id	sid	tid	token	lemma	pos
app01-3959	1	1	acta	acta	PROPN
app01-3959	1	2	polytechnica	polytechnica	PROPN
app01-3959	1	3	ctu	ctu	PROPN
app01-3959	1	4	proceedings	proceeding	NOUN
app01-3959	1	5	doi:10.14311	doi:10.14311	NOUN
app01-3959	1	6	/	/	SYM
app01-3959	1	7	app.2017.7.0033	app.2017.7.0033	PROPN
app01-3959	1	8	acta	acta	PROPN
app01-3959	1	9	polytechnica	polytechnica	PROPN
app01-3959	1	10	ctu	ctu	NOUN
app01-3959	1	11	proceedings	proceeding	NOUN
app01-3959	1	12	7:33–37	7:33–37	NUM
app01-3959	1	13	,	,	PUNCT
app01-3959	1	14	2017	2017	NUM
app01-3959	1	15	©	©	PROPN
app01-3959	1	16	czech	czech	PROPN
app01-3959	1	17	technical	technical	PROPN
app01-3959	1	18	university	university	PROPN
app01-3959	1	19	in	in	ADP
app01-3959	1	20	prague	prague	PROPN
app01-3959	1	21	,	,	PUNCT
app01-3959	1	22	2017	2017	NUM
app01-3959	1	23	available	available	ADJ
app01-3959	1	24	online	online	ADV
app01-3959	1	25	at	at	ADP
app01-3959	1	26	http://ojs.cvut.cz/ojs/index.php/app	http://ojs.cvut.cz/ojs/index.php/app	NOUN
app01-3959	1	27	1d	1d	NUM
app01-3959	1	28	hermite	hermite	ADJ
app01-3959	1	29	elements	element	NOUN
app01-3959	1	30	for	for	ADP
app01-3959	1	31	c1	c1	NOUN
app01-3959	1	32	-	-	PUNCT
app01-3959	1	33	continuous	continuous	ADJ
app01-3959	1	34	solutions	solution	NOUN
app01-3959	1	35	in	in	ADP
app01-3959	1	36	second	second	ADJ
app01-3959	1	37	gradient	gradient	NOUN
app01-3959	1	38	elasticity	elasticity	NOUN
app01-3959	1	39	christian	christian	PROPN
app01-3959	1	40	liebold∗	liebold∗	PROPN
app01-3959	1	41	,	,	PUNCT
app01-3959	1	42	wolfgang	wolfgang	PROPN
app01-3959	1	43	h.	h.	PROPN
app01-3959	1	44	müller	müller	PROPN
app01-3959	1	45	berlin	berlin	PROPN
app01-3959	1	46	university	university	PROPN
app01-3959	1	47	of	of	ADP
app01-3959	1	48	technology	technology	PROPN
app01-3959	1	49	,	,	PUNCT
app01-3959	1	50	chair	chair	NOUN
app01-3959	1	51	of	of	ADP
app01-3959	1	52	continuum	continuum	ADJ
app01-3959	1	53	mechanics	mechanic	NOUN
app01-3959	1	54	and	and	CCONJ
app01-3959	1	55	materials	material	NOUN
app01-3959	1	56	theory	theory	NOUN
app01-3959	1	57	,	,	PUNCT
app01-3959	1	58	einsteinufer	einsteinufer	VERB
app01-3959	1	59	5	5	NUM
app01-3959	1	60	,	,	PUNCT
app01-3959	1	61	10587	10587	NUM
app01-3959	1	62	berlin	berlin	PROPN
app01-3959	1	63	,	,	PUNCT
app01-3959	1	64	germany	germany	PROPN
app01-3959	1	65	∗	∗	NOUN
app01-3959	1	66	corresponding	correspond	VERB
app01-3959	1	67	author	author	NOUN
app01-3959	1	68	:	:	PUNCT
app01-3959	1	69	christian.liebold@tu-berlin.de	christian.liebold@tu-berlin.de	PUNCT
app01-3959	1	70	abstract	abstract	ADJ
app01-3959	1	71	.	.	PUNCT
app01-3959	2	1	we	we	PRON
app01-3959	2	2	present	present	VERB
app01-3959	2	3	a	a	DET
app01-3959	2	4	modified	modify	VERB
app01-3959	2	5	strain	strain	NOUN
app01-3959	2	6	gradient	gradient	NOUN
app01-3959	2	7	theory	theory	NOUN
app01-3959	2	8	of	of	ADP
app01-3959	2	9	elasticity	elasticity	NOUN
app01-3959	2	10	for	for	ADP
app01-3959	2	11	linear	linear	ADJ
app01-3959	2	12	isotropic	isotropic	ADJ
app01-3959	2	13	materials	material	NOUN
app01-3959	2	14	in	in	ADP
app01-3959	2	15	order	order	NOUN
app01-3959	2	16	to	to	PART
app01-3959	2	17	account	account	VERB
app01-3959	2	18	for	for	ADP
app01-3959	2	19	the	the	DET
app01-3959	2	20	so	so	ADV
app01-3959	2	21	-	-	PUNCT
app01-3959	2	22	called	call	VERB
app01-3959	2	23	size	size	NOUN
app01-3959	2	24	effect	effect	NOUN
app01-3959	2	25	.	.	PUNCT
app01-3959	3	1	additional	additional	ADJ
app01-3959	3	2	material	material	NOUN
app01-3959	3	3	length	length	NOUN
app01-3959	3	4	scale	scale	NOUN
app01-3959	3	5	parameters	parameter	NOUN
app01-3959	3	6	are	be	AUX
app01-3959	3	7	introduced	introduce	VERB
app01-3959	3	8	and	and	CCONJ
app01-3959	3	9	the	the	DET
app01-3959	3	10	problem	problem	NOUN
app01-3959	3	11	of	of	ADP
app01-3959	3	12	static	static	ADJ
app01-3959	3	13	beam	beam	NOUN
app01-3959	3	14	bending	bending	NOUN
app01-3959	3	15	is	be	AUX
app01-3959	3	16	analyzed	analyze	VERB
app01-3959	3	17	.	.	PUNCT
app01-3959	4	1	a	a	DET
app01-3959	4	2	numerical	numerical	ADJ
app01-3959	4	3	solution	solution	NOUN
app01-3959	4	4	is	be	AUX
app01-3959	4	5	derived	derive	VERB
app01-3959	4	6	by	by	ADP
app01-3959	4	7	means	mean	NOUN
app01-3959	4	8	of	of	ADP
app01-3959	4	9	a	a	DET
app01-3959	4	10	finite	finite	ADJ
app01-3959	4	11	element	element	NOUN
app01-3959	4	12	approach	approach	NOUN
app01-3959	4	13	.	.	PUNCT
app01-3959	5	1	a	a	DET
app01-3959	5	2	global	global	ADJ
app01-3959	5	3	c1	c1	NOUN
app01-3959	5	4	-	-	PUNCT
app01-3959	5	5	continuous	continuous	ADJ
app01-3959	5	6	displacement	displacement	ADJ
app01-3959	5	7	field	field	NOUN
app01-3959	5	8	is	be	AUX
app01-3959	5	9	applied	apply	VERB
app01-3959	5	10	in	in	ADP
app01-3959	5	11	finite	finite	ADJ
app01-3959	5	12	element	element	NOUN
app01-3959	5	13	solutions	solution	NOUN
app01-3959	5	14	because	because	SCONJ
app01-3959	5	15	the	the	DET
app01-3959	5	16	higher	high	ADJ
app01-3959	5	17	-	-	PUNCT
app01-3959	5	18	order	order	NOUN
app01-3959	5	19	strain	strain	NOUN
app01-3959	5	20	energy	energy	NOUN
app01-3959	5	21	density	density	NOUN
app01-3959	5	22	additionally	additionally	ADV
app01-3959	5	23	depends	depend	VERB
app01-3959	5	24	on	on	ADP
app01-3959	5	25	second	second	ADJ
app01-3959	5	26	gradients	gradient	NOUN
app01-3959	5	27	of	of	ADP
app01-3959	5	28	displacements	displacement	NOUN
app01-3959	5	29	.	.	PUNCT
app01-3959	6	1	so	so	ADV
app01-3959	6	2	-	-	PUNCT
app01-3959	6	3	called	call	VERB
app01-3959	6	4	hermite	hermite	ADJ
app01-3959	6	5	finite	finite	ADJ
app01-3959	6	6	elements	element	NOUN
app01-3959	6	7	are	be	AUX
app01-3959	6	8	used	use	VERB
app01-3959	6	9	that	that	PRON
app01-3959	6	10	allow	allow	VERB
app01-3959	6	11	for	for	ADP
app01-3959	6	12	merging	merge	VERB
app01-3959	6	13	gradients	gradient	NOUN
app01-3959	6	14	between	between	ADP
app01-3959	6	15	elements	element	NOUN
app01-3959	6	16	.	.	PUNCT
app01-3959	7	1	the	the	DET
app01-3959	7	2	element	element	ADJ
app01-3959	7	3	stiffness	stiffness	NOUN
app01-3959	7	4	matrix	matrix	NOUN
app01-3959	7	5	as	as	ADV
app01-3959	7	6	well	well	ADV
app01-3959	7	7	as	as	ADP
app01-3959	7	8	the	the	DET
app01-3959	7	9	global	global	ADJ
app01-3959	7	10	stiffness	stiffness	NOUN
app01-3959	7	11	matrix	matrix	NOUN
app01-3959	7	12	of	of	ADP
app01-3959	7	13	the	the	DET
app01-3959	7	14	problem	problem	NOUN
app01-3959	7	15	is	be	AUX
app01-3959	7	16	developed	develop	VERB
app01-3959	7	17	.	.	PUNCT
app01-3959	8	1	convergence	convergence	NOUN
app01-3959	8	2	,	,	PUNCT
app01-3959	8	3	c1	c1	NOUN
app01-3959	8	4	-	-	PUNCT
app01-3959	8	5	continuity	continuity	NOUN
app01-3959	8	6	and	and	CCONJ
app01-3959	8	7	the	the	DET
app01-3959	8	8	size	size	NOUN
app01-3959	8	9	effect	effect	NOUN
app01-3959	8	10	in	in	ADP
app01-3959	8	11	the	the	DET
app01-3959	8	12	numerical	numerical	ADJ
app01-3959	8	13	solution	solution	NOUN
app01-3959	8	14	is	be	AUX
