id	sid	tid	token	lemma	pos
ap-374	1	1	ap02_04.vp	ap02_04.vp	NOUN
ap-374	1	2	1	1	NUM
ap-374	1	3	introduction	introduction	NOUN
ap-374	1	4	the	the	DET
ap-374	1	5	principal	principal	ADJ
ap-374	1	6	problem	problem	NOUN
ap-374	1	7	of	of	ADP
ap-374	1	8	classical	classical	ADJ
ap-374	1	9	numerical	numerical	ADJ
ap-374	1	10	methods	method	NOUN
ap-374	1	11	,	,	PUNCT
ap-374	1	12	such	such	ADJ
ap-374	1	13	as	as	ADP
ap-374	1	14	finite	finite	ADJ
ap-374	1	15	element	element	NOUN
ap-374	1	16	methods	method	NOUN
ap-374	1	17	,	,	PUNCT
ap-374	1	18	boundary	boundary	ADJ
ap-374	1	19	element	element	NOUN
ap-374	1	20	methods	method	NOUN
ap-374	1	21	,	,	PUNCT
ap-374	1	22	etc	etc	X
ap-374	1	23	.	.	X
ap-374	1	24	,	,	PUNCT
ap-374	1	25	consists	consist	VERB
ap-374	1	26	in	in	ADP
ap-374	1	27	“	"	PUNCT
ap-374	1	28	too	too	ADV
ap-374	1	29	stiff	stiff	ADJ
ap-374	1	30	”	"	PUNCT
ap-374	1	31	models	model	NOUN
ap-374	1	32	,	,	PUNCT
ap-374	1	33	or	or	CCONJ
ap-374	1	34	too	too	ADV
ap-374	1	35	complicated	complicated	ADJ
ap-374	1	36	simulations	simulation	NOUN
ap-374	1	37	of	of	ADP
ap-374	1	38	the	the	DET
ap-374	1	39	real	real	ADJ
ap-374	1	40	states	state	NOUN
ap-374	1	41	when	when	SCONJ
ap-374	1	42	no	no	DET
ap-374	1	43	a	a	DET
ap-374	1	44	priori	priori	ADJ
ap-374	1	45	knowledge	knowledge	NOUN
ap-374	1	46	of	of	ADP
ap-374	1	47	crack	crack	NOUN
ap-374	1	48	initiation	initiation	NOUN
ap-374	1	49	is	be	AUX
ap-374	1	50	available	available	ADJ
ap-374	1	51	.	.	PUNCT
ap-374	2	1	this	this	PRON
ap-374	2	2	is	be	AUX
ap-374	2	3	why	why	SCONJ
ap-374	2	4	discrete	discrete	ADJ
ap-374	2	5	element	element	NOUN
ap-374	2	6	methods	method	NOUN
ap-374	2	7	have	have	AUX
ap-374	2	8	been	be	AUX
ap-374	2	9	introduced	introduce	VERB
ap-374	2	10	to	to	PART
ap-374	2	11	replace	replace	VERB
ap-374	2	12	fracture	fracture	NOUN
ap-374	2	13	mechanics	mechanic	NOUN
ap-374	2	14	problems	problem	NOUN
ap-374	2	15	by	by	ADP
ap-374	2	16	contact	contact	NOUN
ap-374	2	17	problems	problem	NOUN
ap-374	2	18	,	,	PUNCT
ap-374	2	19	which	which	PRON
ap-374	2	20	are	be	AUX
ap-374	2	21	in	in	ADP
ap-374	2	22	many	many	ADJ
ap-374	2	23	respects	respect	NOUN
ap-374	2	24	more	more	ADV
ap-374	2	25	transparent	transparent	ADJ
ap-374	2	26	,	,	PUNCT
ap-374	2	27	and	and	CCONJ
ap-374	2	28	which	which	PRON
ap-374	2	29	lead	lead	VERB
ap-374	2	30	us	we	PRON
ap-374	2	31	to	to	ADP
ap-374	2	32	the	the	DET
ap-374	2	33	same	same	ADJ
ap-374	2	34	results	result	NOUN
ap-374	2	35	.	.	PUNCT
ap-374	3	1	moreover	moreover	ADV
ap-374	3	2	,	,	PUNCT
ap-374	3	3	it	it	PRON
ap-374	3	4	is	be	AUX
ap-374	3	5	not	not	PART
ap-374	3	6	necessary	necessary	ADJ
ap-374	3	7	to	to	PART
ap-374	3	8	know	know	VERB
ap-374	3	9	the	the	DET
ap-374	3	10	crack	crack	NOUN
ap-374	3	11	initiation	initiation	NOUN
ap-374	3	12	in	in	ADP
ap-374	3	13	advance	advance	NOUN
ap-374	3	14	.	.	PUNCT
ap-374	4	1	in	in	ADP
ap-374	4	2	the	the	DET
ap-374	4	3	early	early	ADJ
ap-374	4	4	1970s	1970	NOUN
ap-374	4	5	cundall	cundall	NOUN
ap-374	4	6	,	,	PUNCT
ap-374	4	7	[	[	X
ap-374	4	8	2	2	NUM
ap-374	4	9	]	]	PUNCT
ap-374	4	10	,	,	PUNCT
ap-374	4	11	and	and	CCONJ
ap-374	4	12	others	other	NOUN
ap-374	4	13	,	,	PUNCT
ap-374	4	14	[	[	X
ap-374	4	15	3	3	NUM
ap-374	4	16	]	]	PUNCT
ap-374	4	17	,	,	PUNCT
ap-374	4	18	introduced	introduce	VERB
ap-374	4	19	discrete	discrete	ADJ
ap-374	4	20	elements	element	NOUN
ap-374	4	21	starting	start	VERB
ap-374	4	22	with	with	ADP
ap-374	4	23	dynamic	dynamic	ADJ
ap-374	4	24	equilibrium	equilibrium	NOUN
ap-374	4	25	.	.	PUNCT
ap-374	5	1	first	first	ADV
ap-374	5	2	,	,	PUNCT
ap-374	5	3	brick	brick	NOUN
ap-374	5	4	-	-	PUNCT
ap-374	5	5	like	like	ADJ
ap-374	5	6	elements	element	NOUN
ap-374	5	7	were	be	AUX
ap-374	5	8	used	use	VERB
ap-374	5	9	(	(	PUNCT
ap-374	5	10	professional	professional	ADJ
ap-374	5	11	computer	computer	NOUN
ap-374	5	12	program	program	NOUN
ap-374	5	13	udec	udec	ADJ
ap-374	5	14	)	)	PUNCT
ap-374	5	15	,	,	PUNCT
ap-374	5	16	and	and	CCONJ
ap-374	5	17	later	later	ADV
ap-374	5	18	circular	circular	ADJ
ap-374	5	19	elements	element	NOUN
ap-374	5	20	in	in	ADP
ap-374	5	21	2d	2d	NUM
ap-374	5	22	and	and	CCONJ
ap-374	5	23	spherical	spherical	ADJ
ap-374	5	24	elements	element	NOUN
ap-374	5	25	in	in	ADP
ap-374	5	26	3d	3d	PROPN
ap-374	5	27	(	(	PUNCT
ap-374	5	28	pfc	pfc	NOUN
ap-374	5	29	–	–	PUNCT
ap-374	5	30	particle	particle	NOUN
ap-374	5	31	flow	flow	NOUN
ap-374	5	32	code	code	NOUN
ap-374	5	33	–	–	PUNCT
ap-374	5	34	both	both	DET
ap-374	5	35	computer	computer	NOUN
ap-374	5	36	systems	system	NOUN
ap-374	5	37	issued	issue	VERB
ap-374	5	38	by	by	ADP
ap-374	5	39	itasca	itasca	PROPN
ap-374	5	40	)	)	PUNCT
ap-374	5	41	simulated	simulate	VERB
ap-374	5	42	the	the	DET
ap-374	5	43	continuum	continuum	ADJ
ap-374	5	44	behavior	behavior	NOUN
ap-374	5	45	of	of	ADP
ap-374	5	46	structures	structure	NOUN
ap-374	5	47	.	.	PUNCT
ap-374	6	1	the	the	DET
ap-374	6	2	application	application	NOUN
ap-374	6	3	of	of	ADP
ap-374	6	4	such	such	ADJ
ap-374	6	5	methods	method	NOUN
ap-374	6	6	took	take	VERB
ap-374	6	7	place	place	NOUN
ap-374	6	8	mainly	mainly	ADV
ap-374	6	9	in	in	ADP
ap-374	6	10	geotechnics	geotechnic	NOUN
ap-374	6	11	,	,	PUNCT
ap-374	6	12	where	where	SCONJ
ap-374	6	13	soil	soil	NOUN
ap-374	6	14	is	be	AUX
ap-374	6	15	a	a	DET
ap-374	6	16	typical	typical	ADJ
ap-374	6	17	grain	grain	NOUN
ap-374	6	18	material	material	NOUN
ap-374	6	19	with	with	ADP
ap-374	6	20	the	the	DET
ap-374	6	21	above	above	ADV
ap-374	6	22	-	-	PUNCT
ap-374	6	23	mentioned	mention	VERB
ap-374	6	24	shape	shape	NOUN
ap-374	6	25	,	,	PUNCT
ap-374	6	26	[	[	X
ap-374	6	27	11	11	NUM
ap-374	6	28	]	]	PUNCT
ap-374	6	29	.	.	PUNCT
ap-374	7	1	if	if	SCONJ
ap-374	7	2	the	the	DET
ap-374	7	3	material	material	NOUN
ap-374	7	4	parameters	parameter	NOUN
ap-374	7	5	are	be	AUX
ap-374	7	6	well	well	ADV
ap-374	7	7	chosen	choose	VERB
ap-374	7	8	,	,	PUNCT
ap-374	7	9	the	the	DET
ap-374	7	10	mechanical	mechanical	ADJ
ap-374	7	11	behavior	behavior	NOUN
ap-374	7	12	of	of	ADP
ap-374	7	13	the	the	DET
ap-374	7	14	discrete	discrete	ADJ
ap-374	7	15	elements	element	NOUN
ap-374	7	16	is	be	AUX
ap-374	7	17	very	very	ADV
ap-374	7	18	close	close	ADJ
ap-374	7	19	to	to	ADP
ap-374	7	20	reality	reality	NOUN
ap-374	7	21	.	.	PUNCT
ap-374	8	1	the	the	DET
ap-374	8	2	problem	problem	NOUN
ap-374	8	3	consists	consist	VERB
ap-374	8	4	of	of	ADP
ap-374	8	5	finding	find	VERB
ap-374	8	6	such	such	ADJ
ap-374	8	7	material	material	NOUN
ap-374	8	8	parameters	parameter	NOUN
ap-374	8	9	.	.	PUNCT
ap-374	9	1	there	there	PRON
ap-374	9	2	have	have	AUX
ap-374	9	3	been	be	AUX
ap-374	9	4	many	many	ADJ
ap-374	9	5	attempts	attempt	NOUN
ap-374	9	6	to	to	PART
ap-374	9	7	find	find	VERB
ap-374	9	8	these	these	DET
ap-374	9	9	parameters	parameter	NOUN
ap-374	9	10	,	,	PUNCT
ap-374	9	11	but	but	CCONJ
ap-374	9	12	still	still	ADV
ap-374	9	13	there	there	PRON
ap-374	9	14	is	be	VERB
ap-374	9	15	no	no	DET
ap-374	9	16	satisfactory	satisfactory	ADJ
ap-374	9	17	output	output	NOUN
ap-374	9	18	from	from	ADP
ap-374	9	19	these	these	DET
ap-374	9	20	studies	study	NOUN
ap-374	9	21	.	.	PUNCT
ap-374	10	1	a	a	DET
ap-374	10	2	promising	promising	ADJ
ap-374	10	3	approach	approach	NOUN
ap-374	10	4	may	may	AUX
ap-374	10	5	be	be	AUX
ap-374	10	6	to	to	PART
ap-374	10	7	cover	cover	VERB
ap-374	10	8	the	the	DET
ap-374	10	9	domain	domain	NOUN
ap-374	10	10	,	,	PUNCT
ap-374	10	11	defining	define	VERB
ap-374	10	12	the	the	DET
ap-374	10	13	physical	physical	ADJ
ap-374	10	14	body	body	NOUN
ap-374	10	15	by	by	ADP
ap-374	10	16	hexagonal	hexagonal	ADJ
ap-374	10	17	elements	element	NOUN
ap-374	10	18	,	,	PUNCT
ap-374	10	19	very	very	ADV
ap-374	10	20	close	close	ADV
ap-374	10	21	to	to	ADP
ap-374	10	22	disks	disk	NOUN
ap-374	10	23	,	,	PUNCT
ap-374	10	24	which	which	PRON
ap-374	10	25	can	can	AUX
ap-374	10	26	cover	cover	VERB
ap-374	10	27	the	the	DET
ap-374	10	28	domain	domain	NOUN
ap-374	10	29	with	with	ADP
ap-374	10	30	very	very	ADV
ap-374	10	31	small	small	ADJ
ap-374	10	32	geometrical	geometrical	ADJ
ap-374	10	33	error	error	NOUN
ap-374	10	34	.	.	PUNCT
ap-374	11	1	replacing	replace	VERB
ap-374	11	2	the	the	DET
ap-374	11	3	discrete	discrete	ADJ
ap-374	11	4	elements	element	NOUN
ap-374	11	5	by	by	ADP
ap-374	11	6	elastic	elastic	ADJ
ap-374	11	7	,	,	PUNCT
ap-374	11	8	or	or	CCONJ
ap-374	11	9	elastic	elastic	ADJ
ap-374	11	10	-	-	PUNCT
ap-374	11	11	plastic	plastic	NOUN
ap-374	11	12	,	,	PUNCT
ap-374	11	13	hexagons	hexagon	NOUN
ap-374	11	14	with	with	ADP
ap-374	11	15	the	the	DET
ap-374	11	16	full	full	ADJ
ap-374	11	17	contact	contact	NOUN
ap-374	11	18	of	of	ADP
ap-374	11	19	adjacent	adjacent	ADJ
ap-374	11	20	elements	element	NOUN
ap-374	11	21	along	along	ADP
ap-374	11	22	their	their	PRON
ap-374	11	23	common	common	ADJ
ap-374	11	24	boundaries	boundary	NOUN
ap-374	11	25	yields	yield	VERB
ap-374	11	26	a	a	DET
ap-374	11	27	honeycomb	honeycomb	NOUN
ap-374	11	28	-	-	PUNCT
ap-374	11	29	like	like	ADJ
ap-374	11	30	shape	shape	NOUN
ap-374	11	31	of	of	ADP
ap-374	11	32	the	the	DET
ap-374	11	33	elements	element	NOUN
ap-374	11	34	,	,	PUNCT
ap-374	11	35	see	see	VERB
ap-374	11	36	,	,	PUNCT
ap-374	12	1	e.g.	e.g.	ADV
ap-374	12	2	[	[	X
ap-374	12	3	15	15	NUM
ap-374	12	4	]	]	PUNCT
ap-374	12	5	,	,	PUNCT
ap-374	12	6	covering	cover	VERB
ap-374	12	7	the	the	DET
ap-374	12	8	structure	structure	NOUN
ap-374	12	9	of	of	ADP
ap-374	12	10	the	the	DET
ap-374	12	11	continuous	continuous	ADJ
ap-374	12	12	medium	medium	NOUN
ap-374	12	13	.	.	PUNCT
ap-374	13	1	it	it	PRON
ap-374	13	2	is	be	AUX
ap-374	13	3	necessary	necessary	ADJ
ap-374	13	4	to	to	PART
ap-374	13	5	note	note	VERB
ap-374	13	6	that	that	SCONJ
ap-374	13	7	beams	beam	NOUN
ap-374	13	8	form	form	VERB
ap-374	13	9	the	the	DET
ap-374	13	10	honeycomb	honeycomb	NOUN
ap-374	13	11	boundaries	boundary	NOUN
ap-374	13	12	in	in	ADP
ap-374	13	13	[	[	X
ap-374	13	14	15	15	NUM
ap-374	13	15	]	]	PUNCT
ap-374	13	16	and	and	CCONJ
ap-374	13	17	there	there	PRON
ap-374	13	18	is	be	VERB
ap-374	13	19	no	no	DET
ap-374	13	20	material	material	NOUN
ap-374	13	21	inside	inside	ADP
ap-374	13	22	such	such	ADJ
ap-374	13	23	particles	particle	NOUN
ap-374	13	24	.	.	PUNCT
ap-374	14	1	in	in	ADP
ap-374	14	2	our	our	PRON
ap-374	14	3	case	case	NOUN
ap-374	14	4	some	some	DET
ap-374	14	5	kind	kind	NOUN
ap-374	14	6	of	of	ADP
ap-374	14	7	material	material	NOUN
ap-374	14	8	fills	fill	VERB
ap-374	14	9	the	the	DET
ap-374	14	10	interior	interior	NOUN
ap-374	14	11	of	of	ADP
ap-374	14	12	the	the	DET
ap-374	14	13	hexagonal	hexagonal	ADJ
ap-374	14	14	elements	element	NOUN
ap-374	14	15	.	.	PUNCT
ap-374	15	1	the	the	DET
ap-374	15	2	relations	relation	NOUN
ap-374	15	3	inside	inside	ADP
ap-374	15	4	the	the	DET
ap-374	15	5	hexagonal	hexagonal	ADJ
ap-374	15	6	particles	particle	NOUN
ap-374	15	7	are	be	AUX
ap-374	15	8	solved	solve	VERB
ap-374	15	9	by	by	ADP
ap-374	15	10	a	a	DET
ap-374	15	11	special	special	ADJ
ap-374	15	12	form	form	NOUN
ap-374	15	13	of	of	ADP
ap-374	15	14	the	the	DET
ap-374	15	15	boundary	boundary	ADJ
ap-374	15	16	element	element	NOUN
ap-374	15	17	method	method	NOUN
ap-374	15	18	,	,	PUNCT
ap-374	15	19	[	[	X
ap-374	15	20	1	1	NUM
ap-374	15	21	]	]	PUNCT
ap-374	15	22	.	.	PUNCT
ap-374	16	1	free	free	ADJ
ap-374	16	2	hexagons	hexagon	NOUN
ap-374	16	3	are	be	AUX
ap-374	16	4	used	use	VERB
ap-374	16	5	by	by	ADP
ap-374	16	6	onck	onck	ADJ
ap-374	16	7	and	and	CCONJ
ap-374	16	8	van	van	PROPN
ap-374	16	9	der	der	NOUN
ap-374	16	10	giessen	giessen	VERB
ap-374	16	11	in	in	ADP
ap-374	16	12	[	[	X
ap-374	16	13	12	12	NUM
ap-374	16	14	]	]	PUNCT
ap-374	16	15	,	,	PUNCT
ap-374	16	16	for	for	ADP
ap-374	16	17	example	example	NOUN
ap-374	16	18	,	,	PUNCT
ap-374	16	19	where	where	SCONJ
ap-374	16	20	wide	wide	ADJ
ap-374	16	21	range	range	NOUN
ap-374	16	22	of	of	ADP
ap-374	16	23	references	reference	NOUN
ap-374	16	24	on	on	ADP
ap-374	16	25	this	this	DET
ap-374	16	26	topic	topic	NOUN
ap-374	16	27	can	can	AUX
ap-374	16	28	be	be	AUX
ap-374	16	29	found	find	VERB
ap-374	16	30	.	.	PUNCT
ap-374	17	1	in	in	ADP
ap-374	17	2	[	[	X
ap-374	17	3	12	12	NUM
ap-374	17	4	]	]	PUNCT
ap-374	17	5	,	,	PUNCT
ap-374	17	6	the	the	DET
ap-374	17	7	finite	finite	ADJ
ap-374	17	8	element	element	NOUN
ap-374	17	9	method	method	NOUN
ap-374	17	10	,	,	PUNCT
ap-374	17	11	e.g.	e.g.	ADV
ap-374	17	12	[	[	X
ap-374	17	13	16	16	NUM
ap-374	17	14	]	]	PUNCT
ap-374	17	15	,	,	PUNCT
ap-374	17	16	is	be	AUX
ap-374	17	17	used	use	VERB
ap-374	17	18	to	to	PART
ap-374	17	19	create	create	VERB
ap-374	17	20	the	the	DET
ap-374	17	21	stiffness	stiffness	ADJ
ap-374	17	22	matrices	matrix	NOUN
ap-374	17	23	of	of	ADP
ap-374	17	24	the	the	DET
ap-374	17	25	elements	element	NOUN
ap-374	17	26	,	,	PUNCT
ap-374	17	27	namely	namely	ADV
ap-374	17	28	six	six	NUM
ap-374	17	29	finite	finite	ADJ
ap-374	17	30	elements	element	NOUN
ap-374	17	31	are	be	AUX
ap-374	17	32	substructured	substructure	VERB
ap-374	17	33	to	to	ADP
ap-374	17	34	a	a	DET
ap-374	17	35	hexagon	hexagon	NOUN
ap-374	17	36	.	.	PUNCT
ap-374	18	1	in	in	ADP
ap-374	18	2	applications	application	NOUN
ap-374	18	3	to	to	ADP
ap-374	18	4	geotechnical	geotechnical	ADJ
ap-374	18	5	problems	problem	NOUN
ap-374	18	6	the	the	DET
ap-374	18	7	disturbed	disturbed	ADJ
ap-374	18	8	state	state	NOUN
ap-374	18	9	concept	concept	NOUN
ap-374	18	10	(	(	PUNCT
ap-374	18	11	dsc	dsc	NOUN
ap-374	18	12	)	)	PUNCT
ap-374	18	13	established	establish	VERB
ap-374	18	14	by	by	ADP
ap-374	18	15	desai	desai	PROPN
ap-374	18	16	,	,	PUNCT
ap-374	18	17	[	[	X
ap-374	18	18	4	4	NUM
ap-374	18	19	]	]	PUNCT
ap-374	18	20	,	,	PUNCT
ap-374	18	21	[	[	X
ap-374	18	22	5	5	NUM
ap-374	18	23	]	]	PUNCT
ap-374	18	24	,	,	PUNCT
ap-374	18	25	can	can	AUX
ap-374	18	26	describe	describe	VERB
ap-374	18	27	a	a	DET
ap-374	18	28	wide	wide	ADJ
ap-374	18	29	spectrum	spectrum	NOUN
ap-374	18	30	of	of	ADP
ap-374	18	31	material	material	NOUN
ap-374	18	32	states	state	NOUN
ap-374	18	33	inside	inside	ADP
ap-374	18	34	the	the	DET
ap-374	18	35	elements	element	NOUN
ap-374	18	36	,	,	PUNCT
ap-374	18	37	starting	start	VERB
ap-374	18	38	with	with	ADP
ap-374	18	39	elastic	elastic	ADJ
ap-374	18	40	,	,	PUNCT
ap-374	18	41	elastic	elastic	ADJ
ap-374	18	42	-	-	PUNCT
ap-374	18	43	plastic	plastic	NOUN
ap-374	18	44	,	,	PUNCT
ap-374	18	45	[	[	X
ap-374	18	46	6	6	NUM
ap-374	18	47	]	]	PUNCT
ap-374	18	48	,	,	PUNCT
ap-374	18	49	and	and	CCONJ
ap-374	18	50	even	even	ADV
ap-374	18	51	damage	damage	NOUN
ap-374	18	52	states	state	NOUN
ap-374	18	53	,	,	PUNCT
ap-374	18	54	[	[	X
ap-374	18	55	10	10	NUM
ap-374	18	56	]	]	PUNCT
ap-374	18	57	.	.	PUNCT
ap-374	19	1	the	the	DET
ap-374	19	2	use	use	NOUN
ap-374	19	3	of	of	ADP
ap-374	19	4	eigenparameters	eigenparameter	NOUN
ap-374	19	5	for	for	ADP
ap-374	19	6	plastic	plastic	ADJ
ap-374	19	7	strain	strain	NOUN
ap-374	19	8	,	,	PUNCT
ap-374	19	9	or	or	CCONJ
ap-374	19	10	relaxation	relaxation	NOUN
ap-374	19	11	stress	stress	NOUN
ap-374	19	12	,	,	PUNCT
ap-374	19	13	[	[	X
ap-374	19	14	7	7	NUM
ap-374	19	15	]	]	PUNCT
ap-374	19	16	,	,	PUNCT
ap-374	19	17	[	[	X
ap-374	19	18	8	8	NUM
ap-374	19	19	]	]	PUNCT
ap-374	19	20	,	,	PUNCT
ap-374	19	21	completes	complete	VERB
ap-374	19	22	the	the	DET
ap-374	19	23	description	description	NOUN
ap-374	19	24	of	of	ADP
ap-374	19	25	the	the	DET
ap-374	19	26	possible	possible	ADJ
ap-374	19	27	and	and	CCONJ
ap-374	19	28	suitable	suitable	ADJ
ap-374	19	29	nonlinear	nonlinear	ADJ
ap-374	19	30	constitutive	constitutive	ADJ
ap-374	19	31	laws	law	NOUN
ap-374	19	32	,	,	PUNCT
ap-374	19	33	which	which	PRON
ap-374	19	34	moreover	moreover	ADV
ap-374	19	35	can	can	AUX
ap-374	19	36	be	be	AUX
ap-374	19	37	“	"	PUNCT
ap-374	19	38	tuned	tune	VERB
ap-374	19	39	”	"	PUNCT
ap-374	19	40	from	from	ADP
ap-374	19	41	“	"	PUNCT
ap-374	19	42	in	in	ADP
ap-374	19	43	situ	situ	NOUN
ap-374	19	44	”	"	PUNCT
ap-374	19	45	measurements	measurement	NOUN
ap-374	19	46	,	,	PUNCT
ap-374	19	47	or	or	CCONJ
ap-374	19	48	from	from	ADP
ap-374	19	49	results	result	NOUN
ap-374	19	50	from	from	ADP
ap-374	19	51	scale	scale	NOUN
ap-374	19	52	modeling	modeling	NOUN
ap-374	19	53	.	.	PUNCT
ap-374	20	1	geotechnical	geotechnical	ADJ
ap-374	20	2	properties	property	NOUN
ap-374	20	3	are	be	AUX
ap-374	20	4	defined	define	VERB
ap-374	20	5	on	on	ADP
ap-374	20	6	the	the	DET
ap-374	20	7	boundaries	boundary	NOUN
ap-374	20	8	of	of	ADP
ap-374	20	9	the	the	DET
ap-374	20	10	elements	element	NOUN
ap-374	20	11	.	.	PUNCT
ap-374	21	1	a	a	DET
ap-374	21	2	typical	typical	ADJ
ap-374	21	3	formulation	formulation	NOUN
ap-374	21	4	of	of	ADP
ap-374	21	5	the	the	DET
ap-374	21	6	problem	problem	NOUN
ap-374	21	7	involving	involve	VERB
ap-374	21	8	the	the	DET
ap-374	21	9	generalized	generalize	VERB
ap-374	21	10	mohr	mohr	PROPN
ap-374	21	11	-	-	PUNCT
ap-374	21	12	coulomb	coulomb	PROPN
ap-374	21	13	law	law	NOUN
ap-374	21	14	combined	combine	VERB
ap-374	21	15	with	with	ADP
ap-374	21	16	exclusion	exclusion	NOUN
ap-374	21	17	of	of	ADP
ap-374	21	18	tensile	tensile	NOUN
ap-374	21	19	zones	zone	NOUN
ap-374	21	20	is	be	AUX
ap-374	21	21	proposed	propose	VERB
ap-374	21	22	in	in	ADP
ap-374	21	23	[	[	X
ap-374	21	24	14	14	NUM
ap-374	21	25	]	]	PUNCT
ap-374	21	26	,	,	PUNCT
ap-374	21	27	where	where	SCONJ
ap-374	21	28	the	the	DET
ap-374	21	29	technique	technique	NOUN
ap-374	21	30	using	use	VERB
ap-374	21	31	lagrangian	lagrangian	ADJ
ap-374	21	32	multipliers	multiplier	NOUN
ap-374	21	33	leads	lead	VERB
ap-374	21	34	to	to	ADP
ap-374	21	35	a	a	DET
ap-374	21	36	mixed	mixed	ADJ
ap-374	21	37	problem	problem	NOUN
ap-374	21	38	(	(	PUNCT
ap-374	21	39	both	both	CCONJ
ap-374	21	40	displacements	displacement	NOUN
ap-374	21	41	and	and	CCONJ
ap-374	21	42	stresses	stress	NOUN
ap-374	21	43	–	–	PUNCT
ap-374	21	44	element	element	ADJ
ap-374	21	45	boundary	boundary	ADJ
ap-374	21	46	tractions	traction	NOUN
ap-374	21	47	are	be	AUX
ap-374	21	48	iterated	iterate	VERB
ap-374	21	49	)	)	PUNCT
ap-374	21	50	.	.	PUNCT
ap-374	22	1	in	in	ADP
ap-374	22	2	this	this	DET
ap-374	22	3	paper	paper	NOUN
ap-374	22	4	,	,	PUNCT
ap-374	22	5	the	the	DET
ap-374	22	6	penalty	penalty	NOUN
ap-374	22	7	method	method	NOUN
ap-374	22	8	is	be	AUX
ap-374	22	9	applied	apply	VERB
ap-374	22	10	,	,	PUNCT
ap-374	22	11	and	and	CCONJ
ap-374	22	12	element	element	ADJ
ap-374	22	13	boundary	boundary	ADJ
ap-374	22	14	tractions	traction	NOUN
ap-374	22	15	(	(	PUNCT
ap-374	22	16	formerly	formerly	ADV
ap-374	22	17	lagrangian	lagrangian	ADJ
ap-374	22	18	multipliers	multiplier	NOUN
ap-374	22	19	)	)	PUNCT
ap-374	22	20	are	be	AUX
ap-374	22	21	substituted	substitute	VERB
ap-374	22	22	by	by	ADP
ap-374	22	23	spring	spring	NOUN
ap-374	22	24	stiffnesses	stiffness	NOUN
ap-374	22	25	(	(	PUNCT
ap-374	22	26	i.e.	i.e.	X
ap-374	22	27	,	,	PUNCT
ap-374	22	28	by	by	ADP
ap-374	22	29	penalty	penalty	NOUN
ap-374	22	30	functions	function	NOUN
ap-374	22	31	,	,	PUNCT
ap-374	22	32	or	or	CCONJ
ap-374	22	33	in	in	ADP
ap-374	22	34	our	our	PRON
ap-374	22	35	case	case	NOUN
ap-374	22	36	by	by	ADP
ap-374	22	37	penalty	penalty	NOUN
ap-374	22	38	parameters	parameter	NOUN
ap-374	22	39	)	)	PUNCT
ap-374	22	40	.	.	PUNCT
ap-374	23	1	the	the	DET
ap-374	23	2	springs	spring	NOUN
ap-374	23	3	enable	enable	VERB
ap-374	23	4	us	we	PRON
ap-374	23	5	to	to	PART
ap-374	23	6	simulate	simulate	VERB
ap-374	23	7	the	the	DET
ap-374	23	8	interfacial	interfacial	ADJ
ap-374	23	9	constraint	constraint	NOUN
ap-374	23	10	,	,	PUNCT
ap-374	23	11	namely	namely	ADV
ap-374	23	12	the	the	DET
ap-374	23	13	exclusion	exclusion	NOUN
ap-374	23	14	of	of	ADP
ap-374	23	15	the	the	DET
ap-374	23	16	tensile	tensile	NOUN
ap-374	23	17	tractions	traction	NOUN
ap-374	23	18	and	and	CCONJ
ap-374	23	19	application	application	NOUN
ap-374	23	20	of	of	ADP
ap-374	23	21	the	the	DET
ap-374	23	22	mohr	mohr	PROPN
ap-374	23	23	-	-	PUNCT
ap-374	23	24	coulomb	coulomb	PROPN
ap-374	23	25	law	law	NOUN
ap-374	23	26	.	.	PUNCT
ap-374	24	1	the	the	DET
ap-374	24	2	mohr	mohr	PROPN
ap-374	24	3	-	-	PUNCT
ap-374	24	4	coulomb	coulomb	PROPN
ap-374	24	5	law	law	NOUN
ap-374	24	6	is	be	AUX
ap-374	24	7	used	use	VERB
ap-374	24	8	in	in	ADP
ap-374	24	9	two	two	NUM
ap-374	24	10	basic	basic	ADJ
ap-374	24	11	forms	form	NOUN
ap-374	24	12	,	,	PUNCT
ap-374	24	13	for	for	ADP
ap-374	24	14	brittle	brittle	ADJ
ap-374	24	15	or	or	CCONJ
ap-374	24	16	almost	almost	ADV
ap-374	24	17	brittle	brittle	ADJ
ap-374	24	18	materials	material	NOUN
ap-374	24	19	,	,	PUNCT
ap-374	24	20	and	and	CCONJ
ap-374	24	21	for	for	ADP
ap-374	24	22	soft	soft	ADJ
ap-374	24	23	rocks	rock	NOUN
ap-374	24	24	or	or	CCONJ
ap-374	24	25	soil	soil	NOUN
ap-374	24	26	.	.	PUNCT
ap-374	25	1	several	several	ADJ
ap-374	25	2	phenomena	phenomenon	NOUN
ap-374	25	3	,	,	PUNCT
ap-374	25	4	e.g.	e.g.	ADV
ap-374	25	5	,	,	PUNCT
ap-374	25	6	gas	gas	NOUN
ap-374	25	7	extrusion	extrusion	NOUN
ap-374	25	8	in	in	ADP
ap-374	25	9	a	a	DET
ap-374	25	10	coal	coal	NOUN
ap-374	25	11	seam	seam	NOUN
ap-374	25	12	,	,	PUNCT
ap-374	25	13	swelling	swelling	NOUN
ap-374	25	14	,	,	PUNCT
ap-374	25	15	watering	watering	NOUN
ap-374	25	16	,	,	PUNCT
ap-374	25	17	and	and	CCONJ
ap-374	25	18	even	even	ADV
ap-374	25	19	prestress	prestress	NOUN
ap-374	25	20	,	,	PUNCT
ap-374	25	21	can	can	AUX
ap-374	25	22	be	be	AUX
ap-374	25	23	modeled	model	VERB
ap-374	25	24	by	by	ADP
ap-374	25	25	eshelby	eshelby	ADJ
ap-374	25	26	forces	force	NOUN
ap-374	25	27	[	[	X
ap-374	25	28	9	9	NUM
ap-374	25	29	]	]	PUNCT
ap-374	25	30	.	.	PUNCT
ap-374	26	1	this	this	DET
ap-374	26	2	treatment	treatment	NOUN
ap-374	26	3	seems	seem	VERB
ap-374	26	4	to	to	PART
ap-374	26	5	be	be	AUX
ap-374	26	6	much	much	ADV
ap-374	26	7	more	more	ADV
ap-374	26	8	promising	promising	ADJ
ap-374	26	9	then	then	ADV
ap-374	26	10	the	the	DET
ap-374	26	11	eigenparameters	eigenparameter	NOUN
ap-374	26	12	introduced	introduce	VERB
ap-374	26	13	in	in	ADP
ap-374	26	14	each	each	DET
ap-374	26	15	element	element	NOUN
ap-374	26	16	from	from	ADP
ap-374	26	17	the	the	DET
ap-374	26	18	zone	zone	NOUN
ap-374	26	19	of	of	ADP
ap-374	26	20	some	some	DET
ap-374	26	21	disturbance	disturbance	NOUN
ap-374	26	22	occurrences	occurrence	NOUN
ap-374	26	23	,	,	PUNCT
ap-374	26	24	because	because	SCONJ
ap-374	26	25	only	only	ADV
ap-374	26	26	tractions	traction	NOUN
ap-374	26	27	(	(	PUNCT
ap-374	26	28	eshelby	eshelby	ADJ
ap-374	26	29	forces	force	NOUN
ap-374	26	30	)	)	PUNCT
ap-374	26	31	along	along	ADP
ap-374	26	32	the	the	DET
ap-374	26	33	boundaries	boundary	NOUN
ap-374	26	34	of	of	ADP
ap-374	26	35	those	those	DET
ap-374	26	36	zones	zone	NOUN
ap-374	26	37	have	have	VERB
ap-374	26	38	to	to	PART
ap-374	26	39	be	be	AUX
ap-374	26	40	applied	apply	VERB
ap-374	26	41	.	.	PUNCT
ap-374	27	1	the	the	DET
ap-374	27	2	paper	paper	NOUN
ap-374	27	3	starts	start	VERB
ap-374	27	4	with	with	ADP
ap-374	27	5	the	the	DET
ap-374	27	6	formulation	formulation	NOUN
ap-374	27	7	of	of	ADP
ap-374	27	8	the	the	DET
ap-374	27	9	free	free	ADJ
ap-374	27	10	hexagon	hexagon	PROPN
ap-374	27	11	element	element	NOUN
ap-374	27	12	method	method	NOUN
ap-374	27	13	,	,	PUNCT
ap-374	27	14	and	and	CCONJ
ap-374	27	15	then	then	ADV
ap-374	27	16	statical	statical	PROPN
ap-374	27	17	particle	particle	NOUN
ap-374	27	18	flow	flow	NOUN
ap-374	27	19	is	be	AUX
ap-374	27	20	described	describe	VERB
ap-374	27	21	.	.	PUNCT
ap-374	28	1	applications	application	NOUN
ap-374	28	2	in	in	ADP
ap-374	28	3	several	several	ADJ
ap-374	28	4	fields	field	NOUN
ap-374	28	5	of	of	ADP
ap-374	28	6	practical	practical	ADJ
ap-374	28	7	problems	problem	NOUN
ap-374	28	8	are	be	AUX
ap-374	28	9	discussed	discuss	VERB
ap-374	28	10	in	in	ADP
ap-374	28	11	a	a	DET
ap-374	28	12	forthcoming	forthcoming	ADJ
ap-374	28	13	paper	paper	NOUN
ap-374	28	14	by	by	ADP
ap-374	28	15	the	the	DET
ap-374	28	16	authors	author	NOUN
ap-374	28	17	[	[	X
ap-374	28	18	13	13	NUM
ap-374	28	19	]	]	PUNCT
ap-374	28	20	.	.	PUNCT
ap-374	29	1	2	2	NUM
ap-374	29	2	free	free	ADJ
ap-374	29	3	hexagonal	hexagonal	ADJ
ap-374	29	4	element	element	NOUN
ap-374	29	5	method	method	NOUN
ap-374	29	6	the	the	DET
ap-374	29	7	discrete	discrete	ADJ
ap-374	29	8	free	free	ADJ
ap-374	29	9	hexagonal	hexagonal	ADJ
ap-374	29	10	element	element	NOUN
ap-374	29	11	method	method	NOUN
ap-374	29	12	may	may	AUX
ap-374	29	13	be	be	AUX
ap-374	29	14	considered	consider	VERB
ap-374	29	15	a	a	DET
ap-374	29	16	discrete	discrete	ADJ
ap-374	29	17	element	element	NOUN
ap-374	29	18	method	method	NOUN
ap-374	29	19	.	.	PUNCT
ap-374	30	1	the	the	DET
ap-374	30	2	great	great	ADJ
ap-374	30	3	disadvan42	disadvan42	NOUN
ap-374	30	4	©	©	PROPN
ap-374	30	5	czech	czech	PROPN
ap-374	30	6	technical	technical	PROPN
ap-374	30	7	university	university	PROPN
ap-374	30	8	publishing	publishing	NOUN
ap-374	30	9	house	house	NOUN
ap-374	30	10	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-374	30	11	acta	acta	PROPN
ap-374	30	12	polytechnica	polytechnica	PROPN
ap-374	30	13	vol	vol	NOUN
ap-374	30	14	.	.	PUNCT
ap-374	31	1	42	42	NUM
ap-374	31	2	no	no	INTJ
ap-374	31	3	.	.	PUNCT
ap-374	32	1	4/2002	4/2002	DET
ap-374	32	2	certain	certain	ADJ
ap-374	32	3	discrete	discrete	ADJ
ap-374	32	4	element	element	NOUN
ap-374	32	5	methods	method	NOUN
ap-374	32	6	in	in	ADP
ap-374	32	7	problems	problem	NOUN
ap-374	32	8	of	of	ADP
ap-374	32	9	fracture	fracture	NOUN
ap-374	32	10	mechanics	mechanic	NOUN
ap-374	32	11	p.	p.	PROPN
ap-374	33	1	p.	p.	PROPN
ap-374	33	2	procházka	procházka	PROPN
ap-374	33	3	,	,	PUNCT
ap-374	33	4	m.	m.	NOUN
ap-374	33	5	g.	g.	PROPN
ap-374	33	6	kugblenu	kugblenu	PROPN
ap-374	33	7	in	in	ADP
ap-374	33	8	this	this	DET
ap-374	33	9	paper	paper	NOUN
ap-374	33	10	two	two	NUM
ap-374	33	11	discrete	discrete	ADJ
ap-374	33	12	element	element	NOUN
ap-374	33	13	methods	method	NOUN
ap-374	33	14	(	(	PUNCT
ap-374	33	15	dem	dem	NOUN
ap-374	33	16	)	)	PUNCT
ap-374	33	17	are	be	AUX
ap-374	33	18	discussed	discuss	VERB
ap-374	33	19	.	.	PUNCT
ap-374	34	1	the	the	DET
ap-374	34	2	free	free	ADJ
ap-374	34	3	hexagon	hexagon	PROPN
ap-374	34	4	element	element	NOUN
ap-374	34	5	method	method	NOUN
ap-374	34	6	is	be	AUX
ap-374	34	7	considered	consider	VERB
ap-374	34	8	a	a	DET
ap-374	34	9	powerful	powerful	ADJ
ap-374	34	10	discrete	discrete	ADJ
ap-374	34	11	element	element	NOUN
ap-374	34	12	method	method	NOUN
ap-374	34	13	,	,	PUNCT
ap-374	34	14	which	which	PRON
ap-374	34	15	is	be	AUX
ap-374	34	16	broadly	broadly	ADV
ap-374	34	17	used	use	VERB
ap-374	34	18	in	in	ADP
ap-374	34	19	mechanics	mechanic	NOUN
ap-374	34	20	of	of	ADP
ap-374	34	21	granular	granular	ADJ
ap-374	34	22	media	medium	NOUN
ap-374	34	23	.	.	PUNCT
ap-374	35	1	it	it	PRON
ap-374	35	2	substitutes	substitute	VERB
ap-374	35	3	the	the	DET
ap-374	35	4	methods	method	NOUN
ap-374	35	5	for	for	ADP
ap-374	35	6	solving	solve	VERB
ap-374	35	7	continuum	continuum	ADJ
ap-374	35	8	problems	problem	NOUN
ap-374	35	9	.	.	PUNCT
ap-374	36	1	the	the	DET
ap-374	36	2	great	great	ADJ
ap-374	36	3	disadvantage	disadvantage	NOUN
ap-374	36	4	of	of	ADP
ap-374	36	5	classical	classical	ADJ
ap-374	36	6	dem	dem	NOUN
ap-374	36	7	,	,	PUNCT
ap-374	36	8	such	such	ADJ
ap-374	36	9	as	as	ADP
ap-374	36	10	the	the	DET
ap-374	36	11	particle	particle	NOUN
ap-374	36	12	flow	flow	NOUN
ap-374	36	13	code	code	NOUN
ap-374	36	14	(	(	PUNCT
ap-374	36	15	material	material	NOUN
ap-374	36	16	properties	property	NOUN
ap-374	36	17	are	be	AUX
ap-374	36	18	characterized	characterize	VERB
ap-374	36	19	by	by	ADP
ap-374	36	20	spring	spring	NOUN
ap-374	36	21	stiffness	stiffness	NOUN
ap-374	36	22	)	)	PUNCT
ap-374	36	23	,	,	PUNCT
ap-374	36	24	is	be	AUX
ap-374	36	25	that	that	SCONJ
ap-374	36	26	they	they	PRON
ap-374	36	27	have	have	VERB
ap-374	36	28	to	to	PART
ap-374	36	29	be	be	AUX
ap-374	36	30	fed	feed	VERB
ap-374	36	31	with	with	ADP
ap-374	36	32	material	material	NOUN
ap-374	36	33	properties	property	NOUN
ap-374	36	34	provided	provide	VERB
ap-374	36	35	from	from	ADP
ap-374	36	36	laboratory	laboratory	NOUN
ap-374	36	37	tests	test	NOUN
ap-374	36	38	(	(	PUNCT
ap-374	36	39	young	young	ADJ
ap-374	36	40	’s	’s	PART
ap-374	36	41	modulus	modulus	NOUN
ap-374	36	42	,	,	PUNCT
ap-374	36	43	poisson	poisson	PROPN
ap-374	36	44	’s	’s	PART
ap-374	36	45	ratio	ratio	NOUN
ap-374	36	46	,	,	PUNCT
ap-374	36	47	etc	etc	X
ap-374	36	48	.	.	X
ap-374	36	49	)	)	PUNCT
ap-374	36	50	.	.	PUNCT
ap-374	37	1	the	the	DET
ap-374	37	2	problem	problem	NOUN
ap-374	37	3	consists	consist	VERB
ap-374	37	4	in	in	ADP
ap-374	37	5	the	the	DET
ap-374	37	6	fact	fact	NOUN
ap-374	37	7	that	that	SCONJ
ap-374	37	8	the	the	DET
ap-374	37	9	material	material	NOUN
ap-374	37	10	properties	property	NOUN
ap-374	37	11	of	of	ADP
ap-374	37	12	continuum	continuum	ADJ
ap-374	37	13	methods	method	NOUN
ap-374	37	14	(	(	PUNCT
ap-374	37	15	fem	fem	PROPN
ap-374	37	16	,	,	PUNCT
ap-374	37	17	bem	bem	PROPN
ap-374	37	18	)	)	PUNCT
ap-374	37	19	are	be	AUX
ap-374	37	20	not	not	PART
ap-374	37	21	mutually	mutually	ADV
ap-374	37	22	consistent	consistent	ADJ
ap-374	37	23	with	with	ADP
ap-374	37	24	dem	dem	PROPN
ap-374	37	25	.	.	PUNCT
ap-374	38	1	this	this	PRON
ap-374	38	2	is	be	AUX
ap-374	38	3	why	why	SCONJ
ap-374	38	4	we	we	PRON
ap-374	38	5	utilize	utilize	VERB
ap-374	38	6	the	the	DET
ap-374	38	7	principal	principal	ADJ
ap-374	38	8	idea	idea	NOUN
ap-374	38	9	of	of	ADP
ap-374	38	10	dem	dem	NOUN
ap-374	38	11	,	,	PUNCT
ap-374	38	12	but	but	CCONJ
ap-374	38	13	cover	cover	VERB
ap-374	38	14	the	the	DET