app01-3959	8	15	shown	show	VERB
app01-3959	8	16	.	.	PUNCT
app01-3959	9	1	experiments	experiment	NOUN
app01-3959	9	2	on	on	ADP
app01-3959	9	3	bending	bend	VERB
app01-3959	9	4	stiffnesses	stiffness	NOUN
app01-3959	9	5	of	of	ADP
app01-3959	9	6	different	different	ADJ
app01-3959	9	7	sized	sized	ADJ
app01-3959	9	8	micro	micro	ADJ
app01-3959	9	9	beams	beam	NOUN
app01-3959	9	10	made	make	VERB
app01-3959	9	11	of	of	ADP
app01-3959	9	12	the	the	DET
app01-3959	9	13	polymer	polymer	NOUN
app01-3959	9	14	su-8	su-8	PUNCT
app01-3959	9	15	are	be	AUX
app01-3959	9	16	performed	perform	VERB
app01-3959	9	17	by	by	ADP
app01-3959	9	18	using	use	VERB
app01-3959	9	19	an	an	DET
app01-3959	9	20	atomic	atomic	ADJ
app01-3959	9	21	force	force	NOUN
app01-3959	9	22	microscope	microscope	NOUN
app01-3959	9	23	and	and	CCONJ
app01-3959	9	24	the	the	DET
app01-3959	9	25	results	result	NOUN
app01-3959	9	26	are	be	AUX
app01-3959	9	27	compared	compare	VERB
app01-3959	9	28	to	to	ADP
app01-3959	9	29	the	the	DET
app01-3959	9	30	numerical	numerical	ADJ
app01-3959	9	31	solution	solution	NOUN
app01-3959	9	32	.	.	PUNCT
app01-3959	10	1	keywords	keyword	NOUN
app01-3959	10	2	:	:	PUNCT
app01-3959	10	3	second	second	ADJ
app01-3959	10	4	gradient	gradient	NOUN
app01-3959	10	5	continuum	continuum	ADJ
app01-3959	10	6	,	,	PUNCT
app01-3959	10	7	size	size	NOUN
app01-3959	10	8	effect	effect	NOUN
app01-3959	10	9	,	,	PUNCT
app01-3959	10	10	hermite	hermite	ADJ
app01-3959	10	11	finite	finite	VERB
app01-3959	10	12	elements	element	NOUN
app01-3959	10	13	.	.	PUNCT
app01-3959	11	1	1	1	X
app01-3959	11	2	.	.	X
app01-3959	11	3	introduction	introduction	NOUN
app01-3959	11	4	materials	material	NOUN
app01-3959	11	5	with	with	ADP
app01-3959	11	6	intrinsic	intrinsic	ADJ
app01-3959	11	7	microor	microor	NOUN
app01-3959	11	8	nano	nano	NOUN
app01-3959	11	9	-	-	PUNCT
app01-3959	11	10	structure	structure	NOUN
app01-3959	11	11	can	can	AUX
app01-3959	11	12	show	show	VERB
app01-3959	11	13	size	size	NOUN
app01-3959	11	14	-	-	PUNCT
app01-3959	11	15	dependent	dependent	ADJ
app01-3959	11	16	material	material	NOUN
app01-3959	11	17	behavior	behavior	NOUN
app01-3959	11	18	,	,	PUNCT
app01-3959	11	19	which	which	PRON
app01-3959	11	20	is	be	AUX
app01-3959	11	21	reflected	reflect	VERB
app01-3959	11	22	,	,	PUNCT
app01-3959	11	23	e.g.	e.g.	ADV
app01-3959	11	24	,	,	PUNCT
app01-3959	11	25	by	by	ADP
app01-3959	11	26	a	a	DET
app01-3959	11	27	stiffer	stiffer	ADJ
app01-3959	11	28	elastic	elastic	ADJ
app01-3959	11	29	response	response	NOUN
app01-3959	11	30	to	to	ADP
app01-3959	11	31	external	external	ADJ
app01-3959	11	32	forces	force	NOUN
app01-3959	11	33	when	when	SCONJ
app01-3959	11	34	the	the	DET
app01-3959	11	35	size	size	NOUN
app01-3959	11	36	of	of	ADP
app01-3959	11	37	the	the	DET
app01-3959	11	38	material	material	NOUN
app01-3959	11	39	body	body	NOUN
app01-3959	11	40	is	be	AUX
app01-3959	11	41	reduced	reduce	VERB
app01-3959	11	42	.	.	PUNCT
app01-3959	12	1	a	a	DET
app01-3959	12	2	quantitative	quantitative	ADJ
app01-3959	12	3	understanding	understanding	NOUN
app01-3959	12	4	of	of	ADP
app01-3959	12	5	a	a	DET
app01-3959	12	6	possible	possible	ADJ
app01-3959	12	7	size	size	NOUN
app01-3959	12	8	effect	effect	NOUN
app01-3959	12	9	in	in	ADP
app01-3959	12	10	microand	microand	NOUN
app01-3959	12	11	submicrostructures	submicrostructure	NOUN
app01-3959	12	12	is	be	AUX
app01-3959	12	13	of	of	ADP
app01-3959	12	14	great	great	ADJ
app01-3959	12	15	importance	importance	NOUN
app01-3959	12	16	when	when	SCONJ
app01-3959	12	17	modeling	model	VERB
app01-3959	12	18	microand	microand	NOUN
app01-3959	12	19	nano	nano	NOUN
app01-3959	12	20	-	-	PUNCT
app01-3959	12	21	electro	electro	ADJ
app01-3959	12	22	-	-	PUNCT
app01-3959	12	23	mechanical	mechanical	ADJ
app01-3959	12	24	systems	system	NOUN
app01-3959	12	25	(	(	PUNCT
app01-3959	12	26	mems	mem	NOUN
app01-3959	12	27	/	/	SYM
app01-3959	12	28	nems	nem	NOUN
app01-3959	12	29	)	)	PUNCT
app01-3959	12	30	.	.	PUNCT
app01-3959	13	1	driven	drive	VERB
app01-3959	13	2	by	by	ADP
app01-3959	13	3	miniaturization	miniaturization	NOUN
app01-3959	13	4	,	,	PUNCT
app01-3959	13	5	the	the	DET
app01-3959	13	6	need	need	NOUN
app01-3959	13	7	for	for	ADP
app01-3959	13	8	saving	save	VERB
app01-3959	13	9	materials	material	NOUN
app01-3959	13	10	and	and	CCONJ
app01-3959	13	11	improving	improve	VERB
app01-3959	13	12	the	the	DET
app01-3959	13	13	performance	performance	NOUN
app01-3959	13	14	,	,	PUNCT
app01-3959	13	15	the	the	DET
app01-3959	13	16	requirement	requirement	NOUN
app01-3959	13	17	of	of	ADP
app01-3959	13	18	reliability	reliability	NOUN
app01-3959	13	19	in	in	ADP
app01-3959	13	20	simulation	simulation	NOUN
app01-3959	13	21	technologies	technology	NOUN
app01-3959	13	22	increases	increase	VERB
app01-3959	13	23	.	.	PUNCT
app01-3959	14	1	a	a	DET
app01-3959	14	2	size	size	NOUN
app01-3959	14	3	effect	effect	NOUN
app01-3959	14	4	is	be	AUX
app01-3959	14	5	reflected	reflect	VERB
app01-3959	14	6	in	in	ADP
app01-3959	14	7	a	a	DET
app01-3959	14	8	different	different	ADJ
app01-3959	14	9	elastic	elastic	ADJ
app01-3959	14	10	response	response	NOUN
app01-3959	14	11	to	to	ADP
app01-3959	14	12	external	external	ADJ
app01-3959	14	13	loads	load	NOUN
app01-3959	14	14	if	if	SCONJ
app01-3959	14	15	the	the	DET
app01-3959	14	16	size	size	NOUN
app01-3959	14	17	of	of	ADP
app01-3959	14	18	the	the	DET
app01-3959	14	19	material	material	NOUN
app01-3959	14	20	body	body	NOUN
app01-3959	14	21	is	be	AUX
app01-3959	14	22	reduced	reduce	VERB
app01-3959	14	23	.	.	PUNCT
app01-3959	15	1	experimental	experimental	ADJ
app01-3959	15	2	validation	validation	NOUN
app01-3959	15	3	therefore	therefore	ADV
app01-3959	15	4	is	be	AUX
app01-3959	15	5	given	give	VERB
app01-3959	15	6	in	in	ADP
app01-3959	15	7	,	,	PUNCT
app01-3959	15	8	e.g.	e.g.	ADV
app01-3959	15	9	,	,	PUNCT
app01-3959	15	10	[	[	X
app01-3959	15	11	1–6	1–6	X
app01-3959	15	12	]	]	X
app01-3959	15	13	.	.	PUNCT
app01-3959	16	1	second	second	ADJ
app01-3959	16	2	gradient	gradient	NOUN
app01-3959	16	3	(	(	PUNCT
app01-3959	16	4	sg	sg	NOUN
app01-3959	16	5	)	)	PUNCT
app01-3959	16	6	continuum	continuum	ADJ
app01-3959	16	7	theories	theory	NOUN
app01-3959	16	8	are	be	AUX
app01-3959	16	9	used	use	VERB
app01-3959	16	10	if	if	SCONJ
app01-3959	16	11	,	,	PUNCT
app01-3959	16	12	in	in	ADP
app01-3959	16	13	the	the	DET
app01-3959	16	14	absence	absence	NOUN
app01-3959	16	15	of	of	ADP
app01-3959	16	16	strain	strain	NOUN
app01-3959	16	17	gradients	gradient	NOUN
app01-3959	16	18	(	(	PUNCT
app01-3959	16	19	in	in	ADP
app01-3959	16	20	uniaxial	uniaxial	ADJ
app01-3959	16	21	tensile	tensile	NOUN
app01-3959	16	22	tests	test	NOUN
app01-3959	16	23	)	)	PUNCT
app01-3959	16	24	,	,	PUNCT
app01-3959	16	25	the	the	DET
app01-3959	16	26	elastic	elastic	ADJ
app01-3959	16	27	behavior	behavior	NOUN
app01-3959	16	28	of	of	ADP
app01-3959	16	29	the	the	DET