ap-374	38	15	continuum	continuum	NOUN
ap-374	38	16	by	by	ADP
ap-374	38	17	hexagonal	hexagonal	ADJ
ap-374	38	18	elastic	elastic	ADJ
ap-374	38	19	,	,	PUNCT
ap-374	38	20	or	or	CCONJ
ap-374	38	21	elastic	elastic	ADJ
ap-374	38	22	-	-	PUNCT
ap-374	38	23	plastic	plastic	NOUN
ap-374	38	24	,	,	PUNCT
ap-374	38	25	elements	element	NOUN
ap-374	38	26	.	.	PUNCT
ap-374	39	1	in	in	ADP
ap-374	39	2	order	order	NOUN
ap-374	39	3	to	to	PART
ap-374	39	4	complete	complete	VERB
ap-374	39	5	the	the	DET
ap-374	39	6	study	study	NOUN
ap-374	39	7	,	,	PUNCT
ap-374	39	8	another	another	DET
ap-374	39	9	one	one	NUM
ap-374	39	10	dem	dem	NOUN
ap-374	39	11	is	be	AUX
ap-374	39	12	discussed	discuss	VERB
ap-374	39	13	.	.	PUNCT
ap-374	40	1	the	the	DET
ap-374	40	2	second	second	ADJ
ap-374	40	3	method	method	NOUN
ap-374	40	4	starts	start	VERB
ap-374	40	5	with	with	ADP
ap-374	40	6	the	the	DET
ap-374	40	7	classical	classical	ADJ
ap-374	40	8	particle	particle	NOUN
ap-374	40	9	flow	flow	NOUN
ap-374	40	10	code	code	NOUN
ap-374	40	11	(	(	PUNCT
ap-374	40	12	pfc	pfc	NOUN
ap-374	40	13	–	–	PUNCT
ap-374	40	14	which	which	PRON
ap-374	40	15	uses	use	VERB
ap-374	40	16	dynamic	dynamic	ADJ
ap-374	40	17	equilibrium	equilibrium	NOUN
ap-374	40	18	)	)	PUNCT
ap-374	40	19	,	,	PUNCT
ap-374	40	20	but	but	CCONJ
ap-374	40	21	applies	apply	VERB
ap-374	40	22	static	static	ADJ
ap-374	40	23	equilibrium	equilibrium	NOUN
ap-374	40	24	.	.	PUNCT
ap-374	41	1	the	the	DET
ap-374	41	2	second	second	ADJ
ap-374	41	3	method	method	NOUN
ap-374	41	4	is	be	AUX
ap-374	41	5	called	call	VERB
ap-374	41	6	the	the	DET
ap-374	41	7	static	static	ADJ
ap-374	41	8	particle	particle	NOUN
ap-374	41	9	flow	flow	NOUN
ap-374	41	10	code	code	NOUN
ap-374	41	11	(	(	PUNCT
ap-374	41	12	spfc	spfc	NOUN
ap-374	41	13	)	)	PUNCT
ap-374	41	14	.	.	PUNCT
ap-374	42	1	the	the	DET
ap-374	42	2	numerical	numerical	ADJ
ap-374	42	3	experience	experience	NOUN
ap-374	42	4	and	and	CCONJ
ap-374	42	5	comparison	comparison	NOUN
ap-374	42	6	numerical	numerical	ADJ
ap-374	42	7	with	with	ADP
ap-374	42	8	experimental	experimental	ADJ
ap-374	42	9	results	result	NOUN
ap-374	42	10	from	from	ADP
ap-374	42	11	scaled	scale	VERB
ap-374	42	12	models	model	NOUN
ap-374	42	13	are	be	AUX
ap-374	42	14	discussed	discuss	VERB
ap-374	42	15	in	in	ADP
ap-374	42	16	forthcoming	forthcoming	ADJ
ap-374	42	17	paper	paper	NOUN
ap-374	42	18	by	by	ADP
ap-374	42	19	both	both	DET
ap-374	42	20	authors	author	NOUN
ap-374	42	21	.	.	PUNCT
ap-374	43	1	keywords	keyword	NOUN
ap-374	43	2	:	:	PUNCT
ap-374	43	3	discrete	discrete	ADJ
ap-374	43	4	element	element	NOUN
ap-374	43	5	methods	method	NOUN
ap-374	43	6	,	,	PUNCT
ap-374	43	7	free	free	ADJ
ap-374	43	8	hexagon	hexagon	PROPN
ap-374	43	9	element	element	PROPN
ap-374	43	10	method	method	NOUN
ap-374	43	11	,	,	PUNCT
ap-374	43	12	statical	statical	ADJ
ap-374	43	13	particle	particle	NOUN
ap-374	43	14	flow	flow	NOUN
ap-374	43	15	code	code	NOUN
ap-374	43	16	.	.	PUNCT
ap-374	44	1	tage	tage	NOUN
ap-374	44	2	of	of	ADP
ap-374	44	3	some	some	DET
ap-374	44	4	classical	classical	ADJ
ap-374	44	5	dem	dem	NOUN
ap-374	44	6	,	,	PUNCT
ap-374	44	7	however	however	ADV
ap-374	44	8	,	,	PUNCT
ap-374	44	9	is	be	AUX
ap-374	44	10	to	to	PART
ap-374	44	11	feed	feed	VERB
ap-374	44	12	them	they	PRON
ap-374	44	13	with	with	ADP
ap-374	44	14	material	material	NOUN
ap-374	44	15	properties	property	NOUN
ap-374	44	16	provided	provide	VERB
ap-374	44	17	from	from	ADP
ap-374	44	18	laboratory	laboratory	NOUN
ap-374	44	19	tests	test	NOUN
ap-374	44	20	(	(	PUNCT
ap-374	44	21	this	this	PRON
ap-374	44	22	is	be	AUX
ap-374	44	23	the	the	DET
ap-374	44	24	case	case	NOUN
ap-374	44	25	of	of	ADP
ap-374	44	26	the	the	DET
ap-374	44	27	statical	statical	ADJ
ap-374	44	28	particle	particle	NOUN
ap-374	44	29	flow	flow	PROPN
ap-374	44	30	code	code	NOUN
ap-374	44	31	,	,	PUNCT
ap-374	44	32	formulated	formulate	VERB
ap-374	44	33	in	in	ADP
ap-374	44	34	the	the	DET
ap-374	44	35	next	next	ADJ
ap-374	44	36	section	section	NOUN
ap-374	44	37	,	,	PUNCT
ap-374	44	38	as	as	SCONJ
ap-374	44	39	the	the	DET
ap-374	44	40	discs	disc	NOUN
ap-374	44	41	are	be	AUX
ap-374	44	42	connected	connect	VERB
ap-374	44	43	by	by	ADP
ap-374	44	44	springs	spring	NOUN
ap-374	44	45	,	,	PUNCT
ap-374	44	46	while	while	SCONJ
ap-374	44	47	laboratories	laboratory	NOUN
ap-374	44	48	provide	provide	VERB
ap-374	44	49	completely	completely	ADV
ap-374	44	50	different	different	ADJ
ap-374	44	51	material	material	NOUN
ap-374	44	52	parameters	parameter	NOUN
ap-374	44	53	)	)	PUNCT
ap-374	44	54	.	.	PUNCT
ap-374	45	1	this	this	PRON
ap-374	45	2	is	be	AUX
ap-374	45	3	here	here	ADV
ap-374	45	4	overcome	overcome	VERB
ap-374	45	5	by	by	ADP
ap-374	45	6	considering	consider	VERB
ap-374	45	7	the	the	DET
ap-374	45	8	material	material	NOUN
ap-374	45	9	characteristics	characteristic	NOUN
ap-374	45	10	,	,	PUNCT
ap-374	45	11	which	which	PRON
ap-374	45	12	are	be	AUX
ap-374	45	13	similar	similar	ADJ
ap-374	45	14	to	to	ADP
ap-374	45	15	a	a	DET
ap-374	45	16	continuum	continuum	ADJ
ap-374	45	17	.	.	PUNCT
ap-374	46	1	the	the	DET
ap-374	46	2	principal	principal	ADJ
ap-374	46	3	idea	idea	NOUN
ap-374	46	4	of	of	ADP
ap-374	46	5	classical	classical	ADJ
ap-374	46	6	dem	dem	NOUN
ap-374	46	7	is	be	AUX
ap-374	46	8	adopted	adopt	VERB
ap-374	46	9	,	,	PUNCT
ap-374	46	10	and	and	CCONJ
ap-374	46	11	the	the	DET
ap-374	46	12	domain	domain	NOUN
ap-374	46	13	defining	define	VERB
ap-374	46	14	the	the	DET
ap-374	46	15	structure	structure	NOUN
ap-374	46	16	continuum	continuum	NOUN
ap-374	46	17	is	be	AUX
ap-374	46	18	in	in	ADP
ap-374	46	19	our	our	PRON
ap-374	46	20	case	case	NOUN
ap-374	46	21	covered	cover	VERB
ap-374	46	22	by	by	ADP
ap-374	46	23	the	the	DET
ap-374	46	24	hexagonal	hexagonal	ADJ
ap-374	46	25	element	element	NOUN
ap-374	46	26	,	,	PUNCT
ap-374	46	27	or	or	CCONJ
ap-374	46	28	other	other	ADJ
ap-374	46	29	material	material	NOUN
ap-374	46	30	properties	property	NOUN
ap-374	46	31	can	can	AUX
ap-374	46	32	be	be	AUX
ap-374	46	33	introduced	introduce	VERB
ap-374	46	34	,	,	PUNCT
ap-374	46	35	such	such	ADJ
ap-374	46	36	as	as	ADP
ap-374	46	37	elastic	elastic	ADJ
ap-374	46	38	-	-	PUNCT
ap-374	46	39	plastic	plastic	NOUN
ap-374	46	40	,	,	PUNCT
ap-374	46	41	visco	visco	ADJ
ap-374	46	42	-	-	ADJ
ap-374	46	43	elastic	elastic	ADJ
ap-374	46	44	-	-	PUNCT
ap-374	46	45	plastic	plastic	NOUN
ap-374	46	46	,	,	PUNCT
ap-374	46	47	etc	etc	X
ap-374	46	48	.	.	X
ap-374	47	1	this	this	DET
ap-374	47	2	step	step	NOUN
ap-374	47	3	avoids	avoid	VERB
ap-374	47	4	the	the	DET
ap-374	47	5	necessity	necessity	NOUN
ap-374	47	6	to	to	PART
ap-374	47	7	estimate	estimate	VERB
ap-374	47	8	the	the	DET
ap-374	47	9	material	material	NOUN
ap-374	47	10	properties	property	NOUN
ap-374	47	11	of	of	ADP
ap-374	47	12	springs	spring	NOUN
ap-374	47	13	,	,	PUNCT
ap-374	47	14	which	which	PRON
ap-374	47	15	are	be	AUX
ap-374	47	16	essential	essential	ADJ
ap-374	47	17	,	,	PUNCT
ap-374	47	18	e.g.	e.g.	ADV
ap-374	47	19	,	,	PUNCT
ap-374	47	20	for	for	ADP
ap-374	47	21	pfc	pfc	NOUN
ap-374	47	22	.	.	PUNCT
ap-374	48	1	the	the	DET
ap-374	48	2	free	free	ADJ
ap-374	48	3	hexagonal	hexagonal	ADJ
ap-374	48	4	element	element	NOUN
ap-374	48	5	method	method	NOUN
ap-374	48	6	fulfills	fulfill	VERB
ap-374	48	7	a	a	DET
ap-374	48	8	natural	natural	ADJ
ap-374	48	9	requirement	requirement	NOUN
ap-374	48	10	due	due	ADP
ap-374	48	11	to	to	ADP
ap-374	48	12	the	the	DET
ap-374	48	13	fact	fact	NOUN
ap-374	48	14	that	that	SCONJ
ap-374	48	15	the	the	DET
ap-374	48	16	elastic	elastic	ADJ
ap-374	48	17	properties	property	NOUN
ap-374	48	18	are	be	AUX
ap-374	48	19	assigned	assign	VERB
ap-374	48	20	to	to	ADP
ap-374	48	21	the	the	DET
ap-374	48	22	particles	particle	NOUN
ap-374	48	23	,	,	PUNCT
ap-374	48	24	and	and	CCONJ
ap-374	48	25	other	other	ADJ
ap-374	48	26	geotechnical	geotechnical	ADJ
ap-374	48	27	material	material	NOUN
ap-374	48	28	parameters	parameter	NOUN
ap-374	48	29	(	(	PUNCT
ap-374	48	30	angle	angle	NOUN
ap-374	48	31	of	of	ADP
ap-374	48	32	internal	internal	ADJ
ap-374	48	33	friction	friction	NOUN
ap-374	48	34	,	,	PUNCT
ap-374	48	35	shear	shear	NOUN
ap-374	48	36	strength	strength	NOUN
ap-374	48	37	or	or	CCONJ
ap-374	48	38	cohesion	cohesion	NOUN
ap-374	48	39	)	)	PUNCT
ap-374	48	40	to	to	ADP
ap-374	48	41	the	the	DET
ap-374	48	42	contacts	contact	NOUN
ap-374	48	43	of	of	ADP
ap-374	48	44	the	the	DET
ap-374	48	45	elements	element	NOUN
ap-374	48	46	.	.	PUNCT
ap-374	49	1	since	since	SCONJ
ap-374	49	2	most	most	ADJ
ap-374	49	3	particles	particle	NOUN
ap-374	49	4	are	be	AUX
ap-374	49	5	of	of	ADP
ap-374	49	6	the	the	DET
ap-374	49	7	same	same	ADJ
ap-374	49	8	shape	shape	NOUN
ap-374	49	9	it	it	PRON
ap-374	49	10	is	be	AUX
ap-374	49	11	possible	possible	ADJ
ap-374	49	12	to	to	PART
ap-374	49	13	apply	apply	VERB
ap-374	49	14	very	very	ADV
ap-374	49	15	powerful	powerful	ADJ
ap-374	49	16	iteration	iteration	NOUN
ap-374	49	17	procedures	procedure	NOUN
ap-374	49	18	,	,	PUNCT
ap-374	49	19	because	because	SCONJ
ap-374	49	20	the	the	DET
ap-374	49	21	stiffness	stiffness	ADJ
ap-374	49	22	matrix	matrix	NOUN
ap-374	49	23	can	can	AUX
ap-374	49	24	be	be	AUX
ap-374	49	25	stored	store	VERB
ap-374	49	26	in	in	ADP
ap-374	49	27	the	the	DET
ap-374	49	28	internal	internal	ADJ
ap-374	49	29	memory	memory	NOUN
ap-374	49	30	of	of	ADP
ap-374	49	31	a	a	DET
ap-374	49	32	computer	computer	NOUN
ap-374	49	33	.	.	PUNCT
ap-374	50	1	when	when	SCONJ
ap-374	50	2	dealing	deal	VERB
ap-374	50	3	with	with	ADP
ap-374	50	4	crack	crack	NOUN
ap-374	50	5	problems	problem	NOUN
ap-374	50	6	,	,	PUNCT
ap-374	50	7	two	two	NUM
ap-374	50	8	principal	principal	ADJ
ap-374	50	9	methods	method	NOUN
ap-374	50	10	are	be	AUX
ap-374	50	11	used	use	VERB
ap-374	50	12	.	.	PUNCT
ap-374	51	1	first	first	ADV
ap-374	51	2	,	,	PUNCT
ap-374	51	3	the	the	DET
ap-374	51	4	means	mean	NOUN
ap-374	51	5	of	of	ADP
ap-374	51	6	fracture	fracture	NOUN
ap-374	51	7	mechanics	mechanic	NOUN
ap-374	51	8	are	be	AUX
ap-374	51	9	applied	apply	VERB
ap-374	51	10	,	,	PUNCT
ap-374	51	11	or	or	CCONJ
ap-374	51	12	secondly	secondly	ADV
ap-374	51	13	a	a	DET
ap-374	51	14	contact	contact	NOUN
ap-374	51	15	problem	problem	NOUN
ap-374	51	16	can	can	AUX
ap-374	51	17	be	be	AUX
ap-374	51	18	formulated	formulate	VERB
ap-374	51	19	.	.	PUNCT
ap-374	52	1	the	the	DET
ap-374	52	2	first	first	ADJ
ap-374	52	3	case	case	NOUN
ap-374	52	4	is	be	AUX
ap-374	52	5	generally	generally	ADV
ap-374	52	6	not	not	PART
ap-374	52	7	suitable	suitable	ADJ
ap-374	52	8	,	,	PUNCT
ap-374	52	9	because	because	SCONJ
ap-374	52	10	the	the	DET
ap-374	52	11	direction	direction	NOUN
ap-374	52	12	or	or	CCONJ
ap-374	52	13	way	way	NOUN
ap-374	52	14	of	of	ADP
ap-374	52	15	propagation	propagation	NOUN
ap-374	52	16	of	of	ADP
ap-374	52	17	the	the	DET
ap-374	52	18	cracks	crack	NOUN
ap-374	52	19	needs	need	VERB
ap-374	52	20	to	to	PART
ap-374	52	21	be	be	AUX
ap-374	52	22	known	know	VERB
ap-374	52	23	in	in	ADP
ap-374	52	24	advance	advance	NOUN
ap-374	52	25	.	.	PUNCT
ap-374	53	1	this	this	DET
ap-374	53	2	paper	paper	NOUN
ap-374	53	3	uses	use	VERB
ap-374	53	4	the	the	DET
ap-374	53	5	second	second	ADJ
ap-374	53	6	possibility	possibility	NOUN
ap-374	53	7	,	,	PUNCT
ap-374	53	8	which	which	PRON
ap-374	53	9	avoids	avoid	VERB
ap-374	53	10	the	the	DET
ap-374	53	11	obstacle	obstacle	NOUN
ap-374	53	12	of	of	ADP
ap-374	53	13	a	a	DET
ap-374	53	14	priori	priori	ADJ
ap-374	53	15	unknown	unknown	ADJ
ap-374	53	16	way	way	NOUN
ap-374	53	17	of	of	ADP
ap-374	53	18	propagation	propagation	NOUN
ap-374	53	19	of	of	ADP
ap-374	53	20	the	the	DET
ap-374	53	21	cracks	crack	NOUN
ap-374	53	22	by	by	ADP
ap-374	53	23	creating	create	VERB
ap-374	53	24	a	a	DET
ap-374	53	25	mesh	mesh	NOUN
ap-374	53	26	of	of	ADP
ap-374	53	27	free	free	ADJ
ap-374	53	28	hexagonal	hexagonal	ADJ
ap-374	53	29	elements	element	NOUN
ap-374	53	30	.	.	PUNCT
ap-374	54	1	they	they	PRON
ap-374	54	2	are	be	AUX
ap-374	54	3	in	in	ADP
ap-374	54	4	mutual	mutual	ADJ
ap-374	54	5	contact	contact	NOUN
ap-374	54	6	in	in	ADP
ap-374	54	7	the	the	DET
ap-374	54	8	undeformed	undeformed	ADJ
ap-374	54	9	state	state	NOUN
ap-374	54	10	,	,	PUNCT
ap-374	54	11	but	but	CCONJ
ap-374	54	12	can	can	AUX
ap-374	54	13	be	be	AUX
ap-374	54	14	disconnected	disconnect	VERB
ap-374	54	15	when	when	SCONJ
ap-374	54	16	the	the	DET
ap-374	54	17	contact	contact	NOUN
ap-374	54	18	conditions	condition	NOUN
ap-374	54	19	are	be	AUX
ap-374	54	20	violated	violate	VERB
ap-374	54	21	.	.	PUNCT
ap-374	55	1	the	the	DET
ap-374	55	2	computational	computational	ADJ
ap-374	55	3	model	model	NOUN
ap-374	55	4	is	be	AUX
ap-374	55	5	described	describe	VERB
ap-374	55	6	in	in	ADP
ap-374	55	7	the	the	DET
ap-374	55	8	following	follow	VERB
ap-374	55	9	paragraph	paragraph	NOUN
ap-374	55	10	,	,	PUNCT
ap-374	55	11	where	where	SCONJ
ap-374	55	12	the	the	DET
ap-374	55	13	relations	relation	NOUN
ap-374	55	14	needed	need	VERB
ap-374	55	15	for	for	ADP
ap-374	55	16	numerical	numerical	ADJ
ap-374	55	17	computation	computation	NOUN
ap-374	55	18	are	be	AUX
ap-374	55	19	also	also	ADV
ap-374	55	20	introduced	introduce	VERB
ap-374	55	21	.	.	PUNCT
ap-374	56	1	the	the	DET
ap-374	56	2	interface	interface	NOUN
ap-374	56	3	conditions	condition	NOUN
ap-374	56	4	are	be	AUX
ap-374	56	5	formulated	formulate	VERB
ap-374	56	6	in	in	ADP
ap-374	56	7	paragraph	paragraph	NOUN
ap-374	56	8	2.2	2.2	NUM
ap-374	56	9	,	,	PUNCT
ap-374	56	10	where	where	SCONJ
ap-374	56	11	the	the	DET
ap-374	56	12	lagrangian	lagrangian	ADJ
ap-374	56	13	principle	principle	NOUN
ap-374	56	14	is	be	AUX
ap-374	56	15	based	base	VERB
ap-374	56	16	on	on	ADP
ap-374	56	17	the	the	DET
ap-374	56	18	penalty	penalty	NOUN
ap-374	56	19	method	method	NOUN
ap-374	56	20	.	.	PUNCT
ap-374	57	1	the	the	DET
ap-374	57	2	penalty	penalty	NOUN
ap-374	57	3	parameters	parameter	NOUN
ap-374	57	4	are	be	AUX
ap-374	57	5	spring	spring	NOUN
ap-374	57	6	stiffnesses	stiffness	NOUN
ap-374	57	7	;	;	PUNCT
ap-374	57	8	the	the	DET
ap-374	57	9	springs	spring	NOUN
ap-374	57	10	connect	connect	VERB
ap-374	57	11	the	the	DET
ap-374	57	12	adjacent	adjacent	ADJ
ap-374	57	13	elements	element	NOUN
ap-374	57	14	.	.	PUNCT
ap-374	58	1	the	the	DET
ap-374	58	2	material	material	ADJ
ap-374	58	3	characteristics	characteristic	NOUN
ap-374	58	4	of	of	ADP
ap-374	58	5	springs	spring	NOUN
ap-374	58	6	can	can	AUX
ap-374	58	7	possess	possess	VERB
ap-374	58	8	a	a	DET
ap-374	58	9	large	large	ADJ
ap-374	58	10	value	value	NOUN
ap-374	58	11	to	to	PART
ap-374	58	12	ensure	ensure	VERB
ap-374	58	13	the	the	DET
ap-374	58	14	contact	contact	NOUN
ap-374	58	15	constraints	constraint	NOUN
ap-374	58	16	.	.	PUNCT
ap-374	59	1	on	on	ADP
ap-374	59	2	the	the	DET
ap-374	59	3	other	other	ADJ
ap-374	59	4	hand	hand	NOUN
ap-374	59	5	,	,	PUNCT
ap-374	59	6	if	if	SCONJ
ap-374	59	7	,	,	PUNCT
ap-374	59	8	say	say	INTJ
ap-374	59	9	,	,	PUNCT
ap-374	59	10	the	the	DET
ap-374	59	11	tensile	tensile	NOUN
ap-374	59	12	strength	strength	NOUN
ap-374	59	13	condition	condition	NOUN
ap-374	59	14	is	be	AUX
ap-374	59	15	violated	violate	VERB
ap-374	59	16	,	,	PUNCT
ap-374	59	17	the	the	DET
ap-374	59	18	spring	spring	NOUN
ap-374	59	19	parameters	parameter	NOUN
ap-374	59	20	tend	tend	VERB
ap-374	59	21	to	to	ADP
ap-374	59	22	zero	zero	NUM
ap-374	59	23	,	,	PUNCT
ap-374	59	24	and	and	CCONJ
ap-374	59	25	in	in	ADP
ap-374	59	26	this	this	DET
ap-374	59	27	case	case	NOUN
ap-374	59	28	naturally	naturally	ADV
ap-374	59	29	no	no	DET
ap-374	59	30	energy	energy	NOUN
ap-374	59	31	contribution	contribution	NOUN
ap-374	59	32	in	in	ADP
ap-374	59	33	the	the	DET
ap-374	59	34	normal	normal	ADJ
ap-374	59	35	direction	direction	NOUN
ap-374	59	36	to	to	ADP
ap-374	59	37	the	the	DET
ap-374	59	38	element	element	NOUN
ap-374	59	39	boundary	boundary	NOUN
ap-374	59	40	appears	appear	VERB
ap-374	59	41	in	in	ADP
ap-374	59	42	the	the	DET
ap-374	59	43	energy	energy	NOUN
ap-374	59	44	functional	functional	ADJ
ap-374	59	45	in	in	ADP
ap-374	59	46	this	this	DET
ap-374	59	47	case	case	NOUN
ap-374	59	48	.	.	PUNCT
ap-374	60	1	this	this	DET
ap-374	60	2	process	process	NOUN
ap-374	60	3	excludes	exclude	VERB
ap-374	60	4	the	the	DET
ap-374	60	5	possibility	possibility	NOUN
ap-374	60	6	of	of	ADP
ap-374	60	7	a	a	DET
ap-374	60	8	multivalue	multivalue	NOUN
ap-374	60	9	solution	solution	NOUN
ap-374	60	10	,	,	PUNCT
ap-374	60	11	and	and	CCONJ
ap-374	60	12	uniqueness	uniqueness	NOUN
ap-374	60	13	of	of	ADP
ap-374	60	14	the	the	DET
ap-374	60	15	solution	solution	NOUN
ap-374	60	16	of	of	ADP
ap-374	60	17	the	the	DET
ap-374	60	18	trial	trial	NOUN
ap-374	60	19	problem	problem	NOUN
ap-374	60	20	is	be	AUX
ap-374	60	21	ensured	ensure	VERB
ap-374	60	22	.	.	PUNCT
ap-374	61	1	if	if	SCONJ
ap-374	61	2	we	we	PRON
ap-374	61	3	cut	cut	VERB
ap-374	61	4	out	out	ADP
ap-374	61	5	the	the	DET
ap-374	61	6	springs	spring	NOUN
ap-374	61	7	when	when	SCONJ
ap-374	61	8	a	a	DET
ap-374	61	9	certain	certain	ADJ
ap-374	61	10	interfacial	interfacial	ADJ
ap-374	61	11	condition	condition	NOUN
ap-374	61	12	is	be	AUX
ap-374	61	13	violated	violate	VERB
ap-374	61	14	,	,	PUNCT
ap-374	61	15	the	the	DET
ap-374	61	16	problem	problem	NOUN
ap-374	61	17	turns	turn	VERB
ap-374	61	18	to	to	ADP
ap-374	61	19	singular	singular	NOUN
ap-374	61	20	and	and	CCONJ
ap-374	61	21	has	have	VERB
ap-374	61	22	not	not	PART
ap-374	61	23	unique	unique	ADJ
ap-374	61	24	solution	solution	NOUN
ap-374	61	25	.	.	PUNCT
ap-374	62	1	then	then	ADV
ap-374	62	2	the	the	DET
ap-374	62	3	way	way	NOUN
ap-374	62	4	on	on	ADP
ap-374	62	5	how	how	SCONJ
ap-374	62	6	the	the	DET
ap-374	62	7	particles	particle	NOUN
ap-374	62	8	move	move	VERB
ap-374	62	9	in	in	ADP
ap-374	62	10	some	some	DET
ap-374	62	11	later	later	ADJ
ap-374	62	12	stages	stage	NOUN
ap-374	62	13	of	of	ADP
ap-374	62	14	destruction	destruction	NOUN
ap-374	62	15	of	of	ADP
ap-374	62	16	the	the	DET
ap-374	62	17	trial	trial	NOUN
ap-374	62	18	structure	structure	NOUN
ap-374	62	19	can	can	AUX
ap-374	62	20	not	not	PART
ap-374	62	21	be	be	AUX
ap-374	62	22	described	describe	VERB
ap-374	62	23	.	.	PUNCT
ap-374	63	1	the	the	DET
ap-374	63	2	hexagonal	hexagonal	ADJ
ap-374	63	3	particles	particle	NOUN
ap-374	63	4	are	be	AUX
ap-374	63	5	studied	study	VERB
ap-374	63	6	under	under	ADP
ap-374	63	7	various	various	ADJ
ap-374	63	8	contact	contact	NOUN
ap-374	63	9	(	(	PUNCT
ap-374	63	10	interfacial	interfacial	ADJ
ap-374	63	11	)	)	PUNCT
ap-374	63	12	conditions	condition	NOUN
ap-374	63	13	of	of	ADP
ap-374	63	14	the	the	DET
ap-374	63	15	grain	grain	NOUN
ap-374	63	16	particles	particle	NOUN
ap-374	63	17	(	(	PUNCT
ap-374	63	18	elements	element	NOUN
ap-374	63	19	)	)	PUNCT
ap-374	63	20	.	.	PUNCT
ap-374	64	1	in	in	ADP
ap-374	64	2	our	our	PRON
ap-374	64	3	paper	paper	NOUN
ap-374	64	4	two	two	NUM
ap-374	64	5	contact	contact	NOUN
ap-374	64	6	conditions	condition	NOUN
ap-374	64	7	are	be	AUX
ap-374	64	8	considered	consider	VERB
ap-374	64	9	:	:	PUNCT
ap-374	64	10	�	�	PROPN
ap-374	64	11	the	the	DET
ap-374	64	12	generalized	generalize	VERB
ap-374	64	13	mohr	mohr	PROPN
ap-374	64	14	-	-	PUNCT
ap-374	64	15	coulomb	coulomb	NOUN
ap-374	64	16	hypothesis	hypothesis	NOUN
ap-374	64	17	,	,	PUNCT
ap-374	64	18	with	with	ADP
ap-374	64	19	exclusion	exclusion	NOUN
ap-374	64	20	of	of	ADP
ap-374	64	21	non	non	ADJ
ap-374	64	22	-	-	ADJ
ap-374	64	23	admissible	admissible	ADJ
ap-374	64	24	tensile	tensile	NOUN
ap-374	64	25	stresses	stress	NOUN
ap-374	64	26	along	along	ADP
ap-374	64	27	the	the	DET
ap-374	64	28	contact	contact	NOUN
ap-374	64	29	(	(	PUNCT
ap-374	64	30	a	a	DET
ap-374	64	31	rock	rock	NOUN
ap-374	64	32	mass	mass	NOUN
ap-374	64	33	)	)	PUNCT
ap-374	64	34	,	,	PUNCT
ap-374	64	35	�	�	PROPN
ap-374	64	36	limit	limit	VERB
ap-374	64	37	state	state	NOUN
ap-374	64	38	of	of	ADP
ap-374	64	39	shear	shear	NOUN
ap-374	64	40	stresses	stress	NOUN
ap-374	64	41	and	and	CCONJ
ap-374	64	42	exclusion	exclusion	NOUN
ap-374	64	43	of	of	ADP
ap-374	64	44	tensile	tensile	NOUN
ap-374	64	45	tractions	traction	NOUN
ap-374	64	46	along	along	ADP
ap-374	64	47	the	the	DET
ap-374	64	48	contact	contact	NOUN
ap-374	64	49	(	(	PUNCT
ap-374	64	50	a	a	DET
ap-374	64	51	brittle	brittle	ADJ
ap-374	64	52	coal	coal	NOUN
ap-374	64	53	seam	seam	NOUN
ap-374	64	54	)	)	PUNCT
ap-374	64	55	.	.	PUNCT
ap-374	65	1	the	the	DET
ap-374	65	2	first	first	ADJ
ap-374	65	3	case	case	NOUN
ap-374	65	4	is	be	AUX
ap-374	65	5	generally	generally	ADV
ap-374	65	6	connected	connect	VERB
ap-374	65	7	with	with	ADP
ap-374	65	8	applications	application	NOUN
ap-374	65	9	in	in	ADP
ap-374	65	10	geotechnics	geotechnic	NOUN
ap-374	65	11	,	,	PUNCT
ap-374	65	12	composite	composite	ADJ
ap-374	65	13	materials	material	NOUN
ap-374	65	14	,	,	PUNCT
ap-374	65	15	shotcrete	shotcrete	NOUN
ap-374	65	16	,	,	PUNCT
ap-374	65	17	etc	etc	X
ap-374	65	18	.	.	X
ap-374	65	19	,	,	PUNCT
ap-374	65	20	and	and	CCONJ
ap-374	65	21	the	the	DET
ap-374	65	22	second	second	ADJ
ap-374	65	23	case	case	NOUN
ap-374	65	24	is	be	AUX
ap-374	65	25	more	more	ADV
ap-374	65	26	appropriate	appropriate	ADJ
ap-374	65	27	for	for	ADP
ap-374	65	28	applications	application	NOUN
ap-374	65	29	in	in	ADP
ap-374	65	30	underground	underground	ADJ
ap-374	65	31	bumps	bump	NOUN
ap-374	65	32	or	or	CCONJ
ap-374	65	33	rock	rock	NOUN
ap-374	65	34	bursts	burst	NOUN
ap-374	65	35	.	.	PUNCT
ap-374	66	1	a	a	DET
ap-374	66	2	two	two	NUM
ap-374	66	3	-	-	PUNCT
ap-374	66	4	dimensional	dimensional	ADJ
ap-374	66	5	formulation	formulation	NOUN
ap-374	66	6	and	and	CCONJ
ap-374	66	7	its	its	PRON
ap-374	66	8	solution	solution	NOUN
ap-374	66	9	have	have	AUX
ap-374	66	10	been	be	AUX
ap-374	66	11	prepared	prepare	VERB
ap-374	66	12	and	and	CCONJ
ap-374	66	13	are	be	AUX
ap-374	66	14	studied	study	VERB
ap-374	66	15	in	in	ADP
ap-374	66	16	this	this	DET
ap-374	66	17	paper	paper	NOUN
ap-374	66	18	.	.	PUNCT
ap-374	67	1	the	the	DET
ap-374	67	2	problem	problem	NOUN
ap-374	67	3	formulated	formulate	VERB
ap-374	67	4	in	in	ADP
ap-374	67	5	terms	term	NOUN
ap-374	67	6	of	of	ADP
ap-374	67	7	hexagonal	hexagonal	ADJ
ap-374	67	8	elements	element	NOUN
ap-374	67	9	(	(	PUNCT
ap-374	67	10	which	which	PRON
ap-374	67	11	are	be	AUX
ap-374	67	12	not	not	PART
ap-374	67	13	necessarily	necessarily	ADV
ap-374	67	14	mutually	mutually	ADV
ap-374	67	15	connected	connect	VERB
ap-374	67	16	during	during	ADP
ap-374	67	17	the	the	DET
ap-374	67	18	loading	loading	NOUN
ap-374	67	19	process	process	NOUN
ap-374	67	20	of	of	ADP
ap-374	67	21	the	the	DET
ap-374	67	22	body	body	NOUN
ap-374	67	23	,	,	PUNCT
ap-374	67	24	because	because	SCONJ
ap-374	67	25	of	of	ADP
ap-374	67	26	nonlinearities	nonlinearitie	NOUN
ap-374	67	27	arising	arise	VERB
ap-374	67	28	due	due	ADP
ap-374	67	29	to	to	ADP
ap-374	67	30	the	the	DET
ap-374	67	31	interfacial	interfacial	ADJ
ap-374	67	32	conditions	condition	NOUN
ap-374	67	33	)	)	PUNCT
ap-374	67	34	enables	enable	VERB
ap-374	67	35	us	we	PRON
ap-374	67	36	to	to	PART
ap-374	67	37	simulate	simulate	VERB
ap-374	67	38	that	that	DET
ap-374	67	39	crack	crack	NOUN
ap-374	67	40	propagate	propagate	NOUN
ap-374	67	41	.	.	PUNCT
ap-374	68	1	the	the	DET
ap-374	68	2	cracking	cracking	NOUN
ap-374	68	3	of	of	ADP
ap-374	68	4	the	the	DET
ap-374	68	5	medium	medium	NOUN
ap-374	68	6	can	can	AUX
ap-374	68	7	be	be	AUX
ap-374	68	8	described	describe	VERB
ap-374	68	9	in	in	ADP
ap-374	68	10	such	such	DET
ap-374	68	11	a	a	DET
ap-374	68	12	way	way	NOUN
ap-374	68	13	that	that	PRON
ap-374	68	14	the	the	DET
ap-374	68	15	local	local	ADJ
ap-374	68	16	damage	damage	NOUN
ap-374	68	17	may	may	AUX
ap-374	68	18	be	be	AUX
ap-374	68	19	derived	derive	VERB
ap-374	68	20	.	.	PUNCT
ap-374	69	1	local	local	ADJ
ap-374	69	2	deterioration	deterioration	NOUN
ap-374	69	3	of	of	ADP
ap-374	69	4	the	the	DET
ap-374	69	5	material	material	NOUN
ap-374	69	6	is	be	AUX
ap-374	69	7	also	also	ADV
ap-374	69	8	shown	show	VERB
ap-374	69	9	in	in	ADP
ap-374	69	10	the	the	DET
ap-374	69	11	pictures	picture	NOUN
ap-374	69	12	drawn	draw	VERB
ap-374	69	13	for	for	ADP
ap-374	69	14	particular	particular	ADJ
ap-374	69	15	examples	example	NOUN
ap-374	69	16	.	.	PUNCT
ap-374	70	1	such	such	DET
ap-374	70	2	a	a	DET
ap-374	70	3	movement	movement	NOUN
ap-374	70	4	of	of	ADP
ap-374	70	5	elements	element	NOUN
ap-374	70	6	and	and	CCONJ
ap-374	70	7	change	change	NOUN
ap-374	70	8	of	of	ADP
ap-374	70	9	stresses	stress	NOUN
ap-374	70	10	probably	probably	ADV
ap-374	70	11	can	can	AUX
ap-374	70	12	not	not	PART
ap-374	70	13	be	be	AUX
ap-374	70	14	obtained	obtain	VERB
ap-374	70	15	from	from	ADP
ap-374	70	16	continuous	continuous	ADJ
ap-374	70	17	numerical	numerical	ADJ
ap-374	70	18	methods	method	NOUN
ap-374	70	19	.	.	PUNCT
ap-374	71	1	2.1	2.1	NUM
ap-374	71	2	computational	computational	ADJ
ap-374	71	3	model	model	NOUN
ap-374	71	4	let	let	VERB
ap-374	71	5	us	we	PRON
ap-374	71	6	now	now	ADV
ap-374	71	7	consider	consider	VERB
ap-374	71	8	a	a	DET
ap-374	71	9	single	single	ADJ
ap-374	71	10	hexagonal	hexagonal	ADJ
ap-374	71	11	element	element	NOUN
ap-374	71	12	(	(	PUNCT
ap-374	71	13	described	describe	VERB
ap-374	71	14	by	by	ADP
ap-374	71	15	domain	domain	NOUN
ap-374	71	16	with	with	ADP
ap-374	71	17	its	its	PRON
ap-374	71	18	boundary	boundary	NOUN
ap-374	71	19	)	)	PUNCT
ap-374	71	20	.	.	PUNCT
ap-374	72	1	its	its	PRON
ap-374	72	2	connection	connection	NOUN
ap-374	72	3	with	with	ADP
ap-374	72	4	the	the	DET
ap-374	72	5	adjacent	adjacent	ADJ
ap-374	72	6	elements	element	NOUN
ap-374	72	7	is	be	AUX
ap-374	72	8	shown	show	VERB
ap-374	72	9	in	in	ADP
ap-374	72	10	fig	fig	NOUN
ap-374	72	11	.	.	PUNCT
ap-374	73	1	1	1	X
ap-374	73	2	.	.	X
ap-374	74	1	in	in	ADP
ap-374	74	2	each	each	DET
ap-374	74	3	hexagonal	hexagonal	ADJ
ap-374	74	4	element	element	NOUN
ap-374	74	5	,	,	PUNCT
ap-374	74	6	the	the	DET
ap-374	74	7	pseudo	pseudo	NOUN
ap-374	74	8	-	-	ADJ
ap-374	74	9	elastic	elastic	ADJ
ap-374	74	10	material	material	NOUN
ap-374	74	11	properties	property	NOUN
ap-374	74	12	are	be	AUX
ap-374	74	13	taken	take	VERB
ap-374	74	14	into	into	ADP
ap-374	74	15	consideration	consideration	NOUN
ap-374	74	16	,	,	PUNCT
ap-374	74	17	i.e.	i.e.	X
ap-374	74	18	,	,	PUNCT
ap-374	74	19	in	in	ADP
ap-374	74	20	each	each	DET
ap-374	74	21	iteration	iteration	NOUN
ap-374	74	22	step	step	NOUN
ap-374	74	23	the	the	DET
ap-374	74	24	element	element	NOUN
ap-374	74	25	behaves	behave	VERB
ap-374	74	26	linearly	linearly	ADV
ap-374	74	27	,	,	PUNCT
ap-374	74	28	but	but	CCONJ
ap-374	74	29	the	the	DET
ap-374	74	30	material	material	NOUN
ap-374	74	31	properties	property	NOUN
ap-374	74	32	can	can	AUX
ap-374	74	33	change	change	VERB
ap-374	74	34	during	during	ADP
ap-374	74	35	the	the	DET
ap-374	74	36	process	process	NOUN
ap-374	74	37	of	of	ADP
ap-374	74	38	loading	loading	NOUN
ap-374	74	39	and	and	CCONJ
ap-374	74	40	unloading	unloading	NOUN
ap-374	74	41	.	.	PUNCT
ap-374	75	1	this	this	PRON
ap-374	75	2	makes	make	VERB
ap-374	75	3	it	it	PRON
ap-374	75	4	possible	possible	ADJ
ap-374	75	5	to	to	PART
ap-374	75	6	introduce	introduce	VERB
ap-374	75	7	only	only	ADV
ap-374	75	8	an	an	DET
ap-374	75	9	elastic	elastic	ADJ
ap-374	75	10	material	material	NOUN
ap-374	75	11	stiffness	stiffness	NOUN
ap-374	75	12	matrix	matrix	NOUN
ap-374	75	13	,	,	PUNCT
ap-374	75	14	which	which	PRON
ap-374	75	15	is	be	AUX
ap-374	75	16	homogeneous	homogeneous	ADJ
ap-374	75	17	and	and	CCONJ
ap-374	75	18	isotropic	isotropic	NOUN
ap-374	75	19	,	,	PUNCT
ap-374	75	20	and	and	CCONJ
ap-374	75	21	we	we	PRON
ap-374	75	22	get	get	VERB
ap-374	75	23	well	well	ADV
ap-374	75	24	-	-	PUNCT
ap-374	75	25	known	know	VERB
ap-374	75	26	integral	integral	ADJ
ap-374	75	27	equations	equation	NOUN
ap-374	75	28	that	that	PRON
ap-374	75	29	are	be	AUX
ap-374	75	30	valid	valid	ADJ
ap-374	75	31	along	along	ADP
ap-374	75	32	the	the	DET
ap-374	75	33	boundary	boundary	ADJ
ap-374	75	34	abscissas	abscissa	NOUN
ap-374	75	35	of	of	ADP
ap-374	75	36	the	the	DET
ap-374	75	37	hexagons	hexagon	NOUN
ap-374	75	38	,	,	PUNCT
ap-374	75	39	[	[	X
ap-374	75	40	1	1	NUM
ap-374	75	41	]	]	PUNCT
ap-374	75	42	:	:	PUNCT
ap-374	75	43	�	�	PROPN
ap-374	75	44	�	�	PROPN
ap-374	75	45	�	�	PROPN
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ap-374	80	1	1	1	NUM
ap-374	80	2	:	:	PUNCT
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ap-374	85	1	i	i	PRON
ap-374	86	1	i	i	VERB
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ap-374	87	74	2	2	NUM
ap-374	87	75	2	2	NUM
ap-374	87	76	2	2	NUM
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ap-374	88	20	2	2	NUM
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ap-374	88	33	�	�	PROPN
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ap-374	88	77	1	1	NUM
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ap-374	88	79	1	1	NUM
ap-374	88	80	2	2	NUM
ap-374	88	81	1	1	NUM
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ap-374	88	84	u	u	X
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ap-374	89	1	i	i	PRON
ap-374	89	2	s	s	VERB
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ap-374	90	1	i	i	PRON
ap-374	90	2	s	s	X
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ap-374	91	1	d	d	PROPN
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ap-374	91	25	1	1	NUM
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ap-374	91	34	�	�	PROPN
ap-374	91	35	�	�	PROPN
ap-374	91	36	�	�	PROPN
ap-374	91	37	�	�	PROPN