app01-3959	16	30	material	material	NOUN
app01-3959	16	31	is	be	AUX
app01-3959	16	32	independent	independent	ADJ
app01-3959	16	33	of	of	ADP
app01-3959	16	34	the	the	DET
app01-3959	16	35	thickness	thickness	NOUN
app01-3959	16	36	of	of	ADP
app01-3959	16	37	the	the	DET
app01-3959	16	38	sample	sample	NOUN
app01-3959	17	1	[	[	X
app01-3959	17	2	3	3	NUM
app01-3959	17	3	]	]	PUNCT
app01-3959	17	4	.	.	PUNCT
app01-3959	18	1	they	they	PRON
app01-3959	18	2	are	be	AUX
app01-3959	18	3	applicable	applicable	ADJ
app01-3959	18	4	to	to	ADP
app01-3959	18	5	so	so	ADV
app01-3959	18	6	-	-	PUNCT
app01-3959	18	7	called	call	VERB
app01-3959	18	8	non	non	ADJ
app01-3959	18	9	-	-	ADJ
app01-3959	18	10	simple	simple	ADJ
app01-3959	18	11	materials	material	NOUN
app01-3959	18	12	of	of	ADP
app01-3959	18	13	the	the	DET
app01-3959	18	14	gradient	gradient	NOUN
app01-3959	18	15	type	type	NOUN
app01-3959	18	16	,	,	PUNCT
app01-3959	18	17	for	for	ADP
app01-3959	18	18	example	example	NOUN
app01-3959	18	19	,	,	PUNCT
app01-3959	18	20	polymers	polymer	NOUN
app01-3959	18	21	at	at	ADP
app01-3959	18	22	a	a	DET
app01-3959	18	23	small	small	ADJ
app01-3959	18	24	scale	scale	NOUN
app01-3959	18	25	.	.	PUNCT
app01-3959	19	1	since	since	SCONJ
app01-3959	19	2	conventional	conventional	ADJ
app01-3959	19	3	continuum	continuum	ADJ
app01-3959	19	4	theories	theory	NOUN
app01-3959	19	5	based	base	VERB
app01-3959	19	6	on	on	ADP
app01-3959	19	7	the	the	DET
app01-3959	19	8	cauchy	cauchy	ADJ
app01-3959	19	9	continuum	continuum	NOUN
app01-3959	19	10	are	be	AUX
app01-3959	19	11	not	not	PART
app01-3959	19	12	able	able	ADJ
app01-3959	19	13	to	to	PART
app01-3959	19	14	predict	predict	VERB
app01-3959	19	15	size	size	NOUN
app01-3959	19	16	effects	effect	NOUN
app01-3959	19	17	,	,	PUNCT
app01-3959	19	18	the	the	DET
app01-3959	19	19	present	present	ADJ
app01-3959	19	20	work	work	NOUN
app01-3959	19	21	deals	deal	NOUN
app01-3959	19	22	with	with	ADP
app01-3959	19	23	the	the	DET
app01-3959	19	24	modified	modify	VERB
app01-3959	19	25	strain	strain	NOUN
app01-3959	19	26	gradient	gradient	NOUN
app01-3959	19	27	theory	theory	NOUN
app01-3959	19	28	(	(	PUNCT
app01-3959	19	29	msg	msg	PROPN
app01-3959	19	30	)	)	PUNCT
app01-3959	19	31	developed	develop	VERB
app01-3959	19	32	in	in	ADP
app01-3959	19	33	,	,	PUNCT
app01-3959	19	34	e.g.	e.g.	ADV
app01-3959	19	35	,	,	PUNCT
app01-3959	19	36	[	[	X
app01-3959	19	37	7–9	7–9	NOUN
app01-3959	19	38	]	]	X
app01-3959	19	39	.	.	PUNCT
app01-3959	20	1	by	by	ADP
app01-3959	20	2	employing	employ	VERB
app01-3959	20	3	the	the	DET
app01-3959	20	4	macroscopic	macroscopic	ADJ
app01-3959	20	5	rotation	rotation	NOUN
app01-3959	20	6	vector	vector	NOUN
app01-3959	20	7	and	and	CCONJ
app01-3959	20	8	second	second	ADJ
app01-3959	20	9	order	order	NOUN
app01-3959	20	10	derivatives	derivative	NOUN
app01-3959	20	11	of	of	ADP
app01-3959	20	12	the	the	DET
app01-3959	20	13	displacement	displacement	ADJ
app01-3959	20	14	vector	vector	NOUN
app01-3959	20	15	,	,	PUNCT
app01-3959	20	16	msg	msg	NOUN
app01-3959	20	17	-	-	NOUN
app01-3959	20	18	theory	theory	NOUN
app01-3959	20	19	is	be	AUX
app01-3959	20	20	able	able	ADJ
app01-3959	20	21	to	to	PART
app01-3959	20	22	account	account	VERB
app01-3959	20	23	for	for	ADP
app01-3959	20	24	quantities	quantity	NOUN
app01-3959	20	25	like	like	ADP
app01-3959	20	26	rotation	rotation	NOUN
app01-3959	20	27	and	and	CCONJ
app01-3959	20	28	curvature	curvature	NOUN
app01-3959	20	29	.	.	PUNCT
app01-3959	21	1	a	a	DET
app01-3959	21	2	generalization	generalization	NOUN
app01-3959	21	3	of	of	ADP
app01-3959	21	4	strain	strain	NOUN
app01-3959	21	5	gradient	gradient	NOUN
app01-3959	21	6	continua	continuum	NOUN
app01-3959	21	7	has	have	AUX
app01-3959	21	8	been	be	AUX
app01-3959	21	9	developed	develop	VERB
app01-3959	21	10	by	by	ADP
app01-3959	21	11	eringen	eringen	PROPN
app01-3959	21	12	,	,	PUNCT
app01-3959	21	13	who	who	PRON
app01-3959	21	14	proposed	propose	VERB
app01-3959	21	15	“	"	PUNCT
app01-3959	21	16	nonsimple	nonsimple	ADJ
app01-3959	21	17	materials	material	NOUN
app01-3959	21	18	of	of	ADP
app01-3959	21	19	gradient	gradient	ADJ
app01-3959	21	20	type	type	NOUN
app01-3959	21	21	[	[	X
app01-3959	21	22	10	10	NUM
app01-3959	21	23	]	]	PUNCT
app01-3959	21	24	”	"	PUNCT
app01-3959	21	25	in	in	ADP
app01-3959	21	26	order	order	NOUN
app01-3959	21	27	to	to	PART
app01-3959	21	28	derive	derive	VERB
app01-3959	21	29	the	the	DET
app01-3959	21	30	corresponding	corresponding	ADJ
app01-3959	21	31	higher	high	ADJ
app01-3959	21	32	-	-	PUNCT
app01-3959	21	33	order	order	NOUN
app01-3959	21	34	material	material	NOUN
app01-3959	21	35	dependencies	dependency	NOUN
app01-3959	21	36	in	in	ADP
app01-3959	21	37	a	a	DET
app01-3959	21	38	rational	rational	ADJ
app01-3959	21	39	manner	manner	NOUN
app01-3959	21	40	.	.	PUNCT
app01-3959	22	1	the	the	DET
app01-3959	22	2	application	application	NOUN
app01-3959	22	3	of	of	ADP
app01-3959	22	4	conventional	conventional	ADJ
app01-3959	22	5	finite	finite	ADJ
app01-3959	22	6	element	element	NOUN
app01-3959	22	7	(	(	PUNCT
app01-3959	22	8	fe	fe	NOUN
app01-3959	22	9	)	)	PUNCT
app01-3959	22	10	strategies	strategy	NOUN
app01-3959	22	11	may	may	AUX
app01-3959	22	12	lead	lead	VERB
app01-3959	22	13	to	to	ADP
app01-3959	22	14	inaccurate	inaccurate	ADJ
app01-3959	22	15	results	result	NOUN
app01-3959	22	16	,	,	PUNCT
app01-3959	22	17	if	if	SCONJ
app01-3959	22	18	finite	finite	ADJ
app01-3959	22	19	element	element	NOUN
app01-3959	22	20	formulations	formulation	NOUN
app01-3959	22	21	are	be	AUX
app01-3959	22	22	used	use	VERB
app01-3959	22	23	which	which	PRON
app01-3959	22	24	only	only	ADV
app01-3959	22	25	fullfill	fullfill	PROPN
app01-3959	22	26	global	global	ADJ
app01-3959	22	27	c0	c0	PROPN
app01-3959	22	28	–	–	PUNCT
app01-3959	22	29	continuity	continuity	NOUN
app01-3959	22	30	.	.	PUNCT
app01-3959	23	1	the	the	DET
app01-3959	23	2	scope	scope	NOUN
app01-3959	23	3	of	of	ADP
app01-3959	23	4	this	this	DET
app01-3959	23	5	work	work	NOUN
app01-3959	23	6	is	be	AUX
app01-3959	23	7	to	to	PART
app01-3959	23	8	use	use	VERB
app01-3959	23	9	fe	fe	NOUN
app01-3959	23	10	formulations	formulation	NOUN
app01-3959	23	11	based	base	VERB
app01-3959	23	12	on	on	ADP
app01-3959	23	13	hermite	hermite	ADJ
app01-3959	23	14	polynomials	polynomial	NOUN
app01-3959	23	15	in	in	ADP
app01-3959	23	16	order	order	NOUN
app01-3959	23	17	to	to	PART
app01-3959	23	18	fulfill	fulfill	VERB
app01-3959	23	19	global	global	ADJ
app01-3959	23	20	c1	c1	NOUN
app01-3959	23	21	–	–	PUNCT
app01-3959	23	22	continuity	continuity	NOUN
app01-3959	23	23	for	for	ADP
app01-3959	23	24	solutions	solution	NOUN
app01-3959	23	25	in	in	ADP
app01-3959	23	26	the	the	DET
app01-3959	23	27	modified	modify	VERB
app01-3959	23	28	strain	strain	NOUN
app01-3959	23	29	gradient	gradient	NOUN
app01-3959	23	30	theory	theory	NOUN
app01-3959	23	31	.	.	PUNCT
app01-3959	24	1	section	section	NOUN
app01-3959	24	2	2	2	NUM
app01-3959	24	3	presents	present	VERB
app01-3959	24	4	the	the	DET
app01-3959	24	5	strain	strain	ADJ
app01-3959	24	6	energy	energy	NOUN
app01-3959	24	7	function	function	NOUN
app01-3959	24	8	of	of	ADP
app01-3959	24	9	the	the	DET
app01-3959	24	10	modified	modify	VERB
app01-3959	24	11	strain	strain	NOUN
app01-3959	24	12	gradient	gradient	NOUN
app01-3959	24	13	theory	theory	NOUN
app01-3959	24	14	and	and	CCONJ
app01-3959	24	15	a	a	DET
app01-3959	24	16	one	one	NUM
app01-3959	24	17	dimensional	dimensional	ADJ
app01-3959	24	18	differential	differential	NOUN
app01-3959	24	19	equation	equation	NOUN
app01-3959	24	20	is	be	AUX
app01-3959	24	21	derived	derive	VERB
app01-3959	24	22	by	by	ADP
app01-3959	24	23	making	make	VERB
app01-3959	24	24	use	use	NOUN
app01-3959	24	25	of	of	ADP
app01-3959	24	26	the	the	DET
app01-3959	24	27	euler	euler	NOUN
app01-3959	24	28	-	-	PUNCT
app01-3959	24	29	bernoulli	bernoulli	PROPN
app01-3959	24	30	assumptions	assumption	NOUN
app01-3959	24	31	for	for	ADP
app01-3959	24	32	slender	slender	ADJ
app01-3959	24	33	beams	beam	NOUN
app01-3959	24	34	.	.	PUNCT
app01-3959	25	1	the	the	DET
app01-3959	25	2	finite	finite	PROPN
app01-3959	25	3	element	element	NOUN
app01-3959	25	4	formulation	formulation	NOUN
app01-3959	25	5	based	base	VERB
app01-3959	25	6	on	on	ADP
app01-3959	25	7	hermite	hermite	ADJ
app01-3959	25	8	polynomials	polynomial	NOUN
app01-3959	25	9	is	be	AUX
app01-3959	25	10	presented	present	VERB
app01-3959	25	11	in	in	ADP
app01-3959	25	12	sect	sect	NOUN
app01-3959	25	13	.	.	PUNCT
app01-3959	26	1	3	3	NUM
app01-3959	26	2	as	as	ADV
app01-3959	26	3	well	well	ADV
app01-3959	26	4	as	as	ADP
app01-3959	26	5	the	the	DET
app01-3959	26	6	structure	structure	NOUN
app01-3959	26	7	of	of	ADP
app01-3959	26	8	the	the	DET
app01-3959	26	9	element	element	NOUN
app01-3959	26	10	stiffnessand	stiffnessand	NOUN
app01-3959	26	11	system	system	NOUN
app01-3959	26	12	matrix	matrix	NOUN
app01-3959	26	13	.	.	PUNCT
app01-3959	27	1	a	a	DET
app01-3959	27	2	numerical	numerical	ADJ
app01-3959	27	3	example	example	NOUN
app01-3959	27	4	for	for	ADP
app01-3959	27	5	a	a	DET
app01-3959	27	6	loaded	load	VERB
app01-3959	27	7	cantilever	cantilever	NOUN
app01-3959	27	8	beam	beam	NOUN
app01-3959	27	9	is	be	AUX
app01-3959	27	10	then	then	ADV
app01-3959	27	11	given	give	VERB
app01-3959	27	12	in	in	ADP
app01-3959	27	13	sect	sect	NOUN
app01-3959	27	14	.	.	PUNCT
app01-3959	28	1	4	4	X
app01-3959	28	2	.	.	X
app01-3959	28	3	2	2	NUM
app01-3959	28	4	.	.	NUM
app01-3959	28	5	modified	modify	VERB
app01-3959	28	6	strain	strain	NOUN
app01-3959	28	7	gradient	gradient	NOUN
app01-3959	28	8	theory	theory	NOUN
app01-3959	28	9	2.1	2.1	NUM
app01-3959	28	10	.	.	PUNCT
app01-3959	29	1	strain	strain	NOUN
app01-3959	29	2	energy	energy	NOUN
app01-3959	29	3	function	function	NOUN
app01-3959	29	4	the	the	DET
app01-3959	29	5	present	present	ADJ
app01-3959	29	6	study	study	NOUN
app01-3959	29	7	starts	start	VERB
app01-3959	29	8	with	with	ADP
app01-3959	29	9	one	one	NUM
app01-3959	29	10	of	of	ADP
app01-3959	29	11	the	the	DET
app01-3959	29	12	three	three	NUM
app01-3959	29	13	reduced	reduced	ADJ
app01-3959	29	14	forms	form	NOUN
app01-3959	29	15	of	of	ADP
app01-3959	29	16	the	the	DET
app01-3959	29	17	strain	strain	ADJ
app01-3959	29	18	energy	energy	NOUN
app01-3959	29	19	densities	density	NOUN
app01-3959	29	20	for	for	ADP
app01-3959	29	21	small	small	ADJ
app01-3959	29	22	deformations	deformation	NOUN
app01-3959	29	23	,	,	PUNCT
app01-3959	29	24	usg	usg	INTJ
app01-3959	29	25	,	,	PUNCT
app01-3959	29	26	as	as	SCONJ
app01-3959	29	27	postulated	postulate	VERB
app01-3959	29	28	by	by	ADP
app01-3959	29	29	mindlin	mindlin	PROPN
app01-3959	29	30	(	(	PUNCT
app01-3959	29	31	1962	1962	NUM
app01-3959	29	32	)	)	PUNCT
app01-3959	30	1	[	[	X
app01-3959	30	2	8	8	NUM
app01-3959	30	3	]	]	PUNCT
app01-3959	30	4	.	.	PUNCT
app01-3959	31	1	the	the	DET
app01-3959	31	2	einstein	einstein	PROPN
app01-3959	31	3	summation	summation	PROPN
app01-3959	31	4	convention	convention	PROPN
app01-3959	31	5	on	on	ADP
app01-3959	31	6	repeated	repeat	VERB
app01-3959	31	7	indices	index	NOUN
app01-3959	31	8	is	be	AUX
app01-3959	31	9	used	use	VERB
app01-3959	31	10	and	and	CCONJ
app01-3959	31	11	spatial	spatial	ADJ
app01-3959	31	12	partial	partial	ADJ
app01-3959	31	13	derivatives	derivative	NOUN
app01-3959	31	14	in	in	ADP
app01-3959	31	15	the	the	DET
app01-3959	31	16	cartesian	cartesian	ADJ
app01-3959	31	17	coordinate	coordinate	NOUN
app01-3959	31	18	system	system	NOUN
app01-3959	31	19	are	be	AUX
app01-3959	31	20	denoted	denote	VERB
app01-3959	31	21	by	by	ADP
app01-3959	31	22	commaseparated	commaseparate	VERB
app01-3959	31	23	indices	index	NOUN
app01-3959	31	24	.	.	PUNCT
app01-3959	32	1	mindlin	mindlin	PROPN
app01-3959	32	2	’s	’s	PART
app01-3959	32	3	second	second	ADJ
app01-3959	32	4	form	form	NOUN
app01-3959	32	5	of	of	ADP
app01-3959	32	6	linear	linear	ADJ
app01-3959	32	7	isotropic	isotropic	NOUN
app01-3959	32	8	strain	strain	NOUN
app01-3959	32	9	energy	energy	NOUN
app01-3959	32	10	density	density	NOUN
app01-3959	32	11	reads	read	VERB
app01-3959	32	12	:	:	PUNCT
app01-3959	33	1	usg	usg	PROPN
app01-3959	33	2	=	=	PUNCT
app01-3959	33	3	α1εij	α1εij	PROPN
app01-3959	33	4	εij	εij	NOUN
app01-3959	33	5	+	+	CCONJ
app01-3959	33	6	α2εkk	α2εkk	NUM
app01-3959	33	7	εmm	εmm	VERB
app01-3959	33	8	+	+	NUM
app01-3959	33	9	β1ηijk	β1ηijk	NOUN
app01-3959	33	10	ηijk	ηijk	X
app01-3959	33	11	+	+	CCONJ
app01-3959	33	12	β2ηiik	β2ηiik	PROPN
app01-3959	33	13	ηjjk	ηjjk	ADJ
app01-3959	33	14	+	+	CCONJ
app01-3959	34	1	+	+	CCONJ
app01-3959	34	2	β3ηiik	β3ηiik	ADJ
app01-3959	34	3	ηkjj	ηkjj	NOUN
app01-3959	34	4	+	+	CCONJ
app01-3959	34	5	β4ηijj	β4ηijj	PROPN
app01-3959	34	6	ηikk	ηikk	NOUN
app01-3959	35	1	+	+	CCONJ
app01-3959	35	2	β5ηijk	β5ηijk	NOUN
app01-3959	35	3	ηkji	ηkji	X
app01-3959	35	4	,	,	PUNCT
app01-3959	35	5	(	(	PUNCT
app01-3959	35	6	1	1	X
app01-3959	35	7	)	)	PUNCT
app01-3959	35	8	where	where	SCONJ
app01-3959	35	9	εij	εij	NOUN
app01-3959	35	10	=	=	SYM
app01-3959	35	11	1/2(ui	1/2(ui	NUM
app01-3959	35	12	,	,	PUNCT
app01-3959	35	13	j	j	PROPN
app01-3959	36	1	+	+	CCONJ
app01-3959	37	1	uj	uj	PROPN
app01-3959	37	2	,	,	PUNCT
app01-3959	37	3	i	i	NOUN
app01-3959	37	4	)	)	PUNCT
app01-3959	37	5	denotes	denote	VERB
app01-3959	37	6	the	the	DET
app01-3959	37	7	small	small	ADJ
app01-3959	37	8	strain	strain	NOUN
app01-3959	37	9	tensor	tensor	NOUN
app01-3959	37	10	and	and	CCONJ
app01-3959	37	11	ηijk	ηijk	NOUN
app01-3959	37	12	=	=	SYM
app01-3959	37	13	1/2(uk	1/2(uk	NUM
app01-3959	37	14	,	,	PUNCT
app01-3959	37	15	ij	ij	NOUN
app01-3959	38	1	+	+	CCONJ
app01-3959	38	2	uj	uj	PROPN
app01-3959	38	3	,	,	PUNCT
app01-3959	38	4	ki	ki	PROPN
app01-3959	38	5	)	)	PUNCT
app01-3959	39	1	=	=	SYM
app01-3959	39	2	εkj	εkj	NOUN
app01-3959	39	3	,	,	PUNCT
app01-3959	39	4	i	i	PRON
app01-3959	39	5	the	the	DET