ap-374	91	38	�	�	PROPN
ap-374	91	39	�	�	PROPN
ap-374	91	40	�	�	PROPN
ap-374	91	41	b	b	PROPN
ap-374	91	42	u	u	X
ap-374	91	43	k	k	PROPN
ap-374	91	44	t	t	X
ap-374	92	1	i	i	PRON
ap-374	93	1	i	i	PRON
ap-374	93	2	s	s	AUX
ap-374	93	3	ik	ik	PROPN
ap-374	93	4	d	d	PROPN
ap-374	93	5	*	*	PROPN
ap-374	93	6	,	,	PUNCT
ap-374	93	7	,	,	PUNCT
ap-374	93	8	,	,	PUNCT
ap-374	93	9	;	;	NOUN
ap-374	93	10	,	,	PUNCT
ap-374	93	11	,	,	PUNCT
ap-374	93	12	,	,	PUNCT
ap-374	93	13	x	x	SYM
ap-374	93	14	x	x	PRON
ap-374	93	15	�	�	PROPN
ap-374	93	16	�	�	PROPN
ap-374	93	17	�	�	PROPN
ap-374	93	18	(	(	PUNCT
ap-374	93	19	2	2	NUM
ap-374	93	20	)	)	PUNCT
ap-374	93	21	where	where	SCONJ
ap-374	93	22	ui	ui	PROPN
ap-374	93	23	s	s	PROPN
ap-374	93	24	and	and	CCONJ
ap-374	93	25	pi	pi	PROPN
ap-374	93	26	s	s	PART
ap-374	93	27	are	be	AUX
ap-374	93	28	the	the	DET
ap-374	93	29	values	value	NOUN
ap-374	93	30	of	of	ADP
ap-374	93	31	the	the	DET
ap-374	93	32	relevant	relevant	ADJ
ap-374	93	33	quantities	quantity	NOUN
ap-374	93	34	positioned	position	VERB
ap-374	93	35	at	at	ADP
ap-374	93	36	the	the	DET
ap-374	93	37	�	�	PROPN
ap-374	93	38	s	s	PART
ap-374	93	39	,	,	PUNCT
ap-374	93	40	s	s	VERB
ap-374	93	41	1	1	NUM
ap-374	93	42	,	,	PUNCT
ap-374	93	43	…	…	PUNCT
ap-374	93	44	,	,	PUNCT
ap-374	93	45	6	6	NUM
ap-374	93	46	,	,	PUNCT
ap-374	93	47	i.e.	i.e.	X
ap-374	93	48	,	,	PUNCT
ap-374	93	49	�	�	PROPN
ap-374	93	50	�	�	PROPN
ap-374	93	51	u	u	PROPN
ap-374	93	52	ui	ui	NOUN
ap-374	94	1	s	s	VERB
ap-374	95	1	i	i	PROPN
ap-374	95	2	s	s	PROPN
ap-374	95	3	�	�	PROPN
ap-374	95	4	�	�	PROPN
ap-374	95	5	and	and	CCONJ
ap-374	95	6	�	�	PROPN
ap-374	95	7	�	�	PROPN
ap-374	95	8	p	p	NOUN
ap-374	95	9	pi	pi	NOUN
ap-374	95	10	s	s	PART
ap-374	95	11	i	i	PROPN
ap-374	95	12	s	s	PROPN
ap-374	95	13	�	�	PROPN
ap-374	95	14	�	�	PROPN
ap-374	95	15	.	.	PUNCT
ap-374	96	1	moreover	moreover	ADV
ap-374	96	2	,	,	PUNCT
ap-374	96	3	the	the	DET
ap-374	96	4	vector	vector	NOUN
ap-374	96	5	of	of	ADP
ap-374	96	6	influences	influence	NOUN
ap-374	96	7	of	of	ADP
ap-374	96	8	the	the	DET
ap-374	96	9	volume	volume	NOUN
ap-374	96	10	weight	weight	NOUN
ap-374	96	11	forces	force	NOUN
ap-374	96	12	on	on	ADP
ap-374	96	13	the	the	DET
ap-374	96	14	boundary	boundary	ADJ
ap-374	96	15	abscissas	abscissas	PROPN
ap-374	96	16	is	be	AUX
ap-374	96	17	�	�	PROPN
ap-374	96	18	�	�	PROPN
ap-374	96	19	bs	bs	PROPN
ap-374	96	20	�	�	PROPN
ap-374	96	21	1	1	NUM
ap-374	96	22	2	2	NUM
ap-374	96	23	,	,	PUNCT
ap-374	96	24	,	,	PUNCT
ap-374	96	25	s	s	NOUN
ap-374	96	26	1	1	NUM
ap-374	96	27	,	,	PUNCT
ap-374	96	28	…	…	PUNCT
ap-374	96	29	,	,	PUNCT
ap-374	96	30	6	6	NUM
ap-374	96	31	,	,	PUNCT
ap-374	96	32	and	and	CCONJ
ap-374	96	33	�	�	PROPN
ap-374	96	34	�	�	PROPN
ap-374	96	35	�	�	PROPN
ap-374	96	36	�	�	PROPN
ap-374	97	1	k	k	X
ap-374	97	2	s	s	PROPN
ap-374	98	1	i	i	PRON
ap-374	98	2	s	s	PROPN
ap-374	98	3	ik	ik	PROPN
ap-374	98	4	s	s	PROPN
ap-374	98	5	d	d	PROPN
ap-374	98	6	�	�	PROPN
ap-374	98	7	�	�	PROPN
ap-374	98	8	�	�	PROPN
ap-374	98	9	�	�	PROPN
ap-374	98	10	�	�	PROPN
ap-374	98	11	b	b	PROPN
ap-374	98	12	u	u	X
ap-374	98	13	k	k	PROPN
ap-374	99	1	i	i	PRON
ap-374	99	2	*	*	PUNCT
ap-374	99	3	,	,	PUNCT
ap-374	99	4	,	,	PUNCT
ap-374	99	5	,	,	PUNCT
ap-374	99	6	x	x	SYM
ap-374	99	7	x	x	PRON
ap-374	99	8	�	�	PROPN
ap-374	99	9	�	�	PROPN
ap-374	99	10	�	�	PROPN
ap-374	99	11	1	1	NUM
ap-374	99	12	2	2	NUM
ap-374	99	13	1	1	NUM
ap-374	99	14	2	2	NUM
ap-374	99	15	.	.	PUNCT
ap-374	100	1	for	for	ADP
ap-374	100	2	better	well	ADJ
ap-374	100	3	and	and	CCONJ
ap-374	100	4	more	more	ADV
ap-374	100	5	convenient	convenient	ADJ
ap-374	100	6	computation	computation	NOUN
ap-374	100	7	,	,	PUNCT
ap-374	100	8	the	the	DET
ap-374	100	9	most	most	ADV
ap-374	100	10	important	important	ADJ
ap-374	100	11	integrals	integral	NOUN
ap-374	100	12	are	be	AUX
ap-374	100	13	given	give	VERB
ap-374	100	14	in	in	ADP
ap-374	100	15	the	the	DET
ap-374	100	16	appendix	appendix	NOUN
ap-374	100	17	.	.	PUNCT
ap-374	101	1	in	in	ADP
ap-374	101	2	this	this	DET
ap-374	101	3	way	way	NOUN
ap-374	101	4	,	,	PUNCT
ap-374	101	5	the	the	DET
ap-374	101	6	integrals	integral	NOUN
ap-374	101	7	in	in	ADP
ap-374	101	8	(	(	PUNCT
ap-374	101	9	2	2	NUM
ap-374	101	10	)	)	PUNCT
ap-374	101	11	may	may	AUX
ap-374	101	12	be	be	AUX
ap-374	101	13	calculated	calculate	VERB
ap-374	101	14	directly	directly	ADV
ap-374	101	15	,	,	PUNCT
ap-374	101	16	without	without	ADP
ap-374	101	17	numerical	numerical	ADJ
ap-374	101	18	integration	integration	NOUN
ap-374	101	19	.	.	PUNCT
ap-374	102	1	let	let	VERB
ap-374	102	2	us	we	PRON
ap-374	102	3	introduce	introduce	VERB
ap-374	102	4	vectors	vector	NOUN
ap-374	102	5	�	�	PROPN
ap-374	102	6	s	s	PART
ap-374	102	7	,	,	PUNCT
ap-374	102	8	�	�	PROPN
ap-374	102	9	s	s	PART
ap-374	102	10	,	,	PUNCT
ap-374	102	11	s	s	PART
ap-374	102	12	=	=	SYM
ap-374	102	13	1	1	NUM
ap-374	102	14	,	,	PUNCT
ap-374	102	15	…	…	PUNCT
ap-374	102	16	,	,	PUNCT
ap-374	102	17	6	6	NUM
ap-374	102	18	,	,	PUNCT
ap-374	102	19	and	and	CCONJ
ap-374	102	20	also	also	ADV
ap-374	102	21	u	u	NOUN
ap-374	102	22	and	and	CCONJ
ap-374	102	23	p	p	NOUN
ap-374	102	24	as	as	ADP
ap-374	102	25	:	:	PUNCT
ap-374	102	26	�	�	PROPN
ap-374	102	27	�	�	PROPN
ap-374	102	28	�	�	PROPN
ap-374	102	29	�	�	PROPN
ap-374	102	30	�	�	PROPN
ap-374	102	31	�	�	PROPN
ap-374	102	32	�	�	PROPN
ap-374	102	33	�	�	PROPN
ap-374	102	34	s	s	PART
ap-374	102	35	s	s	NOUN
ap-374	102	36	s	s	X
ap-374	102	37	s	s	X
ap-374	102	38	s	s	X
ap-374	102	39	s	s	PROPN
ap-374	102	40	�	�	PROPN
ap-374	102	41	�	�	PROPN
ap-374	102	42	�	�	PROPN
ap-374	102	43	�	�	PROPN
ap-374	102	44	�	�	PROPN
ap-374	102	45	�	�	PROPN
ap-374	102	46	�	�	PROPN
ap-374	102	47	�	�	PROPN
ap-374	102	48	�	�	PROPN
ap-374	102	49	u	u	PROPN
ap-374	102	50	u	u	NOUN
ap-374	102	51	p	p	NOUN
ap-374	102	52	p	p	PROPN
ap-374	102	53	1	1	NUM
ap-374	102	54	2	2	NUM
ap-374	102	55	1	1	NUM
ap-374	102	56	2	2	NUM
ap-374	102	57	1	1	NUM
ap-374	102	58	2	2	NUM
ap-374	102	59	3	3	NUM
ap-374	102	60	4	4	NUM
ap-374	102	61	5	5	NUM
ap-374	102	62	6	6	NUM
ap-374	102	63	,	,	PUNCT
ap-374	102	64	,	,	PUNCT
ap-374	102	65	u	u	PROPN
ap-374	102	66	�	�	PROPN
ap-374	102	67	�	�	PROPN
ap-374	102	68	�	�	PROPN
ap-374	102	69	�	�	PROPN
ap-374	102	70	�	�	PROPN
ap-374	102	71	�	�	PROPN
ap-374	102	72	�	�	PROPN
ap-374	102	73	,	,	PUNCT
ap-374	102	74	p	p	PROPN
ap-374	102	75	�	�	PROPN
ap-374	102	76	�	�	PROPN
ap-374	102	77	�	�	PROPN
ap-374	102	78	�	�	PROPN
ap-374	102	79	�	�	PROPN
ap-374	102	80	�	�	PROPN
ap-374	102	81	1	1	NUM
ap-374	102	82	2	2	NUM
ap-374	102	83	3	3	NUM
ap-374	102	84	4	4	NUM
ap-374	102	85	5	5	NUM
ap-374	102	86	6	6	NUM
ap-374	102	87	�	�	PROPN
ap-374	102	88	�	�	PROPN
ap-374	102	89	�	�	PROPN
ap-374	102	90	�	�	PROPN
ap-374	102	91	,	,	PUNCT
ap-374	102	92	b	b	PROPN
ap-374	102	93	b	b	PROPN
ap-374	102	94	b	b	PROPN
ap-374	102	95	b	b	PROPN
ap-374	102	96	b	b	PROPN
ap-374	102	97	b	b	PROPN
ap-374	102	98	b	b	PROPN
ap-374	102	99	1	1	NUM
ap-374	102	100	2	2	NUM
ap-374	102	101	3	3	NUM
ap-374	102	102	4	4	NUM
ap-374	102	103	5	5	NUM
ap-374	102	104	6	6	NUM
ap-374	102	105	�	�	PROPN
ap-374	102	106	�	�	PROPN
ap-374	102	107	�	�	PROPN
ap-374	102	108	�	�	PROPN
ap-374	102	109	�	�	PROPN
ap-374	102	110	�	�	PROPN
ap-374	102	111	k	k	PROPN
ap-374	102	112	s	s	X
ap-374	102	113	i	i	PRON
ap-374	102	114	s	s	PROPN
ap-374	102	115	ik	ik	PROPN
ap-374	102	116	s	s	PROPN
ap-374	102	117	k	k	PROPN
ap-374	102	118	s	s	X
ap-374	103	1	i	i	PRON
ap-374	103	2	s	s	VERB
ap-374	103	3	ik	ik	PROPN
ap-374	103	4	s	s	X
ap-374	103	5	s	s	X
ap-374	103	6	s	s	PROPN
ap-374	103	7	d	d	X
ap-374	103	8	d	d	PROPN
ap-374	103	9	�	�	PROPN
ap-374	103	10	�	�	PROPN
ap-374	103	11	�	�	PROPN
ap-374	103	12	�	�	PROPN
ap-374	103	13	�	�	PROPN
ap-374	103	14	�	�	PROPN
ap-374	103	15	�	�	PROPN
ap-374	103	16	�	�	PROPN
ap-374	103	17	u	u	PROPN
ap-374	104	1	p	p	PROPN
ap-374	104	2	p	p	X
ap-374	104	3	u	u	X
ap-374	104	4	i	i	PRON
ap-374	104	5	i	i	PRON
ap-374	104	6	*	*	PUNCT
ap-374	105	1	*	*	PUNCT
ap-374	105	2	,	,	PUNCT
ap-374	105	3	,	,	PUNCT
ap-374	105	4	,	,	PUNCT
ap-374	105	5	x	x	PUNCT
ap-374	105	6	x	x	PUNCT
ap-374	105	7	x	x	SYM
ap-374	105	8	x	x	PRON
ap-374	105	9	�	�	PROPN
ap-374	105	10	�	�	PROPN
ap-374	105	11	�	�	PROPN
ap-374	105	12	�	�	PROPN
ap-374	105	13	1	1	NUM
ap-374	105	14	2	2	NUM
ap-374	105	15	1	1	NUM
ap-374	105	16	2	2	NUM
ap-374	105	17	�	�	PROPN
ap-374	105	18	.	.	PUNCT
ap-374	106	1	using	use	VERB
ap-374	106	2	this	this	DET
ap-374	106	3	notation	notation	NOUN
ap-374	106	4	,	,	PUNCT
ap-374	106	5	the	the	DET
ap-374	106	6	relations	relation	NOUN
ap-374	106	7	on	on	ADP
ap-374	106	8	the	the	DET
ap-374	106	9	elements	element	NOUN
ap-374	106	10	(	(	PUNCT
ap-374	106	11	2	2	X
ap-374	106	12	)	)	PUNCT
ap-374	106	13	can	can	AUX
ap-374	106	14	be	be	AUX
ap-374	106	15	recorded	record	VERB
ap-374	106	16	as	as	ADP
ap-374	106	17	:	:	PUNCT
ap-374	106	18	au	au	PROPN
ap-374	106	19	bp	bp	PROPN
ap-374	106	20	b	b	PROPN
ap-374	106	21	�	�	PROPN
ap-374	106	22	�	�	PROPN
ap-374	106	23	(	(	PUNCT
ap-374	106	24	3	3	NUM
ap-374	106	25	)	)	PUNCT
ap-374	106	26	where	where	SCONJ
ap-374	106	27	a	a	PRON
ap-374	106	28	and	and	CCONJ
ap-374	106	29	b	b	NOUN
ap-374	106	30	are	be	AUX
ap-374	106	31	(	(	PUNCT
ap-374	106	32	12	12	NUM
ap-374	106	33	*	*	NUM
ap-374	106	34	12	12	NUM
ap-374	106	35	)	)	PUNCT
ap-374	106	36	matrices	matrix	NOUN
ap-374	106	37	,	,	PUNCT
ap-374	106	38	and	and	CCONJ
ap-374	106	39	their	their	PRON
ap-374	106	40	components	component	NOUN
ap-374	106	41	are	be	AUX
ap-374	106	42	singular	singular	ADJ
ap-374	106	43	integrals	integral	NOUN
ap-374	106	44	over	over	ADP
ap-374	106	45	the	the	DET
ap-374	106	46	boundary	boundary	ADJ
ap-374	106	47	abscissas	abscissa	NOUN
ap-374	106	48	.	.	PUNCT
ap-374	107	1	matrix	matrix	NOUN
ap-374	107	2	a	a	PRON
ap-374	107	3	is	be	AUX
ap-374	107	4	generally	generally	ADV
ap-374	107	5	singular	singular	ADJ
ap-374	107	6	,	,	PUNCT
ap-374	107	7	while	while	SCONJ
ap-374	107	8	matrix	matrix	NOUN
ap-374	107	9	b	b	NOUN
ap-374	107	10	is	be	AUX
ap-374	107	11	regular	regular	ADJ
ap-374	107	12	.	.	PUNCT
ap-374	108	1	this	this	DET
ap-374	108	2	fact	fact	NOUN
ap-374	108	3	enables	enable	VERB
ap-374	108	4	us	we	PRON
ap-374	108	5	to	to	PART
ap-374	108	6	rearrange	rearrange	VERB
ap-374	108	7	equations	equation	NOUN
ap-374	108	8	(	(	PUNCT
ap-374	108	9	3	3	NUM
ap-374	108	10	)	)	PUNCT
ap-374	108	11	into	into	ADP
ap-374	108	12	the	the	DET
ap-374	108	13	form	form	NOUN
ap-374	108	14	:	:	PUNCT
ap-374	108	15	ku	ku	PROPN
ap-374	108	16	p	p	PROPN
ap-374	108	17	v	v	PROPN
ap-374	108	18	k	k	PROPN
ap-374	108	19	b	b	PROPN
ap-374	108	20	a	a	DET
ap-374	108	21	v	v	PROPN
ap-374	108	22	b	b	PROPN
ap-374	108	23	b	b	PROPN
ap-374	108	24	�	�	PROPN
ap-374	108	25	�	�	PROPN
ap-374	108	26	�	�	PROPN
ap-374	108	27	�	�	PROPN
ap-374	108	28	�	�	PROPN
ap-374	108	29	�	�	PROPN
ap-374	108	30	,	,	PUNCT
ap-374	108	31	,	,	PUNCT
ap-374	108	32	1	1	NUM
ap-374	108	33	1	1	NUM
ap-374	108	34	(	(	PUNCT
ap-374	108	35	4	4	NUM
ap-374	108	36	)	)	PUNCT
ap-374	108	37	where	where	SCONJ
ap-374	108	38	the	the	DET
ap-374	108	39	stiffness	stiffness	ADJ
ap-374	108	40	matrix	matrix	NOUN
ap-374	108	41	k	k	NOUN
ap-374	108	42	is	be	AUX
ap-374	108	43	different	different	ADJ
ap-374	108	44	from	from	ADP
ap-374	108	45	that	that	PRON
ap-374	108	46	arising	arise	VERB
ap-374	108	47	in	in	ADP
ap-374	108	48	applications	application	NOUN
ap-374	108	49	of	of	ADP
ap-374	108	50	finite	finite	ADJ
ap-374	108	51	elements	element	NOUN
ap-374	108	52	(	(	PUNCT
ap-374	108	53	here	here	ADV
ap-374	108	54	it	it	PRON
ap-374	108	55	is	be	AUX
ap-374	108	56	prevailingly	prevailingly	ADV
ap-374	108	57	non	non	ADJ
ap-374	108	58	-	-	ADJ
ap-374	108	59	symmetric	symmetric	ADJ
ap-374	108	60	)	)	PUNCT
ap-374	108	61	,	,	PUNCT
ap-374	108	62	v	v	NOUN
ap-374	108	63	is	be	AUX
ap-374	108	64	the	the	DET
ap-374	108	65	vector	vector	NOUN
ap-374	108	66	of	of	ADP
ap-374	108	67	volume	volume	NOUN
ap-374	108	68	weight	weight	NOUN
ap-374	108	69	forces	force	NOUN
ap-374	108	70	concentrated	concentrate	VERB
ap-374	108	71	on	on	ADP
ap-374	108	72	the	the	DET
ap-374	108	73	boundary	boundary	ADJ
ap-374	108	74	abscissas	abscissa	NOUN
ap-374	108	75	(	(	PUNCT
ap-374	108	76	more	more	ADV
ap-374	108	77	precisely	precisely	ADV
ap-374	108	78	at	at	ADP
ap-374	108	79	the	the	DET
ap-374	108	80	point	point	NOUN
ap-374	108	81	�	�	PROPN
ap-374	108	82	)	)	PUNCT
ap-374	108	83	.	.	PUNCT
ap-374	109	1	in	in	ADP
ap-374	109	2	this	this	DET
ap-374	109	3	way	way	NOUN
ap-374	109	4	,	,	PUNCT
ap-374	109	5	the	the	DET
ap-374	109	6	discretized	discretized	ADJ
ap-374	109	7	problem	problem	NOUN
ap-374	109	8	becomes	become	VERB
ap-374	109	9	a	a	DET
ap-374	109	10	problem	problem	NOUN
ap-374	109	11	similar	similar	ADJ
ap-374	109	12	to	to	ADP
ap-374	109	13	the	the	DET
ap-374	109	14	fem	fem	NOUN
ap-374	109	15	.	.	PUNCT
ap-374	110	1	along	along	ADP
ap-374	110	2	the	the	DET
ap-374	110	3	adjacent	adjacent	ADJ
ap-374	110	4	boundary	boundary	ADJ
ap-374	110	5	abscissas	abscissa	NOUN
ap-374	110	6	it	it	PRON
ap-374	110	7	should	should	AUX
ap-374	110	8	hold	hold	VERB
ap-374	110	9	(	(	PUNCT
ap-374	110	10	pi	pi	PROPN
ap-374	110	11	�	�	PROPN
ap-374	110	12	are	be	AUX
ap-374	110	13	eshelbys	eshelby	NOUN
ap-374	110	14	’	'	PUNCT
ap-374	110	15	forces	force	NOUN
ap-374	110	16	):	):	PUNCT
ap-374	110	17	�	�	PROPN
ap-374	110	18	�	�	PROPN
ap-374	110	19	�	�	PROPN
ap-374	110	20	�	�	PROPN
ap-374	110	21	p	p	NOUN
ap-374	110	22	p	p	NOUN
ap-374	110	23	p	p	NOUN
ap-374	111	1	pi	pi	NOUN
ap-374	112	1	i	i	PRON
ap-374	113	1	i	i	PRON
ap-374	114	1	i	i	PRON
ap-374	114	2	�	�	PROPN
ap-374	114	3	�	�	PROPN
ap-374	114	4	�	�	PROPN
ap-374	114	5	�	�	PROPN
ap-374	114	6	�	�	PROPN
ap-374	114	7	�	�	PROPN
ap-374	114	8	�	�	PROPN
ap-374	114	9	�	�	PROPN
ap-374	114	10	�	�	PROPN
ap-374	114	11	,	,	PUNCT
ap-374	114	12	(	(	PUNCT
ap-374	114	13	5	5	X
ap-374	114	14	)	)	PUNCT
ap-374	114	15	where	where	SCONJ
ap-374	114	16	superscript	superscript	PROPN
ap-374	114	17	plus	plus	CCONJ
ap-374	114	18	means	mean	VERB
ap-374	114	19	from	from	ADP
ap-374	114	20	the	the	DET
ap-374	114	21	right	right	NOUN
ap-374	114	22	and	and	CCONJ
ap-374	114	23	minus	minus	CCONJ
ap-374	114	24	from	from	ADP
ap-374	114	25	the	the	DET
ap-374	114	26	left	left	NOUN
ap-374	114	27	(	(	PUNCT
ap-374	114	28	at	at	ADP
ap-374	114	29	most	most	ADV
ap-374	114	30	two	two	NUM
ap-374	114	31	particles	particle	NOUN
ap-374	114	32	can	can	AUX
ap-374	114	33	be	be	AUX
ap-374	114	34	in	in	ADP
ap-374	114	35	contact	contact	NOUN
ap-374	114	36	)	)	PUNCT
ap-374	114	37	.	.	PUNCT
ap-374	115	1	now	now	ADV
ap-374	115	2	using	use	VERB
ap-374	115	3	the	the	DET
ap-374	115	4	relations	relation	NOUN
ap-374	115	5	(	(	PUNCT
ap-374	115	6	4	4	NUM
ap-374	115	7	)	)	PUNCT
ap-374	115	8	and	and	CCONJ
ap-374	115	9	(	(	PUNCT
ap-374	115	10	5	5	NUM
ap-374	115	11	)	)	PUNCT
ap-374	115	12	,	,	PUNCT
ap-374	115	13	we	we	PRON
ap-374	115	14	get	get	VERB
ap-374	115	15	twice	twice	ADV
ap-374	115	16	as	as	ADV
ap-374	115	17	many	many	ADJ
ap-374	115	18	unknowns	unknown	NOUN
ap-374	115	19	as	as	ADP
ap-374	115	20	equations	equation	NOUN
ap-374	115	21	,	,	PUNCT
ap-374	115	22	because	because	SCONJ
ap-374	115	23	no	no	DET
ap-374	115	24	connection	connection	NOUN
ap-374	115	25	between	between	ADP
ap-374	115	26	the	the	DET
ap-374	115	27	elements	element	NOUN
ap-374	115	28	has	have	AUX
ap-374	115	29	yet	yet	ADV
ap-374	115	30	been	be	AUX
ap-374	115	31	introduced	introduce	VERB
ap-374	115	32	.	.	PUNCT
ap-374	116	1	equations	equation	NOUN
ap-374	116	2	(	(	PUNCT
ap-374	116	3	5	5	X
ap-374	116	4	)	)	PUNCT
ap-374	116	5	have	have	VERB
ap-374	116	6	to	to	PART
ap-374	116	7	be	be	AUX
ap-374	116	8	accomplished	accomplish	VERB
ap-374	116	9	by	by	ADP
ap-374	116	10	a	a	DET
ap-374	116	11	constraint	constraint	NOUN
ap-374	116	12	of	of	ADP
ap-374	116	13	the	the	DET
ap-374	116	14	type	type	NOUN
ap-374	116	15	�	�	PROPN
ap-374	116	16	�	�	PROPN
ap-374	116	17	k	k	PROPN
ap-374	116	18	u	u	NOUN
ap-374	116	19	u	u	NOUN
ap-374	117	1	pi	pi	NOUN
ap-374	118	1	i	i	INTJ
ap-374	119	1	i	i	PRON
ap-374	119	2	i	i	PROPN
ap-374	119	3	�	�	PROPN
ap-374	119	4	�	�	PROPN
ap-374	119	5	�	�	PROPN
ap-374	119	6	�	�	PROPN
ap-374	119	7	.	.	PUNCT
ap-374	120	1	(	(	PUNCT
ap-374	120	2	6	6	X
ap-374	120	3	)	)	PUNCT
ap-374	120	4	the	the	DET
ap-374	120	5	latter	latter	ADJ
ap-374	120	6	conditions	condition	NOUN
ap-374	120	7	are	be	AUX
ap-374	120	8	penalty	penalty	NOUN
ap-374	120	9	-	-	PUNCT
ap-374	120	10	like	like	ADJ
ap-374	120	11	conditions	condition	NOUN
ap-374	120	12	,	,	PUNCT
ap-374	120	13	since	since	SCONJ
ap-374	120	14	if	if	SCONJ
ap-374	120	15	ki	ki	PROPN
ap-374	120	16	is	be	AUX
ap-374	120	17	great	great	ADJ
ap-374	120	18	enough	enough	ADV
ap-374	120	19	,	,	PUNCT
ap-374	120	20	the	the	DET
ap-374	120	21	distribution	distribution	NOUN
ap-374	120	22	of	of	ADP
ap-374	120	23	displacements	displacement	NOUN
ap-374	120	24	is	be	AUX
ap-374	120	25	continuous	continuous	ADJ
ap-374	120	26	,	,	PUNCT
ap-374	120	27	and	and	CCONJ
ap-374	120	28	the	the	DET
ap-374	120	29	displacement	displacement	NOUN
ap-374	120	30	from	from	ADP
ap-374	120	31	the	the	DET
ap-374	120	32	right	right	NOUN
ap-374	120	33	is	be	AUX
ap-374	120	34	equal	equal	ADJ
ap-374	120	35	to	to	ADP
ap-374	120	36	the	the	DET
ap-374	120	37	displacement	displacement	NOUN
ap-374	120	38	from	from	ADP
ap-374	120	39	the	the	DET
ap-374	120	40	left	left	NOUN
ap-374	120	41	.	.	PUNCT
ap-374	121	1	these	these	DET
ap-374	121	2	conditions	condition	NOUN
ap-374	121	3	can	can	AUX
ap-374	121	4	locally	locally	ADV
ap-374	121	5	be	be	AUX
ap-374	121	6	violated	violate	VERB
ap-374	121	7	,	,	PUNCT
ap-374	121	8	because	because	SCONJ
ap-374	121	9	of	of	ADP
ap-374	121	10	the	the	DET
ap-374	121	11	contact	contact	NOUN
ap-374	121	12	conditions	condition	NOUN
ap-374	121	13	,	,	PUNCT
ap-374	121	14	which	which	PRON
ap-374	121	15	are	be	AUX
ap-374	121	16	discussed	discuss	VERB
ap-374	121	17	later	later	ADV
ap-374	121	18	in	in	ADP
ap-374	121	19	this	this	DET
ap-374	121	20	text	text	NOUN
ap-374	121	21	.	.	PUNCT
ap-374	122	1	introducing	introduce	VERB
ap-374	122	2	boundary	boundary	ADJ
ap-374	122	3	conditions	condition	NOUN
ap-374	122	4	and	and	CCONJ
ap-374	122	5	assuming	assume	VERB
ap-374	122	6	that	that	SCONJ
ap-374	122	7	ki	ki	PROPN
ap-374	122	8	remains	remain	VERB
ap-374	122	9	great	great	ADJ
ap-374	122	10	enough	enough	ADV
ap-374	122	11	leads	lead	VERB
ap-374	122	12	us	we	PRON
ap-374	122	13	to	to	ADP
ap-374	122	14	a	a	DET
ap-374	122	15	stable	stable	ADJ
ap-374	122	16	system	system	NOUN
ap-374	122	17	of	of	ADP
ap-374	122	18	equations	equation	NOUN
ap-374	122	19	delivering	deliver	VERB
ap-374	122	20	a	a	DET
ap-374	122	21	unique	unique	ADJ
ap-374	122	22	solution	solution	NOUN
ap-374	122	23	.	.	PUNCT
ap-374	123	1	even	even	ADV
ap-374	123	2	in	in	ADP
ap-374	123	3	the	the	DET
ap-374	123	4	case	case	NOUN
ap-374	123	5	when	when	SCONJ
ap-374	123	6	local	local	ADJ
ap-374	123	7	disturbances	disturbance	NOUN
ap-374	123	8	occur	occur	VERB
ap-374	123	9	,	,	PUNCT
ap-374	123	10	the	the	DET
ap-374	123	11	solution	solution	NOUN
ap-374	123	12	can	can	AUX
ap-374	123	13	be	be	AUX
ap-374	123	14	stable	stable	ADJ
ap-374	123	15	.	.	PUNCT
ap-374	124	1	it	it	PRON
ap-374	124	2	can	can	AUX
ap-374	124	3	happen	happen	VERB
ap-374	124	4	that	that	SCONJ
ap-374	124	5	there	there	PRON
ap-374	124	6	are	be	VERB
ap-374	124	7	too	too	ADV
ap-374	124	8	many	many	ADJ
ap-374	124	9	disturbances	disturbance	NOUN
ap-374	124	10	,	,	PUNCT
ap-374	124	11	e.g.	e.g.	ADV
ap-374	124	12	,	,	PUNCT
ap-374	124	13	dense	dense	ADJ
ap-374	124	14	occurrence	occurrence	NOUN
ap-374	124	15	of	of	ADP
ap-374	124	16	crack	crack	NOUN
ap-374	124	17	,	,	PUNCT
ap-374	124	18	and	and	CCONJ
ap-374	124	19	localized	localized	ADJ
ap-374	124	20	damage	damage	NOUN
ap-374	124	21	along	along	ADP
ap-374	124	22	a	a	DET
ap-374	124	23	path	path	NOUN
ap-374	124	24	(	(	PUNCT
ap-374	124	25	earth	earth	NOUN
ap-374	124	26	slope	slope	NOUN
ap-374	124	27	stability	stability	NOUN
ap-374	124	28	violation	violation	NOUN
ap-374	124	29	)	)	PUNCT
ap-374	124	30	.	.	PUNCT
ap-374	125	1	then	then	ADV
ap-374	125	2	the	the	DET
ap-374	125	3	solution	solution	NOUN
ap-374	125	4	is	be	AUX
ap-374	125	5	unstable	unstable	ADJ
ap-374	125	6	,	,	PUNCT
ap-374	125	7	and	and	CCONJ
ap-374	125	8	there	there	PRON
ap-374	125	9	is	be	VERB
ap-374	125	10	a	a	DET
ap-374	125	11	failure	failure	NOUN
ap-374	125	12	of	of	ADP
ap-374	125	13	the	the	DET
ap-374	125	14	structure	structure	NOUN
ap-374	125	15	.	.	PUNCT
ap-374	126	1	this	this	PRON
ap-374	126	2	is	be	AUX
ap-374	126	3	also	also	ADV
ap-374	126	4	,	,	PUNCT
ap-374	126	5	for	for	ADP
ap-374	126	6	example	example	NOUN
ap-374	126	7	,	,	PUNCT
ap-374	126	8	the	the	DET
ap-374	126	9	case	case	NOUN
ap-374	126	10	of	of	ADP
ap-374	126	11	a	a	DET
ap-374	126	12	rock	rock	NOUN
ap-374	126	13	burst	burst	NOUN
ap-374	126	14	.	.	PUNCT
ap-374	127	1	discretization	discretization	NOUN
ap-374	127	2	in	in	ADP
ap-374	127	3	the	the	DET
ap-374	127	4	previous	previous	ADJ
ap-374	127	5	sense	sense	NOUN
ap-374	127	6	leads	lead	VERB
ap-374	127	7	to	to	ADP
ap-374	127	8	a	a	DET
ap-374	127	9	nonlinear	nonlinear	ADJ
ap-374	127	10	system	system	NOUN
ap-374	127	11	of	of	ADP
ap-374	127	12	algebraic	algebraic	ADJ
ap-374	127	13	equations	equation	NOUN
ap-374	127	14	,	,	PUNCT
ap-374	127	15	which	which	PRON
ap-374	127	16	are	be	AUX
ap-374	127	17	solved	solve	VERB
ap-374	127	18	by	by	ADP
ap-374	127	19	an	an	DET
ap-374	127	20	over	over	ADP
ap-374	127	21	-	-	PUNCT
ap-374	127	22	relaxation	relaxation	NOUN
ap-374	127	23	iterative	iterative	NOUN
ap-374	127	24	procedure	procedure	NOUN
ap-374	127	25	.	.	PUNCT
ap-374	128	1	this	this	DET
ap-374	128	2	method	method	NOUN
ap-374	128	3	is	be	AUX
ap-374	128	4	sufficient	sufficient	ADJ
ap-374	128	5	for	for	ADP
ap-374	128	6	study	study	NOUN
ap-374	128	7	purposes	purpose	NOUN
ap-374	128	8	.	.	PUNCT
ap-374	129	1	for	for	ADP
ap-374	129	2	a	a	DET
ap-374	129	3	larger	large	ADJ
ap-374	129	4	range	range	NOUN
ap-374	129	5	of	of	ADP
ap-374	129	6	equations	equation	NOUN
ap-374	129	7	the	the	DET
ap-374	129	8	conjugate	conjugate	ADJ
ap-374	129	9	gradient	gradient	NOUN
ap-374	129	10	method	method	NOUN
ap-374	129	11	has	have	AUX
ap-374	129	12	been	be	AUX
ap-374	129	13	prepared	prepare	VERB
ap-374	129	14	.	.	PUNCT
ap-374	130	1	for	for	ADP
ap-374	130	2	displacements	displacement	NOUN
ap-374	130	3	inside	inside	ADP
ap-374	130	4	the	the	DET
ap-374	130	5	element	element	NOUN
ap-374	130	6	domain	domain	NOUN
ap-374	130	7	�	�	PROPN
ap-374	130	8	it	it	PRON
ap-374	130	9	holds	hold	VERB
ap-374	130	10	:	:	PUNCT
ap-374	130	11	�	�	PROPN
ap-374	130	12	�	�	PROPN
ap-374	130	13	�	�	PROPN
ap-374	130	14	�	�	PROPN
ap-374	130	15	u	u	PROPN
ap-374	130	16	p	p	X
ap-374	130	17	u	u	X
ap-374	130	18	u	u	NOUN
ap-374	130	19	p	p	NOUN
ap-374	130	20	is	be	AUX
ap-374	130	21	k	k	PROPN
ap-374	131	1	i	i	PRON
ap-374	131	2	s	s	PROPN
ap-374	131	3	ik	ik	PROPN
ap-374	131	4	*	*	PUNCT
ap-374	132	1	i	i	PRON
ap-374	132	2	s	s	VERB
ap-374	132	3	ik	ik	PROPN
ap-374	132	4	*	*	PUNCT
ap-374	132	5	d	d	X
ap-374	132	6	s	s	PROPN
ap-374	132	7	�	�	PROPN
ap-374	132	8	�	�	PROPN
ap-374	132	9	�	�	PROPN
ap-374	132	10	�	�	PROPN
ap-374	132	11	�	�	PROPN
ap-374	132	12	�	�	PROPN
ap-374	132	13	�	�	PROPN
ap-374	132	14	�	�	PROPN
ap-374	132	15	�	�	PROPN
ap-374	132	16	�	�	PROPN
ap-374	132	17	�	�	PROPN
ap-374	132	18	�	�	PROPN
ap-374	132	19	x	x	SYM
ap-374	132	20	x	x	SYM
ap-374	132	21	x	x	X
ap-374	132	22	,	,	PUNCT
ap-374	132	23	�	�	PROPN
ap-374	132	24	1	1	NUM
ap-374	132	25	2	2	NUM
ap-374	132	26	1	1	NUM
ap-374	132	27	6	6	NUM
ap-374	132	28	�	�	PROPN
ap-374	132	29	�	�	PROPN
ap-374	132	30	�	�	PROPN
ap-374	132	31	�	�	PROPN
ap-374	132	32	,	,	PUNCT
ap-374	132	33	,	,	PUNCT
ap-374	132	34	,	,	PUNCT
ap-374	132	35	,	,	PUNCT
ap-374	132	36	,	,	PUNCT
ap-374	132	37	�	�	PROPN
ap-374	132	38	�	�	PROPN
ap-374	132	39	d	d	PROPN
ap-374	132	40	d	d	X
ap-374	132	41	s	s	X
ap-374	133	1	i	i	PRON
ap-374	133	2	s	s	PROPN
ap-374	133	3	ik	ik	PROPN
ap-374	133	4	*	*	PUNCT
ap-374	133	5	x	x	SYM
ap-374	133	6	x	x	SYM
ap-374	133	7	x	x	SYM
ap-374	133	8	�	�	PROPN
ap-374	133	9	�	�	PROPN
ap-374	133	10	�	�	PROPN
ap-374	133	11	�	�	PROPN
ap-374	133	12	�	�	PROPN
ap-374	133	13	�	�	PROPN
ap-374	133	14	�	�	PROPN
ap-374	133	15	�	�	PROPN
ap-374	133	16	�	�	PROPN
ap-374	133	17	�	�	PROPN
ap-374	133	18	�	�	PROPN
ap-374	133	19	�	�	PROPN
ap-374	133	20	b	b	PROPN
ap-374	133	21	u	u	X
ap-374	134	1	k	k	PROPN
ap-374	134	2	i	i	NOUN
ap-374	134	3	1	1	NUM
ap-374	134	4	2	2	NUM
ap-374	134	5	1	1	NUM
ap-374	134	6	2	2	NUM
ap-374	134	7	(	(	PUNCT
ap-374	134	8	7	7	NUM
ap-374	134	9	)	)	PUNCT
ap-374	134	10	where	where	SCONJ
ap-374	134	11	the	the	DET
ap-374	134	12	element	element	ADJ
ap-374	134	13	boundary	boundary	ADJ
ap-374	134	14	displacements	displacement	NOUN
ap-374	134	15	and	and	CCONJ
ap-374	134	16	tractions	traction	NOUN
ap-374	134	17	are	be	AUX
ap-374	134	18	known	know	VERB
ap-374	134	19	from	from	ADP
ap-374	134	20	the	the	DET
ap-374	134	21	previous	previous	ADJ
ap-374	134	22	computation	computation	NOUN
ap-374	134	23	,	,	PUNCT
ap-374	134	24	providing	provide	VERB
ap-374	134	25	the	the	DET
ap-374	134	26	solution	solution	NOUN
ap-374	134	27	is	be	AUX
ap-374	134	28	stable	stable	ADJ
ap-374	134	29	.	.	PUNCT
ap-374	135	1	using	use	VERB
ap-374	135	2	kinematic	kinematic	ADJ
ap-374	135	3	equations	equation	NOUN
ap-374	135	4	and	and	CCONJ
ap-374	135	5	hooke	hooke	PROPN
ap-374	135	6	’s	’s	PART
ap-374	135	7	law	law	NOUN
ap-374	135	8	,	,	PUNCT
ap-374	135	9	the	the	DET
ap-374	135	10	internal	internal	ADJ
ap-374	135	11	stresses	stress	NOUN
ap-374	135	12	can	can	AUX
ap-374	135	13	be	be	AUX
ap-374	135	14	calculated	calculate	VERB
ap-374	135	15	from	from	ADP
ap-374	135	16	(	(	PUNCT
ap-374	135	17	7	7	NUM
ap-374	135	18	)	)	PUNCT
ap-374	135	19	.	.	PUNCT
ap-374	136	1	there	there	PRON
ap-374	136	2	is	be	VERB
ap-374	136	3	no	no	DET
ap-374	136	4	44	44	NUM
ap-374	136	5	©	©	PROPN
ap-374	136	6	czech	czech	PROPN
ap-374	136	7	technical	technical	PROPN
ap-374	136	8	university	university	PROPN
ap-374	136	9	publishing	publishing	NOUN
ap-374	136	10	house	house	NOUN
ap-374	136	11	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-374	136	12	acta	acta	PROPN
ap-374	136	13	polytechnica	polytechnica	PROPN
ap-374	136	14	vol	vol	NOUN
ap-374	136	15	.	.	PUNCT
ap-374	137	1	42	42	NUM
ap-374	137	2	no	no	INTJ
ap-374	137	3	.	.	PUNCT
ap-374	138	1	4/2002	4/2002	DET
ap-374	138	2	danger	danger	NOUN
ap-374	138	3	of	of	ADP
ap-374	138	4	singularities	singularity	NOUN
ap-374	138	5	,	,	PUNCT
ap-374	138	6	as	as	SCONJ
ap-374	138	7	the	the	DET
ap-374	138	8	points	point	NOUN
ap-374	138	9	x	x	X
ap-374	138	10	and	and	CCONJ
ap-374	138	11	�	�	PROPN
ap-374	138	12	never	never	ADV
ap-374	138	13	meet	meet	VERB
ap-374	138	14	(	(	PUNCT
ap-374	138	15	point	point	NOUN
ap-374	138	16	x	x	PUNCT
ap-374	138	17	lies	lie	VERB
ap-374	138	18	inside	inside	ADP
ap-374	138	19	the	the	DET
ap-374	138	20	domain	domain	NOUN
ap-374	138	21	�	�	PROPN
ap-374	138	22	and	and	CCONJ
ap-374	138	23	�	�	PROPN
ap-374	138	24	on	on	ADP
ap-374	138	25	boundary	boundary	ADJ
ap-374	138	26	�	�	PROPN
ap-374	138	27	)	)	PUNCT
ap-374	138	28	.	.	PUNCT
ap-374	139	1	2.2	2.2	NUM
ap-374	139	2	formulation	formulation	NOUN
ap-374	139	3	of	of	ADP
ap-374	139	4	the	the	DET
ap-374	139	5	contact	contact	NOUN
ap-374	139	6	problem	problem	NOUN
ap-374	139	7	recall	recall	VERB
ap-374	139	8	that	that	SCONJ
ap-374	139	9	displacements	displacement	NOUN
ap-374	139	10	are	be	AUX
ap-374	139	11	described	describe	VERB
ap-374	139	12	by	by	ADP
ap-374	139	13	a	a	DET
ap-374	139	14	vector	vector	NOUN
ap-374	139	15	function	function	NOUN
ap-374	139	16	�	�	PROPN
ap-374	139	17	�	�	PROPN
ap-374	139	18	u	u	PROPN
ap-374	139	19	�	�	PROPN
ap-374	139	20	u	u	PROPN
ap-374	139	21	u1	u1	NOUN
ap-374	139	22	2	2	NUM
ap-374	139	23	,	,	PUNCT
ap-374	139	24	of	of	ADP
ap-374	139	25	the	the	DET
ap-374	139	26	variable	variable	ADJ
ap-374	139	27	�	�	PROPN
ap-374	139	28	�	�	PROPN
ap-374	139	29	x	x	PROPN
ap-374	139	30	�	�	PROPN
ap-374	139	31	x	x	SYM
ap-374	139	32	x1	x1	PROPN
ap-374	139	33	2	2	NUM
ap-374	139	34	,	,	PUNCT
ap-374	139	35	.	.	PUNCT
ap-374	140	1	the	the	DET
ap-374	140	2	traction	traction	NOUN
ap-374	140	3	field	field	NOUN
ap-374	140	4	on	on	ADP
ap-374	140	5	the	the	DET
ap-374	140	6	particle	particle	NOUN
ap-374	140	7	boundaries	boundary	NOUN
ap-374	140	8	is	be	AUX
ap-374	140	9	denoted	denote	VERB
ap-374	140	10	either	either	CCONJ
ap-374	140	11	as	as	ADP
ap-374	140	12	�	�	PROPN
ap-374	140	13	�	�	PROPN
ap-374	140	14	p	p	PROPN
ap-374	140	15	�	�	PROPN
ap-374	140	16	p	p	PROPN
ap-374	140	17	p1	p1	PROPN
ap-374	140	18	2	2	NUM
ap-374	140	19	,	,	PUNCT
ap-374	140	20	,	,	PUNCT
ap-374	140	21	or	or	CCONJ
ap-374	140	22	after	after	ADP
ap-374	140	23	projections	projection	NOUN
ap-374	140	24	to	to	ADP
ap-374	140	25	normal	normal	ADJ
ap-374	140	26	and	and	CCONJ
ap-374	140	27	tangential	tangential	ADJ
ap-374	140	28	directions	direction	NOUN
ap-374	140	29	as	as	ADP
ap-374	140	30	�	�	PROPN
ap-374	140	31	�	�	PROPN
ap-374	140	32	p	p	PROPN
ap-374	140	33	�	�	PROPN
ap-374	140	34	p	p	PROPN
ap-374	140	35	pn	pn	PROPN
ap-374	140	36	t	t	PROPN
ap-374	140	37	,	,	PUNCT
ap-374	140	38	.	.	PUNCT
ap-374	141	1	a	a	DET
ap-374	141	2	similar	similar	ADJ
ap-374	141	3	result	result	NOUN
ap-374	141	4	is	be	AUX