app01-3959	39	6	gradient	gradient	NOUN
app01-3959	39	7	33	33	NUM
app01-3959	39	8	http://dx.doi.org/10.14311/app.2017.7.0033	http://dx.doi.org/10.14311/app.2017.7.0033	NOUN
app01-3959	39	9	http://ojs.cvut.cz/ojs/index.php/app	http://ojs.cvut.cz/ojs/index.php/app	X
app01-3959	40	1	christian	christian	PROPN
app01-3959	40	2	liebold	liebold	PROPN
app01-3959	40	3	,	,	PUNCT
app01-3959	40	4	wolfgang	wolfgang	PROPN
app01-3959	40	5	h.	h.	PROPN
app01-3959	40	6	müller	müller	PROPN
app01-3959	40	7	acta	acta	PROPN
app01-3959	40	8	polytechnica	polytechnica	PROPN
app01-3959	40	9	ctu	ctu	NOUN
app01-3959	40	10	proceedings	proceeding	NOUN
app01-3959	40	11	of	of	ADP
app01-3959	40	12	strain	strain	NOUN
app01-3959	40	13	.	.	PUNCT
app01-3959	41	1	α1	α1	PROPN
app01-3959	41	2	and	and	CCONJ
app01-3959	41	3	α2	α2	ADJ
app01-3959	41	4	lead	lead	NOUN
app01-3959	41	5	to	to	ADP
app01-3959	41	6	lamé	lamé	NOUN
app01-3959	41	7	’s	’s	PART
app01-3959	41	8	constants	constant	NOUN
app01-3959	41	9	and	and	CCONJ
app01-3959	41	10	β1,	β1,	NOUN
app01-3959	41	11	...	...	PUNCT
app01-3959	41	12	,5	,5	PUNCT
app01-3959	41	13	are	be	AUX
app01-3959	41	14	five	five	NUM
app01-3959	41	15	additional	additional	ADJ
app01-3959	41	16	higher	high	ADJ
app01-3959	41	17	-	-	PUNCT
app01-3959	41	18	order	order	NOUN
app01-3959	41	19	material	material	NOUN
app01-3959	41	20	constants	constant	NOUN
app01-3959	41	21	[	[	X
app01-3959	41	22	11	11	NUM
app01-3959	41	23	]	]	PUNCT
app01-3959	41	24	.	.	PUNCT
app01-3959	42	1	σij	σij	NOUN
app01-3959	42	2	and	and	CCONJ
app01-3959	42	3	µijk	µijk	NOUN
app01-3959	42	4	denote	denote	VERB
app01-3959	42	5	the	the	DET
app01-3959	42	6	cauchy	cauchy	PROPN
app01-3959	42	7	stress	stress	NOUN
app01-3959	42	8	tensor	tensor	NOUN
app01-3959	42	9	and	and	CCONJ
app01-3959	42	10	the	the	DET
app01-3959	42	11	higher	high	ADJ
app01-3959	42	12	-	-	PUNCT
app01-3959	42	13	order	order	NOUN
app01-3959	42	14	stress	stress	NOUN
app01-3959	42	15	tensor	tensor	NOUN
app01-3959	42	16	,	,	PUNCT
app01-3959	42	17	respectively	respectively	ADV
app01-3959	42	18	:	:	PUNCT
app01-3959	42	19	σij	σij	NOUN
app01-3959	42	20	=	=	SYM
app01-3959	42	21	∂usg	∂usg	X
app01-3959	42	22	∂εij	∂εij	NOUN
app01-3959	42	23	,	,	PUNCT
app01-3959	42	24	µijk	µijk	X
app01-3959	42	25	=	=	SYM
app01-3959	42	26	∂usg	∂usg	X
app01-3959	42	27	∂ηijk	∂ηijk	PROPN
app01-3959	42	28	.	.	PUNCT
app01-3959	43	1	(	(	PUNCT
app01-3959	43	2	2	2	X
app01-3959	43	3	)	)	PUNCT
app01-3959	43	4	the	the	DET
app01-3959	43	5	inclusion	inclusion	NOUN
app01-3959	43	6	of	of	ADP
app01-3959	43	7	the	the	DET
app01-3959	43	8	macroscopic	macroscopic	ADJ
app01-3959	43	9	rotation	rotation	NOUN
app01-3959	43	10	vector	vector	NOUN
app01-3959	43	11	ϕi	ϕi	ADP
app01-3959	43	12	=	=	PROPN
app01-3959	43	13	1/2εijk	1/2εijk	PROPN
app01-3959	43	14	uk	uk	PROPN
app01-3959	43	15	,	,	PUNCT
app01-3959	43	16	j	j	PROPN
app01-3959	43	17	(	(	PUNCT
app01-3959	43	18	εijk	εijk	NOUN
app01-3959	43	19	being	be	AUX
app01-3959	43	20	the	the	DET
app01-3959	43	21	levi	levi	NOUN
app01-3959	43	22	-	-	PUNCT
app01-3959	43	23	civita	civita	NOUN
app01-3959	43	24	symbol	symbol	NOUN
app01-3959	43	25	)	)	PUNCT
app01-3959	44	1	leads	lead	VERB
app01-3959	44	2	to	to	ADP
app01-3959	44	3	a	a	DET
app01-3959	44	4	reduction	reduction	NOUN
app01-3959	44	5	of	of	ADP
app01-3959	44	6	the	the	DET
app01-3959	44	7	additional	additional	ADJ
app01-3959	44	8	material	material	NOUN
app01-3959	44	9	constants	constant	NOUN
app01-3959	44	10	from	from	ADP
app01-3959	44	11	five	five	NUM
app01-3959	44	12	to	to	PART
app01-3959	44	13	three	three	NUM
app01-3959	44	14	.	.	PUNCT
app01-3959	45	1	based	base	VERB
app01-3959	45	2	on	on	ADP
app01-3959	45	3	fleck	fleck	PROPN
app01-3959	45	4	&	&	CCONJ
app01-3959	45	5	hutchinson	hutchinson	PROPN
app01-3959	45	6	(	(	PUNCT
app01-3959	45	7	1997	1997	NUM
app01-3959	45	8	)	)	PUNCT
app01-3959	46	1	[	[	X
app01-3959	46	2	12	12	NUM
app01-3959	46	3	]	]	X
app01-3959	46	4	we	we	PRON
app01-3959	46	5	introduce	introduce	VERB
app01-3959	46	6	independent	independent	ADJ
app01-3959	46	7	expressions	expression	NOUN
app01-3959	46	8	of	of	ADP
app01-3959	46	9	ηijk	ηijk	NOUN
app01-3959	46	10	and	and	CCONJ
app01-3959	46	11	decompose	decompose	VERB
app01-3959	46	12	the	the	DET
app01-3959	46	13	second	second	ADJ
app01-3959	46	14	order	order	NOUN
app01-3959	46	15	displacement	displacement	NOUN
app01-3959	46	16	gradient	gradient	NOUN
app01-3959	46	17	into	into	ADP
app01-3959	46	18	a	a	DET
app01-3959	46	19	symmetric	symmetric	ADJ
app01-3959	46	20	part	part	NOUN
app01-3959	46	21	ηs	ηs	ADP
app01-3959	46	22	ijk	ijk	PROPN
app01-3959	46	23	and	and	CCONJ
app01-3959	46	24	a	a	DET
app01-3959	46	25	remaining	remain	VERB
app01-3959	46	26	part	part	NOUN
app01-3959	46	27	ηr	ηr	X
app01-3959	46	28	ijk	ijk	X
app01-3959	46	29	(	(	PUNCT
app01-3959	46	30	which	which	PRON
app01-3959	46	31	is	be	AUX
app01-3959	46	32	not	not	PART
app01-3959	46	33	necessarily	necessarily	ADV
app01-3959	46	34	anti	anti	ADJ
app01-3959	46	35	-	-	ADJ
app01-3959	46	36	symmetric	symmetric	ADJ
app01-3959	46	37	):	):	PUNCT
app01-3959	46	38	hj	hj	PROPN
app01-3959	46	39	hj	hj	PROPN
app01-3959	46	40	hj	hj	PROPN
app01-3959	46	41	z	z	PROPN
app01-3959	46	42	~	~	PROPN
app01-3959	46	43	hj	hj	PROPN
app01-3959	46	44	�	�	PROPN
app01-3959	46	45	�	�	PROPN
app01-3959	46	46	�	�	PROPN
app01-3959	46	47	�	�	PROPN
app01-3959	46	48	�	�	PROPN
app01-3959	46	49	�	�	PROPN
app01-3959	46	50	�	�	PROPN
app01-3959	46	51	�	�	PROPN
app01-3959	46	52	ηijk	ηijk	PROPN
app01-3959	46	53	ηs	ηs	PROPN
app01-3959	46	54	ijk	ijk	PROPN
app01-3959	46	55	ηr	ηr	PROPN
app01-3959	46	56	ijk	ijk	PROPN
app01-3959	46	57	η̄ij	η̄ij	PROPN
app01-3959	46	58	χs	χs	ADP
app01-3959	46	59	ijχa	ijχa	PROPN
app01-3959	46	60	ij	ij	PROPN
app01-3959	46	61	η	η	PROPN
app01-3959	46	62	(	(	PUNCT
app01-3959	46	63	0	0	NUM
app01-3959	46	64	)	)	PUNCT
app01-3959	46	65	ijk	ijk	PROPN
app01-3959	46	66	η	η	PROPN
app01-3959	46	67	(	(	PUNCT
app01-3959	46	68	1	1	NUM
app01-3959	46	69	)	)	PUNCT
app01-3959	46	70	ijkχa	ijkχa	NOUN
app01-3959	46	71	ijεmm	ijεmm	NOUN
app01-3959	46	72	,	,	PUNCT
app01-3959	46	73	i	i	PRON
app01-3959	46	74	figure	figure	VERB
app01-3959	46	75	1	1	NUM
app01-3959	46	76	.	.	PUNCT
app01-3959	46	77	scheme	scheme	NOUN
app01-3959	46	78	of	of	ADP
app01-3959	46	79	decomposition	decomposition	NOUN
app01-3959	46	80	ηijk	ηijk	NOUN
app01-3959	46	81	=	=	SYM
app01-3959	46	82	ηs	ηs	PROPN
app01-3959	46	83	ijk	ijk	PROPN
app01-3959	46	84	+	+	CCONJ
app01-3959	46	85	ηr	ηr	PROPN
app01-3959	46	86	ijk	ijk	PROPN
app01-3959	46	87	,	,	PUNCT
app01-3959	46	88	ηs	ηs	PROPN
app01-3959	46	89	ijk	ijk	PROPN
app01-3959	47	1	=	=	NOUN
app01-3959	47	2	1	1	NUM
app01-3959	47	3	3	3	NUM
app01-3959	47	4	(	(	PUNCT
app01-3959	47	5	uk	uk	PROPN
app01-3959	47	6	,	,	PUNCT
app01-3959	47	7	ij	ij	NOUN
app01-3959	47	8	+	+	CCONJ
app01-3959	47	9	ui	ui	PROPN
app01-3959	47	10	,	,	PUNCT