ap-374	141	5	valid	valid	ADJ
ap-374	141	6	for	for	ADP
ap-374	141	7	projections	projection	NOUN
ap-374	141	8	of	of	ADP
ap-374	141	9	displacements	displacement	NOUN
ap-374	141	10	,	,	PUNCT
ap-374	141	11	�	�	PROPN
ap-374	141	12	�	�	PROPN
ap-374	141	13	u	u	PROPN
ap-374	141	14	�	�	PROPN
ap-374	141	15	u	u	PROPN
ap-374	141	16	un	un	PROPN
ap-374	141	17	t	t	PROPN
ap-374	141	18	,	,	PUNCT
ap-374	141	19	.	.	PUNCT
ap-374	142	1	assuming	assume	VERB
ap-374	142	2	the	the	DET
ap-374	142	3	“	"	PUNCT
ap-374	142	4	small	small	ADJ
ap-374	142	5	deformation	deformation	NOUN
ap-374	142	6	”	"	PUNCT
ap-374	142	7	theory	theory	NOUN
ap-374	142	8	,	,	PUNCT
ap-374	142	9	the	the	DET
ap-374	142	10	essential	essential	ADJ
ap-374	142	11	contact	contact	NOUN
ap-374	142	12	conditions	condition	NOUN
ap-374	142	13	on	on	ADP
ap-374	142	14	the	the	DET
ap-374	142	15	interface	interface	NOUN
ap-374	142	16	may	may	AUX
ap-374	142	17	be	be	AUX
ap-374	142	18	formulated	formulate	VERB
ap-374	142	19	as	as	SCONJ
ap-374	142	20	follows	follow	VERB
ap-374	142	21	(	(	PUNCT
ap-374	142	22	no	no	DET
ap-374	142	23	penetration	penetration	NOUN
ap-374	142	24	conditions	condition	NOUN
ap-374	142	25	):	):	PUNCT
ap-374	142	26	�	�	PROPN
ap-374	142	27	�	�	PROPN
ap-374	142	28	u	u	PROPN
ap-374	142	29	n	n	CCONJ
ap-374	142	30	k	k	PROPN
ap-374	142	31	n	n	PROPN
ap-374	142	32	k	k	NOUN
ap-374	142	33	,	,	PUNCT
ap-374	142	34	c	c	PROPN
ap-374	142	35	n	n	PROPN
ap-374	142	36	k	k	NOUN
ap-374	142	37	,	,	PUNCT
ap-374	142	38	�	�	PROPN
ap-374	142	39	�	�	PROPN
ap-374	142	40	�	�	PROPN
ap-374	142	41	u	u	NOUN
ap-374	142	42	u	u	NOUN
ap-374	142	43	�	�	PROPN
ap-374	142	44	0	0	NUM
ap-374	142	45	on	on	ADP
ap-374	142	46	�	�	PROPN
ap-374	142	47	c	c	PROPN
ap-374	142	48	k	k	X
ap-374	142	49	,	,	PUNCT
ap-374	142	50	(	(	PUNCT
ap-374	142	51	8)	8)	NUM
ap-374	142	52	where	where	SCONJ
ap-374	142	53	�	�	PROPN
ap-374	142	54	c	c	PROPN
ap-374	142	55	k	k	PROPN
ap-374	142	56	,	,	PUNCT
ap-374	142	57	k	k	PROPN
ap-374	142	58	1	1	NUM
ap-374	142	59	,	,	PUNCT
ap-374	142	60	…	…	PUNCT
ap-374	142	61	,	,	PUNCT
ap-374	142	62	n	n	PRON
ap-374	142	63	are	be	AUX
ap-374	142	64	boundaries	boundary	NOUN
ap-374	142	65	between	between	ADP
ap-374	142	66	adjacent	adjacent	ADJ
ap-374	142	67	particles	particle	NOUN
ap-374	142	68	,	,	PUNCT
ap-374	142	69	un	un	PROPN
ap-374	142	70	k	k	PROPN
ap-374	142	71	,	,	PUNCT
ap-374	142	72	�	�	PROPN
ap-374	142	73	is	be	AUX
ap-374	142	74	the	the	DET
ap-374	142	75	normal	normal	ADJ
ap-374	142	76	displacement	displacement	NOUN
ap-374	142	77	of	of	ADP
ap-374	142	78	current	current	ADJ
ap-374	142	79	element	element	NOUN
ap-374	142	80	�	�	PROPN
ap-374	142	81	c	c	PROPN
ap-374	142	82	and	and	CCONJ
ap-374	142	83	�	�	PROPN
ap-374	142	84	a	a	PRON
ap-374	142	85	belongs	belong	VERB
ap-374	142	86	to	to	ADP
ap-374	142	87	the	the	DET
ap-374	142	88	adjacent	adjacent	ADJ
ap-374	142	89	element	element	NOUN
ap-374	142	90	,	,	PUNCT
ap-374	142	91	both	both	PRON
ap-374	142	92	on	on	ADP
ap-374	142	93	the	the	DET
ap-374	142	94	current	current	ADJ
ap-374	142	95	common	common	ADJ
ap-374	142	96	boundary	boundary	NOUN
ap-374	142	97	,	,	PUNCT
ap-374	142	98	�	�	PROPN
ap-374	142	99	c	c	PROPN
ap-374	142	100	k	k	PROPN
ap-374	142	101	,	,	PUNCT
ap-374	142	102	k	k	PROPN
ap-374	142	103	runs	run	VERB
ap-374	142	104	numbers	number	NOUN
ap-374	142	105	of	of	ADP
ap-374	142	106	all	all	DET
ap-374	142	107	common	common	ADJ
ap-374	142	108	sides	side	NOUN
ap-374	142	109	of	of	ADP
ap-374	142	110	the	the	DET
ap-374	142	111	particles	particle	NOUN
ap-374	142	112	,	,	PUNCT
ap-374	142	113	n	n	PRON
ap-374	142	114	is	be	AUX
ap-374	142	115	the	the	DET
ap-374	142	116	number	number	NOUN
ap-374	142	117	of	of	ADP
ap-374	142	118	common	common	ADJ
ap-374	142	119	sides	side	NOUN
ap-374	142	120	of	of	ADP
ap-374	142	121	hexagons	hexagon	NOUN
ap-374	142	122	(	(	PUNCT
ap-374	142	123	having	have	VERB
ap-374	142	124	exactly	exactly	ADV
ap-374	142	125	two	two	NUM
ap-374	142	126	adjacent	adjacent	ADJ
ap-374	142	127	particles	particle	NOUN
ap-374	142	128	inside	inside	ADP
ap-374	142	129	the	the	DET
ap-374	142	130	domain	domain	NOUN
ap-374	142	131	,	,	PUNCT
ap-374	142	132	one	one	NUM
ap-374	142	133	or	or	CCONJ
ap-374	142	134	none	none	NOUN
ap-374	142	135	on	on	ADP
ap-374	142	136	the	the	DET
ap-374	142	137	external	external	ADJ
ap-374	142	138	boundary	boundary	NOUN
ap-374	142	139	)	)	PUNCT
ap-374	142	140	.	.	PUNCT
ap-374	143	1	let	let	VERB
ap-374	143	2	kn	kn	PROPN
ap-374	143	3	k	k	PROPN
ap-374	143	4	be	be	AUX
ap-374	143	5	the	the	DET
ap-374	143	6	spring	spring	NOUN
ap-374	143	7	stiffness	stiffness	NOUN
ap-374	143	8	in	in	ADP
ap-374	143	9	the	the	DET
ap-374	143	10	normal	normal	ADJ
ap-374	143	11	direction	direction	NOUN
ap-374	143	12	and	and	CCONJ
ap-374	143	13	kn	kn	PROPN
ap-374	143	14	k	k	PROPN
ap-374	143	15	be	be	AUX
ap-374	143	16	the	the	DET
ap-374	143	17	spring	spring	NOUN
ap-374	143	18	stiffness	stiffness	NOUN
ap-374	143	19	in	in	ADP
ap-374	143	20	the	the	DET
ap-374	143	21	tangential	tangential	ADJ
ap-374	143	22	direction	direction	NOUN
ap-374	143	23	on	on	ADP
ap-374	143	24	the	the	DET
ap-374	143	25	boundary	boundary	NOUN
ap-374	143	26	between	between	ADP
ap-374	143	27	particles	particle	NOUN
ap-374	143	28	with	with	ADP
ap-374	143	29	a	a	DET
ap-374	143	30	common	common	ADJ
ap-374	143	31	boundary	boundary	ADJ
ap-374	143	32	�	�	PROPN
ap-374	143	33	c	c	PROPN
ap-374	143	34	k.	k.	PROPN
ap-374	143	35	then	then	ADV
ap-374	143	36	in	in	ADP
ap-374	143	37	the	the	DET
ap-374	143	38	elastic	elastic	ADJ
ap-374	143	39	region	region	NOUN
ap-374	143	40	�	�	PROPN
ap-374	143	41	�	�	PROPN
ap-374	143	42	p	p	PROPN
ap-374	143	43	kn	kn	PROPN
ap-374	143	44	k	k	PROPN
ap-374	143	45	n	n	PROPN
ap-374	143	46	k	k	PROPN
ap-374	143	47	n	n	CCONJ
ap-374	143	48	k	k	PROPN
ap-374	143	49	�	�	PROPN
ap-374	143	50	u	u	PROPN
ap-374	143	51	and	and	CCONJ
ap-374	143	52	�	�	PROPN
ap-374	143	53	�	�	PROPN
ap-374	143	54	p	p	NOUN
ap-374	144	1	kt	kt	PROPN
ap-374	144	2	k	k	PROPN
ap-374	144	3	t	t	PROPN
ap-374	144	4	k	k	PROPN
ap-374	144	5	t	t	PROPN
ap-374	144	6	k	k	PROPN
ap-374	144	7	�	�	PROPN
ap-374	144	8	u	u	PROPN
ap-374	144	9	.	.	PUNCT
ap-374	145	1	denote	denote	VERB
ap-374	145	2	�	�	PROPN
ap-374	145	3	�	�	PROPN
ap-374	145	4	�	�	PROPN
ap-374	145	5	�	�	PROPN
ap-374	145	6	�	�	PROPN
ap-374	145	7	�	�	PROPN
ap-374	145	8	�	�	PROPN
ap-374	145	9	�	�	PROPN
ap-374	145	10	k	k	PROPN
ap-374	146	1	v	v	PROPN
ap-374	146	2	p	p	X
ap-374	146	3	p	p	PROPN
ap-374	146	4	k	k	PROPN
ap-374	146	5	p	p	X
ap-374	146	6	p	p	X
ap-374	146	7	p	p	X
ap-374	146	8	k	k	PROPN
ap-374	146	9	�	�	PROPN
ap-374	146	10	�	�	PROPN
ap-374	146	11	�	�	PROPN
ap-374	146	12	�	�	PROPN
ap-374	146	13	�	�	PROPN
ap-374	146	14	�	�	PROPN
ap-374	146	15	�	�	PROPN
ap-374	146	16	u	u	PROPN
ap-374	146	17	u	u	PROPN
ap-374	146	18	u	u	NOUN
ap-374	146	19	,	,	PUNCT
ap-374	146	20	,	,	PUNCT
ap-374	146	21	n	n	PROPN
ap-374	146	22	+	+	CCONJ
ap-374	147	1	k	k	PROPN
ap-374	147	2	n	n	CCONJ
ap-374	147	3	k	k	PROPN
ap-374	147	4	n	n	CCONJ
ap-374	147	5	k	k	PROPN
ap-374	147	6	n	n	CCONJ
ap-374	147	7	k	k	PROPN
ap-374	147	8	n	n	PROPN
ap-374	147	9	+	+	CCONJ
ap-374	147	10	k	k	PROPN
ap-374	147	11	n	n	CCONJ
ap-374	147	12	k	k	PROPN
ap-374	147	13	n	n	CCONJ
ap-374	147	14	k	k	PROPN
ap-374	147	15	t	t	PROPN
ap-374	148	1	k	k	PROPN
ap-374	148	2	t	t	PROPN
ap-374	149	1	k	k	PROPN
ap-374	149	2	if	if	SCONJ
ap-374	149	3	then	then	ADV
ap-374	149	4	0	0	NUM
ap-374	149	5	�	�	PROPN
ap-374	149	6	�	�	PROPN
ap-374	149	7	�	�	PROPN
ap-374	149	8	�	�	PROPN
ap-374	149	9	�	�	PROPN
ap-374	149	10	�	�	PROPN
ap-374	149	11	�	�	PROPN
ap-374	149	12	�	�	PROPN
ap-374	149	13	�	�	PROPN
ap-374	149	14	�	�	PROPN
ap-374	149	15	�	�	PROPN
ap-374	149	16	c	c	PROPN
ap-374	149	17	k	k	PROPN
ap-374	149	18	n	n	PROPN
ap-374	149	19	u	u	NOUN
ap-374	149	20	uk	uk	PROPN
ap-374	149	21	c	c	PROPN
ap-374	149	22	k	k	PROPN
ap-374	149	23	n	n	PROPN
ap-374	149	24	+	+	CCONJ
ap-374	149	25	k	k	PROPN
ap-374	149	26	t	t	PROPN
ap-374	150	1	k	k	PROPN
ap-374	150	2	t	t	PROPN
ap-374	150	3	k	k	PROPN
ap-374	150	4	,	,	PUNCT
ap-374	150	5	c	c	PROPN
ap-374	150	6	t	t	PROPN
ap-374	150	7	k	k	PROPN
ap-374	150	8	,	,	PUNCT
ap-374	150	9	on	on	ADP
ap-374	150	10	�	�	PROPN
ap-374	150	11	,	,	PUNCT
ap-374	150	12	,	,	PUNCT
ap-374	150	13	,	,	PUNCT
ap-374	150	14	,	,	PUNCT
ap-374	150	15	.1	.1	NUM
ap-374	150	16	u	u	PROPN
ap-374	150	17	�	�	PROPN
ap-374	150	18	where	where	SCONJ
ap-374	150	19	ut	ut	PROPN
ap-374	150	20	k	k	PROPN
ap-374	150	21	,	,	PUNCT
ap-374	150	22	�	�	PROPN
ap-374	150	23	is	be	AUX
ap-374	150	24	the	the	DET
ap-374	150	25	tangential	tangential	ADJ
ap-374	150	26	displacement	displacement	NOUN
ap-374	150	27	on	on	ADP
ap-374	150	28	the	the	DET
ap-374	150	29	side	side	NOUN
ap-374	150	30	k	k	PROPN
ap-374	150	31	,	,	PUNCT
ap-374	150	32	�	�	PROPN
ap-374	150	33	�	�	PROPN
ap-374	150	34	pn	pn	PROPN
ap-374	150	35	+	+	CCONJ
ap-374	150	36	k	k	PROPN
ap-374	150	37	denotes	denote	VERB
ap-374	150	38	the	the	DET
ap-374	150	39	tensile	tensile	NOUN
ap-374	150	40	strength	strength	NOUN
ap-374	150	41	,	,	PUNCT
ap-374	150	42	ck	ck	PROPN
ap-374	150	43	is	be	AUX
ap-374	150	44	the	the	DET
ap-374	150	45	shear	shear	NOUN
ap-374	150	46	strength	strength	NOUN
ap-374	150	47	,	,	PUNCT
ap-374	150	48	v	v	NOUN
ap-374	150	49	is	be	AUX
ap-374	150	50	the	the	DET
ap-374	150	51	set	set	NOUN
ap-374	150	52	of	of	ADP
ap-374	150	53	displacements	displacement	NOUN
ap-374	150	54	that	that	PRON
ap-374	150	55	fulfill	fulfill	VERB
ap-374	150	56	the	the	DET
ap-374	150	57	kinematical	kinematical	ADJ
ap-374	150	58	boundary	boundary	ADJ
ap-374	150	59	conditions	condition	NOUN
ap-374	150	60	and	and	CCONJ
ap-374	150	61	condition	condition	NOUN
ap-374	150	62	(	(	PUNCT
ap-374	150	63	8)	8)	NUM
ap-374	150	64	.	.	PUNCT
ap-374	151	1	if	if	SCONJ
ap-374	151	2	pn	pn	PROPN
ap-374	151	3	k	k	PROPN
ap-374	151	4	�	�	PROPN
ap-374	151	5	0	0	PROPN
ap-374	151	6	then	then	ADV
ap-374	151	7	set	set	VERB
ap-374	151	8	k	k	PROPN
ap-374	151	9	is	be	AUX
ap-374	151	10	a	a	DET
ap-374	151	11	cone	cone	NOUN
ap-374	151	12	of	of	ADP
ap-374	151	13	admissible	admissible	ADJ
ap-374	151	14	displacements	displacement	NOUN
ap-374	151	15	satisfying	satisfy	VERB
ap-374	151	16	the	the	DET
ap-374	151	17	essential	essential	ADJ
ap-374	151	18	boundary	boundary	ADJ
ap-374	151	19	and	and	CCONJ
ap-374	151	20	contact	contact	NOUN
ap-374	151	21	conditions	condition	NOUN
ap-374	151	22	.	.	PUNCT
ap-374	152	1	this	this	PRON
ap-374	152	2	is	be	AUX
ap-374	152	3	valid	valid	ADJ
ap-374	152	4	for	for	ADP
ap-374	152	5	brittle	brittle	ADJ
ap-374	152	6	or	or	CCONJ
ap-374	152	7	almost	almost	ADV
ap-374	152	8	brittle	brittle	ADJ
ap-374	152	9	material	material	NOUN
ap-374	152	10	.	.	PUNCT
ap-374	153	1	if	if	SCONJ
ap-374	153	2	the	the	DET
ap-374	153	3	material	material	NOUN
ap-374	153	4	exhibits	exhibit	VERB
ap-374	153	5	elastoplastic	elastoplastic	ADJ
ap-374	153	6	behavior	behavior	NOUN
ap-374	153	7	,	,	PUNCT
ap-374	153	8	then	then	ADV
ap-374	153	9	cone	cone	PROPN
ap-374	153	10	k	k	PROPN
ap-374	153	11	is	be	AUX
ap-374	153	12	changed	change	VERB
ap-374	153	13	as	as	ADP
ap-374	153	14	:	:	PUNCT
ap-374	153	15	�	�	PROPN
ap-374	153	16	�	�	PROPN
ap-374	153	17	�	�	PROPN
ap-374	153	18	�	�	PROPN
ap-374	153	19	�	�	PROPN
ap-374	153	20	�	�	PROPN
ap-374	153	21	�	�	PROPN
ap-374	153	22	�	�	PROPN
ap-374	153	23	k	k	PROPN
ap-374	154	1	v	v	PROPN
ap-374	154	2	p	p	X
ap-374	154	3	p	p	PROPN
ap-374	154	4	k	k	PROPN
ap-374	154	5	p	p	X
ap-374	154	6	p	p	X
ap-374	154	7	p	p	X
ap-374	154	8	k	k	PROPN
ap-374	154	9	�	�	PROPN
ap-374	154	10	�	�	PROPN
ap-374	154	11	�	�	PROPN
ap-374	154	12	�	�	PROPN
ap-374	154	13	�	�	PROPN
ap-374	154	14	�	�	PROPN
ap-374	154	15	�	�	PROPN
ap-374	154	16	u	u	PROPN
ap-374	154	17	u	u	PROPN
ap-374	154	18	u	u	NOUN
ap-374	154	19	,	,	PUNCT
ap-374	154	20	,	,	PUNCT
ap-374	154	21	n	n	PROPN
ap-374	154	22	+	+	CCONJ
ap-374	155	1	k	k	PROPN
ap-374	155	2	n	n	CCONJ
ap-374	155	3	k	k	PROPN
ap-374	155	4	n	n	CCONJ
ap-374	155	5	k	k	PROPN
ap-374	155	6	n	n	CCONJ
ap-374	155	7	k	k	PROPN
ap-374	155	8	n	n	PROPN
ap-374	155	9	+	+	CCONJ
ap-374	155	10	k	k	PROPN
ap-374	155	11	n	n	CCONJ
ap-374	155	12	k	k	PROPN
ap-374	155	13	n	n	CCONJ
ap-374	155	14	k	k	PROPN
ap-374	155	15	t	t	PROPN
ap-374	156	1	k	k	PROPN
ap-374	156	2	t	t	PROPN
ap-374	157	1	k	k	PROPN
ap-374	157	2	if	if	SCONJ
ap-374	157	3	then	then	ADV
ap-374	157	4	0	0	NUM
ap-374	157	5	�	�	PROPN
ap-374	157	6	�	�	PROPN
ap-374	157	7	�	�	PROPN
ap-374	157	8	�	�	PROPN
ap-374	157	9	�	�	PROPN
ap-374	157	10	�	�	PROPN
ap-374	157	11	�	�	PROPN
ap-374	157	12	�	�	PROPN
ap-374	157	13	�	�	PROPN
ap-374	157	14	�	�	PROPN
ap-374	157	15	�	�	PROPN
ap-374	157	16	�	�	PROPN
ap-374	157	17	�	�	PROPN
ap-374	157	18	�	�	PROPN
ap-374	157	19	c	c	PROPN
ap-374	157	20	p	p	PROPN
ap-374	157	21	p	p	PROPN
ap-374	157	22	k	k	PROPN
ap-374	157	23	n	n	CCONJ
ap-374	157	24	u	u	X
ap-374	157	25	u	u	X
ap-374	157	26	k	k	PROPN
ap-374	157	27	n	n	PROPN
ap-374	157	28	k	k	PROPN
ap-374	157	29	n	n	CCONJ
ap-374	158	1	k	k	PROPN
ap-374	158	2	c	c	PROPN
ap-374	158	3	k	k	PROPN
ap-374	158	4	n	n	PROPN
ap-374	159	1	+	+	CCONJ
ap-374	159	2	k	k	PROPN
ap-374	159	3	t	t	PROPN
ap-374	159	4	k	k	PROPN
ap-374	159	5	t	t	PROPN
ap-374	159	6	k	k	PROPN
ap-374	159	7	,	,	PUNCT
ap-374	159	8	c	c	PROPN
ap-374	159	9	t	t	PROPN
ap-374	159	10	k	k	PROPN
ap-374	159	11	,	,	PUNCT
ap-374	159	12	�	�	PROPN
ap-374	159	13	�	�	PROPN
ap-374	159	14	tan	tan	PROPN
ap-374	159	15	on	on	ADP
ap-374	159	16	�	�	PROPN
ap-374	159	17	,	,	PUNCT
ap-374	159	18	,	,	PUNCT
ap-374	159	19	,	,	PUNCT
ap-374	159	20	,	,	PUNCT
ap-374	159	21	1	1	NUM
ap-374	159	22	u	u	NOUN
ap-374	159	23	.	.	PUNCT
ap-374	160	1	where	where	SCONJ
ap-374	160	2	�	�	PROPN
ap-374	160	3	is	be	AUX
ap-374	160	4	the	the	DET
ap-374	160	5	angle	angle	NOUN
ap-374	160	6	of	of	ADP
ap-374	160	7	internal	internal	ADJ
ap-374	160	8	friction	friction	NOUN
ap-374	160	9	,	,	PUNCT
ap-374	160	10	and	and	CCONJ
ap-374	160	11	pn	pn	PROPN
ap-374	160	12	k	k	PROPN
ap-374	160	13	is	be	AUX
ap-374	160	14	the	the	DET
ap-374	160	15	normal	normal	ADJ
ap-374	160	16	traction	traction	NOUN
ap-374	160	17	on	on	ADP
ap-374	160	18	the	the	DET
ap-374	160	19	side	side	NOUN
ap-374	160	20	k	k	NOUN
ap-374	160	21	,	,	PUNCT
ap-374	160	22	is	be	AUX
ap-374	160	23	the	the	DET
ap-374	160	24	generalized	generalize	VERB
ap-374	160	25	heaviside	heaviside	NOUN
ap-374	160	26	’s	’s	PART
ap-374	160	27	function	function	NOUN
ap-374	160	28	being	be	AUX
ap-374	160	29	equal	equal	ADJ
ap-374	160	30	to	to	ADP
ap-374	160	31	zero	zero	NUM
ap-374	160	32	for	for	ADP
ap-374	160	33	a	a	DET
ap-374	160	34	positive	positive	ADJ
ap-374	160	35	argument	argument	NOUN
ap-374	160	36	and	and	CCONJ
ap-374	160	37	equal	equal	ADJ
ap-374	160	38	to	to	ADP
ap-374	160	39	one	one	NUM
ap-374	160	40	otherwise	otherwise	ADV
ap-374	160	41	.	.	PUNCT
ap-374	161	1	here	here	ADV
ap-374	161	2	the	the	DET
ap-374	161	3	sign	sign	NOUN
ap-374	161	4	convention	convention	NOUN
ap-374	161	5	is	be	AUX
ap-374	161	6	important	important	ADJ
ap-374	161	7	:	:	PUNCT
ap-374	161	8	positive	positive	ADJ
ap-374	161	9	normal	normal	ADJ
ap-374	161	10	traction	traction	NOUN
ap-374	161	11	is	be	AUX
ap-374	161	12	tension	tension	NOUN
ap-374	161	13	.	.	PUNCT
ap-374	162	1	from	from	ADP
ap-374	162	2	the	the	DET
ap-374	162	3	above	above	ADV
ap-374	162	4	defined	define	VERB
ap-374	162	5	spaces	space	NOUN
ap-374	162	6	we	we	PRON
ap-374	162	7	can	can	AUX
ap-374	162	8	deduce	deduce	VERB
ap-374	162	9	that	that	SCONJ
ap-374	162	10	�	�	PROPN
ap-374	162	11	�	�	PROPN
ap-374	162	12	pn	pn	PROPN
ap-374	162	13	k	k	PROPN
ap-374	162	14	n	n	PROPN
ap-374	162	15	k	k	PROPN
ap-374	162	16	,	,	PUNCT
ap-374	162	17	u	u	NOUN
ap-374	162	18	,	,	PUNCT
ap-374	162	19	and	and	CCONJ
ap-374	162	20	�	�	PROPN
ap-374	162	21	�	�	PROPN
ap-374	162	22	pt	pt	PROPN
ap-374	162	23	k	k	PROPN
ap-374	162	24	t	t	PROPN
ap-374	162	25	k	k	PROPN
ap-374	162	26	,	,	PUNCT
ap-374	162	27	u	u	PRON
ap-374	162	28	behave	behave	VERB
ap-374	162	29	linearly	linearly	ADV
ap-374	162	30	between	between	ADP
ap-374	162	31	certain	certain	ADJ
ap-374	162	32	limits	limit	NOUN
ap-374	162	33	,	,	PUNCT
ap-374	162	34	which	which	PRON
ap-374	162	35	are	be	AUX
ap-374	162	36	given	give	VERB
ap-374	162	37	by	by	ADP
ap-374	162	38	the	the	DET
ap-374	162	39	material	material	ADJ
ap-374	162	40	nature	nature	NOUN
ap-374	162	41	of	of	ADP
ap-374	162	42	the	the	DET
ap-374	162	43	body	body	NOUN
ap-374	162	44	.	.	PUNCT
ap-374	163	1	the	the	DET
ap-374	163	2	total	total	ADJ
ap-374	163	3	energy	energy	NOUN
ap-374	163	4	j	j	PROPN
ap-374	163	5	of	of	ADP
ap-374	163	6	the	the	DET
ap-374	163	7	system	system	NOUN
ap-374	163	8	reads	read	VERB
ap-374	163	9	:	:	PUNCT
ap-374	163	10	�	�	PROPN
ap-374	163	11	�	�	PROPN
ap-374	163	12	�	�	PROPN
ap-374	163	13	�	�	PROPN
ap-374	163	14	�	�	PROPN
ap-374	163	15	�	�	PROPN
ap-374	163	16	�	�	PROPN
ap-374	163	17	�	�	PROPN
ap-374	163	18	�	�	PROPN
ap-374	163	19	�	�	PROPN
ap-374	163	20	j	j	PROPN
ap-374	163	21	a	a	PROPN
ap-374	163	22	k	k	PROPN
ap-374	163	23	a	a	X
ap-374	163	24	c	c	NOUN
ap-374	163	25	k	k	PROPN
ap-374	163	26	n	n	CCONJ
ap-374	163	27	u	u	X
ap-374	163	28	u	u	X
ap-374	163	29	u	u	NOUN
ap-374	163	30	u	u	NOUN
ap-374	163	31	b	b	PROPN
ap-374	163	32	u	u	X
ap-374	163	33	u	u	X
ap-374	163	34	u	u	ADJ
ap-374	163	35	�	�	PROPN
ap-374	163	36	�	�	PROPN
ap-374	163	37	�	�	PROPN
ap-374	163	38	�	�	PROPN
ap-374	163	39	�	�	PROPN
ap-374	163	40	�	�	PROPN
ap-374	163	41	�	�	PROPN
ap-374	163	42	�	�	PROPN
ap-374	163	43	�	�	PROPN
ap-374	163	44	�	�	PROPN
ap-374	163	45	�	�	PROPN
ap-374	163	46	1	1	NUM
ap-374	163	47	2	2	NUM
ap-374	163	48	2	2	NUM
ap-374	163	49	1	1	NUM
ap-374	163	50	,	,	PUNCT
ap-374	163	51	,	,	PUNCT
ap-374	163	52	n	n	CCONJ
ap-374	163	53	k	k	PROPN
ap-374	163	54	n	n	PROPN
ap-374	164	1	k	k	PROPN
ap-374	165	1	d	d	PROPN
ap-374	165	2	d	d	PROPN
ap-374	165	3	c	c	PROPN
ap-374	165	4	t	t	PROPN
ap-374	165	5	t	t	PROPN
ap-374	165	6	�	�	PROPN
ap-374	165	7	�	�	PROPN
ap-374	165	8	�	�	PROPN
ap-374	165	9	�	�	PROPN
ap-374	165	10	�	�	PROPN
ap-374	165	11	�	�	PROPN
ap-374	165	12	d	d	PROPN
ap-374	165	13	�	�	PROPN
ap-374	165	14	�	�	PROPN
ap-374	165	15	�	�	PROPN
ap-374	165	16	0	0	NUM
ap-374	165	17	1	1	NUM
ap-374	165	18	2	2	NUM
ap-374	165	19	�	�	PROPN
ap-374	165	20	�	�	PROPN
ap-374	165	21	�	�	PROPN
ap-374	165	22	�	�	PROPN
ap-374	165	23	�	�	PROPN
ap-374	165	24	�	�	PROPN
ap-374	165	25	�	�	PROPN
ap-374	165	26	,	,	PUNCT
ap-374	165	27	,	,	PUNCT
ap-374	165	28	,	,	PUNCT
ap-374	165	29	�	�	PROPN
ap-374	165	30	�	�	PROPN
ap-374	165	31	�	�	PROPN
ap-374	165	32	�	�	PROPN
ap-374	165	33	�	�	PROPN
ap-374	165	34	�	�	PROPN
ap-374	165	35	�	�	PROPN
ap-374	165	36	�	�	PROPN
ap-374	165	37	�	�	PROPN
ap-374	165	38	u	u	PROPN
ap-374	165	39	x	x	PROPN
ap-374	165	40	u	u	NOUN
ap-374	165	41	x	x	X
ap-374	165	42	u	u	NOUN
ap-374	165	43	x	x	X
ap-374	165	44	u	u	NOUN
ap-374	165	45	x	x	PROPN
ap-374	165	46	n	n	ADP
ap-374	165	47	n	n	NOUN
ap-374	166	1	t	t	NOUN
ap-374	166	2	t	t	PROPN
ap-374	166	3	t	t	PROPN
ap-374	166	4	n	n	CCONJ
ap-374	166	5	n	n	PROPN
ap-374	166	6	t	t	PROPN
ap-374	166	7	�	�	PROPN
ap-374	166	8	�	�	PROPN
ap-374	166	9	.	.	PUNCT
ap-374	167	1	(	(	PUNCT
ap-374	167	2	9	9	X
ap-374	167	3	)	)	PUNCT
ap-374	167	4	where	where	SCONJ
ap-374	167	5	�	�	PROPN
ap-374	167	6	is	be	AUX
ap-374	167	7	the	the	DET
ap-374	167	8	strain	strain	NOUN
ap-374	167	9	tensor	tensor	NOUN
ap-374	167	10	,	,	PUNCT
ap-374	167	11	c	c	PROPN
ap-374	167	12	is	be	AUX
ap-374	167	13	the	the	DET
ap-374	167	14	stiffness	stiffness	ADJ
ap-374	167	15	matrix	matrix	NOUN
ap-374	167	16	of	of	ADP
ap-374	167	17	the	the	DET
ap-374	167	18	particle	particle	NOUN
ap-374	167	19	,	,	PUNCT
ap-374	167	20	t	t	PROPN
ap-374	167	21	denotes	denote	VERB
ap-374	167	22	transposition	transposition	NOUN
ap-374	167	23	,	,	PUNCT
ap-374	167	24	�	�	PROPN
ap-374	167	25	0	0	NUM
ap-374	167	26	is	be	AUX
ap-374	167	27	the	the	DET
ap-374	167	28	sum	sum	NOUN
ap-374	167	29	of	of	ADP
ap-374	167	30	subdomains	subdomain	NOUN
ap-374	167	31	�	�	PROPN
ap-374	167	32	,	,	PUNCT
ap-374	167	33	i.e.	i.e.	X
ap-374	167	34	,	,	PUNCT
ap-374	167	35	of	of	ADP
ap-374	167	36	hexagonal	hexagonal	ADJ
ap-374	167	37	elements	element	NOUN
ap-374	167	38	,	,	PUNCT
ap-374	167	39	b	b	X
ap-374	167	40	is	be	AUX
ap-374	167	41	the	the	DET
ap-374	167	42	volume	volume	NOUN
ap-374	167	43	weight	weight	NOUN
ap-374	167	44	vector	vector	NOUN
ap-374	167	45	.	.	PUNCT
ap-374	168	1	note	note	VERB
ap-374	168	2	that	that	SCONJ
ap-374	168	3	the	the	DET
ap-374	168	4	spring	spring	NOUN
ap-374	168	5	stiffness	stiffness	NOUN
ap-374	168	6	kn	kn	PROPN
ap-374	168	7	k	k	PROPN
ap-374	168	8	plays	play	VERB
ap-374	168	9	the	the	DET
ap-374	168	10	role	role	NOUN
ap-374	168	11	of	of	ADP
ap-374	168	12	a	a	DET
ap-374	168	13	penalty	penalty	NOUN
ap-374	168	14	.	.	PUNCT
ap-374	169	1	recall	recall	VERB
ap-374	169	2	that	that	SCONJ
ap-374	169	3	the	the	DET
ap-374	169	4	problem	problem	NOUN
ap-374	169	5	can	can	AUX
ap-374	169	6	also	also	ADV
ap-374	169	7	be	be	AUX
ap-374	169	8	formulated	formulate	VERB
ap-374	169	9	in	in	ADP
ap-374	169	10	terms	term	NOUN
ap-374	169	11	of	of	ADP
ap-374	169	12	lagrangian	lagrangian	ADJ
ap-374	169	13	multipliers	multiplier	NOUN
ap-374	169	14	,	,	PUNCT
ap-374	169	15	and	and	CCONJ
ap-374	169	16	then	then	ADV
ap-374	169	17	leads	lead	VERB
ap-374	169	18	to	to	ADP
ap-374	169	19	mixed	mixed	ADJ
ap-374	169	20	formulation	formulation	NOUN
ap-374	169	21	.	.	PUNCT
ap-374	170	1	the	the	DET
ap-374	170	2	latter	latter	ADJ
ap-374	170	3	case	case	NOUN
ap-374	170	4	is	be	AUX
ap-374	170	5	more	more	ADV
ap-374	170	6	suitable	suitable	ADJ
ap-374	170	7	for	for	ADP
ap-374	170	8	a	a	DET
ap-374	170	9	small	small	ADJ
ap-374	170	10	number	number	NOUN
ap-374	170	11	of	of	ADP
ap-374	170	12	boundary	boundary	ADJ
ap-374	170	13	variables	variable	NOUN
ap-374	170	14	;	;	PUNCT
ap-374	170	15	the	the	DET
ap-374	170	16	problem	problem	NOUN
ap-374	170	17	discussed	discuss	VERB
ap-374	170	18	in	in	ADP
ap-374	170	19	this	this	DET
ap-374	170	20	paper	paper	NOUN
ap-374	170	21	decreases	decrease	VERB
ap-374	170	22	the	the	DET
ap-374	170	23	number	number	NOUN
ap-374	170	24	of	of	ADP
ap-374	170	25	unknowns	unknown	NOUN
ap-374	170	26	introducing	introduce	VERB
ap-374	170	27	the	the	DET
ap-374	170	28	penalty	penalty	NOUN
ap-374	170	29	parameters	parameter	NOUN
ap-374	170	30	.	.	PUNCT
ap-374	171	1	3	3	NUM
ap-374	171	2	statical	statical	ADJ
ap-374	171	3	pfc	pfc	NOUN
ap-374	171	4	this	this	DET
ap-374	171	5	section	section	NOUN
ap-374	171	6	deals	deal	VERB
ap-374	171	7	with	with	ADP
ap-374	171	8	the	the	DET
ap-374	171	9	idea	idea	NOUN
ap-374	171	10	of	of	ADP
ap-374	171	11	modeling	model	VERB
ap-374	171	12	a	a	DET
ap-374	171	13	structure	structure	NOUN
ap-374	171	14	,	,	PUNCT
ap-374	171	15	e.g.	e.g.	ADV
ap-374	171	16	,	,	PUNCT
ap-374	171	17	an	an	DET
ap-374	171	18	earth	earth	NOUN
ap-374	171	19	body	body	NOUN
ap-374	171	20	,	,	PUNCT
ap-374	171	21	by	by	ADP
ap-374	171	22	using	use	VERB
ap-374	171	23	a	a	DET
ap-374	171	24	statical	statical	ADJ
ap-374	171	25	version	version	NOUN
ap-374	171	26	of	of	ADP
ap-374	171	27	pfc	pfc	NOUN
ap-374	171	28	.	.	PUNCT
ap-374	172	1	recall	recall	VERB
ap-374	172	2	that	that	SCONJ
ap-374	172	3	the	the	DET
ap-374	172	4	pfc	pfc	NOUN
ap-374	172	5	is	be	AUX
ap-374	172	6	based	base	VERB
ap-374	172	7	on	on	ADP
ap-374	172	8	dynamic	dynamic	ADJ
ap-374	172	9	equilibrium	equilibrium	NOUN
ap-374	172	10	;	;	PUNCT
ap-374	172	11	for	for	ADP
ap-374	172	12	slow	slow	ADJ
ap-374	172	13	movements	movement	NOUN
ap-374	172	14	of	of	ADP
ap-374	172	15	structures	structure	NOUN
ap-374	172	16	,	,	PUNCT
ap-374	172	17	which	which	PRON
ap-374	172	18	appear	appear	VERB
ap-374	172	19	in	in	ADP
ap-374	172	20	most	most	ADJ
ap-374	172	21	geotechnical	geotechnical	ADJ
ap-374	172	22	problems	problem	NOUN
ap-374	172	23	,	,	PUNCT
ap-374	172	24	for	for	ADP
ap-374	172	25	example	example	NOUN
ap-374	172	26	,	,	PUNCT
ap-374	172	27	it	it	PRON
ap-374	172	28	seems	seem	VERB
ap-374	172	29	to	to	PART
ap-374	172	30	be	be	AUX
ap-374	172	31	better	well	ADJ
ap-374	172	32	to	to	PART
ap-374	172	33	employ	employ	VERB
ap-374	172	34	statical	statical	ADJ
ap-374	172	35	equilibrium	equilibrium	NOUN
ap-374	172	36	.	.	PUNCT
ap-374	173	1	the	the	DET
ap-374	173	2	earth	earth	NOUN
ap-374	173	3	mass	mass	NOUN
ap-374	173	4	is	be	AUX
ap-374	173	5	modeled	model	VERB
ap-374	173	6	in	in	ADP
ap-374	173	7	a	a	DET
ap-374	173	8	statical	statical	ADJ
ap-374	173	9	version	version	NOUN
ap-374	173	10	by	by	ADP
ap-374	173	11	balls	ball	NOUN
ap-374	173	12	in	in	ADP
ap-374	173	13	3d	3d	NUM
ap-374	173	14	or	or	CCONJ
ap-374	173	15	disks	disk	NOUN
ap-374	173	16	in	in	ADP
ap-374	173	17	2d	2d	NUM
ap-374	173	18	in	in	ADP
ap-374	173	19	a	a	DET
ap-374	173	20	similar	similar	ADJ
ap-374	173	21	way	way	NOUN
ap-374	173	22	as	as	ADP
ap-374	173	23	in	in	ADP
ap-374	173	24	the	the	DET
ap-374	173	25	dynamic	dynamic	ADJ
ap-374	173	26	version	version	NOUN
ap-374	173	27	.	.	PUNCT
ap-374	174	1	the	the	DET
ap-374	174	2	balls	ball	NOUN
ap-374	174	3	are	be	AUX
ap-374	174	4	connected	connect	VERB
ap-374	174	5	by	by	ADP
ap-374	174	6	springs	spring	NOUN
ap-374	174	7	that	that	PRON
ap-374	174	8	relate	relate	VERB
ap-374	174	9	forces	force	NOUN
ap-374	174	10	and	and	CCONJ
ap-374	174	11	the	the	DET
ap-374	174	12	appropriate	appropriate	ADJ
ap-374	174	13	difference	difference	NOUN
ap-374	174	14	of	of	ADP
ap-374	174	15	displacements	displacement	NOUN
ap-374	174	16	in	in	ADP
ap-374	174	17	the	the	DET
ap-374	174	18	direction	direction	NOUN
ap-374	174	19	of	of	ADP
ap-374	174	20	the	the	DET
ap-374	174	21	springs	spring	NOUN
ap-374	174	22	.	.	PUNCT
ap-374	175	1	the	the	DET
ap-374	175	2	springs	spring	NOUN
ap-374	175	3	are	be	AUX
ap-374	175	4	considered	consider	VERB
ap-374	175	5	either	either	CCONJ
ap-374	175	6	in	in	ADP
ap-374	175	7	normal	normal	ADJ
ap-374	175	8	and	and	CCONJ
ap-374	175	9	tangential	tangential	ADJ
ap-374	175	10	directions	direction	NOUN
ap-374	175	11	to	to	ADP
ap-374	175	12	the	the	DET
ap-374	175	13	boundary	boundary	NOUN
ap-374	175	14	of	of	ADP
ap-374	175	15	the	the	DET
ap-374	175	16	particles	particle	NOUN
ap-374	175	17	,	,	PUNCT
ap-374	175	18	or	or	CCONJ
ap-374	175	19	in	in	ADP
ap-374	175	20	the	the	DET
ap-374	175	21	direction	direction	NOUN
ap-374	175	22	of	of	ADP
ap-374	175	23	the	the	DET
ap-374	175	24	coordinate	coordinate	NOUN
ap-374	175	25	axes	axis	NOUN
ap-374	175	26	x	x	PUNCT
ap-374	175	27	and	and	CCONJ
ap-374	175	28	y.	y.	PROPN
ap-374	175	29	in	in	ADP
ap-374	175	30	our	our	PRON
ap-374	175	31	case	case	NOUN
ap-374	175	32	,	,	PUNCT
ap-374	175	33	statical	statical	PROPN
ap-374	175	34	equilibrium	equilibrium	NOUN
ap-374	175	35	has	have	VERB
ap-374	175	36	to	to	PART
ap-374	175	37	be	be	AUX
ap-374	175	38	fulfilled	fulfil	VERB
ap-374	175	39	all	all	ADV
ap-374	175	40	over	over	ADP
ap-374	175	41	each	each	DET
ap-374	175	42	ball	ball	NOUN
ap-374	175	43	,	,	PUNCT
ap-374	175	44	and	and	CCONJ
ap-374	175	45	at	at	ADP
ap-374	175	46	the	the	DET
ap-374	175	47	contact	contact	NOUN
ap-374	175	48	points	point	NOUN
ap-374	175	49	between	between	ADP
ap-374	175	50	the	the	DET
ap-374	175	51	adjacent	adjacent	ADJ
ap-374	175	52	balls	ball	NOUN
ap-374	175	53	.	.	PUNCT
ap-374	176	1	the	the	DET
ap-374	176	2	balls	ball	NOUN
ap-374	176	3	(	(	PUNCT
ap-374	176	4	disks	disk	NOUN
ap-374	176	5	)	)	PUNCT
ap-374	176	6	are	be	AUX
ap-374	176	7	considered	consider	VERB
ap-374	176	8	rigid	rigid	ADJ
ap-374	176	9	.	.	PUNCT
ap-374	177	1	introduce	introduce	VERB
ap-374	177	2	coordinate	coordinate	NOUN
ap-374	177	3	system	system	NOUN
ap-374	177	4	0xyz	0xyz	NOUN
ap-374	177	5	in	in	ADP
ap-374	177	6	3d	3d	NUM
ap-374	177	7	.	.	PUNCT
ap-374	178	1	then	then	ADV
ap-374	178	2	each	each	DET
ap-374	178	3	disk	disk	NOUN
ap-374	178	4	has	have	VERB
ap-374	178	5	six	six	NUM
ap-374	178	6	degrees	degree	NOUN
ap-374	178	7	of	of	ADP
ap-374	178	8	freedom	freedom	NOUN
ap-374	178	9	(	(	PUNCT
ap-374	178	10	displacement	displacement	NOUN
ap-374	178	11	u	u	NOUN
ap-374	178	12	in	in	ADP
ap-374	178	13	direction	direction	NOUN
ap-374	178	14	x	x	NOUN
ap-374	178	15	,	,	PUNCT
ap-374	178	16	displacement	displacement	NOUN
ap-374	178	17	v	v	NOUN
ap-374	178	18	in	in	ADP
ap-374	178	19	direction	direction	NOUN
ap-374	178	20	y	y	PROPN
ap-374	178	21	,	,	PUNCT
ap-374	178	22	and	and	CCONJ
ap-374	178	23	displacement	displacement	NOUN
ap-374	178	24	w	w	NOUN
ap-374	178	25	in	in	ADP
ap-374	178	26	direction	direction	NOUN
ap-374	178	27	z	z	NOUN
ap-374	178	28	,	,	PUNCT
ap-374	178	29	and	and	CCONJ
ap-374	178	30	three	three	NUM
ap-374	178	31	rotations	rotation	NOUN
ap-374	178	32	with	with	ADP
ap-374	178	33	respect	respect	NOUN
ap-374	178	34	to	to	ADP
ap-374	178	35	the	the	DET
ap-374	178	36	three	three	NUM
ap-374	178	37	axes	axis	NOUN
ap-374	178	38	x	x	NOUN
ap-374	178	39	,	,	PUNCT
ap-374	178	40	y	y	PROPN
ap-374	178	41	and	and	CCONJ
ap-374	178	42	z.	z.	PROPN
ap-374	178	43	in	in	ADP
ap-374	178	44	what	what	PRON
ap-374	178	45	follows	follow	VERB
ap-374	178	46	we	we	PRON
ap-374	178	47	restrict	restrict	VERB
ap-374	178	48	our	our	PRON
ap-374	178	49	considerations	consideration	NOUN
ap-374	178	50	to	to	ADP
ap-374	178	51	2d	2d	NOUN
ap-374	178	52	for	for	ADP
ap-374	178	53	simplicity	simplicity	NOUN
ap-374	178	54	;	;	PUNCT