app01-3959	47	11	jk	jk	PROPN
app01-3959	48	1	+	+	CCONJ
app01-3959	48	2	uj	uj	PROPN
app01-3959	48	3	,	,	PUNCT
app01-3959	48	4	ki	ki	PROPN
app01-3959	48	5	)	)	PUNCT
app01-3959	48	6	,	,	PUNCT
app01-3959	48	7	ηr	ηr	PROPN
app01-3959	48	8	ijk	ijk	X
app01-3959	48	9	=	=	PROPN
app01-3959	48	10	2	2	NUM
app01-3959	48	11	3	3	NUM
app01-3959	48	12	(	(	PUNCT
app01-3959	48	13	εikl	εikl	PROPN
app01-3959	48	14	η̄lj	η̄lj	PROPN
app01-3959	48	15	+	+	CCONJ
app01-3959	48	16	εjkl	εjkl	VERB
app01-3959	48	17	η̄li	η̄li	PROPN
app01-3959	48	18	)	)	PUNCT
app01-3959	49	1	+	+	CCONJ
app01-3959	49	2	εkjl	εkjl	VERB
app01-3959	49	3	η̄li	η̄li	PROPN
app01-3959	49	4	,	,	PUNCT
app01-3959	49	5	(	(	PUNCT
app01-3959	49	6	3	3	X
app01-3959	49	7	)	)	PUNCT
app01-3959	50	1	where	where	SCONJ
app01-3959	50	2	η̄ij	η̄ij	NOUN
app01-3959	50	3	=	=	PUNCT
app01-3959	50	4	ϕj	ϕj	PROPN
app01-3959	50	5	,	,	PUNCT
app01-3959	50	6	i	i	PRON
app01-3959	50	7	is	be	AUX
app01-3959	50	8	the	the	DET
app01-3959	50	9	gradient	gradient	NOUN
app01-3959	50	10	of	of	ADP
app01-3959	50	11	rotation	rotation	NOUN
app01-3959	50	12	,	,	PUNCT
app01-3959	50	13	which	which	PRON
app01-3959	50	14	we	we	PRON
app01-3959	50	15	decompose	decompose	VERB
app01-3959	50	16	into	into	ADP
app01-3959	50	17	its	its	PRON
app01-3959	50	18	symmetric	symmetric	ADJ
app01-3959	50	19	and	and	CCONJ
app01-3959	50	20	anti	anti	ADJ
app01-3959	50	21	-	-	ADJ
app01-3959	50	22	symmetric	symmetric	ADJ
app01-3959	50	23	parts	part	NOUN
app01-3959	50	24	,	,	PUNCT
app01-3959	50	25	χs	χs	NOUN
app01-3959	50	26	ij	ij	NOUN
app01-3959	50	27	and	and	CCONJ
app01-3959	50	28	χa	χa	ADJ
app01-3959	50	29	ij	ij	INTJ
app01-3959	50	30	,	,	PUNCT
app01-3959	50	31	respectively	respectively	ADV
app01-3959	50	32	:	:	PUNCT
app01-3959	50	33	χa	χa	NOUN
app01-3959	50	34	ij	ij	NOUN
app01-3959	50	35	=	=	NOUN
app01-3959	50	36	1	1	NUM
app01-3959	50	37	2	2	NUM
app01-3959	50	38	(	(	PUNCT
app01-3959	50	39	ϕi	ϕi	PROPN
app01-3959	50	40	,	,	PUNCT
app01-3959	50	41	j	j	PROPN
app01-3959	51	1	−	−	PROPN
app01-3959	52	1	ϕj	ϕj	PROPN
app01-3959	52	2	,	,	PUNCT
app01-3959	52	3	i	i	PROPN
app01-3959	52	4	)	)	PUNCT
app01-3959	52	5	,	,	PUNCT
app01-3959	52	6	χs	χs	X
app01-3959	52	7	ij	ij	NOUN
app01-3959	53	1	=	=	NOUN
app01-3959	54	1	1	1	NUM
app01-3959	54	2	2	2	NUM
app01-3959	54	3	(	(	PUNCT
app01-3959	54	4	ϕi	ϕi	PROPN
app01-3959	54	5	,	,	PUNCT
app01-3959	54	6	j	j	PROPN
app01-3959	54	7	+	+	CCONJ
app01-3959	54	8	ϕj	ϕj	PROPN
app01-3959	54	9	,	,	PUNCT
app01-3959	54	10	i	i	PROPN
app01-3959	54	11	)	)	PUNCT
app01-3959	54	12	.	.	PUNCT
app01-3959	55	1	(	(	PUNCT
app01-3959	55	2	4	4	X
app01-3959	55	3	)	)	PUNCT
app01-3959	55	4	the	the	DET
app01-3959	55	5	tensor	tensor	NOUN
app01-3959	55	6	ηs	ηs	PROPN
app01-3959	55	7	ijk	ijk	PROPN
app01-3959	55	8	is	be	AUX
app01-3959	55	9	further	far	ADV
app01-3959	55	10	decomposed	decompose	VERB
app01-3959	55	11	into	into	ADP
app01-3959	55	12	its	its	PRON
app01-3959	55	13	spherical	spherical	ADJ
app01-3959	55	14	and	and	CCONJ
app01-3959	55	15	deviatoric	deviatoric	ADJ
app01-3959	55	16	part	part	NOUN
app01-3959	55	17	,	,	PUNCT
app01-3959	55	18	η(0	η(0	PROPN
app01-3959	55	19	)	)	PUNCT
app01-3959	55	20	ijk	ijk	PROPN
app01-3959	55	21	and	and	CCONJ
app01-3959	55	22	η(1	η(1	PROPN
app01-3959	55	23	)	)	PUNCT
app01-3959	55	24	ijk	ijk	PROPN
app01-3959	55	25	,	,	PUNCT
app01-3959	55	26	cf	cf	NOUN
app01-3959	55	27	.	.	PUNCT
app01-3959	55	28	,	,	PUNCT
app01-3959	55	29	fig	fig	NOUN
app01-3959	55	30	.	.	PUNCT
app01-3959	56	1	1	1	NUM
app01-3959	56	2	.	.	PUNCT
app01-3959	57	1	the	the	DET
app01-3959	57	2	quantity	quantity	NOUN
app01-3959	57	3	η(0	η(0	PROPN
app01-3959	57	4	)	)	PUNCT
app01-3959	57	5	ijk	ijk	PROPN
app01-3959	57	6	is	be	AUX
app01-3959	57	7	related	relate	VERB
app01-3959	57	8	to	to	ADP
app01-3959	57	9	χa	χa	PROPN
app01-3959	58	1	ij	ij	INTJ
app01-3959	58	2	and	and	CCONJ
app01-3959	58	3	the	the	DET
app01-3959	58	4	dilatation	dilatation	NOUN
app01-3959	58	5	gradient	gradient	NOUN
app01-3959	58	6	εmm	εmm	PROPN
app01-3959	58	7	,	,	PUNCT
app01-3959	58	8	i	i	PRON
app01-3959	58	9	in	in	ADP
app01-3959	58	10	the	the	DET
app01-3959	58	11	following	following	ADJ
app01-3959	58	12	manner	manner	NOUN
app01-3959	58	13	:	:	PUNCT
app01-3959	58	14	η	η	PROPN
app01-3959	58	15	(	(	PUNCT
app01-3959	58	16	0	0	NUM
app01-3959	58	17	)	)	PUNCT
app01-3959	58	18	ijk	ijk	NOUN
app01-3959	58	19	=	=	NOUN
app01-3959	58	20	1	1	NUM
app01-3959	58	21	5	5	NUM
app01-3959	58	22	(	(	PUNCT
app01-3959	58	23	δij	δij	NOUN
app01-3959	58	24	η	η	PROPN
app01-3959	58	25	s	s	PART
app01-3959	58	26	mmk	mmk	NOUN
app01-3959	58	27	+	+	CCONJ
app01-3959	58	28	δjk	δjk	PROPN
app01-3959	58	29	η	η	PROPN
app01-3959	58	30	s	s	PROPN
app01-3959	58	31	mmi	mmi	NOUN
app01-3959	58	32	+	+	CCONJ
app01-3959	58	33	δki	δki	PROPN
app01-3959	58	34	η	η	PROPN
app01-3959	58	35	s	s	PROPN
app01-3959	58	36	mmj	mmj	NOUN
app01-3959	58	37	)	)	PUNCT
app01-3959	58	38	ηs	ηs	ADP
app01-3959	58	39	mmi	mmi	PROPN
app01-3959	59	1	=	=	SYM
app01-3959	59	2	εmm	εmm	PROPN
app01-3959	59	3	,	,	PUNCT
app01-3959	59	4	i	i	PRON
app01-3959	59	5	+	+	X
app01-3959	59	6	2	2	NUM
app01-3959	59	7	3εilnχ	3εilnχ	NUM
app01-3959	59	8	a	a	DET
app01-3959	59	9	ln	ln	NOUN
app01-3959	59	10	,	,	PUNCT
app01-3959	59	11	η	η	PROPN
app01-3959	59	12	(	(	PUNCT
app01-3959	59	13	1	1	NUM
app01-3959	59	14	)	)	PUNCT
app01-3959	59	15	ijk	ijk	NOUN
app01-3959	59	16	=	=	PUNCT
app01-3959	59	17	ηs	ηs	PROPN
app01-3959	59	18	ijk	ijk	PROPN
app01-3959	59	19	−	−	PROPN
app01-3959	59	20	η	η	PROPN
app01-3959	59	21	(	(	PUNCT
app01-3959	59	22	0	0	NUM
app01-3959	59	23	)	)	PUNCT
app01-3959	59	24	ijk	ijk	NOUN
app01-3959	59	25	.	.	PUNCT
app01-3959	60	1	(	(	PUNCT
app01-3959	60	2	5	5	NUM
app01-3959	60	3	)	)	PUNCT
app01-3959	60	4	as	as	SCONJ
app01-3959	60	5	shown	show	VERB
app01-3959	60	6	in	in	ADP
app01-3959	60	7	[	[	X
app01-3959	60	8	13	13	NUM
app01-3959	60	9	,	,	PUNCT
app01-3959	60	10	14	14	NUM
app01-3959	60	11	]	]	PUNCT
app01-3959	60	12	χa	χa	NOUN
app01-3959	60	13	ij	ij	NOUN
app01-3959	60	14	does	do	AUX
app01-3959	60	15	not	not	PART
app01-3959	60	16	influence	influence	VERB
app01-3959	60	17	the	the	DET
app01-3959	60	18	strain	strain	NOUN
app01-3959	60	19	energy	energy	NOUN
app01-3959	60	20	if	if	SCONJ
app01-3959	60	21	symmetry	symmetry	NOUN
app01-3959	60	22	of	of	ADP
app01-3959	60	23	the	the	DET
app01-3959	60	24	couple	couple	NOUN
app01-3959	60	25	stress	stress	NOUN
app01-3959	60	26	tensor	tensor	NOUN
app01-3959	60	27	µij	µij	ADV
app01-3959	60	28	is	be	AUX
app01-3959	60	29	assumed	assume	VERB
app01-3959	60	30	.	.	PUNCT
app01-3959	61	1	as	as	ADP
app01-3959	61	2	a	a	DET
app01-3959	61	3	consequence	consequence	NOUN
app01-3959	61	4	the	the	DET
app01-3959	61	5	linear	linear	ADJ
app01-3959	61	6	isotropic	isotropic	NOUN
app01-3959	61	7	strain	strain	NOUN
app01-3959	61	8	energy	energy	NOUN
app01-3959	61	9	density	density	NOUN
app01-3959	61	10	for	for	ADP