ap-374	178	55	generalization	generalization	NOUN
ap-374	178	56	to	to	ADP
ap-374	178	57	3d	3d	PROPN
ap-374	178	58	is	be	AUX
ap-374	178	59	straightforward	straightforward	ADJ
ap-374	178	60	.	.	PUNCT
ap-374	179	1	the	the	DET
ap-374	179	2	movement	movement	NOUN
ap-374	179	3	of	of	ADP
ap-374	179	4	each	each	DET
ap-374	179	5	disk	disk	NOUN
ap-374	179	6	is	be	AUX
ap-374	179	7	described	describe	VERB
ap-374	179	8	by	by	ADP
ap-374	179	9	two	two	NUM
ap-374	179	10	displacements	displacement	NOUN
ap-374	179	11	u	u	NOUN
ap-374	179	12	,	,	PUNCT
ap-374	179	13	v	v	NOUN
ap-374	179	14	and	and	CCONJ
ap-374	179	15	rotation	rotation	NOUN
ap-374	179	16	�	�	PROPN
ap-374	179	17	.	.	PUNCT
ap-374	180	1	the	the	DET
ap-374	180	2	forces	force	NOUN
ap-374	180	3	concentrated	concentrate	VERB
ap-374	180	4	at	at	ADP
ap-374	180	5	one	one	NUM
ap-374	180	6	contact	contact	NOUN
ap-374	180	7	point	point	NOUN
ap-374	180	8	of	of	ADP
ap-374	180	9	the	the	DET
ap-374	180	10	adjacent	adjacent	ADJ
ap-374	180	11	balls	ball	NOUN
ap-374	180	12	obey	obey	VERB
ap-374	180	13	the	the	DET
ap-374	180	14	contact	contact	NOUN
ap-374	180	15	conditions	condition	NOUN
ap-374	180	16	that	that	PRON
ap-374	180	17	are	be	AUX
ap-374	180	18	typical	typical	ADJ
ap-374	180	19	for	for	ADP
ap-374	180	20	soil	soil	NOUN
ap-374	180	21	in	in	ADP
ap-374	180	22	our	our	PRON
ap-374	180	23	study	study	NOUN
ap-374	180	24	.	.	PUNCT
ap-374	181	1	they	they	PRON
ap-374	181	2	determine	determine	VERB
ap-374	181	3	the	the	DET
ap-374	181	4	change	change	NOUN
ap-374	181	5	of	of	ADP
ap-374	181	6	stages	stage	NOUN
ap-374	181	7	in	in	ADP
ap-374	181	8	the	the	DET
ap-374	181	9	dsc	dsc	NOUN
ap-374	181	10	model	model	NOUN
ap-374	181	11	.	.	PUNCT
ap-374	182	1	the	the	DET
ap-374	182	2	plastic	plastic	ADJ
ap-374	182	3	behavior	behavior	NOUN
ap-374	182	4	,	,	PUNCT
ap-374	182	5	providing	provide	VERB
ap-374	182	6	rigid	rigid	ADJ
ap-374	182	7	balls	ball	NOUN
ap-374	182	8	,	,	PUNCT
ap-374	182	9	is	be	AUX
ap-374	182	10	imposed	impose	VERB
ap-374	182	11	only	only	ADV
ap-374	182	12	by	by	ADP
ap-374	182	13	the	the	DET
ap-374	182	14	forces	force	NOUN
ap-374	182	15	brought	bring	VERB
ap-374	182	16	about	about	ADP
ap-374	182	17	by	by	ADP
ap-374	182	18	spring	spring	NOUN
ap-374	182	19	stiffnesses	stiffness	NOUN
ap-374	182	20	and	and	CCONJ
ap-374	182	21	eigenparameters	eigenparameter	NOUN
ap-374	182	22	,	,	PUNCT
ap-374	182	23	e.g.	e.g.	ADV
ap-374	182	24	,	,	PUNCT
ap-374	182	25	plastic	plastic	NOUN
ap-374	182	26	strains	strain	NOUN
ap-374	182	27	(	(	PUNCT
ap-374	182	28	displacements	displacement	NOUN
ap-374	182	29	)	)	PUNCT
ap-374	182	30	,	,	PUNCT
ap-374	182	31	or	or	CCONJ
ap-374	182	32	relaxation	relaxation	NOUN
ap-374	182	33	stresses	stress	NOUN
ap-374	182	34	(	(	PUNCT
ap-374	182	35	forces	force	NOUN
ap-374	182	36	)	)	PUNCT
ap-374	182	37	.	.	PUNCT
ap-374	183	1	when	when	SCONJ
ap-374	183	2	introducing	introduce	VERB
ap-374	183	3	some	some	DET
ap-374	183	4	spring	spring	NOUN
ap-374	183	5	(	(	PUNCT
ap-374	183	6	of	of	ADP
ap-374	183	7	the	the	DET
ap-374	183	8	shape	shape	NOUN
ap-374	183	9	of	of	ADP
ap-374	183	10	a	a	DET
ap-374	183	11	straight	straight	ADJ
ap-374	183	12	line	line	NOUN
ap-374	183	13	,	,	PUNCT
ap-374	183	14	or	or	CCONJ
ap-374	183	15	more	more	ADV
ap-374	183	16	precisely	precisely	ADV
ap-374	183	17	of	of	ADP
ap-374	183	18	an	an	DET
ap-374	183	19	abscissa	abscissa	NOUN
ap-374	183	20	)	)	PUNCT
ap-374	183	21	spanned	span	VERB
ap-374	183	22	between	between	ADP
ap-374	183	23	two	two	NUM
ap-374	183	24	points	point	NOUN
ap-374	183	25	,	,	PUNCT
ap-374	183	26	its	its	PRON
ap-374	183	27	stiffness	stiffness	NOUN
ap-374	183	28	is	be	AUX
ap-374	183	29	k	k	PROPN
ap-374	183	30	,	,	PUNCT
ap-374	183	31	the	the	DET
ap-374	183	32	relation	relation	NOUN
ap-374	183	33	force	force	NOUN
ap-374	183	34	f	f	PROPN
ap-374	183	35	–	–	PUNCT
ap-374	183	36	displacement	displacement	ADJ
ap-374	183	37	u	u	NOUN
ap-374	183	38	in	in	ADP
ap-374	183	39	the	the	DET
ap-374	183	40	elastic	elastic	ADJ
ap-374	183	41	case	case	NOUN
ap-374	183	42	may	may	AUX
ap-374	183	43	generally	generally	ADV
ap-374	183	44	be	be	AUX
ap-374	183	45	written	write	VERB
ap-374	183	46	as	as	ADP
ap-374	183	47	(	(	PUNCT
ap-374	183	48	considering	consider	VERB
ap-374	183	49	one	one	NUM
ap-374	183	50	-	-	PUNCT
ap-374	183	51	dimensional	dimensional	ADJ
ap-374	183	52	case	case	NOUN
ap-374	183	53	):	):	PUNCT
ap-374	183	54	f	f	PROPN
ap-374	183	55	ku	ku	PROPN
ap-374	183	56	�	�	PROPN
ap-374	183	57	�	�	PROPN
ap-374	183	58	�	�	PROPN
ap-374	183	59	,	,	PUNCT
ap-374	183	60	or	or	CCONJ
ap-374	183	61	�	�	PROPN
ap-374	183	62	�	�	PROPN
ap-374	183	63	f	f	PROPN
ap-374	183	64	k	k	PROPN
ap-374	183	65	u	u	PROPN
ap-374	183	66	�	�	PROPN
ap-374	183	67	�	�	PROPN
ap-374	183	68	�	�	PROPN
ap-374	183	69	(	(	PUNCT
ap-374	183	70	10	10	NUM
ap-374	183	71	)	)	PUNCT
ap-374	183	72	where	where	SCONJ
ap-374	183	73	respectively	respectively	ADV
ap-374	183	74	�	�	PROPN
ap-374	183	75	is	be	AUX
ap-374	183	76	the	the	DET
ap-374	183	77	eigenstress	eigenstress	NOUN
ap-374	183	78	(	(	PUNCT
ap-374	183	79	eigenforce	eigenforce	NOUN
ap-374	183	80	)	)	PUNCT
ap-374	183	81	,	,	PUNCT
ap-374	183	82	and	and	CCONJ
ap-374	183	83	�	�	PROPN
ap-374	183	84	is	be	AUX
ap-374	183	85	the	the	DET
ap-374	183	86	eigenstrain	eigenstrain	NOUN
ap-374	183	87	(	(	PUNCT
ap-374	183	88	eigendisplacement	eigendisplacement	NOUN
ap-374	183	89	)	)	PUNCT
ap-374	183	90	.	.	PUNCT
ap-374	184	1	another	another	DET
ap-374	184	2	possibility	possibility	NOUN
ap-374	184	3	is	be	AUX
ap-374	184	4	to	to	PART
ap-374	184	5	drop	drop	VERB
ap-374	184	6	out	out	ADP
ap-374	184	7	the	the	DET
ap-374	184	8	eigenparameters	eigenparameter	NOUN
ap-374	184	9	and	and	CCONJ
ap-374	184	10	impose	impose	VERB
ap-374	184	11	the	the	DET
ap-374	184	12	nonlinear	nonlinear	ADJ
ap-374	184	13	conditions	condition	NOUN
ap-374	184	14	exceptionally	exceptionally	ADV
ap-374	184	15	on	on	ADP
ap-374	184	16	the	the	DET
ap-374	184	17	springs	spring	NOUN
ap-374	184	18	.	.	PUNCT
ap-374	185	1	the	the	DET
ap-374	185	2	eigenparameters	eigenparameter	NOUN
ap-374	185	3	©	©	PROPN
ap-374	185	4	czech	czech	PROPN
ap-374	185	5	technical	technical	PROPN
ap-374	185	6	university	university	PROPN
ap-374	185	7	publishing	publishing	NOUN
ap-374	185	8	house	house	NOUN
ap-374	185	9	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-374	185	10	45	45	NUM
ap-374	185	11	acta	acta	PROPN
ap-374	185	12	polytechnica	polytechnica	PROPN
ap-374	185	13	vol	vol	NOUN
ap-374	185	14	.	.	PUNCT
ap-374	186	1	42	42	NUM
ap-374	186	2	no	no	INTJ
ap-374	186	3	.	.	PUNCT
ap-374	187	1	4/2002	4/2002	PROPN
ap-374	187	2	enable	enable	VERB
ap-374	187	3	a	a	DET
ap-374	187	4	larger	large	ADJ
ap-374	187	5	range	range	NOUN
ap-374	187	6	of	of	ADP
ap-374	187	7	physical	physical	ADJ
ap-374	187	8	laws	law	NOUN
ap-374	187	9	to	to	PART
ap-374	187	10	be	be	AUX
ap-374	187	11	used	use	VERB
ap-374	187	12	in	in	ADP
ap-374	187	13	the	the	DET
ap-374	187	14	material	material	NOUN
ap-374	187	15	models	model	NOUN
ap-374	187	16	.	.	PUNCT
ap-374	188	1	this	this	PRON
ap-374	188	2	is	be	AUX
ap-374	188	3	why	why	SCONJ
ap-374	188	4	they	they	PRON
ap-374	188	5	are	be	AUX
ap-374	188	6	mostly	mostly	ADV
ap-374	188	7	applied	apply	VERB
ap-374	188	8	in	in	ADP
ap-374	188	9	the	the	DET
ap-374	188	10	mechanical	mechanical	ADJ
ap-374	188	11	models	model	NOUN
ap-374	188	12	.	.	PUNCT
ap-374	189	1	3.1	3.1	NUM
ap-374	189	2	relations	relation	NOUN
ap-374	189	3	between	between	ADP
ap-374	189	4	disks	disk	NOUN
ap-374	189	5	let	let	VERB
ap-374	189	6	us	we	PRON
ap-374	189	7	take	take	VERB
ap-374	189	8	a	a	DET
ap-374	189	9	set	set	NOUN
ap-374	189	10	of	of	ADP
ap-374	189	11	disks	disk	NOUN
ap-374	189	12	describing	describe	VERB
ap-374	189	13	a	a	DET
ap-374	189	14	discontinuous	discontinuous	ADJ
ap-374	189	15	medium	medium	NOUN
ap-374	189	16	positioned	position	VERB
ap-374	189	17	in	in	ADP
ap-374	189	18	a	a	DET
ap-374	189	19	coordinate	coordinate	NOUN
ap-374	189	20	system	system	NOUN
ap-374	189	21	0xy	0xy	NOUN
ap-374	189	22	,	,	PUNCT
ap-374	189	23	see	see	VERB
ap-374	189	24	fig	fig	NOUN
ap-374	189	25	.	.	PUNCT
ap-374	190	1	2	2	X
ap-374	190	2	.	.	X
ap-374	190	3	at	at	ADP
ap-374	190	4	the	the	DET
ap-374	190	5	contact	contact	NOUN
ap-374	190	6	points	point	NOUN
ap-374	190	7	(	(	PUNCT
ap-374	190	8	nodal	nodal	NOUN
ap-374	190	9	points	point	NOUN
ap-374	190	10	)	)	PUNCT
ap-374	190	11	,	,	PUNCT
ap-374	190	12	the	the	DET
ap-374	190	13	springs	spring	NOUN
ap-374	190	14	in	in	ADP
ap-374	190	15	the	the	DET
ap-374	190	16	tangential	tangential	ADJ
ap-374	190	17	and	and	CCONJ
ap-374	190	18	normal	normal	ADJ
ap-374	190	19	directions	direction	NOUN
ap-374	190	20	are	be	AUX
ap-374	190	21	introduced	introduce	VERB
ap-374	190	22	,	,	PUNCT
ap-374	190	23	which	which	PRON
ap-374	190	24	have	have	AUX
ap-374	190	25	stiffnesses	stiffness	NOUN
ap-374	190	26	kt	kt	PROPN
ap-374	190	27	in	in	ADP
ap-374	190	28	the	the	DET
ap-374	190	29	tangential	tangential	ADJ
ap-374	190	30	direction	direction	NOUN
ap-374	190	31	to	to	ADP
ap-374	190	32	the	the	DET
ap-374	190	33	boundary	boundary	NOUN
ap-374	190	34	of	of	ADP
ap-374	190	35	the	the	DET
ap-374	190	36	disk	disk	NOUN
ap-374	190	37	and	and	CCONJ
ap-374	190	38	kn	kn	PROPN
ap-374	190	39	in	in	ADP
ap-374	190	40	the	the	DET
ap-374	190	41	normal	normal	ADJ
ap-374	190	42	direction	direction	NOUN
ap-374	190	43	to	to	ADP
ap-374	190	44	the	the	DET
ap-374	190	45	boundary	boundary	NOUN
ap-374	190	46	at	at	ADP
ap-374	190	47	the	the	DET
ap-374	190	48	interface	interface	NOUN
ap-374	190	49	nodal	nodal	NOUN
ap-374	190	50	point	point	NOUN
ap-374	190	51	connecting	connect	VERB
ap-374	190	52	two	two	NUM
ap-374	190	53	adjacent	adjacent	ADJ
ap-374	190	54	disks	disk	NOUN
ap-374	190	55	.	.	PUNCT
ap-374	191	1	such	such	DET
ap-374	191	2	a	a	DET
ap-374	191	3	connection	connection	NOUN
ap-374	191	4	is	be	AUX
ap-374	191	5	described	describe	VERB
ap-374	191	6	in	in	ADP
ap-374	191	7	more	more	ADJ
ap-374	191	8	detail	detail	NOUN
ap-374	191	9	in	in	ADP
ap-374	191	10	fig	fig	NOUN
ap-374	191	11	.	.	PUNCT
ap-374	192	1	3	3	NUM
ap-374	192	2	for	for	ADP
ap-374	192	3	three	three	NUM
ap-374	192	4	disks	disk	NOUN
ap-374	192	5	in	in	ADP
ap-374	192	6	mutual	mutual	ADJ
ap-374	192	7	contact	contact	NOUN
ap-374	192	8	.	.	PUNCT
ap-374	193	1	fig	fig	NOUN
ap-374	193	2	.	.	PUNCT
ap-374	194	1	3	3	NUM
ap-374	194	2	depicts	depict	VERB
ap-374	194	3	external	external	ADJ
ap-374	194	4	(	(	PUNCT
ap-374	194	5	volume	volume	NOUN
ap-374	194	6	weight	weight	NOUN
ap-374	194	7	)	)	PUNCT
ap-374	194	8	forces	force	NOUN
ap-374	194	9	fi	fi	NOUN
ap-374	194	10	,	,	PUNCT
ap-374	194	11	i	i	PRON
ap-374	194	12	1	1	NUM
ap-374	194	13	,	,	PUNCT
ap-374	194	14	…	…	PUNCT
ap-374	194	15	,	,	PUNCT
ap-374	194	16	n	n	CCONJ
ap-374	194	17	(	(	PUNCT
ap-374	194	18	n	n	X
ap-374	194	19	is	be	AUX
ap-374	194	20	the	the	DET
ap-374	194	21	number	number	NOUN
ap-374	194	22	of	of	ADP
ap-374	194	23	all	all	DET
ap-374	194	24	disks	disk	NOUN
ap-374	194	25	)	)	PUNCT
ap-374	194	26	,	,	PUNCT
ap-374	194	27	contact	contact	NOUN
ap-374	194	28	forces	force	NOUN
ap-374	194	29	in	in	ADP
ap-374	194	30	normal	normal	ADJ
ap-374	194	31	and	and	CCONJ
ap-374	194	32	tangential	tangential	ADJ
ap-374	194	33	directions	direction	NOUN
ap-374	194	34	nij	nij	PROPN
ap-374	194	35	,	,	PUNCT
ap-374	194	36	qij	qij	PROPN
ap-374	194	37	,	,	PUNCT
ap-374	194	38	respectively	respectively	ADV
ap-374	194	39	,	,	PUNCT
ap-374	194	40	where	where	SCONJ
ap-374	194	41	i	i	PRON
ap-374	194	42	,	,	PUNCT
ap-374	194	43	j	j	PROPN
ap-374	194	44	1	1	NUM
ap-374	194	45	,	,	PUNCT
ap-374	194	46	2	2	NUM
ap-374	194	47	,	,	PUNCT
ap-374	194	48	and	and	CCONJ
ap-374	194	49	reactions	reaction	NOUN
ap-374	194	50	at	at	ADP
ap-374	194	51	the	the	DET
ap-374	194	52	supports	support	NOUN
ap-374	194	53	(	(	PUNCT
ap-374	194	54	created	create	VERB
ap-374	194	55	in	in	ADP
ap-374	194	56	this	this	DET
ap-374	194	57	case	case	NOUN
ap-374	194	58	by	by	ADP
ap-374	194	59	a	a	DET
ap-374	194	60	flat	flat	ADJ
ap-374	194	61	plate	plate	NOUN
ap-374	194	62	in	in	ADP
ap-374	194	63	3d	3d	NUM
ap-374	194	64	,	,	PUNCT
ap-374	194	65	or	or	CCONJ
ap-374	194	66	by	by	ADP
ap-374	194	67	a	a	DET
ap-374	194	68	straight	straight	ADJ
ap-374	194	69	line	line	NOUN
ap-374	194	70	in	in	ADP
ap-374	194	71	2d	2d	NOUN
ap-374	194	72	)	)	PUNCT
ap-374	194	73	a	a	DET
ap-374	194	74	,	,	PUNCT
ap-374	194	75	b	b	NOUN
ap-374	194	76	,	,	PUNCT
ap-374	194	77	ha	ha	INTJ
ap-374	194	78	,	,	PUNCT
ap-374	194	79	hb	hb	PROPN
ap-374	194	80	.	.	PUNCT
ap-374	195	1	the	the	DET
ap-374	195	2	first	first	ADJ
ap-374	195	3	index	index	NOUN
ap-374	195	4	denotes	denote	VERB
ap-374	195	5	the	the	DET
ap-374	195	6	number	number	NOUN
ap-374	195	7	of	of	ADP
ap-374	195	8	the	the	DET
ap-374	195	9	current	current	ADJ
ap-374	195	10	disk	disk	NOUN
ap-374	195	11	and	and	CCONJ
ap-374	195	12	the	the	DET
ap-374	195	13	second	second	ADJ
ap-374	195	14	index	index	NOUN
ap-374	195	15	stands	stand	VERB
ap-374	195	16	for	for	ADP
ap-374	195	17	the	the	DET
ap-374	195	18	number	number	NOUN
ap-374	195	19	of	of	ADP
ap-374	195	20	the	the	DET
ap-374	195	21	adjacent	adjacent	ADJ
ap-374	195	22	disk	disk	NOUN
ap-374	195	23	.	.	PUNCT
ap-374	196	1	this	this	DET
ap-374	196	2	notation	notation	NOUN
ap-374	196	3	is	be	AUX
ap-374	196	4	kept	keep	VERB
ap-374	196	5	in	in	ADP
ap-374	196	6	the	the	DET
ap-374	196	7	following	follow	VERB
ap-374	196	8	text	text	NOUN
ap-374	196	9	.	.	PUNCT
ap-374	197	1	the	the	DET
ap-374	197	2	main	main	ADJ
ap-374	197	3	objective	objective	NOUN
ap-374	197	4	is	be	AUX
ap-374	197	5	to	to	PART
ap-374	197	6	formulate	formulate	VERB
ap-374	197	7	the	the	DET
ap-374	197	8	equations	equation	NOUN
ap-374	197	9	of	of	ADP
ap-374	197	10	equilibrium	equilibrium	NOUN
ap-374	197	11	in	in	ADP
ap-374	197	12	each	each	DET
ap-374	197	13	disk	disk	NOUN
ap-374	197	14	i	i	PRON
ap-374	197	15	,	,	PUNCT
ap-374	197	16	i	i	PRON
ap-374	197	17	1	1	NUM
ap-374	197	18	,	,	PUNCT
ap-374	197	19	…	…	PUNCT
ap-374	197	20	,	,	PUNCT
ap-374	197	21	n	n	NOUN
ap-374	197	22	and	and	CCONJ
ap-374	197	23	from	from	ADP
ap-374	197	24	this	this	DET
ap-374	197	25	equilibrium	equilibrium	NOUN
ap-374	197	26	to	to	PART
ap-374	197	27	determine	determine	VERB
ap-374	197	28	the	the	DET
ap-374	197	29	displacements	displacement	NOUN
ap-374	197	30	of	of	ADP
ap-374	197	31	the	the	DET
ap-374	197	32	center	center	NOUN
ap-374	197	33	ui	ui	PROPN
ap-374	197	34	,	,	PUNCT
ap-374	197	35	vi	vi	PROPN
ap-374	197	36	and	and	CCONJ
ap-374	197	37	the	the	DET
ap-374	197	38	rotations	rotation	NOUN
ap-374	197	39	�	�	PROPN
ap-374	197	40	i	i	PRON
ap-374	197	41	of	of	ADP
ap-374	197	42	each	each	DET
ap-374	197	43	disk	disk	NOUN
ap-374	197	44	.	.	PUNCT
ap-374	198	1	the	the	DET
ap-374	198	2	connection	connection	NOUN
ap-374	198	3	with	with	ADP
ap-374	198	4	the	the	DET
ap-374	198	5	adjacent	adjacent	ADJ
ap-374	198	6	disks	disk	NOUN
ap-374	198	7	is	be	AUX
ap-374	198	8	created	create	VERB
ap-374	198	9	by	by	ADP
ap-374	198	10	the	the	DET
ap-374	198	11	quantities	quantity	NOUN
ap-374	198	12	with	with	ADP
ap-374	198	13	indices	index	NOUN
ap-374	198	14	i	i	PRON
ap-374	198	15	(	(	PUNCT
ap-374	198	16	the	the	DET
ap-374	198	17	current	current	ADJ
ap-374	198	18	disk	disk	NOUN
ap-374	198	19	)	)	PUNCT
ap-374	198	20	and	and	CCONJ
ap-374	198	21	j	j	PROPN
ap-374	198	22	(	(	PUNCT
ap-374	198	23	the	the	DET
ap-374	198	24	adjacent	adjacent	ADJ
ap-374	198	25	disk	disk	NOUN
ap-374	198	26	)	)	PUNCT
ap-374	198	27	.	.	PUNCT
ap-374	199	1	in	in	ADP
ap-374	199	2	the	the	DET
ap-374	199	3	sense	sense	NOUN
ap-374	199	4	of	of	ADP
ap-374	199	5	(	(	PUNCT
ap-374	199	6	10	10	NUM
ap-374	199	7	)	)	PUNCT
ap-374	199	8	the	the	DET
ap-374	199	9	physical	physical	ADJ
ap-374	199	10	equations	equation	NOUN
ap-374	199	11	at	at	ADP
ap-374	199	12	each	each	DET
ap-374	199	13	nodal	nodal	NOUN
ap-374	199	14	point	point	NOUN
ap-374	199	15	are	be	AUX
ap-374	199	16	formulated	formulate	VERB
ap-374	199	17	as	as	ADP
ap-374	199	18	:	:	PUNCT
ap-374	199	19	n	n	PRON
ap-374	199	20	q	q	PROPN
ap-374	199	21	k	k	X
ap-374	199	22	k	k	X
ap-374	200	1	ij	ij	INTJ
ap-374	200	2	ij	ij	INTJ
ap-374	200	3	n	n	PRON
ap-374	200	4	ij	ij	INTJ
ap-374	201	1	t	t	X
ap-374	202	1	ij	ij	INTJ
ap-374	203	1	n	n	PRON
ap-374	203	2	ij	ij	INTJ
ap-374	203	3	t	t	X
ap-374	203	4	ij	ij	NOUN
ap-374	203	5	n0	n0	PROPN
ap-374	203	6	0	0	NUM
ap-374	203	7	�	�	PROPN
ap-374	203	8	�	�	PROPN
ap-374	203	9	�	�	PROPN
ap-374	203	10	�	�	PROPN
ap-374	203	11	�	�	PROPN
ap-374	203	12	�	�	PROPN
ap-374	203	13	�	�	PROPN
ap-374	203	14	�	�	PROPN
ap-374	203	15	�	�	PROPN
ap-374	203	16	�	�	PROPN
ap-374	203	17	�	�	PROPN
ap-374	203	18	�	�	PROPN
ap-374	203	19	�	�	PROPN
ap-374	203	20	�	�	PROPN
ap-374	203	21	�	�	PROPN
ap-374	203	22	�	�	PROPN
ap-374	203	23	�	�	PROPN
ap-374	204	1	ij	ij	NOUN
ap-374	204	2	t	t	PROPN
ap-374	204	3	ij	ij	INTJ
ap-374	204	4	�	�	PROPN
ap-374	204	5	�	�	PROPN
ap-374	204	6	�	�	PROPN
ap-374	204	7	�	�	PROPN
ap-374	204	8	(	(	PUNCT
ap-374	204	9	11	11	NUM
ap-374	204	10	)	)	PUNCT
ap-374	204	11	where	where	SCONJ
ap-374	204	12	�	�	NOUN
ap-374	204	13	n	n	PRON
ap-374	204	14	ij	ij	NOUN
ap-374	204	15	and	and	CCONJ
ap-374	204	16	�	�	PROPN
ap-374	204	17	t	t	PROPN
ap-374	204	18	ij	ij	NOUN
ap-374	204	19	are	be	AUX
ap-374	204	20	respectively	respectively	ADV
ap-374	204	21	eigenforces	eigenforce	NOUN
ap-374	204	22	in	in	ADP
ap-374	204	23	normal	normal	ADJ
ap-374	204	24	and	and	CCONJ
ap-374	204	25	tangential	tangential	ADJ
ap-374	204	26	directions	direction	NOUN
ap-374	204	27	.	.	PUNCT
ap-374	205	1	indices	indice	VERB
ap-374	205	2	i	i	PRON
ap-374	205	3	,	,	PUNCT
ap-374	205	4	j	j	PROPN
ap-374	205	5	describe	describe	VERB
ap-374	205	6	the	the	DET
ap-374	205	7	numbers	number	NOUN
ap-374	205	8	of	of	ADP
ap-374	205	9	disks	disk	NOUN
ap-374	205	10	in	in	ADP
ap-374	205	11	mutual	mutual	ADJ
ap-374	205	12	contact	contact	NOUN
ap-374	205	13	and	and	CCONJ
ap-374	205	14	�	�	PROPN
ap-374	205	15	n	n	PART
ap-374	205	16	ij	ij	NOUN
ap-374	205	17	,	,	PUNCT
ap-374	205	18	�	�	PROPN
ap-374	205	19	t	t	PROPN
ap-374	205	20	ij	ij	NOUN
ap-374	205	21	are	be	AUX
ap-374	205	22	the	the	DET
ap-374	205	23	differences	difference	NOUN
ap-374	205	24	of	of	ADP
ap-374	205	25	displacements	displacement	NOUN
ap-374	205	26	in	in	ADP
ap-374	205	27	normal	normal	ADJ
ap-374	205	28	and	and	CCONJ
ap-374	205	29	tangential	tangential	ADJ
ap-374	205	30	directions	direction	NOUN
ap-374	205	31	,	,	PUNCT
ap-374	205	32	respectively	respectively	ADV
ap-374	205	33	,	,	PUNCT
ap-374	205	34	between	between	ADP
ap-374	205	35	disk	disk	NOUN
ap-374	205	36	i	i	PROPN
ap-374	205	37	and	and	CCONJ
ap-374	205	38	disk	disk	NOUN
ap-374	205	39	j	j	PROPN
ap-374	205	40	,	,	PUNCT
ap-374	205	41	i.e.	i.e.	X
ap-374	205	42	,	,	PUNCT
ap-374	205	43	�	�	PROPN
ap-374	205	44	n	n	ADP
ap-374	205	45	ij	ij	NOUN
ap-374	205	46	n	n	CCONJ
ap-374	205	47	ij	ij	INTJ
ap-374	205	48	n	n	CCONJ
ap-374	205	49	ji	ji	PROPN
ap-374	205	50	�	�	PROPN
ap-374	205	51	�	�	PROPN
ap-374	205	52	u	u	PROPN
ap-374	205	53	u	u	PROPN
ap-374	205	54	,	,	PUNCT
ap-374	205	55	�	�	PROPN
ap-374	205	56	t	t	PROPN
ap-374	206	1	ij	ij	X
ap-374	206	2	t	t	X
ap-374	206	3	ij	ij	INTJ
ap-374	206	4	t	t	PROPN
ap-374	206	5	ji	ji	PROPN
ap-374	206	6	�	�	PROPN
ap-374	206	7	�	�	PROPN
ap-374	206	8	u	u	NOUN
ap-374	206	9	u	u	NOUN
ap-374	206	10	.	.	PUNCT
ap-374	207	1	let	let	VERB
ap-374	207	2	the	the	DET
ap-374	207	3	nodal	nodal	NOUN
ap-374	207	4	point	point	NOUN
ap-374	207	5	ij	ij	NOUN
ap-374	207	6	under	under	ADP
ap-374	207	7	consideration	consideration	NOUN
ap-374	207	8	be	be	AUX
ap-374	207	9	deviated	deviate	VERB
ap-374	207	10	from	from	ADP
ap-374	207	11	the	the	DET
ap-374	207	12	x	x	NOUN
ap-374	207	13	-	-	NOUN
ap-374	207	14	direction	direction	NOUN
ap-374	207	15	by	by	ADP
ap-374	207	16	an	an	DET
ap-374	207	17	angle	angle	NOUN
ap-374	207	18	�	�	PROPN
ap-374	207	19	ij	ij	NOUN
ap-374	207	20	.	.	PUNCT
ap-374	208	1	then	then	ADV
ap-374	208	2	the	the	DET
ap-374	208	3	transformation	transformation	NOUN
ap-374	208	4	of	of	ADP
ap-374	208	5	forces	force	NOUN
ap-374	208	6	to	to	ADP
ap-374	208	7	the	the	DET
ap-374	208	8	0xy	0xy	ADJ
ap-374	208	9	coordinate	coordinate	NOUN
ap-374	208	10	system	system	NOUN
ap-374	208	11	is	be	AUX
ap-374	208	12	written	write	VERB
ap-374	208	13	by	by	ADP
ap-374	208	14	:	:	PUNCT
ap-374	208	15	n	n	CCONJ
ap-374	208	16	n	n	CCONJ
ap-374	208	17	nx	nx	INTJ
ap-374	209	1	ij	ij	INTJ
ap-374	209	2	y	y	PROPN
ap-374	210	1	ij	ij	INTJ
ap-374	210	2	ij	ij	INTJ
ap-374	210	3	ij	ij	INTJ
ap-374	210	4	ij	ij	INTJ
ap-374	210	5	ij	ij	INTJ
ap-374	211	1	i	i	PROPN
ap-374	211	2	�	�	PROPN
ap-374	211	3	�	�	PROPN
ap-374	211	4	�	�	PROPN
ap-374	211	5	�	�	PROPN
ap-374	211	6	�	�	PROPN
ap-374	211	7	�	�	PROPN
ap-374	211	8	�	�	PROPN
ap-374	211	9	�	�	PROPN
ap-374	211	10	�	�	PROPN
ap-374	211	11	�	�	PROPN
ap-374	211	12	�	�	PROPN
ap-374	211	13	cos	cos	PROPN
ap-374	211	14	sin	sin	PROPN
ap-374	211	15	sin	sin	PROPN
ap-374	211	16	cos	cos	PROPN
ap-374	211	17	�	�	PROPN
ap-374	211	18	�	�	PROPN
ap-374	211	19	�	�	PROPN
ap-374	211	20	�	�	PROPN
ap-374	211	21	j	j	PROPN
ap-374	212	1	ij	ij	INTJ
ap-374	212	2	ij	ij	INTJ
ap-374	212	3	t	t	X
ap-374	212	4	ij	ij	X
ap-374	212	5	ijq	ijq	VERB
ap-374	212	6	n	n	CCONJ
ap-374	212	7	q	q	PROPN
ap-374	212	8	�	�	PROPN
ap-374	212	9	�	�	PROPN
ap-374	212	10	�	�	PROPN
ap-374	212	11	�	�	PROPN
ap-374	212	12	�	�	PROPN
ap-374	212	13	�	�	PROPN
ap-374	212	14	�	�	PROPN
ap-374	212	15	t	t	PROPN
ap-374	212	16	(	(	PUNCT
ap-374	212	17	12	12	NUM
ap-374	212	18	)	)	PUNCT
ap-374	212	19	where	where	SCONJ
ap-374	212	20	nx	nx	PROPN
ap-374	212	21	ij	ij	NOUN
ap-374	212	22	,	,	PUNCT
ap-374	212	23	ny	ny	PROPN
ap-374	212	24	ij	ij	NOUN
ap-374	212	25	are	be	AUX
ap-374	212	26	forces	force	NOUN
ap-374	212	27	in	in	ADP
ap-374	212	28	x	x	PUNCT
ap-374	212	29	and	and	CCONJ
ap-374	212	30	y	y	PROPN
ap-374	212	31	directions	direction	NOUN
ap-374	212	32	,	,	PUNCT
ap-374	212	33	tij	tij	PROPN
ap-374	212	34	is	be	AUX
ap-374	212	35	the	the	DET
ap-374	212	36	transformation	transformation	NOUN
ap-374	212	37	matrix	matrix	NOUN
ap-374	212	38	and	and	CCONJ
ap-374	212	39	superscript	superscript	PROPN
ap-374	212	40	t	t	PROPN
ap-374	212	41	denotes	denote	VERB
ap-374	212	42	transposition	transposition	PROPN
ap-374	212	43	.	.	PUNCT
ap-374	213	1	recall	recall	VERB
ap-374	213	2	that	that	DET
ap-374	213	3	matrix	matrix	NOUN
ap-374	213	4	tij	tij	NOUN
ap-374	213	5	is	be	AUX
ap-374	213	6	unitary	unitary	ADJ
ap-374	213	7	,	,	PUNCT
ap-374	213	8	which	which	PRON
ap-374	213	9	means	mean	VERB
ap-374	213	10	that	that	SCONJ
ap-374	213	11	t	t	PROPN
ap-374	213	12	tij	tij	PROPN
ap-374	213	13	ij	ij	NUM
ap-374	213	14	t	t	PROPN
ap-374	213	15	�	�	PROPN
ap-374	213	16	�	�	PROPN
ap-374	213	17	1	1	NUM
ap-374	213	18	.	.	PUNCT
ap-374	214	1	since	since	SCONJ
ap-374	214	2	the	the	DET
ap-374	214	3	same	same	ADJ
ap-374	214	4	equations	equation	NOUN
ap-374	214	5	hold	hold	VERB
ap-374	214	6	for	for	ADP
ap-374	214	7	displacements	displacement	NOUN
ap-374	214	8	,	,	PUNCT
ap-374	214	9	the	the	DET
ap-374	214	10	following	follow	VERB
ap-374	214	11	forces	force	NOUN
ap-374	214	12	–	–	PUNCT
ap-374	214	13	displacements	displacement	NOUN
ap-374	214	14	relation	relation	NOUN
ap-374	214	15	holds	hold	VERB
ap-374	214	16	valid	valid	ADJ
ap-374	214	17	as	as	ADP
ap-374	214	18	:	:	PUNCT
ap-374	214	19	n	n	CCONJ
ap-374	214	20	n	n	NOUN
ap-374	215	1	k	k	NOUN
ap-374	216	1	k	k	PUNCT
ap-374	217	1	x	x	PUNCT
ap-374	218	1	ij	ij	INTJ
ap-374	219	1	y	y	NOUN
ap-374	220	1	ij	ij	INTJ
ap-374	220	2	ij	ij	INTJ
ap-374	220	3	t	t	NOUN
ap-374	220	4	n	n	CCONJ
ap-374	220	5	ij	ij	INTJ
ap-374	220	6	t	t	X
ap-374	220	7	ij	ij	INTJ
ap-374	220	8	n	n	PRON
ap-374	221	1	ij	ij	INTJ
ap-374	222	1	t	t	X
ap-374	222	2	ij	ij	NOUN
ap-374	222	3	0	0	NUM
ap-374	222	4	0	0	NUM
ap-374	222	5	�	�	PROPN
ap-374	222	6	�	�	PROPN
ap-374	222	7	�	�	PROPN
ap-374	222	8	�	�	PROPN
ap-374	222	9	�	�	PROPN
ap-374	222	10	�	�	PROPN
ap-374	222	11	�	�	PROPN
ap-374	222	12	�	�	PROPN
ap-374	222	13	�	�	PROPN
ap-374	222	14	�	�	PROPN
ap-374	222	15	�	�	PROPN
ap-374	222	16	�	�	PROPN
ap-374	222	17	�	�	PROPN
ap-374	222	18	�	�	PROPN
ap-374	222	19	�	�	PROPN
ap-374	222	20	�	�	PROPN
ap-374	222	21	�	�	PROPN
ap-374	222	22	�	�	PROPN
ap-374	222	23	�	�	PROPN
ap-374	222	24	�	�	PROPN
ap-374	222	25	�	�	PROPN
ap-374	222	26	�	�	PROPN
ap-374	222	27	�	�	PROPN
ap-374	222	28	�	�	PROPN
ap-374	222	29	�	�	PROPN
ap-374	222	30	�	�	PROPN
ap-374	222	31	�	�	PROPN
ap-374	222	32	�	�	PROPN
ap-374	222	33	�	�	PROPN
ap-374	222	34	�	�	PROPN
ap-374	222	35	�	�	PROPN
ap-374	222	36	�	�	PROPN
ap-374	222	37	n	n	CCONJ
ap-374	223	1	ij	ij	NOUN
ap-374	224	1	t	t	X
ap-374	224	2	ij	ij	INTJ
ap-374	225	1	xx	xx	NUM
ap-374	226	1	ij	ij	INTJ
ap-374	227	1	xy	xy	INTJ
ap-374	227	2	ij	ij	INTJ
ap-374	227	3	yx	yx	INTJ
ap-374	228	1	ij	ij	INTJ
ap-374	228	2	yy	yy	INTJ
ap-374	229	1	ij	ij	INTJ
ap-374	229	2	k	k	PROPN
ap-374	229	3	k	k	PROPN
ap-374	229	4	k	k	PROPN
ap-374	229	5	k	k	PROPN
ap-374	229	6	�	�	PROPN
ap-374	229	7	�	�	PROPN
ap-374	229	8	n	n	CCONJ
ap-374	230	1	ij	ij	NOUN
ap-374	231	1	t	t	X
ap-374	232	1	ij	ij	INTJ
ap-374	233	1	n	n	PRON
ap-374	233	2	ij	ij	NOUN
ap-374	233	3	t	t	X
ap-374	233	4	ij	ij	INTJ
ap-374	233	5	�	�	PROPN
ap-374	233	6	�	�	PROPN
ap-374	233	7	�	�	PROPN
ap-374	233	8	�	�	PROPN
ap-374	233	9	�	�	PROPN
ap-374	233	10	�	�	PROPN
ap-374	233	11	�	�	PROPN
ap-374	233	12	�	�	PROPN
ap-374	233	13	�	�	PROPN
ap-374	233	14	(	(	PUNCT
ap-374	233	15	13	13	NUM
ap-374	233	16	)	)	PUNCT
ap-374	233	17	where	where	SCONJ
ap-374	233	18	k	k	PROPN
ap-374	233	19	k	k	PROPN
ap-374	233	20	kxx	kxx	PROPN
ap-374	233	21	ij	ij	INTJ
ap-374	233	22	n	n	ADV
ap-374	233	23	ij	ij	INTJ
ap-374	234	1	ij	ij	INTJ
ap-374	234	2	t	t	X
ap-374	235	1	ij	ij	INTJ
ap-374	235	2	ij	ij	PROPN
ap-374	235	3	�	�	PROPN
ap-374	235	4	�	�	PROPN
ap-374	235	5	cos	cos	PROPN
ap-374	235	6	sin2	sin2	PROPN
ap-374	235	7	2	2	NUM
ap-374	235	8	�	�	PROPN
ap-374	235	9	�	�	PROPN
ap-374	235	10	;	;	NOUN
ap-374	235	11	k	k	PROPN
ap-374	235	12	k	k	PROPN
ap-374	235	13	kyy	kyy	PROPN
ap-374	236	1	ij	ij	X
ap-374	236	2	t	t	X
ap-374	237	1	ij	ij	INTJ
ap-374	238	1	ij	ij	INTJ
ap-374	238	2	n	n	ADP
ap-374	238	3	ij	ij	INTJ
ap-374	238	4	ij	ij	PROPN
ap-374	238	5	�	�	PROPN
ap-374	238	6	�	�	PROPN
ap-374	238	7	cos	cos	PROPN
ap-374	238	8	sin2	sin2	PROPN
ap-374	238	9	2	2	NUM
ap-374	238	10	�	�	PROPN
ap-374	238	11	�	�	PROPN
ap-374	238	12	;	;	NOUN
ap-374	238	13	�	�	PROPN
ap-374	238	14	�	�	PROPN
ap-374	239	1	k	k	PROPN
ap-374	239	2	k	k	PROPN
ap-374	239	3	k	k	PROPN
ap-374	239	4	kxy	kxy	NOUN
ap-374	239	5	ij	ij	NOUN
ap-374	239	6	yx	yx	NOUN
ap-374	239	7	ij	ij	INTJ
ap-374	239	8	n	n	CCONJ
ap-374	239	9	ij	ij	INTJ
ap-374	239	10	t	t	X
ap-374	239	11	ij	ij	INTJ
ap-374	239	12	ij	ij	INTJ
ap-374	239	13	�	�	PROPN
ap-374	239	14	�	�	PROPN
ap-374	239	15	�	�	PROPN
ap-374	239	16	1	1	NUM
ap-374	239	17	2	2	NUM
ap-374	239	18	2sin	2sin	NUM
ap-374	239	19	�	�	PROPN
ap-374	239	20	�	�	PROPN
ap-374	239	21	�	�	PROPN
ap-374	239	22	�	�	PROPN
ap-374	239	23	�	�	PROPN
ap-374	239	24	�	�	PROPN
ap-374	239	25	x	x	PROPN
ap-374	239	26	ij	ij	NOUN
ap-374	239	27	n	n	ADV
ap-374	239	28	ij	ij	INTJ
ap-374	239	29	ij	ij	INTJ
ap-374	239	30	t	t	X
ap-374	239	31	ij	ij	INTJ
ap-374	239	32	ij	ij	PROPN
ap-374	239	33	�	�	PROPN
ap-374	239	34	�	�	PROPN
ap-374	239	35	cos	cos	PROPN
ap-374	239	36	sin	sin	NOUN
ap-374	239	37	;	;	PUNCT
ap-374	239	38	�	�	PROPN
ap-374	239	39	�	�	PROPN
ap-374	239	40	�	�	PROPN
ap-374	239	41	�	�	PROPN
ap-374	239	42	�	�	PROPN
ap-374	239	43	y	y	PROPN
ap-374	239	44	ij	ij	NOUN
ap-374	239	45	n	n	ADV
ap-374	239	46	ij	ij	INTJ
ap-374	239	47	ij	ij	INTJ
ap-374	239	48	t	t	X
ap-374	240	1	ij	ij	INTJ
ap-374	240	2	ij	ij	INTJ
ap-374	240	3	�	�	PROPN
ap-374	240	4	�	�	PROPN
ap-374	240	5	sin	sin	PROPN
ap-374	240	6	cos	cos	PROPN
ap-374	240	7	(	(	PUNCT
ap-374	240	8	14	14	NUM
ap-374	240	9	)	)	PUNCT
ap-374	240	10	and	and	CCONJ
ap-374	240	11	�	�	NOUN
ap-374	240	12	x	x	SYM
ap-374	240	13	ij	ij	PROPN
ap-374	240	14	,	,	PUNCT
ap-374	240	15	�	�	PROPN
ap-374	240	16	y	y	PROPN
ap-374	240	17	ij	ij	NOUN
ap-374	240	18	are	be	AUX
ap-374	240	19	differences	difference	NOUN
ap-374	240	20	of	of	ADP
ap-374	240	21	displacements	displacement	NOUN
ap-374	240	22	in	in	ADP
ap-374	240	23	x	x	PUNCT
ap-374	240	24	and	and	CCONJ
ap-374	240	25	y	y	PROPN
ap-374	240	26	directions	direction	NOUN
ap-374	240	27	,	,	PUNCT
ap-374	240	28	respectively	respectively	ADV
ap-374	240	29	,	,	PUNCT
ap-374	240	30	in	in	ADP
ap-374	240	31	disks	disk	NOUN
ap-374	240	32	i	i	PROPN
ap-374	240	33	and	and	CCONJ
ap-374	240	34	j	j	PROPN
ap-374	240	35	,	,	PUNCT
ap-374	240	36	i.e.	i.e.	X
ap-374	240	37	,	,	PUNCT
ap-374	240	38	�	�	PROPN
ap-374	240	39	x	x	SYM
ap-374	240	40	ij	ij	INTJ
ap-374	240	41	x	x	X
ap-374	240	42	ij	ij	INTJ
ap-374	240	43	x	x	X
ap-374	240	44	ji	ji	PRON
ap-374	240	45	�	�	PROPN
ap-374	240	46	�	�	PROPN
ap-374	240	47	u	u	PROPN
ap-374	240	48	u	u	PROPN
ap-374	240	49	,	,	PUNCT
ap-374	240	50	�	�	PROPN
ap-374	240	51	y	y	PROPN
ap-374	241	1	ij	ij	INTJ
ap-374	241	2	y	y	PROPN
ap-374	241	3	ij	ij	INTJ
ap-374	241	4	y	y	PROPN
ap-374	241	5	ji	ji	PROPN
ap-374	241	6	�	�	PROPN
ap-374	241	7	�	�	PROPN
ap-374	241	8	u	u	NOUN
ap-374	241	9	u	u	NOUN
ap-374	241	10	.	.	PUNCT
ap-374	242	1	a	a	DET
ap-374	242	2	typical	typical	ADJ
ap-374	242	3	disk	disk	NOUN