app01-3959	61	11	non	non	ADJ
app01-3959	61	12	-	-	ADJ
app01-3959	61	13	simple	simple	ADJ
app01-3959	61	14	materials	material	NOUN
app01-3959	61	15	of	of	ADP
app01-3959	61	16	gradient	gradient	ADJ
app01-3959	61	17	type	type	NOUN
app01-3959	61	18	reads	read	NOUN
app01-3959	61	19	:	:	PUNCT
app01-3959	61	20	umsg	umsg	NOUN
app01-3959	61	21	=	=	SYM
app01-3959	61	22	2gεij	2gεij	NUM
app01-3959	61	23	εij	εij	NOUN
app01-3959	61	24	+	+	CCONJ
app01-3959	61	25	λεkk	λεkk	NOUN
app01-3959	61	26	εii	εii	NOUN
app01-3959	61	27	+	+	CCONJ
app01-3959	61	28	2g`2	2g`2	NOUN
app01-3959	61	29	0εmm	0εmm	NOUN
app01-3959	61	30	,	,	PUNCT
app01-3959	61	31	i	i	PRON
app01-3959	61	32	εkk	εkk	VERB
app01-3959	61	33	,	,	PUNCT
app01-3959	61	34	i	i	PRON
app01-3959	61	35	+	+	X
app01-3959	61	36	+	+	CCONJ
app01-3959	61	37	2g`2	2g`2	NOUN
app01-3959	61	38	1η	1η	NOUN
app01-3959	61	39	(	(	PUNCT
app01-3959	61	40	1	1	X
app01-3959	61	41	)	)	PUNCT
app01-3959	61	42	ijk	ijk	PROPN
app01-3959	61	43	η	η	PROPN
app01-3959	61	44	(	(	PUNCT
app01-3959	61	45	1	1	NUM
app01-3959	61	46	)	)	PUNCT
app01-3959	61	47	ijk	ijk	NOUN
app01-3959	61	48	+	+	CCONJ
app01-3959	61	49	2g`2	2g`2	NOUN
app01-3959	61	50	2χ	2χ	NOUN
app01-3959	61	51	s	s	VERB
app01-3959	61	52	ijχ	ijχ	NOUN
app01-3959	61	53	s	s	X
app01-3959	61	54	ij	ij	NOUN
app01-3959	61	55	,	,	PUNCT
app01-3959	61	56	(	(	PUNCT
app01-3959	61	57	6	6	NUM
app01-3959	61	58	)	)	PUNCT
app01-3959	61	59	where	where	SCONJ
app01-3959	61	60	λ	λ	PROPN
app01-3959	61	61	and	and	CCONJ
app01-3959	61	62	g	g	PROPN
app01-3959	61	63	are	be	AUX
app01-3959	61	64	lamé	lamé	NOUN
app01-3959	61	65	’s	’s	PART
app01-3959	61	66	constants	constant	NOUN
app01-3959	61	67	,	,	PUNCT
app01-3959	61	68	whereas	whereas	SCONJ
app01-3959	61	69	`	`	PUNCT
app01-3959	61	70	0	0	NUM
app01-3959	61	71	,	,	PUNCT
app01-3959	61	72	`	`	PUNCT
app01-3959	61	73	1	1	NUM
app01-3959	61	74	and	and	CCONJ
app01-3959	61	75	`	`	PUNCT
app01-3959	61	76	2	2	NUM
app01-3959	61	77	denote	denote	VERB
app01-3959	61	78	additional	additional	ADJ
app01-3959	61	79	material	material	NOUN
app01-3959	61	80	length	length	NOUN
app01-3959	61	81	scale	scale	NOUN
app01-3959	61	82	parameters	parameter	NOUN
app01-3959	61	83	.	.	PUNCT
app01-3959	62	1	these	these	DET
app01-3959	62	2	parameters	parameter	NOUN
app01-3959	62	3	are	be	AUX
app01-3959	62	4	chosen	choose	VERB
app01-3959	62	5	to	to	PART
app01-3959	62	6	be	be	AUX
app01-3959	62	7	of	of	ADP
app01-3959	62	8	the	the	DET
app01-3959	62	9	dimension	dimension	NOUN
app01-3959	62	10	of	of	ADP
app01-3959	62	11	a	a	DET
app01-3959	62	12	length	length	NOUN
app01-3959	62	13	and	and	CCONJ
app01-3959	62	14	squared	square	VERB
app01-3959	62	15	in	in	ADP
app01-3959	62	16	order	order	NOUN
app01-3959	62	17	to	to	PART
app01-3959	62	18	guarantee	guarantee	VERB
app01-3959	62	19	a	a	DET
app01-3959	62	20	positive	positive	ADJ
app01-3959	62	21	definite	definite	ADJ
app01-3959	62	22	problem	problem	NOUN
app01-3959	62	23	in	in	ADP
app01-3959	62	24	the	the	DET
app01-3959	62	25	energy	energy	NOUN
app01-3959	62	26	minimization	minimization	NOUN
app01-3959	62	27	.	.	PUNCT
app01-3959	63	1	the	the	DET
app01-3959	63	2	normalization	normalization	NOUN
app01-3959	63	3	of	of	ADP
app01-3959	63	4	the	the	DET
app01-3959	63	5	higher	high	ADJ
app01-3959	63	6	-	-	PUNCT
app01-3959	63	7	order	order	NOUN
app01-3959	63	8	terms	term	NOUN
app01-3959	63	9	by	by	ADP
app01-3959	63	10	g	g	PROPN
app01-3959	63	11	is	be	AUX
app01-3959	63	12	arbitrary	arbitrary	ADJ
app01-3959	63	13	.	.	PUNCT
app01-3959	64	1	2.2	2.2	NUM
app01-3959	64	2	.	.	PUNCT
app01-3959	65	1	governing	govern	VERB
app01-3959	65	2	euler	euler	PROPN
app01-3959	65	3	-	-	PUNCT
app01-3959	65	4	bernoulli	bernoulli	PROPN
app01-3959	65	5	differential	differential	NOUN
app01-3959	65	6	equation	equation	NOUN
app01-3959	65	7	by	by	ADP
app01-3959	65	8	using	use	VERB
app01-3959	65	9	the	the	DET
app01-3959	65	10	displacement	displacement	ADJ
app01-3959	65	11	field	field	NOUN
app01-3959	65	12	of	of	ADP
app01-3959	65	13	an	an	DET
app01-3959	65	14	eulerbernoulli	eulerbernoulli	NOUN
app01-3959	65	15	beam	beam	NOUN
app01-3959	65	16	of	of	ADP
app01-3959	65	17	length	length	NOUN
app01-3959	65	18	l	l	PROPN
app01-3959	65	19	,	,	PUNCT
app01-3959	65	20	thickness	thickness	PROPN
app01-3959	65	21	t	t	PROPN
app01-3959	65	22	,	,	PUNCT
app01-3959	65	23	crosssection	crosssection	NOUN
app01-3959	65	24	a	a	PRON
app01-3959	65	25	,	,	PUNCT
app01-3959	65	26	young	young	ADJ
app01-3959	65	27	’s	’s	PART
app01-3959	65	28	modulus	modulus	ADJ
app01-3959	65	29	e	e	NOUN
app01-3959	65	30	,	,	PUNCT
app01-3959	65	31	and	and	CCONJ
app01-3959	65	32	second	second	ADJ
app01-3959	65	33	moment	moment	NOUN
app01-3959	65	34	of	of	ADP
app01-3959	65	35	inertia	inertia	NOUN
app01-3959	65	36	i	i	PRON
app01-3959	65	37	cf	cf	VERB
app01-3959	65	38	.	.	PUNCT
app01-3959	65	39	,	,	PUNCT
app01-3959	65	40	fig	fig	NOUN
app01-3959	65	41	.	.	PUNCT
app01-3959	66	1	2	2	NUM
app01-3959	66	2	,	,	PUNCT
app01-3959	66	3	ux	ux	NOUN
app01-3959	66	4	=	=	SYM
app01-3959	66	5	−zdw(x	−zdw(x	PROPN
app01-3959	66	6	)	)	PUNCT
app01-3959	66	7	dx	dx	PROPN
app01-3959	66	8	,	,	PUNCT
app01-3959	66	9	uy	uy	NOUN
app01-3959	66	10	=	=	SYM
app01-3959	66	11	0	0	PROPN
app01-3959	66	12	,	,	PUNCT
app01-3959	66	13	uz	uz	PROPN
app01-3959	66	14	=	=	SYM
app01-3959	66	15	w(x	w(x	PROPN
app01-3959	66	16	)	)	PUNCT
app01-3959	66	17	,	,	PUNCT
app01-3959	66	18	(	(	PUNCT
app01-3959	66	19	7	7	X
app01-3959	66	20	)	)	PUNCT
app01-3959	66	21	l	l	NOUN
app01-3959	66	22	,	,	PUNCT
app01-3959	66	23	ei	ei	PROPN
app01-3959	66	24	,	,	PUNCT
app01-3959	66	25	a	a	DET
app01-3959	66	26	w(x	w(x	NOUN
app01-3959	66	27	)	)	PUNCT
app01-3959	66	28	dw(x	dw(x	NUM
app01-3959	66	29	)	)	PUNCT
app01-3959	67	1	dx	dx	PROPN
app01-3959	68	1	f	f	PROPN
app01-3959	68	2	xy	xy	PROPN
app01-3959	68	3	z	z	NOUN
app01-3959	68	4	figure	figure	NOUN
app01-3959	68	5	2	2	NUM
app01-3959	68	6	.	.	PUNCT
app01-3959	69	1	bending	bend	VERB
app01-3959	69	2	line	line	NOUN
app01-3959	69	3	of	of	ADP
app01-3959	69	4	a	a	DET
app01-3959	69	5	cantilever	cantilever	NOUN
app01-3959	69	6	where	where	SCONJ
app01-3959	69	7	w(x	w(x	NOUN
app01-3959	69	8	)	)	PUNCT
app01-3959	69	9	characterizes	characterize	VERB
app01-3959	69	10	the	the	DET
app01-3959	69	11	bending	bend	VERB
app01-3959	69	12	line	line	NOUN
app01-3959	69	13	and	and	CCONJ
app01-3959	69	14	f	f	PROPN
app01-3959	69	15	denotes	denote	VERB
app01-3959	69	16	the	the	DET
app01-3959	69	17	force	force	NOUN
app01-3959	69	18	at	at	ADP
app01-3959	69	19	the	the	DET
app01-3959	69	20	free	free	ADJ
app01-3959	69	21	end	end	NOUN
app01-3959	69	22	,	,	PUNCT
app01-3959	69	23	eqs	eqs	PROPN
app01-3959	69	24	.	.	PUNCT
app01-3959	70	1	(	(	PUNCT
app01-3959	70	2	3)–(6	3)–(6	X
app01-3959	70	3	)	)	PUNCT
app01-3959	70	4	lead	lead	NOUN
app01-3959	70	5	to	to	ADP
app01-3959	70	6	the	the	DET
app01-3959	70	7	strain	strain	ADJ