ap-374	242	4	with	with	ADP
ap-374	242	5	springs	spring	NOUN
ap-374	242	6	introduced	introduce	VERB
ap-374	242	7	at	at	ADP
ap-374	242	8	nodes	node	NOUN
ap-374	242	9	in	in	ADP
ap-374	242	10	x	x	X
ap-374	242	11	and	and	CCONJ
ap-374	242	12	in	in	ADP
ap-374	242	13	y	y	PROPN
ap-374	242	14	directions	direction	NOUN
ap-374	242	15	and	and	CCONJ
ap-374	242	16	the	the	DET
ap-374	242	17	induced	induced	ADJ
ap-374	242	18	forces	force	NOUN
ap-374	242	19	in	in	ADP
ap-374	242	20	the	the	DET
ap-374	242	21	normal	normal	ADJ
ap-374	242	22	and	and	CCONJ
ap-374	242	23	tangential	tangential	ADJ
ap-374	242	24	directions	direction	NOUN
ap-374	242	25	are	be	AUX
ap-374	242	26	illustrated	illustrate	VERB
ap-374	242	27	in	in	ADP
ap-374	242	28	fig	fig	NOUN
ap-374	242	29	.	.	PUNCT
ap-374	243	1	4	4	X
ap-374	243	2	.	.	X
ap-374	243	3	if	if	SCONJ
ap-374	243	4	no	no	DET
ap-374	243	5	rotations	rotation	NOUN
ap-374	243	6	were	be	AUX
ap-374	243	7	considered	consider	VERB
ap-374	243	8	,	,	PUNCT
ap-374	243	9	the	the	DET
ap-374	243	10	above	above	ADJ
ap-374	243	11	formulas	formula	NOUN
ap-374	243	12	would	would	AUX
ap-374	243	13	be	be	AUX
ap-374	243	14	valid	valid	ADJ
ap-374	243	15	without	without	ADP
ap-374	243	16	improvement	improvement	NOUN
ap-374	243	17	and	and	CCONJ
ap-374	243	18	the	the	DET
ap-374	243	19	computation	computation	NOUN
ap-374	243	20	may	may	AUX
ap-374	243	21	start	start	VERB
ap-374	243	22	with	with	ADP
ap-374	243	23	(	(	PUNCT
ap-374	243	24	13	13	NUM
ap-374	243	25	)	)	PUNCT
ap-374	243	26	.	.	PUNCT
ap-374	244	1	for	for	ADP
ap-374	244	2	each	each	DET
ap-374	244	3	disk	disk	NOUN
ap-374	244	4	two	two	NUM
ap-374	244	5	degrees	degree	NOUN
ap-374	244	6	of	of	ADP
ap-374	244	7	freedom	freedom	NOUN
ap-374	244	8	in	in	ADP
ap-374	244	9	2d	2d	NUM
ap-374	244	10	(	(	PUNCT
ap-374	244	11	two	two	NUM
ap-374	244	12	independent	independent	ADJ
ap-374	244	13	displacements	displacement	NOUN
ap-374	244	14	are	be	AUX
ap-374	244	15	unknown	unknown	ADJ
ap-374	244	16	)	)	PUNCT
ap-374	244	17	,	,	PUNCT
ap-374	244	18	and	and	CCONJ
ap-374	244	19	three	three	NUM
ap-374	244	20	dof	dof	NOUN
ap-374	244	21	in	in	ADP
ap-374	244	22	3d	3d	PROPN
ap-374	244	23	(	(	PUNCT
ap-374	244	24	three	three	NUM
ap-374	244	25	independent	independent	ADJ
ap-374	244	26	displacements	displacement	NOUN
ap-374	244	27	)	)	PUNCT
ap-374	244	28	are	be	AUX
ap-374	244	29	sought	seek	VERB
ap-374	244	30	.	.	PUNCT
ap-374	245	1	in	in	ADP
ap-374	245	2	the	the	DET
ap-374	245	3	case	case	NOUN
ap-374	245	4	of	of	ADP
ap-374	245	5	admitted	admit	VERB
ap-374	245	6	rotations	rotation	NOUN
ap-374	245	7	of	of	ADP
ap-374	245	8	disks	disk	NOUN
ap-374	245	9	,	,	PUNCT
ap-374	245	10	additional	additional	ADJ
ap-374	245	11	unknown	unknown	ADJ
ap-374	245	12	angles	angle	NOUN
ap-374	245	13	�	�	PROPN
ap-374	245	14	i	i	PRON
ap-374	245	15	describing	describe	VERB
ap-374	245	16	the	the	DET
ap-374	245	17	rotations	rotation	NOUN
ap-374	245	18	of	of	ADP
ap-374	245	19	the	the	DET
ap-374	245	20	disks	disk	NOUN
ap-374	245	21	have	have	VERB
ap-374	245	22	to	to	PART
ap-374	245	23	be	be	AUX
ap-374	245	24	introduced	introduce	VERB
ap-374	245	25	.	.	PUNCT
ap-374	246	1	recall	recall	VERB
ap-374	246	2	that	that	SCONJ
ap-374	246	3	three	three	NUM
ap-374	246	4	dof	dof	NOUN
ap-374	246	5	(	(	PUNCT
ap-374	246	6	two	two	NUM
ap-374	246	7	displacements	displacement	NOUN
ap-374	246	8	ui	ui	PROPN
ap-374	246	9	,	,	PUNCT
ap-374	246	10	vi	vi	PROPN
ap-374	246	11	and	and	CCONJ
ap-374	246	12	one	one	NUM
ap-374	246	13	angle	angle	NOUN
ap-374	246	14	of	of	ADP
ap-374	246	15	rotation	rotation	NOUN
ap-374	246	16	�	�	PROPN
ap-374	246	17	i	i	PRON
ap-374	246	18	in	in	ADP
ap-374	246	19	2d	2d	NUM
ap-374	246	20	are	be	AUX
ap-374	246	21	to	to	PART
ap-374	246	22	be	be	AUX
ap-374	246	23	sought	seek	VERB
ap-374	246	24	.	.	PUNCT
ap-374	247	1	the	the	DET
ap-374	247	2	situation	situation	NOUN
ap-374	247	3	is	be	AUX
ap-374	247	4	depicted	depict	VERB
ap-374	247	5	in	in	ADP
ap-374	247	6	fig	fig	NOUN
ap-374	247	7	.	.	PUNCT
ap-374	248	1	5	5	X
ap-374	248	2	.	.	X
ap-374	248	3	let	let	VERB
ap-374	248	4	us	we	PRON
ap-374	248	5	focus	focus	VERB
ap-374	248	6	on	on	ADP
ap-374	248	7	one	one	NUM
ap-374	248	8	typical	typical	ADJ
ap-374	248	9	disk	disk	NOUN
ap-374	248	10	.	.	PUNCT
ap-374	249	1	its	its	PRON
ap-374	249	2	basic	basic	ADJ
ap-374	249	3	movements	movement	NOUN
ap-374	249	4	and	and	CCONJ
ap-374	249	5	their	their	PRON
ap-374	249	6	denotations	denotation	NOUN
ap-374	249	7	are	be	AUX
ap-374	249	8	clear	clear	ADJ
ap-374	249	9	from	from	ADP
ap-374	249	10	fig	fig	NOUN
ap-374	249	11	.	.	PUNCT
ap-374	250	1	6	6	NUM
ap-374	250	2	.	.	X
ap-374	250	3	with	with	ADP
ap-374	250	4	respect	respect	NOUN
ap-374	250	5	to	to	ADP
ap-374	250	6	the	the	DET
ap-374	250	7	46	46	NUM
ap-374	250	8	©	©	PROPN
ap-374	250	9	czech	czech	PROPN
ap-374	250	10	technical	technical	PROPN
ap-374	250	11	university	university	PROPN
ap-374	250	12	publishing	publishing	NOUN
ap-374	250	13	house	house	NOUN
ap-374	250	14	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-374	250	15	acta	acta	PROPN
ap-374	250	16	polytechnica	polytechnica	PROPN
ap-374	250	17	vol	vol	NOUN
ap-374	250	18	.	.	PUNCT
ap-374	251	1	42	42	NUM
ap-374	251	2	no	no	INTJ
ap-374	251	3	.	.	PUNCT
ap-374	252	1	4/2002	4/2002	NUM
ap-374	252	2	fig	fig	NOUN
ap-374	252	3	.	.	PUNCT
ap-374	253	1	2	2	NUM
ap-374	253	2	:	:	PUNCT
ap-374	253	3	structure	structure	NOUN
ap-374	253	4	of	of	ADP
ap-374	253	5	the	the	DET
ap-374	253	6	balls	ball	NOUN
ap-374	253	7	fig	fig	VERB
ap-374	253	8	.	.	PUNCT
ap-374	254	1	3	3	NUM
ap-374	254	2	:	:	PUNCT
ap-374	254	3	forces	force	NOUN
ap-374	254	4	between	between	ADP
ap-374	254	5	disks	disk	NOUN
ap-374	254	6	above	above	ADP
ap-374	254	7	-	-	PUNCT
ap-374	254	8	mentioned	mention	VERB
ap-374	254	9	arguments	argument	NOUN
ap-374	254	10	,	,	PUNCT
ap-374	254	11	the	the	DET
ap-374	254	12	three	three	NUM
ap-374	254	13	movements	movement	NOUN
ap-374	254	14	and	and	CCONJ
ap-374	254	15	their	their	PRON
ap-374	254	16	parts	part	NOUN
ap-374	254	17	are	be	AUX
ap-374	254	18	described	describe	VERB
ap-374	254	19	in	in	ADP
ap-374	254	20	this	this	DET
ap-374	254	21	picture	picture	NOUN
ap-374	254	22	.	.	PUNCT
ap-374	255	1	the	the	DET
ap-374	255	2	total	total	ADJ
ap-374	255	3	displacement	displacement	NOUN
ap-374	255	4	at	at	ADP
ap-374	255	5	any	any	DET
ap-374	255	6	point	point	NOUN
ap-374	255	7	on	on	ADP
ap-374	255	8	the	the	DET
ap-374	255	9	boundary	boundary	NOUN
ap-374	255	10	of	of	ADP
ap-374	255	11	the	the	DET
ap-374	255	12	disk	disk	NOUN
ap-374	255	13	in	in	ADP
ap-374	255	14	the	the	DET
ap-374	255	15	x	x	NOUN
ap-374	255	16	direction	direction	NOUN
ap-374	255	17	,	,	PUNCT
ap-374	255	18	or	or	CCONJ
ap-374	255	19	in	in	ADP
ap-374	255	20	the	the	DET
ap-374	255	21	y	y	PROPN
ap-374	255	22	direction	direction	NOUN
ap-374	255	23	,	,	PUNCT
ap-374	255	24	consists	consist	VERB
ap-374	255	25	of	of	ADP
ap-374	255	26	two	two	NUM
ap-374	255	27	kinds	kind	NOUN
ap-374	255	28	of	of	ADP
ap-374	255	29	displacements	displacement	NOUN
ap-374	255	30	that	that	PRON
ap-374	255	31	are	be	AUX
ap-374	255	32	related	relate	VERB
ap-374	255	33	to	to	ADP
ap-374	255	34	the	the	DET
ap-374	255	35	rotation	rotation	NOUN
ap-374	255	36	(	(	PUNCT
ap-374	255	37	subscript	subscript	NOUN
ap-374	255	38	rot	rot	VERB
ap-374	255	39	)	)	PUNCT
ap-374	255	40	,	,	PUNCT
ap-374	255	41	and	and	CCONJ
ap-374	255	42	translation	translation	NOUN
ap-374	255	43	(	(	PUNCT
ap-374	255	44	subscript	subscript	PROPN
ap-374	255	45	tran	tran	PROPN
ap-374	255	46	)	)	PUNCT
ap-374	255	47	,	,	PUNCT
ap-374	255	48	i.e.	i.e.	X
ap-374	255	49	,	,	PUNCT
ap-374	255	50	u	u	NOUN
ap-374	255	51	u	u	NOUN
ap-374	255	52	ux	ux	INTJ
ap-374	255	53	i	i	PRON
ap-374	255	54	x	x	VERB
ap-374	255	55	,	,	PUNCT
ap-374	255	56	rot	rot	VERB
ap-374	255	57	i	i	PRON
ap-374	255	58	x	x	PROPN
ap-374	255	59	,	,	PUNCT
ap-374	255	60	tran	tran	PROPN
ap-374	255	61	i	i	PROPN
ap-374	255	62	�	�	PROPN
ap-374	255	63	�	�	PROPN
ap-374	255	64	,	,	PUNCT
ap-374	255	65	u	u	NOUN
ap-374	255	66	u	u	NOUN
ap-374	255	67	uy	uy	INTJ
ap-374	255	68	i	i	PRON
ap-374	255	69	y	y	PROPN
ap-374	255	70	,	,	PUNCT
ap-374	255	71	rot	rot	VERB
ap-374	255	72	i	i	PRON
ap-374	255	73	y	y	PROPN
ap-374	255	74	,	,	PUNCT
ap-374	255	75	tran	tran	PROPN
ap-374	255	76	i	i	PROPN
ap-374	255	77	�	�	PROPN
ap-374	255	78	�	�	PROPN
ap-374	255	79	.	.	PUNCT
ap-374	256	1	since	since	SCONJ
ap-374	256	2	the	the	DET
ap-374	256	3	2d	2d	NUM
ap-374	256	4	case	case	NOUN
ap-374	256	5	is	be	AUX
ap-374	256	6	under	under	ADP
ap-374	256	7	consideration	consideration	NOUN
ap-374	256	8	,	,	PUNCT
ap-374	256	9	the	the	DET
ap-374	256	10	unknown	unknown	ADJ
ap-374	256	11	quantities	quantity	NOUN
ap-374	256	12	in	in	ADP
ap-374	256	13	each	each	DET
ap-374	256	14	disk	disk	NOUN
ap-374	256	15	i	i	PRON
ap-374	256	16	are	be	AUX
ap-374	256	17	ux	ux	PROPN
ap-374	256	18	,	,	PUNCT
ap-374	256	19	tran	tran	PROPN
ap-374	257	1	i	i	PRON
ap-374	257	2	,	,	PUNCT
ap-374	257	3	uy	uy	PROPN
ap-374	257	4	,	,	PUNCT
ap-374	257	5	tran	tran	PROPN
ap-374	258	1	i	i	PROPN
ap-374	258	2	and	and	CCONJ
ap-374	258	3	�	�	PROPN
ap-374	258	4	i.	i.	NOUN
ap-374	258	5	it	it	PRON
ap-374	258	6	only	only	ADV
ap-374	258	7	remains	remain	VERB
ap-374	258	8	to	to	PART
ap-374	258	9	express	express	VERB
ap-374	258	10	the	the	DET
ap-374	258	11	influence	influence	NOUN
ap-374	258	12	of	of	ADP
ap-374	258	13	rotation	rotation	NOUN
ap-374	258	14	of	of	ADP
ap-374	258	15	each	each	DET
ap-374	258	16	node	node	NOUN
ap-374	258	17	.	.	PUNCT
ap-374	259	1	from	from	ADP
ap-374	259	2	fig	fig	NOUN
ap-374	259	3	.	.	PUNCT
ap-374	260	1	6	6	NUM
ap-374	260	2	it	it	PRON
ap-374	260	3	obviously	obviously	ADV
ap-374	260	4	holds	hold	VERB
ap-374	260	5	:	:	PUNCT
ap-374	261	1	�	�	PROPN
ap-374	261	2	�	�	PROPN
ap-374	261	3	�	�	PROPN
ap-374	261	4	�	�	PROPN
ap-374	261	5	�	�	PROPN
ap-374	261	6	�	�	PROPN
ap-374	261	7	u	u	PROPN
ap-374	261	8	r	r	NOUN
ap-374	261	9	u	u	NOUN
ap-374	261	10	r	r	NOUN
ap-374	261	11	x	x	NOUN
ap-374	261	12	,	,	PUNCT
ap-374	261	13	rot	rot	VERB
ap-374	261	14	i	i	PRON
ap-374	261	15	y	y	NOUN
ap-374	261	16	,	,	PUNCT
ap-374	261	17	rot	rot	VERB
ap-374	261	18	i	i	PRON
ap-374	261	19	�	�	PROPN
ap-374	261	20	�	�	PROPN
ap-374	261	21	�	�	PROPN
ap-374	261	22	�	�	PROPN
ap-374	261	23	�	�	PROPN
ap-374	261	24	�	�	PROPN
ap-374	261	25	�	�	PROPN
ap-374	262	1	i	i	PRON
ap-374	262	2	ij	ij	INTJ
ap-374	263	1	i	i	PRON
ap-374	263	2	ij	ij	INTJ
ap-374	264	1	i	i	PRON
ap-374	264	2	ij	ij	INTJ
ap-374	265	1	i	i	PROPN
ap-374	265	2	cos	cos	PROPN
ap-374	265	3	cos	cos	PROPN
ap-374	265	4	,	,	PUNCT
ap-374	265	5	sin	sin	PROPN
ap-374	265	6	�	�	PROPN
ap-374	265	7	�	�	PROPN
ap-374	265	8	�	�	PROPN
ap-374	265	9	�	�	PROPN
ap-374	265	10	�	�	PROPN
ap-374	265	11	�	�	PROPN
ap-374	265	12	�	�	PROPN
ap-374	265	13	sin	sin	NOUN
ap-374	265	14	,	,	PUNCT
ap-374	265	15	�	�	NOUN
ap-374	265	16	ij	ij	X
ap-374	265	17	(	(	PUNCT
ap-374	265	18	15	15	NUM
ap-374	265	19	)	)	PUNCT
ap-374	265	20	where	where	SCONJ
ap-374	265	21	�	�	PROPN
ap-374	265	22	ij	ij	NOUN
ap-374	265	23	is	be	AUX
ap-374	265	24	given	give	VERB
ap-374	265	25	for	for	ADP
ap-374	265	26	each	each	DET
ap-374	265	27	node	node	NOUN
ap-374	265	28	and	and	CCONJ
ap-374	265	29	ri	ri	PROPN
ap-374	265	30	is	be	AUX
ap-374	265	31	the	the	DET
ap-374	265	32	radius	radius	NOUN
ap-374	265	33	of	of	ADP
ap-374	265	34	disk	disk	NOUN
ap-374	265	35	i.	i.	NOUN
ap-374	265	36	the	the	DET
ap-374	265	37	forces	force	NOUN
ap-374	265	38	nx	nx	X
ap-374	265	39	ij	ij	NOUN
ap-374	265	40	,	,	PUNCT
ap-374	265	41	and	and	CCONJ
ap-374	265	42	ny	ny	PROPN
ap-374	265	43	ij	ij	NOUN
ap-374	265	44	acting	act	VERB
ap-374	265	45	between	between	ADP
ap-374	265	46	disk	disk	NOUN
ap-374	265	47	i	i	PROPN
ap-374	265	48	and	and	CCONJ
ap-374	265	49	disk	disk	NOUN
ap-374	265	50	j	j	PROPN
ap-374	265	51	are	be	AUX
ap-374	265	52	then	then	ADV
ap-374	265	53	given	give	VERB
ap-374	265	54	by	by	ADP
ap-374	265	55	(	(	PUNCT
ap-374	265	56	13	13	NUM
ap-374	265	57	)	)	PUNCT
ap-374	265	58	.	.	PUNCT
ap-374	266	1	3.2	3.2	NUM
ap-374	266	2	governing	govern	VERB
ap-374	266	3	equations	equation	NOUN
ap-374	266	4	equation	equation	NOUN
ap-374	266	5	(	(	PUNCT
ap-374	266	6	13	13	NUM
ap-374	266	7	)	)	PUNCT
ap-374	266	8	can	can	AUX
ap-374	266	9	be	be	AUX
ap-374	266	10	rearranged	rearrange	VERB
ap-374	266	11	in	in	ADP
ap-374	266	12	a	a	DET
ap-374	266	13	more	more	ADV
ap-374	266	14	suitable	suitable	ADJ
ap-374	266	15	way	way	NOUN
ap-374	266	16	for	for	ADP
ap-374	266	17	algorithmization	algorithmization	NOUN
ap-374	266	18	:	:	PUNCT
ap-374	266	19	n	n	CCONJ
ap-374	266	20	n	n	CCONJ
ap-374	266	21	n	n	CCONJ
ap-374	266	22	n	n	NOUN
ap-374	267	1	k	k	NOUN
ap-374	267	2	k	k	PROPN
ap-374	267	3	k	k	PROPN
ap-374	267	4	kx	kx	PROPN
ap-374	268	1	ij	ij	INTJ
ap-374	268	2	y	y	PROPN
ap-374	269	1	ij	ij	INTJ
ap-374	269	2	x	x	PUNCT
ap-374	270	1	ji	ji	NOUN
ap-374	270	2	y	y	PROPN
ap-374	270	3	ji	ji	PROPN
ap-374	271	1	xx	xx	INTJ
ap-374	272	1	ij	ij	INTJ
ap-374	273	1	xy	xy	INTJ
ap-374	273	2	ij	ij	INTJ
ap-374	274	1	xx	xx	NUM
ap-374	275	1	ij	ij	INTJ
ap-374	275	2	x	x	X
ap-374	275	3	�	�	PROPN
ap-374	275	4	�	�	PROPN
ap-374	275	5	�	�	PROPN
ap-374	275	6	�	�	PROPN
ap-374	275	7	�	�	PROPN
ap-374	275	8	�	�	PROPN
ap-374	275	9	y	y	PROPN
ap-374	276	1	ij	ij	INTJ
ap-374	277	1	xy	xy	INTJ
ap-374	277	2	ij	ij	INTJ
ap-374	278	1	yy	yy	INTJ
ap-374	278	2	ij	ij	INTJ
ap-374	279	1	xy	xy	INTJ
ap-374	279	2	ij	ij	INTJ
ap-374	280	1	yy	yy	INTJ
ap-374	281	1	ij	ij	INTJ
ap-374	281	2	xx	xx	INTJ
ap-374	282	1	ji	ji	INTJ
ap-374	282	2	xy	xy	INTJ
ap-374	283	1	ji	ji	INTJ
ap-374	283	2	xx	xx	INTJ
ap-374	284	1	ji	ji	INTJ
ap-374	284	2	xy	xy	INTJ
ap-374	285	1	ji	ji	INTJ
ap-374	286	1	x	x	PUNCT
ap-374	286	2	k	k	PROPN
ap-374	287	1	k	k	PROPN
ap-374	287	2	k	k	PROPN
ap-374	288	1	k	k	PROPN
ap-374	289	1	k	k	PROPN
ap-374	290	1	k	k	PROPN
ap-374	291	1	k	k	PROPN
ap-374	291	2	k	k	PROPN
ap-374	291	3	k	k	PROPN
ap-374	291	4	�	�	PROPN
ap-374	291	5	�	�	PROPN
ap-374	291	6	�	�	PROPN
ap-374	291	7	�	�	PROPN
ap-374	291	8	�	�	PROPN
ap-374	291	9	y	y	PROPN
ap-374	291	10	ji	ji	PROPN
ap-374	292	1	yy	yy	INTJ
ap-374	293	1	ji	ji	INTJ
ap-374	293	2	xy	xy	INTJ
ap-374	294	1	ji	ji	INTJ
ap-374	295	1	yy	yy	INTJ
ap-374	295	2	ji	ji	INTJ
ap-374	296	1	x	x	PUNCT
ap-374	297	1	i	i	PRON
ap-374	297	2	y	y	VERB
ap-374	298	1	i	i	VERB
ap-374	298	2	x	x	PROPN
ap-374	298	3	j	j	PROPN
ap-374	298	4	y	y	PROPN
ap-374	298	5	j	j	PROPN
ap-374	298	6	�	�	PROPN
ap-374	298	7	�	�	PROPN
ap-374	298	8	�	�	PROPN
ap-374	298	9	�	�	PROPN
ap-374	298	10	�	�	PROPN
ap-374	298	11	�	�	PROPN
ap-374	298	12	�	�	PROPN
ap-374	298	13	�	�	PROPN
ap-374	298	14	�	�	PROPN
ap-374	298	15	�	�	PROPN
ap-374	298	16	�	�	PROPN
ap-374	298	17	�	�	PROPN
ap-374	298	18	�	�	PROPN
ap-374	298	19	�	�	PROPN
ap-374	298	20	�	�	PROPN
ap-374	298	21	�	�	PROPN
ap-374	298	22	k	k	PROPN
ap-374	298	23	k	k	PROPN
ap-374	298	24	k	k	PROPN
ap-374	298	25	u	u	X
ap-374	298	26	u	u	X
ap-374	298	27	u	u	X
ap-374	298	28	u	u	ADJ
ap-374	298	29	�	�	PROPN
ap-374	298	30	�	�	PROPN
ap-374	298	31	�	�	PROPN
ap-374	298	32	�	�	PROPN
ap-374	298	33	�	�	PROPN
ap-374	298	34	�	�	PROPN
ap-374	298	35	�	�	PROPN
ap-374	298	36	�	�	PROPN
ap-374	298	37	�	�	PROPN
ap-374	298	38	�	�	PROPN
ap-374	298	39	x	x	PUNCT
ap-374	299	1	i	i	PRON
ap-374	299	2	y	y	VERB
ap-374	300	1	i	i	VERB
ap-374	300	2	x	x	PROPN
ap-374	300	3	j	j	PROPN
ap-374	300	4	y	y	PROPN
ap-374	300	5	j	j	PROPN
ap-374	300	6	(	(	PUNCT
ap-374	300	7	16	16	NUM
ap-374	300	8	)	)	PUNCT
ap-374	300	9	and	and	CCONJ
ap-374	300	10	from	from	ADP
ap-374	300	11	(	(	PUNCT
ap-374	300	12	15	15	NUM
ap-374	300	13	):	):	PUNCT
ap-374	300	14	u	u	PRON
ap-374	300	15	u	u	NOUN
ap-374	300	16	u	u	X
ap-374	300	17	u	u	X
ap-374	300	18	u	u	X
ap-374	300	19	u	u	NOUN
ap-374	300	20	u	u	NOUN
ap-374	300	21	x	x	PROPN
ap-374	300	22	i	i	NOUN
ap-374	300	23	y	y	VERB
ap-374	301	1	i	i	VERB
ap-374	301	2	x	x	PROPN
ap-374	302	1	j	j	PROPN
ap-374	302	2	y	y	PROPN
ap-374	302	3	j	j	PROPN
ap-374	302	4	x	x	PROPN
ap-374	302	5	,	,	PUNCT
ap-374	302	6	tran	tran	PROPN
ap-374	302	7	i	i	PROPN
ap-374	302	8	y	y	PROPN
ap-374	302	9	,	,	PUNCT
ap-374	302	10	tran	tran	PROPN
ap-374	303	1	i	i	PROPN
ap-374	303	2	x	x	PROPN
ap-374	303	3	,	,	PUNCT
ap-374	303	4	tran	tran	PROPN
ap-374	303	5	�	�	PROPN
ap-374	303	6	�	�	PROPN
ap-374	303	7	�	�	PROPN
ap-374	303	8	�	�	PROPN
ap-374	303	9	�	�	PROPN
ap-374	303	10	�	�	PROPN
ap-374	303	11	�	�	PROPN
ap-374	303	12	�	�	PROPN
ap-374	303	13	j	j	PROPN
ap-374	303	14	y	y	PROPN
ap-374	303	15	,	,	PUNCT
ap-374	303	16	tran	tran	PROPN
ap-374	303	17	j	j	PROPN
ap-374	304	1	i	i	PRON
ap-374	304	2	ij	ij	INTJ
ap-374	305	1	i	i	PRON
ap-374	306	1	ij	ij	INTJ
ap-374	307	1	i	i	PRON
ap-374	307	2	u	u	NOUN
ap-374	307	3	r	r	NOUN
ap-374	307	4	r	r	NOUN
ap-374	307	5	�	�	PROPN
ap-374	307	6	�	�	PROPN
ap-374	307	7	�	�	PROPN
ap-374	307	8	�	�	PROPN
ap-374	307	9	�	�	PROPN
ap-374	307	10	�	�	PROPN
ap-374	307	11	�	�	PROPN
ap-374	307	12	cos	cos	PROPN
ap-374	307	13	cos	cos	PROPN
ap-374	307	14	sin	sin	PROPN
ap-374	307	15	�	�	PROPN
ap-374	307	16	�	�	PROPN
ap-374	307	17	�	�	PROPN
ap-374	307	18	�	�	PROPN
ap-374	307	19	�	�	PROPN
ap-374	307	20	�	�	PROPN
ap-374	307	21	�	�	PROPN
ap-374	307	22	�	�	PROPN
ap-374	307	23	�	�	PROPN
ap-374	307	24	�	�	PROPN
ap-374	307	25	�	�	PROPN
ap-374	307	26	�	�	PROPN
ap-374	307	27	�	�	PROPN
ap-374	307	28	�	�	PROPN
ap-374	307	29	�	�	PROPN
ap-374	307	30	�	�	PROPN
ap-374	307	31	�	�	PROPN
ap-374	307	32	�	�	PROPN
ap-374	307	33	�	�	PROPN
ap-374	307	34	�	�	PROPN
ap-374	307	35	�	�	PROPN
ap-374	307	36	�	�	PROPN
ap-374	307	37	�	�	PROPN
ap-374	307	38	�	�	PROPN
ap-374	308	1	ij	ij	NOUN
ap-374	309	1	i	i	PRON
ap-374	309	2	ij	ij	INTJ
ap-374	309	3	j	j	PROPN
ap-374	310	1	ji	ji	INTJ
ap-374	311	1	i	i	INTJ
ap-374	311	2	ji	ji	INTJ
ap-374	312	1	j	j	PROPN
ap-374	313	1	ji	ji	INTJ
ap-374	313	2	i	i	PRON
ap-374	313	3	ji	ji	PROPN
ap-374	313	4	�	�	PROPN
ap-374	313	5	�	�	PROPN
ap-374	313	6	�	�	PROPN
ap-374	313	7	�	�	PROPN
ap-374	313	8	�	�	PROPN
ap-374	313	9	�	�	PROPN
ap-374	313	10	�	�	PROPN
ap-374	313	11	sin	sin	PROPN
ap-374	313	12	cos	cos	PROPN
ap-374	313	13	cos	cos	PROPN
ap-374	313	14	sin	sin	PROPN
ap-374	313	15	sin	sin	NOUN
ap-374	313	16	r	r	NOUN
ap-374	313	17	r	r	NOUN
ap-374	313	18	�	�	PROPN
ap-374	313	19	�	�	PROPN
ap-374	313	20	�	�	PROPN
ap-374	313	21	(	(	PUNCT
ap-374	313	22	17	17	NUM
ap-374	313	23	)	)	PUNCT
ap-374	313	24	the	the	DET
ap-374	313	25	third	third	ADJ
ap-374	313	26	unknown	unknown	ADJ
ap-374	313	27	�	�	PROPN
ap-374	313	28	i	i	PRON
ap-374	313	29	appears	appear	VERB
ap-374	313	30	in	in	ADP
ap-374	313	31	the	the	DET
ap-374	313	32	conditions	condition	NOUN
ap-374	313	33	of	of	ADP
ap-374	313	34	equilibrium	equilibrium	NOUN
ap-374	313	35	in	in	ADP
ap-374	313	36	nonlinear	nonlinear	ADJ
ap-374	313	37	terms	term	NOUN
ap-374	313	38	,	,	PUNCT
ap-374	313	39	namely	namely	ADV
ap-374	313	40	in	in	ADP
ap-374	313	41	cosines	cosine	NOUN
ap-374	313	42	and	and	CCONJ
ap-374	313	43	sines	sine	NOUN
ap-374	313	44	(	(	PUNCT
ap-374	313	45	recall	recall	VERB
ap-374	313	46	that	that	SCONJ
ap-374	313	47	�	�	PROPN
ap-374	313	48	ij	ij	NOUN
ap-374	313	49	is	be	AUX
ap-374	313	50	the	the	DET
ap-374	313	51	angle	angle	NOUN
ap-374	313	52	of	of	ADP
ap-374	313	53	deviation	deviation	NOUN
ap-374	313	54	from	from	ADP
ap-374	313	55	the	the	DET
ap-374	313	56	x	x	NOUN
ap-374	313	57	-	-	NOUN
ap-374	313	58	axis	axis	NOUN
ap-374	313	59	of	of	ADP
ap-374	313	60	the	the	DET
ap-374	313	61	point	point	NOUN
ap-374	313	62	ij	ij	NOUN
ap-374	313	63	on	on	ADP
ap-374	313	64	the	the	DET
ap-374	313	65	boundary	boundary	NOUN
ap-374	313	66	of	of	ADP
ap-374	313	67	disk	disk	NOUN
ap-374	313	68	i	i	PRON
ap-374	313	69	being	be	AUX
ap-374	313	70	in	in	ADP
ap-374	313	71	contact	contact	NOUN
ap-374	313	72	with	with	ADP
ap-374	313	73	disk	disk	NOUN
ap-374	313	74	j	j	PROPN
ap-374	313	75	)	)	PUNCT
ap-374	313	76	.	.	PUNCT
ap-374	314	1	in	in	ADP
ap-374	314	2	order	order	NOUN
ap-374	314	3	to	to	PART
ap-374	314	4	avoid	avoid	VERB
ap-374	314	5	very	very	ADV
ap-374	314	6	complicated	complicated	ADJ
ap-374	314	7	and	and	CCONJ
ap-374	314	8	unreliable	unreliable	ADJ
ap-374	314	9	nonlinear	nonlinear	ADJ
ap-374	314	10	computation	computation	NOUN
ap-374	314	11	,	,	PUNCT
ap-374	314	12	the	the	DET
ap-374	314	13	load	load	NOUN
ap-374	314	14	(	(	PUNCT
ap-374	314	15	for	for	ADP
ap-374	314	16	example	example	NOUN
ap-374	314	17	volume	volume	NOUN
ap-374	314	18	weight	weight	NOUN
ap-374	314	19	)	)	PUNCT
ap-374	314	20	will	will	AUX
ap-374	314	21	be	be	AUX
ap-374	314	22	divided	divide	VERB
ap-374	314	23	into	into	ADP
ap-374	314	24	increments	increment	NOUN
ap-374	314	25	,	,	PUNCT
ap-374	314	26	and	and	CCONJ
ap-374	314	27	in	in	ADP
ap-374	314	28	each	each	DET
ap-374	314	29	increment	increment	NOUN
ap-374	314	30	the	the	DET
ap-374	314	31	small	small	ADJ
ap-374	314	32	displacement	displacement	NOUN
ap-374	314	33	(	(	PUNCT
ap-374	314	34	or	or	CCONJ
ap-374	314	35	more	more	ADV
ap-374	314	36	precisely	precisely	ADV
ap-374	314	37	small	small	ADJ
ap-374	314	38	rotation	rotation	NOUN
ap-374	314	39	)	)	PUNCT
ap-374	314	40	theory	theory	NOUN
ap-374	314	41	will	will	AUX
ap-374	314	42	be	be	AUX
ap-374	314	43	considered	consider	VERB
ap-374	314	44	.	.	PUNCT
ap-374	315	1	assuming	assume	VERB
ap-374	315	2	small	small	ADJ
ap-374	315	3	enough	enough	ADJ
ap-374	315	4	increments	increment	NOUN
ap-374	315	5	,	,	PUNCT
ap-374	315	6	small	small	ADJ
ap-374	315	7	enough	enough	ADJ
ap-374	315	8	angle	angle	NOUN
ap-374	315	9	�	�	PROPN
ap-374	315	10	also	also	ADV
ap-374	315	11	results	result	VERB
ap-374	315	12	,	,	PUNCT
ap-374	315	13	and	and	CCONJ
ap-374	315	14	(	(	PUNCT
ap-374	315	15	17	17	NUM
ap-374	315	16	)	)	PUNCT
ap-374	315	17	is	be	AUX
ap-374	315	18	substituted	substitute	VERB
ap-374	315	19	by	by	ADP
ap-374	315	20	:	:	PUNCT
ap-374	315	21	u	u	NOUN
ap-374	315	22	u	u	NOUN
ap-374	315	23	u	u	X
ap-374	315	24	u	u	X
ap-374	315	25	u	u	X
ap-374	315	26	u	u	NOUN
ap-374	315	27	u	u	NOUN
ap-374	315	28	x	x	PROPN
ap-374	315	29	i	i	NOUN
ap-374	315	30	y	y	VERB
ap-374	316	1	i	i	VERB
ap-374	316	2	x	x	PROPN
ap-374	317	1	j	j	PROPN
ap-374	317	2	y	y	PROPN
ap-374	317	3	j	j	PROPN
ap-374	317	4	x	x	PROPN
ap-374	317	5	,	,	PUNCT
ap-374	317	6	tran	tran	PROPN
ap-374	317	7	i	i	PROPN
ap-374	317	8	y	y	PROPN
ap-374	317	9	,	,	PUNCT
ap-374	317	10	tran	tran	PROPN
ap-374	318	1	i	i	PROPN
ap-374	318	2	x	x	PROPN
ap-374	318	3	,	,	PUNCT
ap-374	318	4	tran	tran	PROPN
ap-374	318	5	�	�	PROPN
ap-374	318	6	�	�	PROPN
ap-374	318	7	�	�	PROPN
ap-374	318	8	�	�	PROPN
ap-374	318	9	j	j	PROPN
ap-374	318	10	y	y	PROPN
ap-374	318	11	,	,	PUNCT
ap-374	318	12	tran	tran	PROPN
ap-374	319	1	j	j	PROPN
ap-374	320	1	i	i	PRON
ap-374	320	2	i	i	PRON
ap-374	321	1	ij	ij	INTJ
ap-374	321	2	i	i	PRON
ap-374	322	1	i	i	PRON
ap-374	322	2	ij	ij	VERB
ap-374	322	3	j	j	NOUN
ap-374	323	1	i	i	PRON
ap-374	323	2	u	u	VERB
ap-374	323	3	r	r	NOUN
ap-374	323	4	r	r	NOUN
ap-374	323	5	r	r	NOUN
ap-374	323	6	�	�	PROPN
ap-374	323	7	�	�	PROPN
ap-374	323	8	�	�	PROPN
ap-374	323	9	�	�	PROPN
ap-374	323	10	�	�	PROPN
ap-374	323	11	�	�	PROPN
ap-374	323	12	�	�	PROPN
ap-374	323	13	�	�	PROPN
ap-374	323	14	�	�	PROPN
ap-374	323	15	sin	sin	PROPN
ap-374	323	16	cos	cos	PROPN
ap-374	323	17	sin	sin	PROPN
ap-374	323	18	cos	cos	PROPN
ap-374	323	19	�	�	PROPN
ap-374	323	20	�	�	PROPN
ap-374	323	21	�	�	PROPN
ap-374	324	1	ji	ji	PROPN
ap-374	324	2	j	j	PROPN
ap-374	324	3	i	i	PROPN
ap-374	324	4	jir	jir	PROPN
ap-374	324	5	�	�	PROPN
ap-374	324	6	�	�	PROPN
ap-374	324	7	�	�	PROPN
ap-374	324	8	(	(	PUNCT
ap-374	324	9	17a	17a	X
ap-374	324	10	)	)	PUNCT
ap-374	324	11	in	in	ADP
ap-374	324	12	each	each	DET
ap-374	324	13	increment	increment	NOUN
ap-374	324	14	ux	ux	PROPN
ap-374	324	15	,	,	PUNCT
ap-374	324	16	tran	tran	PROPN
ap-374	325	1	i	i	PRON
ap-374	325	2	,	,	PUNCT
ap-374	325	3	uy	uy	PROPN
ap-374	325	4	,	,	PUNCT
ap-374	325	5	tran	tran	PROPN
ap-374	325	6	i	i	PRON
ap-374	325	7	,	,	PUNCT
ap-374	325	8	and	and	CCONJ
ap-374	325	9	�	�	NOUN
ap-374	325	10	i	i	PRON
ap-374	325	11	are	be	AUX
ap-374	325	12	parts	part	NOUN
ap-374	325	13	of	of	ADP
ap-374	325	14	the	the	DET
ap-374	325	15	total	total	ADJ
ap-374	325	16	values	value	NOUN
ap-374	325	17	,	,	PUNCT
ap-374	325	18	as	as	SCONJ
ap-374	325	19	also	also	ADV
ap-374	325	20	are	be	AUX
ap-374	325	21	the	the	DET
ap-374	325	22	forces	force	NOUN
ap-374	325	23	computed	compute	VERB
ap-374	325	24	from	from	ADP
ap-374	325	25	these	these	DET
ap-374	325	26	movements	movement	NOUN
ap-374	325	27	.	.	PUNCT
ap-374	326	1	another	another	DET
ap-374	326	2	advantage	advantage	NOUN
ap-374	326	3	of	of	ADP
ap-374	326	4	this	this	DET
ap-374	326	5	incremental	incremental	ADJ
ap-374	326	6	process	process	NOUN
ap-374	326	7	is	be	AUX
ap-374	326	8	©	©	PROPN
ap-374	326	9	czech	czech	PROPN
ap-374	326	10	technical	technical	PROPN
ap-374	326	11	university	university	PROPN
ap-374	326	12	publishing	publishing	NOUN
ap-374	326	13	house	house	NOUN
ap-374	326	14	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-374	326	15	47	47	NUM
ap-374	326	16	acta	acta	PROPN
ap-374	326	17	polytechnica	polytechnica	PROPN
ap-374	326	18	vol	vol	NOUN
ap-374	326	19	.	.	PUNCT
ap-374	327	1	42	42	NUM
ap-374	327	2	no	no	INTJ
ap-374	327	3	.	.	PUNCT
ap-374	328	1	4/2002	4/2002	NUM
ap-374	328	2	fig	fig	NOUN
ap-374	328	3	.	.	PUNCT
ap-374	329	1	4	4	NUM
ap-374	329	2	:	:	PUNCT
ap-374	329	3	starting	start	VERB
ap-374	329	4	model	model	NOUN
ap-374	329	5	of	of	ADP
ap-374	329	6	one	one	NUM
ap-374	329	7	disk	disk	NOUN
ap-374	329	8	for	for	ADP
ap-374	329	9	further	further	ADJ
ap-374	329	10	computation	computation	NOUN
ap-374	329	11	fig	fig	NOUN
ap-374	329	12	.	.	PUNCT
ap-374	330	1	5	5	NUM
ap-374	330	2	:	:	PUNCT
ap-374	330	3	additional	additional	ADJ
ap-374	330	4	displacements	displacement	NOUN
ap-374	330	5	at	at	ADP
ap-374	330	6	the	the	DET
ap-374	330	7	point	point	NOUN
ap-374	330	8	ij	ij	NOUN
ap-374	330	9	from	from	ADP
ap-374	330	10	rotation	rotation	NOUN
ap-374	330	11	fig	fig	NOUN
ap-374	330	12	.	.	PUNCT
ap-374	331	1	6	6	NUM
ap-374	331	2	:	:	SYM
ap-374	331	3	three	three	NUM
ap-374	331	4	basic	basic	ADJ
ap-374	331	5	movements	movement	NOUN
ap-374	331	6	of	of	ADP
ap-374	331	7	a	a	DET
ap-374	331	8	disk	disk	NOUN
ap-374	331	9	the	the	DET
ap-374	331	10	possibility	possibility	NOUN
ap-374	331	11	to	to	PART
ap-374	331	12	test	test	VERB
ap-374	331	13	the	the	DET
ap-374	331	14	contact	contact	NOUN
ap-374	331	15	conditions	condition	NOUN
ap-374	331	16	,	,	PUNCT
ap-374	331	17	as	as	SCONJ
ap-374	331	18	described	describe	VERB
ap-374	331	19	in	in	ADP
ap-374	331	20	the	the	DET
ap-374	331	21	following	follow	VERB
ap-374	331	22	section	section	NOUN
ap-374	331	23	.	.	PUNCT
ap-374	332	1	an	an	DET
ap-374	332	2	additional	additional	ADJ
ap-374	332	3	condition	condition	NOUN
ap-374	332	4	is	be	AUX
ap-374	332	5	necessary	necessary	ADJ
ap-374	332	6	to	to	PART
ap-374	332	7	complete	complete	VERB
ap-374	332	8	the	the	DET
ap-374	332	9	equations	equation	NOUN
ap-374	332	10	for	for	ADP
ap-374	332	11	three	three	NUM
ap-374	332	12	unknowns	unknown	NOUN
ap-374	332	13	in	in	ADP
ap-374	332	14	each	each	DET
ap-374	332	15	disk	disk	NOUN
ap-374	332	16	.	.	PUNCT
ap-374	333	1	this	this	PRON
ap-374	333	2	is	be	AUX
ap-374	333	3	the	the	DET
ap-374	333	4	moment	moment	NOUN
ap-374	333	5	condition	condition	NOUN
ap-374	333	6	with	with	ADP
ap-374	333	7	respect	respect	NOUN
ap-374	333	8	,	,	PUNCT
ap-374	333	9	for	for	ADP
ap-374	333	10	example	example	NOUN
ap-374	333	11	,	,	PUNCT
ap-374	333	12	to	to	ADP
ap-374	333	13	the	the	DET
ap-374	333	14	center	center	NOUN
ap-374	333	15	of	of	ADP
ap-374	333	16	the	the	DET
ap-374	333	17	disk	disk	NOUN
ap-374	333	18	under	under	ADP
ap-374	333	19	study	study	NOUN
ap-374	333	20	:	:	PUNCT
ap-374	333	21	q	q	PUNCT
ap-374	334	1	ij	ij	INTJ
ap-374	334	2	i	i	INTJ
ap-374	335	1	i	i	PRON
ap-374	336	1	r	r	VERB
ap-374	336	2	j	j	PROPN
ap-374	336	3	m	m	PROPN
ap-374	336	4	�	�	PROPN
ap-374	336	5	�	�	PROPN
ap-374	336	6	�	�	PROPN
ap-374	336	7	1	1	NUM
ap-374	336	8	0	0	NUM
ap-374	336	9	,	,	PUNCT
ap-374	336	10	(	(	PUNCT
ap-374	336	11	18	18	NUM
ap-374	336	12	)	)	PUNCT
ap-374	336	13	where	where	SCONJ
ap-374	336	14	mi	mi	PROPN
ap-374	336	15	is	be	AUX
ap-374	336	16	the	the	DET
ap-374	336	17	number	number	NOUN
ap-374	336	18	of	of	ADP
ap-374	336	19	nodes	node	NOUN
ap-374	336	20	on	on	ADP
ap-374	336	21	the	the	DET
ap-374	336	22	boundary	boundary	NOUN
ap-374	336	23	of	of	ADP
ap-374	336	24	disk	disk	NOUN
ap-374	336	25	i.	i.	NOUN
ap-374	336	26	since	since	SCONJ
ap-374	336	27	ri	ri	PROPN
ap-374	336	28	is	be	AUX
ap-374	336	29	constant	constant	ADJ
ap-374	336	30	in	in	ADP
ap-374	336	31	each	each	DET
ap-374	336	32	disk	disk	NOUN
ap-374	336	33	i	i	PRON
ap-374	336	34	,	,	PUNCT
ap-374	336	35	it	it	PRON
ap-374	336	36	may	may	AUX
ap-374	336	37	be	be	AUX
ap-374	336	38	dropped	drop	VERB
ap-374	336	39	out	out	ADP
ap-374	336	40	and	and	CCONJ
ap-374	336	41	the	the	DET
ap-374	336	42	three	three	NUM
ap-374	336	43	conditions	condition	NOUN
ap-374	336	44	in	in	ADP
ap-374	336	45	disk	disk	NOUN
ap-374	336	46	i	i	PRON
ap-374	336	47	are	be	AUX
ap-374	336	48	obtained	obtain	VERB
ap-374	336	49	as	as	ADP
ap-374	336	50	:	:	PUNCT
ap-374	336	51	n	n	PROPN
ap-374	336	52	f	f	PROPN
ap-374	337	1	n	n	CCONJ
ap-374	337	2	f	f	PROPN
ap-374	337	3	q	q	PROPN
ap-374	337	4	n	n	PROPN
ap-374	337	5	j	j	PROPN
ap-374	337	6	m	m	PROPN
ap-374	337	7	j	j	PROPN
ap-374	337	8	m	m	PROPN
ap-374	337	9	j	j	NOUN
ap-374	337	10	m	m	VERB
ap-374	337	11	x	x	VERB
ap-374	337	12	ij	ij	INTJ
ap-374	337	13	x	x	INTJ
ap-374	337	14	i	i	PRON
ap-374	337	15	y	y	VERB
ap-374	338	1	ij	ij	INTJ
ap-374	338	2	y	y	INTJ
ap-374	339	1	i	i	PRON
ap-374	339	2	t	t	X
ap-374	340	1	ij	ij	INTJ
ap-374	340	2	x	x	INTJ
ap-374	341	1	ij	ij	INTJ
ap-374	341	2	i	i	INTJ
ap-374	342	1	i	i	PRON
ap-374	342	2	i	i	PRON
ap-374	342	3	�	�	PROPN
ap-374	342	4	�	�	PROPN
ap-374	342	5	�	�	PROPN
ap-374	342	6	�	�	PROPN
ap-374	342	7	�	�	PROPN
ap-374	342	8	�	�	PROPN
ap-374	342	9	�	�	PROPN
ap-374	342	10	�	�	PROPN
ap-374	342	11	�	�	PROPN
ap-374	342	12	�	�	PROPN
ap-374	342	13	1	1	NUM
ap-374	342	14	1	1	NUM
ap-374	342	15	1	1	NUM
ap-374	342	16	,	,	PUNCT
ap-374	342	17	,	,	PUNCT
ap-374	342	18	sin	sin	PROPN
ap-374	342	19	�	�	PROPN
ap-374	342	20	�	�	PROPN
ap-374	342	21	�	�	PROPN
ap-374	342	22	ij	ij	NOUN
ap-374	342	23	y	y	PROPN
ap-374	343	1	ij	ij	INTJ
ap-374	343	2	ij	ij	INTJ
ap-374	344	1	i	i	PROPN
ap-374	344	2	�	�	PROPN
ap-374	344	3	�	�	PROPN
ap-374	344	4	�	�	PROPN
ap-374	344	5	�	�	PROPN
ap-374	344	6	n	n	CCONJ
ap-374	344	7	j	j	PROPN
ap-374	344	8	m	m	VERB
ap-374	344	9	cos	cos	PROPN
ap-374	344	10	�	�	PROPN
ap-374	344	11	1	1	NUM
ap-374	344	12	0	0	NUM
ap-374	344	13	(	(	PUNCT
ap-374	344	14	19	19	NUM
ap-374	344	15	)	)	PUNCT
ap-374	344	16	where	where	SCONJ
ap-374	344	17	fx	fx	PROPN
ap-374	345	1	i	i	PRON
ap-374	345	2	and	and	CCONJ
ap-374	345	3	fy	fy	PROPN
ap-374	345	4	i	i	PRON
ap-374	345	5	are	be	AUX
ap-374	345	6	volume	volume	NOUN
ap-374	345	7	weight	weight	NOUN
ap-374	345	8	forces	force	NOUN
ap-374	345	9	.	.	PUNCT
ap-374	346	1	if	if	SCONJ
ap-374	346	2	only	only	ADJ
ap-374	346	3	gravitation	gravitation	NOUN
ap-374	346	4	is	be	AUX
ap-374	346	5	considered	consider	VERB
ap-374	346	6	,	,	PUNCT
ap-374	346	7	the	the	DET
ap-374	346	8	denotation	denotation	NOUN
ap-374	346	9	f	f	PROPN
ap-374	346	10	fi	fi	NOUN
ap-374	346	11	y	y	PROPN
ap-374	346	12	i	i	PRON
ap-374	346	13	�	�	PROPN
ap-374	346	14	,	,	PUNCT
ap-374	346	15	and	and	CCONJ
ap-374	346	16	assumption	assumption	NOUN
ap-374	346	17	fx	fx	PROPN
ap-374	346	18	i	i	PROPN
ap-374	346	19	�	�	PROPN
ap-374	346	20	0	0	NUM
ap-374	346	21	can	can	AUX
ap-374	346	22	be	be	AUX
ap-374	346	23	used	use	VERB
ap-374	346	24	,	,	PUNCT
ap-374	346	25	as	as	ADP
ap-374	346	26	in	in	ADP
ap-374	346	27	fig	fig	NOUN
ap-374	346	28	.	.	PUNCT
ap-374	347	1	3	3	X
ap-374	347	2	.	.	X
ap-374	347	3	after	after	ADP
ap-374	347	4	introducing	introduce	VERB
ap-374	347	5	boundary	boundary	ADJ
ap-374	347	6	conditions	condition	NOUN
ap-374	347	7	and	and	CCONJ
ap-374	347	8	eigenforces	eigenforce	NOUN
ap-374	347	9	,	,	PUNCT
ap-374	347	10	the	the	DET
ap-374	347	11	equations	equation	NOUN
ap-374	347	12	(	(	PUNCT
ap-374	347	13	19	19	NUM
ap-374	347	14	)	)	PUNCT
ap-374	347	15	create	create	VERB
ap-374	347	16	an	an	DET
ap-374	347	17	algebraic	algebraic	ADJ
ap-374	347	18	system	system	NOUN
ap-374	347	19	for	for	ADP
ap-374	347	20	unknown	unknown	ADJ
ap-374	347	21	displacements	displacement	NOUN
ap-374	347	22	ux	ux	PROPN
ap-374	347	23	,	,	PUNCT
ap-374	347	24	tran	tran	PROPN
ap-374	348	1	i	i	PRON
ap-374	348	2	,	,	PUNCT
ap-374	348	3	uy	uy	PROPN
ap-374	348	4	,	,	PUNCT
ap-374	348	5	tran	tran	PROPN
ap-374	348	6	i	i	PRON
ap-374	348	7	,	,	PUNCT
ap-374	348	8	and	and	CCONJ
ap-374	348	9	rotations	rotation	NOUN
ap-374	348	10	�	�	VERB
ap-374	348	11	i	i	PRON
ap-374	348	12	of	of	ADP
ap-374	348	13	the	the	DET
ap-374	348	14	disks	disk	NOUN
ap-374	348	15	.	.	PUNCT
ap-374	349	1	solving	solve	VERB
ap-374	349	2	this	this	PRON
ap-374	349	3	,	,	PUNCT
ap-374	349	4	the	the	DET
ap-374	349	5	forces	force	NOUN
ap-374	349	6	can	can	AUX
ap-374	349	7	be	be	AUX
ap-374	349	8	determined	determine	VERB
ap-374	349	9	from	from	ADP
ap-374	349	10	(	(	PUNCT
ap-374	349	11	16	16	NUM
ap-374	349	12	)	)	PUNCT
ap-374	349	13	.	.	PUNCT
ap-374	350	1	note	note	VERB
ap-374	350	2	that	that	SCONJ
ap-374	350	3	when	when	SCONJ
ap-374	350	4	properly	properly	ADV
ap-374	350	5	stated	state	VERB
ap-374	350	6	,	,	PUNCT
ap-374	350	7	system	system	NOUN
ap-374	350	8	(	(	PUNCT
ap-374	350	9	19	19	NUM
ap-374	350	10	)	)	PUNCT
ap-374	350	11	has	have	VERB
ap-374	350	12	a	a	DET
ap-374	350	13	unique	unique	ADJ
ap-374	350	14	elastic	elastic	ADJ
ap-374	350	15	solution	solution	NOUN
ap-374	350	16	,	,	PUNCT
ap-374	350	17	providing	provide	VERB
ap-374	350	18	that	that	SCONJ
ap-374	350	19	the	the	DET
ap-374	350	20	incremental	incremental	ADJ
ap-374	350	21	formulation	formulation	NOUN
ap-374	350	22	(	(	PUNCT
ap-374	350	23	17a	17a	X
ap-374	350	24	)	)	PUNCT
ap-374	350	25	is	be	AUX
ap-374	350	26	assumed	assume	VERB
ap-374	350	27	,	,	PUNCT
ap-374	350	28	i.e.	i.e.	X
ap-374	350	29	,	,	PUNCT
ap-374	350	30	small	small	ADJ
ap-374	350	31	displacement	displacement	NOUN
ap-374	350	32	theory	theory	NOUN
ap-374	350	33	may	may	AUX
ap-374	350	34	be	be	AUX
ap-374	350	35	employed	employ	VERB
ap-374	350	36	.	.	PUNCT
ap-374	351	1	3.3	3.3	NUM
ap-374	351	2	interfacial	interfacial	ADJ
ap-374	351	3	conditions	condition	NOUN
ap-374	351	4	in	in	ADP
ap-374	351	5	geotechnics	geotechnic	NOUN
ap-374	351	6	and	and	CCONJ
ap-374	351	7	mining	mining	NOUN
ap-374	351	8	engineering	engineering	NOUN
ap-374	351	9	it	it	PRON
ap-374	351	10	is	be	AUX
ap-374	351	11	well	well	ADV
ap-374	351	12	known	know	VERB
ap-374	351	13	that	that	SCONJ
ap-374	351	14	the	the	DET
ap-374	351	15	material	material	ADJ
ap-374	351	16	behavior	behavior	NOUN
ap-374	351	17	of	of	ADP
ap-374	351	18	the	the	DET
ap-374	351	19	soil	soil	NOUN
ap-374	351	20	mass	mass	NOUN
ap-374	351	21	is	be	AUX
ap-374	351	22	not	not	PART
ap-374	351	23	elastic	elastic	ADJ
ap-374	351	24	,	,	PUNCT
ap-374	351	25	but	but	CCONJ
ap-374	351	26	exhibits	exhibit	VERB
ap-374	351	27	either	either	CCONJ
ap-374	351	28	plastic	plastic	ADJ
ap-374	351	29	behavior	behavior	NOUN
ap-374	351	30	,	,	PUNCT
ap-374	351	31	or	or	CCONJ
ap-374	351	32	localized	localized	ADJ
ap-374	351	33	damage	damage	NOUN
ap-374	351	34	,	,	PUNCT
ap-374	351	35	or	or	CCONJ
ap-374	351	36	both	both	PRON
ap-374	351	37	.	.	PUNCT
ap-374	352	1	contrary	contrary	ADJ
ap-374	352	2	to	to	ADP
ap-374	352	3	the	the	DET
ap-374	352	4	case	case	NOUN
ap-374	352	5	of	of	ADP
ap-374	352	6	free	free	ADJ
ap-374	352	7	hexagons	hexagon	NOUN
ap-374	352	8	,	,	PUNCT
ap-374	352	9	plastic	plastic	ADJ
ap-374	352	10	behavior	behavior	NOUN
ap-374	352	11	has	have	VERB
ap-374	352	12	to	to	PART
ap-374	352	13	be	be	AUX
ap-374	352	14	employed	employ	VERB
ap-374	352	15	only	only	ADV
ap-374	352	16	for	for	ADP
ap-374	352	17	spring	spring	NOUN
ap-374	352	18	properties	property	NOUN
ap-374	352	19	.	.	PUNCT
ap-374	353	1	for	for	ADP
ap-374	353	2	the	the	DET
ap-374	353	3	sake	sake	NOUN
ap-374	353	4	of	of	ADP
ap-374	353	5	completeness	completeness	NOUN
ap-374	353	6	,	,	PUNCT
ap-374	353	7	an	an	DET
ap-374	353	8	example	example	NOUN
ap-374	353	9	of	of	ADP
ap-374	353	10	such	such	ADJ
ap-374	353	11	properties	property	NOUN
ap-374	353	12	is	be	AUX
ap-374	353	13	discussed	discuss	VERB
ap-374	353	14	here	here	ADV
ap-374	353	15	.	.	PUNCT
ap-374	354	1	consider	consider	VERB
ap-374	354	2	two	two	NUM
ap-374	354	3	balls	ball	NOUN
ap-374	354	4	that	that	PRON
ap-374	354	5	are	be	AUX
ap-374	354	6	connected	connect	VERB
ap-374	354	7	by	by	ADP
ap-374	354	8	the	the	DET
ap-374	354	9	above	above	ADV
ap-374	354	10	-	-	PUNCT
ap-374	354	11	described	describe	VERB
ap-374	354	12	system	system	NOUN
ap-374	354	13	of	of	ADP
ap-374	354	14	springs	spring	NOUN
ap-374	354	15	.	.	PUNCT
ap-374	355	1	for	for	ADP
ap-374	355	2	the	the	DET
ap-374	355	3	sake	sake	NOUN
ap-374	355	4	of	of	ADP
ap-374	355	5	simplicity	simplicity	NOUN
ap-374	355	6	,	,	PUNCT
ap-374	355	7	we	we	PRON
ap-374	355	8	again	again	ADV
ap-374	355	9	concentrate	concentrate	VERB
ap-374	355	10	our	our	PRON
ap-374	355	11	attention	attention	NOUN
ap-374	355	12	on	on	ADP
ap-374	355	13	the	the	DET
ap-374	355	14	2d	2d	NUM
ap-374	355	15	case	case	NOUN
ap-374	355	16	.	.	PUNCT
ap-374	356	1	using	use	VERB
ap-374	356	2	formula	formula	NOUN
ap-374	356	3	(	(	PUNCT
ap-374	356	4	11	11	NUM
ap-374	356	5	)	)	PUNCT
ap-374	356	6	,	,	PUNCT
ap-374	356	7	the	the	DET
ap-374	356	8	normal	normal	ADJ
ap-374	356	9	forces	force	NOUN
ap-374	356	10	nij	nij	NOUN
ap-374	356	11	and	and	CCONJ
ap-374	356	12	tangential	tangential	ADJ
ap-374	356	13	forces	force	NOUN
ap-374	356	14	qij	qij	NOUN
ap-374	356	15	can	can	AUX
ap-374	356	16	be	be	AUX
ap-374	356	17	obtained	obtain	VERB
ap-374	356	18	for	for	ADP
ap-374	356	19	each	each	DET
ap-374	356	20	linear	linear	ADJ
ap-374	356	21	state	state	NOUN
ap-374	356	22	.	.	PUNCT
ap-374	357	1	vector	vector	NOUN
ap-374	357	2	transformation	transformation	NOUN
ap-374	357	3	of	of	ADP
ap-374	357	4	the	the	DET
ap-374	357	5	coordinates	coordinate	NOUN
ap-374	357	6	applied	apply	VERB
ap-374	357	7	to	to	ADP
ap-374	357	8	(	(	PUNCT
ap-374	357	9	17	17	NUM
ap-374	357	10	)	)	PUNCT
ap-374	357	11	provides	provide	VERB
ap-374	357	12	displacements	displacement	NOUN
ap-374	357	13	un	un	PROPN
ap-374	358	1	ij	ij	INTJ
ap-374	358	2	and	and	CCONJ
ap-374	358	3	ut	ut	PROPN
ap-374	358	4	ij	ij	INTJ
ap-374	358	5	.	.	PUNCT
ap-374	359	1	in	in	ADP
ap-374	359	2	a	a	DET
ap-374	359	3	wide	wide	ADJ
ap-374	359	4	range	range	NOUN
ap-374	359	5	of	of	ADP
ap-374	359	6	problems	problem	NOUN
ap-374	359	7	,	,	PUNCT
ap-374	359	8	the	the	DET
ap-374	359	9	classical	classical	ADJ
ap-374	359	10	plastic	plastic	NOUN
ap-374	359	11	laws	law	NOUN
ap-374	359	12	of	of	ADP
ap-374	359	13	deformation	deformation	NOUN
ap-374	359	14	and	and	CCONJ
ap-374	359	15	stress	stress	NOUN
ap-374	359	16	state	state	NOUN
ap-374	359	17	,	,	PUNCT
ap-374	359	18	e.g.	e.g.	ADV
ap-374	359	19	,	,	PUNCT
ap-374	359	20	elasto	elasto	NOUN
ap-374	359	21	-	-	PUNCT
ap-374	359	22	plastic	plastic	NOUN
ap-374	359	23	law	law	NOUN
ap-374	359	24	,	,	PUNCT
ap-374	359	25	are	be	AUX
ap-374	359	26	formulated	formulate	VERB
ap-374	359	27	as	as	ADP
ap-374	359	28	:	:	PUNCT
ap-374	359	29	n	n	PRON
ap-374	359	30	q	q	NOUN
ap-374	359	31	kij	kij	ADJ
ap-374	359	32	ij	ij	NOUN
ap-374	359	33	0	0	NUM
ap-374	359	34	2	2	NUM
ap-374	359	35	2	2	NUM
ap-374	359	36	24	24	NUM
ap-374	359	37	�	�	PROPN
ap-374	359	38	�	�	PROPN
ap-374	359	39	,	,	PUNCT
ap-374	359	40	i.e.	i.e.	X
ap-374	359	41	,	,	PUNCT
ap-374	359	42	�	�	PROPN
ap-374	359	43	�	�	PROPN
ap-374	359	44	�	�	PROPN
ap-374	359	45	�	�	PROPN
ap-374	359	46	k	k	PROPN
ap-374	359	47	u	u	PROPN
ap-374	359	48	k	k	PROPN
ap-374	359	49	u	u	X
ap-374	359	50	kn	kn	PROPN
ap-374	359	51	ij	ij	INTJ
ap-374	359	52	n	n	ADV
ap-374	359	53	ij	ij	INTJ
ap-374	360	1	t	t	X
ap-374	361	1	ij	ij	INTJ
ap-374	361	2	t	t	X
ap-374	361	3	ij	ij	NOUN
ap-374	361	4	0	0	NUM
ap-374	361	5	2	2	NUM
ap-374	361	6	2	2	NUM
ap-374	361	7	24	24	NUM
ap-374	361	8	�	�	PROPN
ap-374	361	9	�	�	PROPN
ap-374	361	10	(	(	PUNCT
ap-374	361	11	20	20	NUM
ap-374	361	12	)	)	PUNCT
ap-374	361	13	where	where	SCONJ
ap-374	361	14	k0	k0	PROPN
ap-374	361	15	is	be	AUX
ap-374	361	16	a	a	DET
ap-374	361	17	given	give	VERB
ap-374	361	18	positive	positive	ADJ
ap-374	361	19	number	number	NOUN
ap-374	361	20	.	.	PUNCT
ap-374	362	1	in	in	ADP
ap-374	362	2	the	the	DET
ap-374	362	3	case	case	NOUN
ap-374	362	4	of	of	ADP
ap-374	362	5	violating	violate	VERB
ap-374	362	6	conditions	condition	NOUN
ap-374	362	7	(	(	PUNCT
ap-374	362	8	20	20	NUM
ap-374	362	9	)	)	PUNCT
ap-374	362	10	,	,	PUNCT
ap-374	362	11	new	new	ADJ
ap-374	362	12	kt	kt	PROPN
ap-374	362	13	ij	ij	NOUN
ap-374	362	14	may	may	AUX
ap-374	362	15	be	be	AUX
ap-374	362	16	determined	determine	VERB
ap-374	362	17	.	.	PUNCT
ap-374	363	1	while	while	SCONJ
ap-374	363	2	the	the	DET
ap-374	363	3	value	value	NOUN
ap-374	363	4	of	of	ADP
ap-374	363	5	kt	kt	PROPN
ap-374	363	6	ij	ij	NOUN
ap-374	363	7	is	be	AUX
ap-374	363	8	restricted	restrict	VERB
ap-374	363	9	by	by	ADP
ap-374	363	10	(	(	PUNCT
ap-374	363	11	20	20	NUM
ap-374	363	12	)	)	PUNCT
ap-374	363	13	,	,	PUNCT
ap-374	363	14	un	un	PROPN
ap-374	363	15	ij	ij	PROPN
ap-374	363	16	is	be	AUX
ap-374	363	17	mostly	mostly	ADV
ap-374	363	18	bounded	bound	VERB
ap-374	363	19	by	by	ADP
ap-374	363	20	some	some	DET
ap-374	363	21	value	value	NOUN
ap-374	363	22	that	that	PRON
ap-374	363	23	can	can	AUX
ap-374	363	24	not	not	PART
ap-374	363	25	be	be	AUX
ap-374	363	26	exceeded	exceed	VERB
ap-374	363	27	.	.	PUNCT
ap-374	364	1	moreover	moreover	ADV
ap-374	364	2	,	,	PUNCT
ap-374	364	3	kn	kn	PROPN
ap-374	364	4	ij	ij	NOUN
ap-374	364	5	changes	change	VERB
ap-374	364	6	nonlinearly	nonlinearly	ADV
ap-374	364	7	with	with	ADP
ap-374	364	8	un	un	PROPN
ap-374	364	9	ij	ij	PROPN
ap-374	364	10	.	.	PUNCT
ap-374	365	1	a	a	DET
ap-374	365	2	parabolic	parabolic	ADJ
ap-374	365	3	rule	rule	NOUN
ap-374	365	4	is	be	AUX
ap-374	365	5	mostly	mostly	ADV
ap-374	365	6	applied	apply	VERB
ap-374	365	7	as	as	ADP
ap-374	365	8	:	:	PUNCT
ap-374	365	9	�	�	PROPN
ap-374	365	10	�	�	PROPN
ap-374	365	11	k	k	PROPN
ap-374	365	12	k	k	PROPN
ap-374	365	13	un	un	PROPN
ap-374	365	14	ij	ij	PROPN
ap-374	365	15	n0	n0	PROPN
ap-374	365	16	ij	ij	PROPN
ap-374	365	17	n	n	PRON
ap-374	365	18	ij	ij	NOUN
ap-374	365	19	s	s	PROPN
ap-374	365	20	�	�	PROPN
ap-374	365	21	�	�	PROPN
ap-374	365	22	1	1	NUM
ap-374	365	23	(	(	PUNCT
ap-374	365	24	21	21	NUM
ap-374	365	25	)	)	PUNCT
ap-374	365	26	where	where	SCONJ
ap-374	365	27	s	s	NOUN
ap-374	365	28	is	be	AUX
ap-374	365	29	an	an	DET
ap-374	365	30	exponent	exponent	NOUN
ap-374	365	31	to	to	PART
ap-374	365	32	be	be	AUX
ap-374	365	33	stated	state	VERB
ap-374	365	34	from	from	ADP
ap-374	365	35	laboratory	laboratory	NOUN
ap-374	365	36	tests	test	NOUN
ap-374	365	37	,	,	PUNCT
ap-374	365	38	as	as	ADV
ap-374	365	39	well	well	ADV
ap-374	365	40	as	as	ADP
ap-374	365	41	the	the	DET
ap-374	365	42	starting	starting	NOUN
ap-374	365	43	value	value	NOUN
ap-374	365	44	of	of	ADP
ap-374	365	45	kn0	kn0	PROPN
ap-374	365	46	ij	ij	INTJ
ap-374	365	47	.	.	PUNCT
ap-374	366	1	the	the	DET
ap-374	366	2	value	value	NOUN
ap-374	366	3	of	of	ADP
ap-374	366	4	nij	nij	PROPN
ap-374	366	5	increases	increase	NOUN
ap-374	366	6	nonlinearly	nonlinearly	ADV
ap-374	366	7	and	and	CCONJ
ap-374	366	8	when	when	SCONJ
ap-374	366	9	the	the	DET
ap-374	366	10	strength	strength	NOUN
ap-374	366	11	is	be	AUX
ap-374	366	12	reached	reach	VERB
ap-374	366	13	,	,	PUNCT
ap-374	366	14	a	a	DET
ap-374	366	15	crack	crack	NOUN
ap-374	366	16	is	be	AUX
ap-374	366	17	assumed	assume	VERB
ap-374	366	18	at	at	ADP
ap-374	366	19	point	point	NOUN
ap-374	366	20	ij	ij	NOUN
ap-374	366	21	and	and	CCONJ
ap-374	366	22	the	the	DET
ap-374	366	23	spring	spring	NOUN
ap-374	366	24	is	be	AUX
ap-374	366	25	suddenly	suddenly	ADV
ap-374	366	26	removed	remove	VERB
ap-374	366	27	.	.	PUNCT
ap-374	367	1	in	in	ADP
ap-374	367	2	practical	practical	ADJ
ap-374	367	3	examples	example	NOUN
ap-374	367	4	,	,	PUNCT
ap-374	367	5	the	the	DET
ap-374	367	6	spring	spring	NOUN
ap-374	367	7	that	that	PRON
ap-374	367	8	is	be	AUX
ap-374	367	9	in	in	ADP
ap-374	367	10	tension	tension	NOUN
ap-374	367	11	is	be	AUX
ap-374	367	12	removed	remove	VERB
ap-374	367	13	gradually	gradually	ADV
ap-374	367	14	to	to	PART
ap-374	367	15	stabilize	stabilize	VERB
ap-374	367	16	the	the	DET
ap-374	367	17	convergence	convergence	NOUN
ap-374	367	18	and	and	CCONJ
ap-374	367	19	speed	speed	VERB
ap-374	367	20	up	up	ADP
ap-374	367	21	the	the	DET
ap-374	367	22	iteration	iteration	NOUN
ap-374	367	23	process	process	NOUN
ap-374	367	24	.	.	PUNCT
ap-374	368	1	on	on	ADP
ap-374	368	2	the	the	DET
ap-374	368	3	other	other	ADJ
ap-374	368	4	hand	hand	NOUN
ap-374	368	5	,	,	PUNCT
ap-374	368	6	at	at	ADP
ap-374	368	7	this	this	DET
ap-374	368	8	point	point	NOUN
ap-374	368	9	“	"	PUNCT
ap-374	368	10	penetration	penetration	NOUN
ap-374	368	11	”	"	PUNCT
ap-374	368	12	of	of	ADP
ap-374	368	13	one	one	NUM
ap-374	368	14	disk	disk	NOUN
ap-374	368	15	into	into	ADP
ap-374	368	16	the	the	DET
ap-374	368	17	adjacent	adjacent	ADJ
ap-374	368	18	disk	disk	NOUN
ap-374	368	19	is	be	AUX
ap-374	368	20	fully	fully	ADV
ap-374	368	21	permitted	permit	VERB
ap-374	368	22	.	.	PUNCT
ap-374	369	1	this	this	PRON
ap-374	369	2	is	be	AUX
ap-374	369	3	an	an	DET
ap-374	369	4	impact	impact	NOUN
ap-374	369	5	of	of	ADP
ap-374	369	6	the	the	DET
ap-374	369	7	nonlinear	nonlinear	ADJ
ap-374	369	8	behavior	behavior	NOUN
ap-374	369	9	(	(	PUNCT
ap-374	369	10	21	21	NUM
ap-374	369	11	)	)	PUNCT
ap-374	369	12	of	of	ADP
ap-374	369	13	the	the	DET
ap-374	369	14	spring	spring	NOUN
ap-374	369	15	being	be	AUX
ap-374	369	16	compressed	compress	VERB
ap-374	369	17	in	in	ADP
ap-374	369	18	the	the	DET
ap-374	369	19	normal	normal	ADJ
ap-374	369	20	direction	direction	NOUN
ap-374	369	21	.	.	PUNCT
ap-374	370	1	damage	damage	NOUN
ap-374	370	2	occurs	occur	VERB
ap-374	370	3	when	when	SCONJ
ap-374	370	4	the	the	DET
ap-374	370	5	mohr	mohr	PROPN
ap-374	370	6	-	-	PUNCT
ap-374	370	7	coulomb	coulomb	PROPN
ap-374	370	8	hypothesis	hypothesis	NOUN
ap-374	370	9	is	be	AUX
ap-374	370	10	violated	violate	VERB
ap-374	370	11	or	or	CCONJ
ap-374	370	12	tensile	tensile	NOUN
ap-374	370	13	strength	strength	NOUN
ap-374	370	14	is	be	AUX
ap-374	370	15	reached	reach	VERB
ap-374	370	16	.	.	PUNCT
ap-374	371	1	in	in	ADP
ap-374	371	2	this	this	DET
ap-374	371	3	case	case	NOUN
ap-374	371	4	,	,	PUNCT
ap-374	371	5	it	it	PRON
ap-374	371	6	means	mean	VERB
ap-374	371	7	that	that	SCONJ
ap-374	371	8	a	a	X
ap-374	371	9	)	)	PUNCT
ap-374	371	10	�	�	PROPN
ap-374	371	11	�	�	PROPN
ap-374	371	12	q	q	PROPN
ap-374	371	13	n	n	NUM
ap-374	371	14	nij	nij	PROPN
ap-374	371	15	ij	ij	PROPN
ap-374	371	16	b	b	PROPN
ap-374	371	17	ij	ij	INTJ
ap-374	371	18	�	�	PROPN
ap-374	371	19	�	�	PROPN
ap-374	371	20	�	�	PROPN
ap-374	371	21	tan	tan	PROPN
ap-374	371	22	�	�	PROPN
ap-374	371	23	�	�	PROPN
ap-374	371	24	,	,	PUNCT
ap-374	371	25	where	where	SCONJ
ap-374	371	26	�	�	PROPN
ap-374	371	27	b	b	PROPN
ap-374	371	28	is	be	AUX
ap-374	371	29	the	the	DET
ap-374	371	30	shear	shear	NOUN
ap-374	371	31	strength	strength	NOUN
ap-374	371	32	(	(	PUNCT
ap-374	371	33	cohesion	cohesion	NOUN
ap-374	371	34	)	)	PUNCT
ap-374	371	35	,	,	PUNCT
ap-374	371	36	is	be	AUX
ap-374	371	37	the	the	DET
ap-374	371	38	heaviside	heaviside	ADJ
ap-374	371	39	function	function	NOUN
ap-374	371	40	,	,	PUNCT
ap-374	371	41	and	and	CCONJ
ap-374	371	42	�	�	PROPN
ap-374	371	43	is	be	AUX
ap-374	371	44	the	the	DET
ap-374	371	45	angle	angle	NOUN
ap-374	371	46	of	of	ADP
ap-374	371	47	internal	internal	ADJ
ap-374	371	48	friction	friction	NOUN
ap-374	371	49	,	,	PUNCT
ap-374	371	50	b	b	X
ap-374	371	51	)	)	PUNCT
ap-374	372	1	n	n	NOUN
ap-374	372	2	nij	nij	NOUN
ap-374	372	3	ij	ij	PROPN
ap-374	372	4	+	+	PROPN
ap-374	372	5	�	�	PROPN
ap-374	372	6	,	,	PUNCT
ap-374	372	7	where	where	SCONJ
ap-374	372	8	nij	nij	PROPN
ap-374	372	9	+	+	CCONJ
ap-374	372	10	is	be	AUX
ap-374	372	11	the	the	DET
ap-374	372	12	tensile	tensile	NOUN
ap-374	372	13	strength	strength	NOUN
ap-374	372	14	.	.	PUNCT
ap-374	373	1	when	when	SCONJ
ap-374	373	2	condition	condition	NOUN
ap-374	373	3	a	a	X
ap-374	373	4	)	)	PUNCT
ap-374	373	5	is	be	AUX
ap-374	373	6	not	not	PART
ap-374	373	7	fulfilled	fulfil	VERB
ap-374	373	8	,	,	PUNCT
ap-374	373	9	then	then	ADV
ap-374	373	10	a	a	DET
ap-374	373	11	“	"	PUNCT
ap-374	373	12	cut	cut	NOUN
ap-374	373	13	”	"	PUNCT
ap-374	373	14	of	of	ADP
ap-374	373	15	qij	qij	NOUN
ap-374	373	16	is	be	AUX
ap-374	373	17	supposed	suppose	VERB
ap-374	373	18	according	accord	VERB
ap-374	373	19	the	the	DET
ap-374	373	20	following	follow	VERB
ap-374	373	21	rule	rule	NOUN
ap-374	373	22	:	:	PUNCT
ap-374	373	23	�	�	PROPN
ap-374	373	24	�	�	PROPN
ap-374	373	25	q	q	PROPN
ap-374	373	26	n	n	NUM
ap-374	373	27	nij	nij	NOUN
ap-374	374	1	ij	ij	PROPN
ap-374	374	2	b	b	PROPN
ap-374	374	3	ij	ij	INTJ
ap-374	374	4	t	t	PROPN
ap-374	374	5	ij	ij	INTJ
ap-374	374	6	�	�	PROPN
ap-374	374	7	�	�	PROPN
ap-374	374	8	�	�	PROPN
ap-374	374	9	�	�	PROPN
ap-374	374	10	tan	tan	PROPN
ap-374	374	11	�	�	PROPN
ap-374	374	12	�	�	PROPN
ap-374	374	13	�	�	PROPN
ap-374	374	14	.	.	PUNCT
ap-374	375	1	note	note	VERB
ap-374	375	2	that	that	SCONJ
ap-374	375	3	more	more	ADV
ap-374	375	4	complicated	complicated	ADJ
ap-374	375	5	rules	rule	NOUN
ap-374	375	6	may	may	AUX
ap-374	375	7	be	be	AUX
ap-374	375	8	imposed	impose	VERB
ap-374	375	9	.	.	PUNCT
ap-374	376	1	for	for	ADP
ap-374	376	2	example	example	NOUN
ap-374	376	3	,	,	PUNCT
ap-374	376	4	both	both	DET
ap-374	376	5	internal	internal	ADJ
ap-374	376	6	parameters	parameter	NOUN
ap-374	376	7	,	,	PUNCT
ap-374	376	8	angle	angle	NOUN
ap-374	376	9	of	of	ADP
ap-374	376	10	internal	internal	ADJ
ap-374	376	11	friction	friction	NOUN
ap-374	376	12	and	and	CCONJ
ap-374	376	13	shear	shear	NOUN
ap-374	376	14	strength	strength	NOUN
ap-374	376	15	,	,	PUNCT
ap-374	376	16	may	may	AUX
ap-374	376	17	change	change	VERB
ap-374	376	18	with	with	ADP
ap-374	376	19	the	the	DET
ap-374	376	20	values	value	NOUN
ap-374	376	21	of	of	ADP
ap-374	376	22	qij	qij	PROPN
ap-374	376	23	.	.	PUNCT
ap-374	377	1	in	in	ADP
ap-374	377	2	the	the	DET
ap-374	377	3	case	case	NOUN
ap-374	377	4	of	of	ADP
ap-374	377	5	violation	violation	NOUN
ap-374	377	6	of	of	ADP
ap-374	377	7	condition	condition	NOUN
ap-374	377	8	b	b	PROPN
ap-374	377	9	)	)	PUNCT
ap-374	377	10	,	,	PUNCT
ap-374	377	11	a	a	DET
ap-374	377	12	local	local	ADJ
ap-374	377	13	disconnection	disconnection	NOUN
ap-374	377	14	(	(	PUNCT
ap-374	377	15	debond	debond	ADJ
ap-374	377	16	)	)	PUNCT
ap-374	377	17	occurs	occur	VERB
ap-374	377	18	and	and	CCONJ
ap-374	377	19	the	the	DET
ap-374	377	20	spring	spring	NOUN
ap-374	377	21	is	be	AUX
ap-374	377	22	removed	remove	VERB
ap-374	377	23	again	again	ADV
ap-374	377	24	.	.	PUNCT
ap-374	378	1	this	this	PRON
ap-374	378	2	is	be	AUX
ap-374	378	3	not	not	PART
ap-374	378	4	due	due	ADJ
ap-374	378	5	to	to	ADP
ap-374	378	6	local	local	ADJ
ap-374	378	7	cracking	cracking	NOUN
ap-374	378	8	but	but	CCONJ
ap-374	378	9	because	because	SCONJ
ap-374	378	10	of	of	ADP
ap-374	378	11	disconnection	disconnection	NOUN
ap-374	378	12	of	of	ADP
ap-374	378	13	the	the	DET
ap-374	378	14	disks	disk	NOUN
ap-374	378	15	that	that	PRON
ap-374	378	16	were	be	AUX
ap-374	378	17	originally	originally	ADV
ap-374	378	18	in	in	ADP
ap-374	378	19	contact	contact	NOUN
ap-374	378	20	at	at	ADP
ap-374	378	21	point	point	NOUN
ap-374	378	22	ij	ij	NOUN
ap-374	378	23	.	.	PUNCT
ap-374	379	1	eigenforces	eigenforce	NOUN
ap-374	379	2	have	have	AUX
ap-374	379	3	not	not	PART
ap-374	379	4	been	be	AUX
ap-374	379	5	discussed	discuss	VERB
ap-374	379	6	in	in	ADP
ap-374	379	7	this	this	DET
ap-374	379	8	paper	paper	NOUN
ap-374	379	9	.	.	PUNCT
ap-374	380	1	they	they	PRON
ap-374	380	2	are	be	AUX
ap-374	380	3	additional	additional	ADJ
ap-374	380	4	design	design	NOUN
ap-374	380	5	parameters	parameter	NOUN
ap-374	380	6	for	for	ADP
ap-374	380	7	optimal	optimal	ADJ
ap-374	380	8	approximation	approximation	NOUN
ap-374	380	9	of	of	ADP
ap-374	380	10	reality	reality	NOUN
ap-374	380	11	or	or	CCONJ
ap-374	380	12	of	of	ADP
ap-374	380	13	laboratory	laboratory	NOUN
ap-374	380	14	tests	test	NOUN
ap-374	380	15	in	in	ADP
ap-374	380	16	such	such	DET
ap-374	380	17	a	a	DET
ap-374	380	18	numerical	numerical	ADJ
ap-374	380	19	model	model	NOUN
ap-374	380	20	.	.	PUNCT
ap-374	381	1	they	they	PRON
ap-374	381	2	may	may	AUX
ap-374	381	3	also	also	ADV
ap-374	381	4	simulate	simulate	VERB
ap-374	381	5	other	other	ADJ
ap-374	381	6	phenomena	phenomenon	NOUN
ap-374	381	7	,	,	PUNCT
ap-374	381	8	such	such	ADJ
ap-374	381	9	as	as	ADP
ap-374	381	10	change	change	NOUN
ap-374	381	11	of	of	ADP
ap-374	381	12	temperature	temperature	NOUN
ap-374	381	13	,	,	PUNCT
ap-374	381	14	gas	gas	NOUN
ap-374	381	15	emission	emission	NOUN
ap-374	381	16	,	,	PUNCT
ap-374	381	17	blasting	blast	VERB
ap-374	381	18	at	at	ADP
ap-374	381	19	some	some	DET
ap-374	381	20	local	local	ADJ
ap-374	381	21	sources	source	NOUN
ap-374	381	22	,	,	PUNCT
ap-374	381	23	etc	etc	X
ap-374	381	24	.	.	X
ap-374	381	25	conclusions	conclusion	NOUN
ap-374	381	26	two	two	NUM
ap-374	381	27	new	new	ADJ
ap-374	381	28	discrete	discrete	ADJ
ap-374	381	29	element	element	NOUN
ap-374	381	30	methods	method	NOUN
ap-374	381	31	have	have	AUX
ap-374	381	32	been	be	AUX
ap-374	381	33	introduced	introduce	VERB
ap-374	381	34	in	in	ADP
ap-374	381	35	this	this	DET
ap-374	381	36	paper	paper	NOUN
ap-374	381	37	.	.	PUNCT
ap-374	382	1	one	one	NUM
ap-374	382	2	of	of	ADP
ap-374	382	3	them	they	PRON
ap-374	382	4	is	be	AUX
ap-374	382	5	an	an	DET
ap-374	382	6	extension	extension	NOUN
ap-374	382	7	of	of	ADP
ap-374	382	8	the	the	DET
ap-374	382	9	well	well	ADV
ap-374	382	10	-	-	PUNCT
ap-374	382	11	known	know	VERB
ap-374	382	12	particle	particle	NOUN
ap-374	382	13	flow	flow	NOUN
ap-374	382	14	code	code	NOUN
ap-374	382	15	.	.	PUNCT
ap-374	383	1	the	the	DET
ap-374	383	2	solution	solution	NOUN
ap-374	383	3	of	of	ADP
ap-374	383	4	this	this	DET
ap-374	383	5	method	method	NOUN
ap-374	383	6	is	be	AUX
ap-374	383	7	very	very	ADV
ap-374	383	8	easy	easy	ADJ
ap-374	383	9	and	and	CCONJ
ap-374	383	10	fast	fast	ADJ
ap-374	383	11	.	.	PUNCT
ap-374	384	1	on	on	ADP
ap-374	384	2	the	the	DET
ap-374	384	3	other	other	ADJ
ap-374	384	4	hand	hand	NOUN
ap-374	384	5	,	,	PUNCT
ap-374	384	6	it	it	PRON
ap-374	384	7	bears	bear	VERB
ap-374	384	8	the	the	DET
ap-374	384	9	same	same	ADJ
ap-374	384	10	disadvantages	disadvantage	NOUN
ap-374	384	11	as	as	ADP
ap-374	384	12	pfc	pfc	NOUN
ap-374	384	13	itself	itself	PRON
ap-374	384	14	.	.	PUNCT
ap-374	385	1	the	the	DET
ap-374	385	2	interpretation	interpretation	NOUN
ap-374	385	3	of	of	ADP
ap-374	385	4	the	the	DET
ap-374	385	5	material	material	NOUN
ap-374	385	6	properties	property	NOUN
ap-374	385	7	currently	currently	ADV
ap-374	385	8	obtained	obtain	VERB
ap-374	385	9	from	from	ADP
ap-374	385	10	laboratory	laboratory	NOUN
ap-374	385	11	tests	test	NOUN
ap-374	385	12	is	be	AUX
ap-374	385	13	quite	quite	ADV
ap-374	385	14	complicated	complicated	ADJ
ap-374	385	15	,	,	PUNCT
ap-374	385	16	if	if	SCONJ
ap-374	385	17	possible	possible	ADJ
ap-374	385	18	at	at	ADV
ap-374	385	19	all	all	ADV
ap-374	385	20	.	.	PUNCT
ap-374	386	1	if	if	SCONJ
ap-374	386	2	the	the	DET
ap-374	386	3	material	material	NOUN
ap-374	386	4	properties	property	NOUN
ap-374	386	5	are	be	AUX
ap-374	386	6	properly	properly	ADV
ap-374	386	7	chosen	choose	VERB
ap-374	386	8	,	,	PUNCT
ap-374	386	9	the	the	DET
ap-374	386	10	results	result	NOUN
ap-374	386	11	seem	seem	VERB
ap-374	386	12	to	to	PART
ap-374	386	13	be	be	AUX
ap-374	386	14	realistic	realistic	ADJ
ap-374	386	15	,	,	PUNCT
ap-374	386	16	as	as	SCONJ
ap-374	386	17	shown	show	VERB
ap-374	386	18	in	in	ADP
ap-374	386	19	the	the	DET
ap-374	386	20	forthcoming	forthcoming	ADJ
ap-374	386	21	paper	paper	NOUN
ap-374	386	22	by	by	ADP
ap-374	386	23	the	the	DET
ap-374	386	24	authors	author	NOUN
ap-374	386	25	.	.	PUNCT
ap-374	387	1	a	a	DET
ap-374	387	2	much	much	ADV
ap-374	387	3	more	more	ADV
ap-374	387	4	complex	complex	ADJ
ap-374	387	5	and	and	CCONJ
ap-374	387	6	suitable	suitable	ADJ
ap-374	387	7	method	method	NOUN
ap-374	387	8	for	for	ADP
ap-374	387	9	predicting	predict	VERB
ap-374	387	10	the	the	DET
ap-374	387	11	real	real	ADJ
ap-374	387	12	behavior	behavior	NOUN
ap-374	387	13	of	of	ADP
ap-374	387	14	the	the	DET
ap-374	387	15	test	test	NOUN
ap-374	387	16	material	material	NOUN
ap-374	387	17	is	be	AUX
ap-374	387	18	the	the	DET
ap-374	387	19	method	method	NOUN
ap-374	387	20	of	of	ADP
ap-374	387	21	free	free	ADJ
ap-374	387	22	hexagons	hexagon	NOUN
ap-374	387	23	,	,	PUNCT
ap-374	387	24	which	which	PRON
ap-374	387	25	involves	involve	VERB
ap-374	387	26	both	both	CCONJ
ap-374	387	27	mechanical	mechanical	ADJ
ap-374	387	28	and	and	CCONJ
ap-374	387	29	geotechnical	geotechnical	ADJ
ap-374	387	30	properties	property	NOUN
ap-374	387	31	received	receive	VERB
ap-374	387	32	from	from	ADP
ap-374	387	33	the	the	DET
ap-374	387	34	experiments	experiment	NOUN
ap-374	387	35	.	.	PUNCT
ap-374	388	1	the	the	DET
ap-374	388	2	hexagons	hexagon	NOUN
ap-374	388	3	can	can	AUX
ap-374	388	4	cover	cover	VERB
ap-374	388	5	the	the	DET
ap-374	388	6	entire	entire	ADJ
ap-374	388	7	domain	domain	NOUN
ap-374	388	8	describing	describe	VERB
ap-374	388	9	the	the	DET
ap-374	388	10	physical	physical	ADJ
ap-374	388	11	body	body	NOUN
ap-374	388	12	,	,	PUNCT
ap-374	388	13	and	and	CCONJ
ap-374	388	14	along	along	ADP
ap-374	388	15	the	the	DET
ap-374	388	16	local	local	ADJ
ap-374	388	17	boundaries	boundary	NOUN
ap-374	388	18	between	between	ADP
ap-374	388	19	elements	element	NOUN
ap-374	388	20	the	the	DET
ap-374	388	21	geotechnical	geotechnical	ADJ
ap-374	388	22	properties	property	NOUN
ap-374	388	23	can	can	AUX
ap-374	388	24	be	be	AUX
ap-374	388	25	imposed	impose	VERB
ap-374	388	26	.	.	PUNCT
ap-374	389	1	the	the	DET
ap-374	389	2	material	material	ADJ
ap-374	389	3	behavior	behavior	NOUN
ap-374	389	4	inside	inside	ADP
ap-374	389	5	the	the	DET
ap-374	389	6	elements	element	NOUN
ap-374	389	7	is	be	AUX
ap-374	389	8	described	describe	VERB
ap-374	389	9	by	by	ADP
ap-374	389	10	virtue	virtue	NOUN
ap-374	389	11	of	of	ADP
ap-374	389	12	boundary	boundary	ADJ
ap-374	389	13	elements	element	NOUN
ap-374	389	14	,	,	PUNCT
ap-374	389	15	which	which	PRON
ap-374	389	16	are	be	AUX
ap-374	389	17	more	more	ADV
ap-374	389	18	appropriate	appropriate	ADJ
ap-374	389	19	than	than	ADP
ap-374	389	20	finite	finite	ADJ
ap-374	389	21	elements	element	NOUN
ap-374	389	22	in	in	ADP
ap-374	389	23	this	this	DET
ap-374	389	24	case	case	NOUN
ap-374	389	25	.	.	PUNCT
ap-374	390	1	when	when	SCONJ
ap-374	390	2	using	use	VERB
ap-374	390	3	the	the	DET
ap-374	390	4	finite	finite	ADJ
ap-374	390	5	element	element	NOUN
ap-374	390	6	method	method	NOUN
ap-374	390	7	,	,	PUNCT
ap-374	390	8	the	the	DET
ap-374	390	9	local	local	ADJ
ap-374	390	10	tractions	traction	NOUN
ap-374	390	11	are	be	AUX
ap-374	390	12	polynomials	polynomial	NOUN
ap-374	390	13	of	of	ADP
ap-374	390	14	one	one	NUM
ap-374	390	15	48	48	NUM
ap-374	390	16	©	©	PROPN
ap-374	390	17	czech	czech	PROPN
ap-374	390	18	technical	technical	PROPN
ap-374	390	19	university	university	PROPN
ap-374	390	20	publishing	publishing	NOUN
ap-374	390	21	house	house	NOUN
ap-374	390	22	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-374	390	23	acta	acta	PROPN
ap-374	390	24	polytechnica	polytechnica	PROPN
ap-374	390	25	vol	vol	NOUN
ap-374	390	26	.	.	PUNCT
ap-374	391	1	42	42	NUM
ap-374	391	2	no	no	INTJ
ap-374	391	3	.	.	PUNCT
ap-374	392	1	4/2002	4/2002	DET
ap-374	392	2	order	order	NOUN
ap-374	392	3	higher	high	ADJ
ap-374	392	4	than	than	ADP
ap-374	392	5	the	the	DET
ap-374	392	6	boundary	boundary	ADJ
ap-374	392	7	displacements	displacement	NOUN
ap-374	392	8	,	,	PUNCT
ap-374	392	9	while	while	SCONJ
ap-374	392	10	the	the	DET
ap-374	392	11	boundary	boundary	ADJ
ap-374	392	12	element	element	NOUN
ap-374	392	13	method	method	NOUN
ap-374	392	14	delivers	deliver	VERB
ap-374	392	15	polynomials	polynomial	NOUN
ap-374	392	16	of	of	ADP
ap-374	392	17	the	the	DET
ap-374	392	18	same	same	ADJ
ap-374	392	19	order	order	NOUN
ap-374	392	20	along	along	ADP
ap-374	392	21	the	the	DET
ap-374	392	22	boundary	boundary	NOUN
ap-374	392	23	.	.	PUNCT
ap-374	393	1	the	the	DET
ap-374	393	2	spring	spring	NOUN
ap-374	393	3	condition	condition	NOUN
ap-374	393	4	is	be	AUX
ap-374	393	5	then	then	ADV
ap-374	393	6	better	well	ADV
ap-374	393	7	fulfilled	fulfil	VERB
ap-374	393	8	by	by	ADP
ap-374	393	9	the	the	DET
ap-374	393	10	boundary	boundary	ADJ
ap-374	393	11	elements	element	NOUN
ap-374	393	12	.	.	PUNCT
ap-374	394	1	acknowledgment	acknowledgment	NOUN
ap-374	394	2	this	this	DET
ap-374	394	3	research	research	NOUN
ap-374	394	4	was	be	AUX
ap-374	394	5	supported	support	VERB
ap-374	394	6	by	by	ADP
ap-374	394	7	the	the	DET
ap-374	394	8	grant	grant	PROPN
ap-374	394	9	agency	agency	NOUN
ap-374	394	10	of	of	ADP
ap-374	394	11	the	the	DET
ap-374	394	12	czech	czech	PROPN
ap-374	394	13	republic	republic	NOUN
ap-374	394	14	–	–	PUNCT
ap-374	394	15	grant	grant	NOUN
ap-374	394	16	number	number	NOUN
ap-374	394	17	103/00/0530	103/00/0530	NUM
ap-374	394	18	and	and	CCONJ
ap-374	394	19	by	by	ADP
ap-374	394	20	the	the	DET
ap-374	394	21	ministry	ministry	PROPN
ap-374	394	22	of	of	ADP
ap-374	394	23	education	education	NOUN
ap-374	394	24	of	of	ADP
ap-374	394	25	the	the	DET
ap-374	394	26	czech	czech	PROPN
ap-374	394	27	republic	republic	NOUN
ap-374	394	28	,	,	PUNCT
ap-374	394	29	project	project	NOUN
ap-374	394	30	msm:210000001,3	msm:210000001,3	PROPN
ap-374	394	31	.	.	PUNCT
ap-374	395	1	references	reference	NOUN
ap-374	395	2	[	[	X
ap-374	395	3	1	1	NUM
ap-374	395	4	]	]	X
ap-374	395	5	brebbia	brebbia	PROPN
ap-374	395	6	,	,	PUNCT
ap-374	395	7	c.	c.	PROPN
ap-374	395	8	a.	a.	PROPN
ap-374	395	9	,	,	PUNCT
ap-374	395	10	telles	telles	PROPN
ap-374	395	11	,	,	PUNCT
ap-374	395	12	j.	j.	PROPN
ap-374	395	13	f.	f.	PROPN
ap-374	395	14	c.	c.	PROPN
ap-374	395	15	,	,	PUNCT
ap-374	395	16	wrobel	wrobel	PROPN
ap-374	395	17	,	,	PUNCT
ap-374	395	18	l.	l.	PROPN
ap-374	395	19	c.	c.	PROPN
ap-374	395	20	:	:	PUNCT
ap-374	395	21	boundary	boundary	ADJ
ap-374	395	22	element	element	NOUN
ap-374	395	23	techniques	technique	NOUN
ap-374	395	24	.	.	PUNCT
ap-374	396	1	berlin	berlin	ADJ
ap-374	396	2	:	:	PUNCT
ap-374	396	3	springer	springer	NOUN
ap-374	396	4	-	-	PUNCT
ap-374	396	5	verlag	verlag	PROPN
ap-374	396	6	,	,	PUNCT
ap-374	396	7	1984	1984	NUM
ap-374	396	8	.	.	PUNCT
ap-374	397	1	[	[	X
ap-374	397	2	2	2	NUM
ap-374	397	3	]	]	PUNCT
ap-374	397	4	cundall	cundall	NOUN
ap-374	397	5	,	,	PUNCT
ap-374	397	6	p.	p.	NOUN
ap-374	397	7	a.	a.	NOUN
ap-374	397	8	:	:	PUNCT
ap-374	397	9	a	a	DET
ap-374	397	10	computer	computer	NOUN
ap-374	397	11	model	model	NOUN
ap-374	397	12	for	for	ADP
ap-374	397	13	simulation	simulation	NOUN
ap-374	397	14	of	of	ADP
ap-374	397	15	progressive	progressive	ADJ
ap-374	397	16	large	large	ADJ
ap-374	397	17	scale	scale	NOUN
ap-374	397	18	movements	movement	NOUN
ap-374	397	19	of	of	ADP
ap-374	397	20	blocky	blocky	ADJ
ap-374	397	21	rock	rock	NOUN
ap-374	397	22	systems	system	NOUN
ap-374	397	23	.	.	PUNCT
ap-374	398	1	symposium	symposium	NOUN
ap-374	398	2	of	of	ADP
ap-374	398	3	the	the	DET
ap-374	398	4	international	international	ADJ
ap-374	398	5	society	society	NOUN
ap-374	398	6	of	of	ADP
ap-374	398	7	rock	rock	NOUN
ap-374	398	8	mechanics	mechanic	NOUN
ap-374	398	9	,	,	PUNCT
ap-374	398	10	1971	1971	NUM
ap-374	398	11	,	,	PUNCT
ap-374	398	12	p.	p.	NOUN
ap-374	398	13	132–150	132–150	NUM
ap-374	398	14	.	.	PUNCT
ap-374	399	1	[	[	X
ap-374	399	2	3	3	NUM
ap-374	399	3	]	]	X
ap-374	399	4	cundall	cundall	NOUN
ap-374	399	5	,	,	PUNCT
ap-374	399	6	p.	p.	NOUN
ap-374	399	7	a.	a.	NOUN
ap-374	399	8	,	,	PUNCT
ap-374	399	9	strack	strack	NOUN
ap-374	399	10	,	,	PUNCT
ap-374	399	11	o.	o.	PROPN
ap-374	399	12	d.	d.	PROPN
ap-374	399	13	l.	l.	PROPN
ap-374	399	14	:	:	PUNCT
ap-374	399	15	a	a	DET
ap-374	399	16	discrete	discrete	ADJ
ap-374	399	17	numerical	numerical	ADJ
ap-374	399	18	model	model	NOUN
ap-374	399	19	for	for	ADP
ap-374	399	20	granular	granular	ADJ
ap-374	399	21	assemblies	assembly	NOUN
ap-374	399	22	.	.	PUNCT
ap-374	400	1	geotechnique	geotechnique	PROPN
ap-374	400	2	,	,	PUNCT
ap-374	400	3	1979	1979	NUM
ap-374	400	4	,	,	PUNCT
ap-374	400	5	p.	p.	NOUN
ap-374	400	6	47–65	47–65	NUM
ap-374	400	7	.	.	PUNCT
ap-374	401	1	[	[	X
ap-374	401	2	4	4	NUM
ap-374	401	3	]	]	X
ap-374	401	4	desai	desai	PROPN
ap-374	401	5	,	,	PUNCT
ap-374	401	6	c.	c.	PROPN
ap-374	401	7	s.	s.	PROPN
ap-374	401	8	:	:	PUNCT
ap-374	401	9	a	a	DET
ap-374	401	10	consistent	consistent	ADJ
ap-374	401	11	finite	finite	ADJ
ap-374	401	12	element	element	NOUN
ap-374	401	13	technique	technique	NOUN
ap-374	401	14	for	for	ADP
ap-374	401	15	work	work	NOUN
ap-374	401	16	-	-	PUNCT
ap-374	401	17	softening	soften	VERB
ap-374	401	18	behavior	behavior	NOUN
ap-374	401	19	.	.	PUNCT
ap-374	402	1	in	in	ADP
ap-374	402	2	:	:	PUNCT
ap-374	402	3	j.	j.	PROPN
ap-374	402	4	t.	t.	PROPN
ap-374	402	5	oden	oden	PROPN
ap-374	402	6	et	et	PROPN
ap-374	402	7	al	al	PROPN
ap-374	402	8	(	(	PUNCT
ap-374	402	9	eds	eds	PROPN
ap-374	402	10	.	.	PUNCT
ap-374	402	11	)	)	PUNCT
ap-374	402	12	,	,	PUNCT
ap-374	402	13	int	int	NOUN
ap-374	402	14	.	.	PUNCT
ap-374	402	15	conf	conf	PROPN
ap-374	402	16	.	.	PUNCT
ap-374	403	1	on	on	ADP
ap-374	403	2	comp	comp	PROPN
ap-374	403	3	.	.	PUNCT
ap-374	403	4	meth	meth	NOUN
ap-374	403	5	.	.	PUNCT
ap-374	404	1	in	in	ADP
ap-374	404	2	nonlinear	nonlinear	ADJ
ap-374	404	3	mech	mech	PROPN
ap-374	404	4	.	.	PUNCT
ap-374	405	1	univ	univ	PROPN
ap-374	405	2	.	.	PROPN
ap-374	406	1	of	of	ADP
ap-374	406	2	texas	texas	PROPN
ap-374	406	3	at	at	ADP
ap-374	406	4	austin	austin	PROPN
ap-374	406	5	,	,	PUNCT
ap-374	406	6	1974	1974	NUM
ap-374	406	7	.	.	PUNCT
ap-374	407	1	[	[	X
ap-374	407	2	5	5	NUM
ap-374	407	3	]	]	X
ap-374	407	4	desai	desai	PROPN
ap-374	407	5	,	,	PUNCT
ap-374	407	6	c.	c.	PROPN
ap-374	407	7	s.	s.	PROPN
ap-374	407	8	:	:	PUNCT
ap-374	407	9	constitutive	constitutive	ADJ
ap-374	407	10	modeling	modeling	NOUN
ap-374	407	11	using	use	VERB
ap-374	407	12	the	the	DET
ap-374	407	13	disturbed	disturbed	ADJ
ap-374	407	14	state	state	NOUN
ap-374	407	15	concept	concept	NOUN
ap-374	407	16	.	.	PUNCT
ap-374	408	1	chapter	chapter	NOUN
ap-374	408	2	8	8	NUM
ap-374	408	3	,	,	PUNCT
ap-374	408	4	continuum	continuum	ADJ
ap-374	408	5	models	model	NOUN
ap-374	408	6	for	for	ADP
ap-374	408	7	materials	material	NOUN
ap-374	408	8	with	with	ADP
ap-374	408	9	microstructure	microstructure	ADJ
ap-374	408	10	,	,	PUNCT
ap-374	408	11	ed	ed	NOUN
ap-374	408	12	.	.	PUNCT
ap-374	408	13	h.	h.	PROPN
ap-374	408	14	mulhaus	mulhaus	PROPN
ap-374	408	15	,	,	PUNCT
ap-374	408	16	uk	uk	PROPN
ap-374	408	17	:	:	PUNCT
ap-374	408	18	john	john	PROPN
ap-374	408	19	wiley	wiley	PROPN
ap-374	408	20	&	&	CCONJ
ap-374	408	21	sons	son	NOUN
ap-374	408	22	,	,	PUNCT
ap-374	408	23	1994	1994	NUM
ap-374	408	24	.	.	PUNCT
ap-374	409	1	[	[	X
ap-374	409	2	6	6	NUM
ap-374	409	3	]	]	PUNCT
ap-374	409	4	duvaut	duvaut	PROPN
ap-374	409	5	,	,	PUNCT
ap-374	409	6	g.	g.	PROPN
ap-374	409	7	,	,	PUNCT
ap-374	409	8	lions	lion	NOUN
ap-374	409	9	,	,	PUNCT
ap-374	409	10	j.-l	j.-l	PROPN
ap-374	409	11	.	.	PUNCT
ap-374	409	12	:	:	PUNCT
ap-374	409	13	les	les	X
ap-374	409	14	inequations	inequation	NOUN
ap-374	409	15	en	en	X
ap-374	409	16	mecanique	mecanique	X
ap-374	409	17	et	et	PROPN
ap-374	409	18	en	en	X
ap-374	409	19	physique	physique	PROPN
ap-374	409	20	.	.	PUNCT
ap-374	410	1	paris	paris	PROPN
ap-374	410	2	:	:	PUNCT
ap-374	410	3	dunod	dunod	PROPN
ap-374	410	4	,	,	PUNCT
ap-374	410	5	1972	1972	NUM
ap-374	410	6	.	.	PUNCT
ap-374	411	1	[	[	X
ap-374	411	2	7	7	NUM
ap-374	411	3	]	]	X
ap-374	411	4	dvorak	dvorak	PROPN
ap-374	411	5	,	,	PUNCT
ap-374	411	6	g.	g.	PROPN
ap-374	411	7	j.	j.	PROPN
ap-374	411	8	,	,	PUNCT
ap-374	411	9	procházka	procházka	ADJ
ap-374	411	10	,	,	PUNCT
ap-374	411	11	p.	p.	PROPN
ap-374	411	12	p.	p.	NOUN
ap-374	412	1	:	:	PUNCT
ap-374	412	2	thick	thick	ADJ
ap-374	412	3	-	-	PUNCT
ap-374	412	4	walled	wall	VERB
ap-374	412	5	composite	composite	ADJ
ap-374	412	6	cylinders	cylinder	NOUN
ap-374	412	7	with	with	ADP
ap-374	412	8	optimal	optimal	ADJ
ap-374	412	9	fiber	fiber	NOUN
ap-374	412	10	prestress	prestress	NOUN
ap-374	412	11	.	.	PUNCT
ap-374	413	1	composites	composite	NOUN
ap-374	413	2	,	,	PUNCT
ap-374	413	3	part	part	NOUN
ap-374	413	4	b	b	PROPN
ap-374	413	5	,	,	PUNCT
ap-374	413	6	27b	27b	NUM
ap-374	413	7	,	,	PUNCT
ap-374	413	8	1996	1996	NUM
ap-374	413	9	,	,	PUNCT
ap-374	413	10	p.	p.	NOUN
ap-374	413	11	643–649	643–649	NUM
ap-374	413	12	.	.	PUNCT
ap-374	414	1	[	[	X
ap-374	414	2	8	8	NUM
ap-374	414	3	]	]	X
ap-374	414	4	dvorak	dvorak	PROPN
ap-374	414	5	,	,	PUNCT
ap-374	414	6	g.	g.	PROPN
ap-374	414	7	j.	j.	PROPN
ap-374	414	8	,	,	PUNCT
ap-374	414	9	procházka	procházka	ADJ
ap-374	414	10	,	,	PUNCT
ap-374	414	11	p.	p.	PROPN
ap-374	414	12	p.	p.	PROPN
ap-374	414	13	,	,	PUNCT
ap-374	415	1	srinivas	srinivas	PROPN
ap-374	415	2	,	,	PUNCT
ap-374	415	3	s.	s.	PROPN
ap-374	415	4	:	:	PUNCT
ap-374	415	5	design	design	NOUN
ap-374	415	6	and	and	CCONJ
ap-374	415	7	fabrication	fabrication	NOUN
ap-374	415	8	of	of	ADP
ap-374	415	9	submerged	submerge	VERB
ap-374	415	10	cylindrical	cylindrical	ADJ
ap-374	415	11	laminates	laminate	NOUN
ap-374	415	12	.	.	PUNCT
ap-374	416	1	part	part	NOUN
ap-374	416	2	i	i	PRON
ap-374	416	3	and	and	CCONJ
ap-374	416	4	part	part	PROPN
ap-374	416	5	ii	ii	PROPN
ap-374	416	6	,	,	PUNCT
ap-374	416	7	int	int	PROPN
ap-374	416	8	.	.	PUNCT
ap-374	417	1	j.	j.	PROPN
ap-374	417	2	solids	solids	PROPN
ap-374	417	3	&	&	CCONJ
ap-374	417	4	structures	structure	NOUN
ap-374	417	5	,	,	PUNCT
ap-374	417	6	1999	1999	NUM
ap-374	417	7	,	,	PUNCT
ap-374	417	8	p.	p.	NOUN
ap-374	417	9	1248–1295	1248–1295	NUM
ap-374	417	10	.	.	PUNCT
ap-374	418	1	[	[	X
ap-374	418	2	9	9	NUM
ap-374	418	3	]	]	X
ap-374	418	4	eshelby	eshelby	PROPN
ap-374	418	5	,	,	PUNCT
ap-374	418	6	j.	j.	PROPN
ap-374	418	7	d.	d.	PROPN
ap-374	418	8	:	:	PUNCT
ap-374	418	9	the	the	DET
ap-374	418	10	determination	determination	NOUN
ap-374	418	11	of	of	ADP
ap-374	418	12	the	the	DET
ap-374	418	13	elastic	elastic	ADJ
ap-374	418	14	field	field	NOUN
ap-374	418	15	of	of	ADP
ap-374	418	16	an	an	DET
ap-374	418	17	ellipsoidal	ellipsoidal	ADJ
ap-374	418	18	inclusion	inclusion	NOUN
ap-374	418	19	,	,	PUNCT
ap-374	418	20	and	and	CCONJ
ap-374	418	21	related	related	ADJ
ap-374	418	22	problems	problem	NOUN
ap-374	418	23	.	.	PUNCT
ap-374	419	1	jmps	jmps	PROPN
ap-374	419	2	,	,	PUNCT
ap-374	419	3	vol	vol	NOUN
ap-374	419	4	.	.	PROPN
ap-374	419	5	11	11	NUM
ap-374	419	6	,	,	PUNCT
ap-374	419	7	1963	1963	NUM
ap-374	419	8	,	,	PUNCT
ap-374	419	9	p.	p.	NOUN
ap-374	419	10	376–396	376–396	NUM
ap-374	419	11	.	.	PUNCT
ap-374	420	1	[	[	X
ap-374	420	2	10	10	NUM
ap-374	420	3	]	]	X
ap-374	420	4	kachanov	kachanov	NOUN
ap-374	420	5	,	,	PUNCT
ap-374	420	6	l.	l.	PROPN
ap-374	420	7	m.	m.	PROPN
ap-374	420	8	:	:	PUNCT
ap-374	420	9	introduction	introduction	NOUN
ap-374	420	10	to	to	ADP
ap-374	420	11	continuum	continuum	ADJ
ap-374	420	12	damage	damage	NOUN
ap-374	420	13	mechanics	mechanic	NOUN
ap-374	420	14	.	.	PUNCT
ap-374	421	1	dordrecht	dordrecht	PROPN
ap-374	421	2	(	(	PUNCT
ap-374	421	3	netherlands	netherlands	PROPN
ap-374	421	4	):	):	PUNCT
ap-374	421	5	martinus	martinus	PROPN
ap-374	421	6	nijhoff	nijhoff	PROPN
ap-374	421	7	publishers	publisher	NOUN
ap-374	421	8	,	,	PUNCT
ap-374	421	9	1986	1986	NUM
ap-374	421	10	.	.	PUNCT
ap-374	422	1	[	[	X
ap-374	422	2	11	11	NUM
ap-374	422	3	]	]	X
ap-374	422	4	moreau	moreau	PROPN
ap-374	422	5	,	,	PUNCT
ap-374	422	6	j.	j.	PROPN
ap-374	422	7	j.	j.	PROPN
ap-374	422	8	:	:	PUNCT
ap-374	422	9	some	some	DET
ap-374	422	10	numerical	numerical	ADJ
ap-374	422	11	methods	method	NOUN
ap-374	422	12	in	in	ADP
ap-374	422	13	multibody	multibody	ADJ
ap-374	422	14	dynamics	dynamic	NOUN
ap-374	422	15	:	:	PUNCT
ap-374	422	16	application	application	NOUN
ap-374	422	17	to	to	ADP
ap-374	422	18	granular	granular	ADJ
ap-374	422	19	materials	material	NOUN
ap-374	422	20	.	.	PUNCT
ap-374	423	1	eur	eur	PROPN
ap-374	423	2	.	.	PUNCT
ap-374	424	1	j.	j.	PROPN
ap-374	424	2	mech	mech	PROPN
ap-374	424	3	.	.	PUNCT
ap-374	425	1	solids	solid	NOUN
ap-374	425	2	vol	vol	NOUN
ap-374	425	3	.	.	PROPN
ap-374	426	1	13	13	NUM
ap-374	426	2	,	,	PUNCT
ap-374	426	3	no	no	INTJ
ap-374	426	4	.	.	NOUN
ap-374	426	5	4	4	NUM
ap-374	426	6	,	,	PUNCT
ap-374	426	7	1994	1994	NUM
ap-374	426	8	,	,	PUNCT
ap-374	426	9	p.	p.	NOUN
ap-374	426	10	93–114	93–114	NUM
ap-374	426	11	.	.	PUNCT
ap-374	427	1	[	[	X
ap-374	427	2	12	12	NUM
ap-374	427	3	]	]	SYM
ap-374	427	4	onck	onck	NOUN
ap-374	427	5	,	,	PUNCT
ap-374	427	6	p.	p.	NOUN
ap-374	427	7	,	,	PUNCT
ap-374	427	8	van	van	PROPN
ap-374	427	9	der	der	NOUN
ap-374	427	10	giessen	giessen	VERB
ap-374	427	11	,	,	PUNCT
ap-374	427	12	e.	e.	NOUN
ap-374	427	13	:	:	PUNCT
ap-374	427	14	growth	growth	NOUN
ap-374	427	15	of	of	ADP
ap-374	427	16	an	an	DET
ap-374	427	17	initially	initially	ADV
ap-374	427	18	sharp	sharp	ADJ
ap-374	427	19	crack	crack	NOUN
ap-374	427	20	by	by	ADP
ap-374	427	21	grain	grain	NOUN
ap-374	427	22	boundary	boundary	ADJ
ap-374	427	23	cavitation	cavitation	NOUN
ap-374	427	24	.	.	PUNCT
ap-374	428	1	jmps	jmps	PROPN
ap-374	428	2	,	,	PUNCT
ap-374	428	3	vol	vol	NOUN
ap-374	428	4	.	.	PROPN
ap-374	429	1	47	47	NUM
ap-374	429	2	,	,	PUNCT
ap-374	429	3	1999	1999	NUM
ap-374	429	4	,	,	PUNCT
ap-374	429	5	p.	p.	NOUN
ap-374	429	6	99–139	99–139	NUM
ap-374	429	7	.	.	PUNCT
ap-374	430	1	[	[	X
ap-374	430	2	13	13	NUM
ap-374	430	3	]	]	X
ap-374	430	4	procházka	procházka	ADJ
ap-374	430	5	,	,	PUNCT
ap-374	430	6	p.	p.	PROPN
ap-374	430	7	p.	p.	PROPN
ap-374	430	8	,	,	PUNCT
ap-374	430	9	kugblenu	kugblenu	NOUN
ap-374	430	10	,	,	PUNCT
ap-374	430	11	m.	m.	NOUN
ap-374	430	12	:	:	PUNCT
ap-374	430	13	application	application	NOUN
ap-374	430	14	of	of	ADP
ap-374	430	15	certain	certain	ADJ
ap-374	430	16	discrete	discrete	ADJ
ap-374	430	17	element	element	NOUN
ap-374	430	18	methods	method	NOUN
ap-374	430	19	to	to	ADP
ap-374	430	20	the	the	DET
ap-374	430	21	problems	problem	NOUN
ap-374	430	22	of	of	ADP
ap-374	430	23	fracture	fracture	NOUN
ap-374	430	24	mechanics	mechanic	NOUN
ap-374	430	25	.	.	PUNCT
ap-374	431	1	acta	acta	PROPN
ap-374	431	2	polytechnica	polytechnica	PROPN
ap-374	431	3	,	,	PUNCT
ap-374	431	4	vol	vol	NOUN
ap-374	431	5	.	.	PROPN
ap-374	432	1	42	42	NUM
ap-374	432	2	,	,	PUNCT
ap-374	432	3	no	no	INTJ
ap-374	432	4	.	.	NOUN
ap-374	432	5	4	4	NUM
ap-374	432	6	,	,	PUNCT
ap-374	432	7	p.	p.	NOUN
ap-374	432	8	57–67	57–67	NUM
ap-374	432	9	.	.	PUNCT
ap-374	433	1	[	[	X
ap-374	433	2	14	14	NUM
ap-374	433	3	]	]	X
ap-374	433	4	procházka	procházka	ADJ
ap-374	433	5	,	,	PUNCT
ap-374	433	6	p.	p.	PROPN
ap-374	433	7	p.	p.	PROPN
ap-374	433	8	,	,	PUNCT
ap-374	433	9	šejnoha	šejnoha	PROPN
ap-374	433	10	,	,	PUNCT
ap-374	433	11	m.	m.	NOUN
ap-374	433	12	:	:	PUNCT
ap-374	433	13	development	development	NOUN
ap-374	433	14	of	of	ADP
ap-374	433	15	debond	debond	ADJ
ap-374	433	16	region	region	NOUN
ap-374	433	17	of	of	ADP
ap-374	433	18	lag	lag	PROPN
ap-374	433	19	model	model	NOUN
ap-374	433	20	.	.	PUNCT
ap-374	434	1	computers	computer	NOUN
ap-374	434	2	&	&	CCONJ
ap-374	434	3	structures	structure	NOUN
ap-374	434	4	,	,	PUNCT
ap-374	434	5	vol	vol	NOUN
ap-374	434	6	.	.	PROPN
ap-374	434	7	55	55	NUM
ap-374	434	8	,	,	PUNCT
ap-374	434	9	no	no	INTJ
ap-374	434	10	.	.	NOUN
ap-374	434	11	2	2	NUM
ap-374	434	12	,	,	PUNCT
ap-374	434	13	1995	1995	NUM
ap-374	434	14	,	,	PUNCT
ap-374	434	15	p.	p.	NOUN
ap-374	434	16	249–260	249–260	NUM
ap-374	434	17	.	.	PUNCT
ap-374	435	1	[	[	X
ap-374	435	2	15	15	NUM
ap-374	435	3	]	]	X
ap-374	435	4	triantafillidis	triantafillidi	NOUN
ap-374	435	5	,	,	PUNCT
ap-374	435	6	n.	n.	NOUN
ap-374	435	7	,	,	PUNCT
ap-374	435	8	schraad	schraad	NOUN
ap-374	435	9	,	,	PUNCT
ap-374	435	10	m.	m.	NOUN
ap-374	435	11	w.	w.	PROPN
ap-374	435	12	:	:	PUNCT
ap-374	435	13	failure	failure	NOUN
ap-374	435	14	in	in	ADP
ap-374	435	15	aluminium	aluminium	NOUN
ap-374	435	16	honeycombs	honeycomb	NOUN
ap-374	435	17	.	.	PUNCT
ap-374	436	1	jmps	jmps	PROPN
ap-374	436	2	,	,	PUNCT
ap-374	436	3	vol	vol	NOUN
ap-374	436	4	.	.	PROPN
ap-374	437	1	47	47	NUM
ap-374	437	2	,	,	PUNCT
ap-374	437	3	1999	1999	NUM
ap-374	437	4	,	,	PUNCT
ap-374	437	5	p.	p.	NOUN
ap-374	437	6	1093–1124	1093–1124	NUM
ap-374	437	7	.	.	PUNCT
ap-374	438	1	[	[	X
ap-374	438	2	16	16	NUM
ap-374	438	3	]	]	X
ap-374	438	4	zienkiewicz	zienkiewicz	PROPN
ap-374	438	5	,	,	PUNCT
ap-374	438	6	o.	o.	PROPN
ap-374	438	7	c.	c.	PROPN
ap-374	438	8	:	:	PUNCT
ap-374	438	9	the	the	DET
ap-374	438	10	finite	finite	PROPN
ap-374	438	11	element	element	NOUN
ap-374	438	12	method	method	NOUN
ap-374	438	13	.	.	PUNCT
ap-374	439	1	new	new	PROPN
ap-374	439	2	york	york	PROPN
ap-374	439	3	:	:	PUNCT
ap-374	439	4	mcgraw	mcgraw	PROPN
ap-374	439	5	-	-	PUNCT
ap-374	439	6	hill	hill	NOUN
ap-374	439	7	book	book	NOUN
ap-374	439	8	company	company	NOUN
ap-374	439	9	,	,	PUNCT
ap-374	439	10	1977	1977	NUM
ap-374	439	11	.	.	PUNCT
ap-374	440	1	appendix	appendix	VERB
ap-374	440	2	�	�	PROPN
ap-374	440	3	�	�	PROPN
ap-374	440	4	log	log	VERB
ap-374	440	5	d	d	NOUN
ap-374	440	6	log	log	NOUN
ap-374	441	1	d	d	PROPN
ap-374	441	2	a	a	DET
ap-374	441	3	b	b	NOUN
ap-374	441	4	a	a	DET
ap-374	441	5	b	b	NOUN
ap-374	441	6	r	r	NOUN
ap-374	441	7	x	x	PROPN
ap-374	441	8	x	x	X
ap-374	441	9	a	a	PRON
ap-374	441	10	x	x	X
ap-374	441	11	b	b	PROPN
ap-374	441	12	a	a	DET
ap-374	441	13	b	b	PROPN
ap-374	441	14	b	b	PROPN
ap-374	441	15	a	a	NOUN
ap-374	441	16	x	x	NOUN
ap-374	442	1	x	x	SYM
ap-374	442	2	x	x	SYM
ap-374	442	3	x	x	SYM
ap-374	442	4	1	1	NUM
ap-374	442	5	1	1	NUM
ap-374	442	6	2	2	NUM
ap-374	442	7	2	2	NUM
ap-374	442	8	1	1	NUM
ap-374	442	9	2	2	NUM
ap-374	442	10	21	21	NUM
ap-374	442	11	2	2	NUM
ap-374	442	12	2	2	NUM
ap-374	442	13	2	2	NUM
ap-374	442	14	�	�	PROPN
ap-374	442	15	�	�	PROPN
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ap-374	442	17	�	�	PROPN
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ap-374	442	24	arctan	arctan	PROPN
ap-374	442	25	b	b	PROPN
ap-374	442	26	a	a	DET
ap-374	442	27	�	�	PROPN
ap-374	442	28	�	�	PROPN
ap-374	442	29	�	�	PROPN
ap-374	442	30	(	(	PUNCT
ap-374	442	31	a.1	a.1	NOUN
ap-374	442	32	)	)	PUNCT
ap-374	442	33	x	x	X
ap-374	443	1	x	x	PUNCT
ap-374	443	2	r	r	NOUN
ap-374	443	3	x	x	NOUN
ap-374	443	4	x	x	PUNCT
ap-374	443	5	x	x	PUNCT
ap-374	443	6	i	i	PRON
ap-374	443	7	j	j	PROPN
ap-374	444	1	d	d	X
ap-374	444	2	a	a	DET
ap-374	444	3	b	b	NOUN
ap-374	444	4	2	2	NUM
ap-374	444	5	1	1	NUM
ap-374	444	6	�	�	PROPN
ap-374	444	7	�	�	PROPN
ap-374	444	8	1	1	NUM
ap-374	444	9	.	.	PUNCT
ap-374	444	10	�	�	PROPN
ap-374	444	11	�	�	PROPN
ap-374	444	12	�	�	PROPN
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ap-374	444	19	�	�	PROPN
ap-374	444	20	x	x	PUNCT
ap-374	444	21	x	x	PUNCT
ap-374	444	22	a	a	PRON
ap-374	444	23	x	x	X
ap-374	444	24	a	a	DET
ap-374	444	25	b	b	NOUN
ap-374	444	26	x	x	SYM
ap-374	444	27	a	a	PRON
ap-374	444	28	x	x	SYM
ap-374	444	29	a	a	DET
ap-374	444	30	x	x	SYM
ap-374	444	31	x	x	SYM
ap-374	444	32	1	1	NUM
ap-374	444	33	2	2	NUM
ap-374	444	34	1	1	NUM
ap-374	444	35	2	2	NUM
ap-374	444	36	2	2	NUM
ap-374	444	37	1d	1d	NUM
ap-374	444	38	a	a	DET
ap-374	444	39	b	b	NOUN
ap-374	444	40	a	a	DET
ap-374	444	41	barctan	barctan	PROPN
ap-374	444	42	arctan	arctan	PROPN
ap-374	444	43	�	�	PROPN
ap-374	444	44	�	�	PROPN
ap-374	444	45	�	�	PROPN
ap-374	444	46	�	�	PROPN
ap-374	444	47	�	�	PROPN
ap-374	444	48	2	2	NUM
ap-374	444	49	.	.	PUNCT
ap-374	444	50	�	�	PROPN
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ap-374	444	57	x	x	NOUN
ap-374	444	58	a	a	PRON
ap-374	444	59	x	x	X
ap-374	444	60	a	a	DET
ap-374	444	61	x	x	SYM
ap-374	444	62	a	a	DET
ap-374	444	63	x	x	SYM
ap-374	444	64	a	a	PRON
ap-374	444	65	x	x	SYM
ap-374	444	66	x	x	SYM
ap-374	444	67	1	1	NUM
ap-374	444	68	b	b	PROPN
ap-374	444	69	a	a	X
ap-374	444	70	d	d	NOUN
ap-374	444	71	a	a	DET
ap-374	444	72	b	b	NUM
ap-374	444	73	1	1	NUM
ap-374	444	74	2	2	NUM
ap-374	444	75	2	2	NUM
ap-374	444	76	1	1	NUM
ap-374	444	77	2	2	NUM
ap-374	444	78	2	2	NUM
ap-374	444	79	2	2	NUM
ap-374	444	80	2log	2log	NUM
ap-374	444	81	3	3	NUM
ap-374	444	82	.	.	PUNCT
ap-374	444	83	�	�	PROPN
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ap-374	444	92	�	�	PROPN
ap-374	445	1	a	a	PRON
ap-374	445	2	x	x	SYM
ap-374	445	3	a	a	PRON
ap-374	445	4	x	x	NOUN
ap-374	445	5	a	a	DET
ap-374	445	6	b	b	NOUN
ap-374	445	7	x	x	SYM
ap-374	445	8	a	a	PRON
ap-374	445	9	x	x	SYM
ap-374	445	10	a	a	DET
ap-374	445	11	x	x	SYM
ap-374	445	12	x	x	SYM
ap-374	445	13	2	2	NUM
ap-374	445	14	1	1	NUM
ap-374	445	15	2	2	NUM
ap-374	445	16	2	2	NUM
ap-374	445	17	1	1	NUM
ap-374	445	18	2	2	NUM
ap-374	445	19	d	d	NOUN
ap-374	445	20	a	a	DET
ap-374	445	21	b	b	PROPN
ap-374	445	22	b	b	PROPN
ap-374	445	23	aarctan	aarctan	PROPN
ap-374	445	24	arctan	arctan	PROPN
ap-374	445	25	�	�	PROPN
ap-374	445	26	�	�	PROPN
ap-374	445	27	�	�	PROPN
ap-374	445	28	�	�	PROPN
ap-374	445	29	�	�	PROPN
ap-374	445	30	2	2	NUM
ap-374	445	31	(	(	PUNCT
ap-374	445	32	a.2	a.2	SYM
ap-374	445	33	)	)	PUNCT
ap-374	445	34	x	x	X
ap-374	446	1	r	r	NOUN
ap-374	446	2	x	x	PUNCT
ap-374	446	3	x	x	PUNCT
ap-374	446	4	x	x	PUNCT
ap-374	446	5	i	i	NOUN
ap-374	446	6	d	d	X
ap-374	446	7	a	a	DET
ap-374	446	8	b	b	NUM
ap-374	446	9	2	2	NUM
ap-374	446	10	1	1	NUM
ap-374	446	11	�	�	PROPN
ap-374	446	12	�	�	PROPN
ap-374	446	13	1	1	NUM
ap-374	446	14	.	.	PUNCT
ap-374	447	1	x	x	PUNCT
ap-374	448	1	x	x	PUNCT
ap-374	448	2	a	a	X
ap-374	448	3	x	x	X
ap-374	448	4	x	x	X
ap-374	448	5	a	a	PRON
ap-374	448	6	x	x	SYM
ap-374	448	7	a	a	DET
ap-374	448	8	x	x	SYM
ap-374	448	9	x	x	SYM
ap-374	448	10	1	1	NUM
ap-374	448	11	b	b	PROPN
ap-374	448	12	a	a	X
ap-374	448	13	d	d	NOUN
ap-374	448	14	a	a	DET
ap-374	448	15	b	b	NUM
ap-374	448	16	1	1	NUM
ap-374	448	17	2	2	NUM
ap-374	448	18	2	2	NUM
ap-374	448	19	1	1	NUM
ap-374	448	20	2	2	NUM
ap-374	448	21	2	2	NUM
ap-374	448	22	2	2	NUM
ap-374	448	23	2	2	NUM
ap-374	448	24	�	�	PROPN
ap-374	448	25	�	�	PROPN
ap-374	448	26	�	�	PROPN
ap-374	448	27	�	�	PROPN
ap-374	448	28	�	�	PROPN
ap-374	448	29	log	log	VERB
ap-374	448	30	2	2	NUM
ap-374	448	31	.	.	PUNCT
ap-374	449	1	a	a	DET
ap-374	449	2	x	x	SYM
ap-374	449	3	a	a	X
ap-374	449	4	x	x	X
ap-374	449	5	x	x	X
ap-374	449	6	a	a	PRON
ap-374	449	7	x	x	SYM
ap-374	449	8	a	a	DET
ap-374	449	9	x	x	SYM
ap-374	449	10	x	x	SYM
ap-374	449	11	1	1	NUM
ap-374	449	12	2	2	NUM
ap-374	449	13	2	2	NUM
ap-374	449	14	1	1	NUM
ap-374	449	15	�	�	PROPN
ap-374	449	16	�	�	PROPN
ap-374	449	17	�	�	PROPN
ap-374	449	18	�	�	PROPN
ap-374	449	19	�	�	PROPN
ap-374	449	20	�	�	PROPN
ap-374	449	21	�	�	PROPN
ap-374	449	22	�	�	PROPN
ap-374	449	23	�	�	PROPN
ap-374	449	24	�	�	PROPN
ap-374	449	25	d	d	PROPN
ap-374	449	26	a	a	DET
ap-374	449	27	b	b	PROPN
ap-374	449	28	b	b	PROPN
ap-374	449	29	aarctan	aarctan	PROPN
ap-374	449	30	arctan	arctan	PROPN
ap-374	449	31	(	(	PUNCT
ap-374	449	32	a.3	a.3	NOUN
ap-374	449	33	)	)	PUNCT
ap-374	449	34	©	©	PROPN
ap-374	449	35	czech	czech	PROPN
ap-374	449	36	technical	technical	PROPN
ap-374	449	37	university	university	PROPN
ap-374	449	38	publishing	publishing	NOUN
ap-374	449	39	house	house	NOUN
ap-374	449	40	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-374	449	41	49	49	NUM
ap-374	449	42	acta	acta	PROPN
ap-374	449	43	polytechnica	polytechnica	PROPN
ap-374	449	44	vol	vol	NOUN
ap-374	449	45	.	.	PUNCT
ap-374	450	1	42	42	NUM
ap-374	450	2	no	no	INTJ
ap-374	450	3	.	.	PUNCT
ap-374	451	1	4/2002	4/2002	NUM
ap-374	451	2	fig	fig	NOUN
ap-374	451	3	.	.	PUNCT
ap-374	452	1	7	7	NUM
ap-374	452	2	:	:	PUNCT
ap-374	452	3	geometry	geometry	NOUN
ap-374	452	4	for	for	ADP
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ap-374	452	6	boundary	boundary	ADJ
ap-374	452	7	integrals	integral	NOUN
ap-374	452	8	d	d	X
ap-374	452	9	a	a	DET
ap-374	452	10	b	b	NOUN
ap-374	452	11	b	b	NOUN
ap-374	452	12	ax	ax	NOUN
ap-374	452	13	r	r	NOUN
ap-374	452	14	a	a	NOUN
ap-374	452	15	x	x	NOUN
ap-374	452	16	a	a	PRON
ap-374	452	17	x	x	SYM
ap-374	452	18	a	a	PRON
ap-374	452	19	x	x	SYM
ap-374	452	20	x	x	SYM
ap-374	452	21	1	1	NUM
ap-374	452	22	2	2	NUM
ap-374	452	23	1	1	NUM
ap-374	452	24	�	�	PROPN
ap-374	452	25	�	�	PROPN
ap-374	452	26	�	�	PROPN
ap-374	452	27	�	�	PROPN
ap-374	452	28	�	�	PROPN
ap-374	452	29	�	�	PROPN
ap-374	452	30	�	�	PROPN
ap-374	452	31	�	�	PROPN
ap-374	452	32	�	�	PROPN
ap-374	452	33	�	�	PROPN
ap-374	452	34	�	�	PROPN
ap-374	452	35	�	�	PROPN
ap-374	452	36	arctan	arctan	PROPN
ap-374	452	37	arctan	arctan	PROPN
ap-374	452	38	(	(	PUNCT
ap-374	452	39	a.4	a.4	PROPN
ap-374	452	40	)	)	PUNCT
ap-374	452	41	x	x	SYM
ap-374	453	1	x	x	PUNCT
ap-374	453	2	x	x	PUNCT
ap-374	453	3	n	n	PRON
ap-374	453	4	r	r	NOUN
ap-374	453	5	x	x	NOUN
ap-374	453	6	x	x	SYM
ap-374	453	7	x	x	PUNCT
ap-374	453	8	a	a	DET
ap-374	453	9	r	r	NOUN
ap-374	453	10	x	x	NOUN
ap-374	453	11	x	x	PUNCT
ap-374	453	12	x	x	PUNCT
ap-374	453	13	x	x	PUNCT
ap-374	453	14	x	x	PUNCT
ap-374	453	15	i	i	PRON
ap-374	453	16	j	j	PROPN
ap-374	454	1	k	k	PROPN
ap-374	454	2	j	j	PROPN
ap-374	455	1	i	i	PRON
ap-374	455	2	kd	kd	PROPN
ap-374	456	1	d	d	PROPN
ap-374	456	2	a	a	DET
ap-374	456	3	b	b	NOUN
ap-374	456	4	a	a	DET
ap-374	456	5	b	b	NOUN
ap-374	456	6	2	2	NUM
ap-374	456	7	1	1	NUM
ap-374	456	8	2	2	NUM
ap-374	456	9	1	1	NUM
ap-374	456	10	�	�	PROPN
ap-374	456	11	�	�	PROPN
ap-374	456	12	�	�	PROPN
ap-374	456	13	�	�	PROPN
ap-374	456	14	see	see	VERB
ap-374	456	15	(	(	PUNCT
ap-374	456	16	a.2	a.2	NOUN
ap-374	456	17	)	)	PUNCT
ap-374	456	18	prof	prof	NOUN
ap-374	456	19	.	.	PUNCT
ap-374	457	1	ing	ing	PROPN
ap-374	457	2	.	.	PUNCT
ap-374	458	1	rndr	rndr	PROPN
ap-374	458	2	.	.	PUNCT
ap-374	459	1	petr	petr	PROPN
ap-374	459	2	p.	p.	PROPN
ap-374	459	3	procházka	procházka	PROPN
ap-374	459	4	,	,	PUNCT
ap-374	459	5	drsc	drsc	PROPN
ap-374	459	6	.	.	PUNCT
ap-374	460	1	phone	phone	NOUN
ap-374	460	2	:	:	PUNCT
ap-374	460	3	+420	+420	PROPN
ap-374	460	4	224	224	NUM
ap-374	460	5	354	354	NUM
ap-374	460	6	480	480	NUM
ap-374	460	7	fax	fax	NOUN
ap-374	460	8	:	:	PUNCT
ap-374	460	9	+420	+420	PROPN
ap-374	460	10	224	224	NUM
ap-374	460	11	310	310	NUM
ap-374	460	12	775	775	NUM
ap-374	460	13	e	e	NOUN
ap-374	460	14	-	-	NOUN
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ap-374	460	16	:	:	PUNCT
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ap-374	460	18	ing	ing	PROPN
ap-374	460	19	.	.	PUNCT
ap-374	461	1	michael	michael	PROPN
ap-374	461	2	kugblenu	kugblenu	PROPN
ap-374	461	3	dept	dept	PROPN
ap-374	461	4	.	.	PROPN
ap-374	461	5	of	of	ADP
ap-374	461	6	structural	structural	ADJ
ap-374	461	7	mechanics	mechanic	NOUN
ap-374	461	8	ctu	ctu	NOUN
ap-374	461	9	in	in	ADP
ap-374	461	10	prague	prague	PROPN
ap-374	461	11	,	,	PUNCT
ap-374	461	12	faculty	faculty	NOUN
ap-374	461	13	of	of	ADP
ap-374	461	14	civil	civil	ADJ
ap-374	461	15	engineering	engineering	NOUN
ap-374	461	16	thákurova	thákurova	VERB
ap-374	461	17	7	7	NUM
ap-374	461	18	166	166	NUM
ap-374	461	19	29	29	NUM
ap-374	461	20	prague	prague	NOUN
ap-374	461	21	6	6	NUM
ap-374	461	22	,	,	PUNCT
ap-374	461	23	czech	czech	PROPN
ap-374	461	24	republic	republic	NOUN
ap-374	461	25	50	50	NUM
ap-374	461	26	©	©	PROPN
ap-374	461	27	czech	czech	PROPN
ap-374	461	28	technical	technical	PROPN
ap-374	461	29	university	university	PROPN
ap-374	461	30	publishing	publishing	NOUN
ap-374	461	31	house	house	NOUN
ap-374	461	32	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-374	461	33	acta	acta	PROPN
ap-374	461	34	polytechnica	polytechnica	PROPN
ap-374	461	35	vol	vol	NOUN
ap-374	461	36	.	.	PUNCT
ap-374	462	1	42	42	NUM
ap-374	462	2	no	no	INTJ
ap-374	462	3	.	.	PUNCT
ap-374	463	1	4/2002	4/2002	NUM