app01-3959	70	8	energy	energy	NOUN
app01-3959	70	9	density	density	NOUN
app01-3959	70	10	of	of	ADP
app01-3959	70	11	the	the	DET
app01-3959	70	12	body	body	NOUN
app01-3959	70	13	.	.	PUNCT
app01-3959	71	1	by	by	ADP
app01-3959	71	2	applying	apply	VERB
app01-3959	71	3	the	the	DET
app01-3959	71	4	principle	principle	NOUN
app01-3959	71	5	of	of	ADP
app01-3959	71	6	virtual	virtual	ADJ
app01-3959	71	7	work	work	NOUN
app01-3959	71	8	to	to	ADP
app01-3959	71	9	the	the	DET
app01-3959	71	10	variation	variation	NOUN
app01-3959	71	11	of	of	ADP
app01-3959	71	12	the	the	DET
app01-3959	71	13	function	function	NOUN
app01-3959	71	14	w(x	w(x	PROPN
app01-3959	71	15	)	)	PUNCT
app01-3959	71	16	,	,	PUNCT
app01-3959	71	17	a	a	DET
app01-3959	71	18	triple	triple	ADJ
app01-3959	71	19	integration	integration	NOUN
app01-3959	71	20	by	by	ADP
app01-3959	71	21	parts	part	NOUN
app01-3959	71	22	leads	lead	VERB
app01-3959	71	23	to	to	ADP
app01-3959	71	24	the	the	DET
app01-3959	71	25	ordinary	ordinary	ADJ
app01-3959	71	26	differential	differential	ADJ
app01-3959	71	27	equation	equation	NOUN
app01-3959	71	28	(	(	PUNCT
app01-3959	71	29	ode	ode	PROPN
app01-3959	71	30	)	)	PUNCT
app01-3959	71	31	of	of	ADP
app01-3959	71	32	the	the	DET
app01-3959	71	33	problem	problem	NOUN
app01-3959	71	34	[	[	X
app01-3959	71	35	15	15	NUM
app01-3959	71	36	]	]	X
app01-3959	71	37	:	:	PUNCT
app01-3959	71	38	s	s	AUX
app01-3959	71	39	d4w	d4w	PROPN
app01-3959	71	40	dx4	dx4	VERB
app01-3959	71	41	−k	−k	PROPN
app01-3959	71	42	d6w	d6w	PROPN
app01-3959	71	43	dx6	dx6	VERB
app01-3959	71	44	=	=	SYM
app01-3959	71	45	0	0	NUM
app01-3959	71	46	,	,	PUNCT
app01-3959	71	47	∀	∀	X
app01-3959	71	48	x	x	SYM
app01-3959	71	49	∈	∈	PROPN
app01-3959	72	1	[	[	X
app01-3959	72	2	0	0	NUM
app01-3959	72	3	,	,	PUNCT
app01-3959	72	4	l	l	NOUN
app01-3959	72	5	]	]	PUNCT
app01-3959	72	6	.	.	PUNCT
app01-3959	73	1	(	(	PUNCT
app01-3959	73	2	8)	8)	NUM
app01-3959	73	3	the	the	DET
app01-3959	73	4	resulting	result	VERB
app01-3959	73	5	ode	ode	NOUN
app01-3959	73	6	is	be	AUX
app01-3959	73	7	of	of	ADP
app01-3959	73	8	rank	rank	NOUN
app01-3959	73	9	six	six	NUM
app01-3959	73	10	,	,	PUNCT
app01-3959	73	11	where	where	SCONJ
app01-3959	73	12	s	s	NOUN
app01-3959	73	13	=	=	SYM
app01-3959	73	14	ei(1	ei(1	PROPN
app01-3959	73	15	+	+	CCONJ
app01-3959	73	16	4308	4308	NUM
app01-3959	73	17	225	225	NUM
app01-3959	73	18	`	`	PUNCT
app01-3959	73	19	2	2	NUM
app01-3959	73	20	t2	t2	NOUN
app01-3959	73	21	)	)	PUNCT
app01-3959	73	22	and	and	CCONJ
app01-3959	73	23	k	k	X
app01-3959	73	24	=	=	SYM
app01-3959	73	25	7	7	NUM
app01-3959	73	26	5ei	5ei	ADJ
app01-3959	73	27	`	`	PUNCT
app01-3959	73	28	2	2	NUM
app01-3959	73	29	(	(	PUNCT
app01-3959	73	30	9	9	NUM
app01-3959	73	31	)	)	PUNCT
app01-3959	73	32	are	be	AUX
app01-3959	73	33	given	give	VERB
app01-3959	73	34	constants	constant	NOUN
app01-3959	73	35	,	,	PUNCT
app01-3959	73	36	if	if	SCONJ
app01-3959	73	37	a	a	DET
app01-3959	73	38	rectangular	rectangular	ADJ
app01-3959	73	39	cross	cross	NOUN
app01-3959	73	40	-	-	NOUN
app01-3959	73	41	section	section	NOUN
app01-3959	73	42	and	and	CCONJ
app01-3959	73	43	`	`	PUNCT
app01-3959	73	44	0	0	X
app01-3959	73	45	=	=	SYM
app01-3959	73	46	`	`	PUNCT
app01-3959	73	47	1	1	X
app01-3959	73	48	=	=	SYM
app01-3959	73	49	`	`	PUNCT
app01-3959	73	50	2	2	X
app01-3959	73	51	=	=	PUNCT
app01-3959	73	52	`	`	PUNCT
app01-3959	73	53	is	be	AUX
app01-3959	73	54	assumed	assume	VERB
app01-3959	73	55	.	.	PUNCT
app01-3959	74	1	3	3	X
app01-3959	74	2	.	.	X
app01-3959	74	3	finite	finite	PROPN
app01-3959	74	4	element	element	PROPN
app01-3959	74	5	implementation	implementation	NOUN
app01-3959	74	6	3.1	3.1	NUM
app01-3959	74	7	.	.	PUNCT
app01-3959	74	8	weak	weak	ADJ
app01-3959	74	9	form	form	NOUN
app01-3959	74	10	and	and	CCONJ
app01-3959	74	11	discretization	discretization	VERB
app01-3959	74	12	a	a	DET
app01-3959	74	13	multiplication	multiplication	NOUN
app01-3959	74	14	of	of	ADP
app01-3959	74	15	eq	eq	NOUN
app01-3959	74	16	.	.	PUNCT
app01-3959	75	1	(	(	PUNCT
app01-3959	75	2	8)	8)	NUM
app01-3959	75	3	with	with	ADP
app01-3959	75	4	a	a	DET
app01-3959	75	5	test	test	NOUN
app01-3959	75	6	function	function	NOUN
app01-3959	75	7	v(x	v(x	PROPN
app01-3959	75	8	)	)	PUNCT
app01-3959	75	9	and	and	CCONJ
app01-3959	75	10	triple	triple	ADJ
app01-3959	75	11	integration	integration	NOUN
app01-3959	75	12	by	by	ADP
app01-3959	75	13	parts	part	NOUN
app01-3959	75	14	yields	yield	NOUN
app01-3959	75	15	in	in	ADP
app01-3959	75	16	the	the	DET
app01-3959	75	17	following	follow	VERB
app01-3959	75	18	weak	weak	ADJ
app01-3959	75	19	integral	integral	ADJ
app01-3959	75	20	form	form	NOUN
app01-3959	75	21	of	of	ADP
app01-3959	75	22	the	the	DET
app01-3959	75	23	ode	ode	PROPN
app01-3959	75	24	:	:	PUNCT
app01-3959	75	25	l∫	l∫	ADJ
app01-3959	75	26	0	0	NUM
app01-3959	75	27	(	(	PUNCT
app01-3959	75	28	s	s	PROPN
app01-3959	75	29	d2w	d2w	PROPN
app01-3959	75	30	dx2	dx2	PROPN
app01-3959	75	31	d2v	d2v	PROPN
app01-3959	75	32	dx2	dx2	PROPN
app01-3959	75	33	+	+	PROPN
app01-3959	75	34	k	k	PROPN
app01-3959	75	35	d3w	d3w	PROPN
app01-3959	75	36	dx3	dx3	PROPN
app01-3959	75	37	d3v	d3v	PROPN
app01-3959	75	38	dx3	dx3	PROPN
app01-3959	75	39	)	)	PUNCT
app01-3959	75	40	dx	dx	PROPN
app01-3959	76	1	=	=	SYM
app01-3959	76	2	0	0	PROPN
app01-3959	76	3	.	.	PUNCT
app01-3959	77	1	(	(	PUNCT
app01-3959	77	2	10	10	NUM
app01-3959	77	3	)	)	PUNCT
app01-3959	77	4	now	now	ADV
app01-3959	77	5	thegalerkinmethod	thegalerkinmethod	NOUN
app01-3959	77	6	is	be	AUX
app01-3959	77	7	applied	apply	VERB
app01-3959	77	8	to	to	PART
app01-3959	77	9	discretize	discretize	VERB
app01-3959	77	10	the	the	DET
app01-3959	77	11	interval	interval	NOUN
app01-3959	77	12	[	[	X
app01-3959	77	13	0	0	NUM
app01-3959	77	14	,	,	PUNCT
app01-3959	77	15	l	l	NOUN
app01-3959	77	16	]	]	PUNCT
app01-3959	77	17	by	by	ADP
app01-3959	77	18	using	use	VERB
app01-3959	77	19	linear	linear	ADJ
app01-3959	77	20	combinations	combination	NOUN
app01-3959	77	21	of	of	ADP
app01-3959	77	22	independent	independent	ADJ
app01-3959	77	23	base	base	NOUN
app01-3959	77	24	functions	function	NOUN
app01-3959	77	25	φα	φα	X
app01-3959	77	26	for	for	ADP
app01-3959	77	27	each	each	DET
app01-3959	77	28	element	element	NOUN
app01-3959	77	29	e	e	NOUN
app01-3959	77	30	=	=	SYM
app01-3959	77	31	1	1	NUM
app01-3959	77	32	,	,	PUNCT
app01-3959	77	33	.	.	PUNCT
app01-3959	77	34	.	.	PUNCT
app01-3959	78	1	.	.	PUNCT
app01-3959	79	1	,	,	PUNCT
app01-3959	79	2	n	n	X
app01-3959	79	3	,	,	PUNCT
app01-3959	79	4	which	which	PRON
app01-3959	79	5	are	be	AUX
app01-3959	79	6	uniformly	uniformly	ADV
app01-3959	79	7	defined	define	VERB
app01-3959	79	8	on	on	ADP
app01-3959	79	9	the	the	DET
app01-3959	79	10	element	element	NOUN
app01-3959	79	11	’s	’s	PART
app01-3959	79	12	coordinate	coordinate	NOUN
app01-3959	79	13	0	0	NUM
app01-3959	79	14	≤	≤	NUM
app01-3959	79	15	ζ	ζ	NOUN
app01-3959	79	16	≤	≤	NUM
app01-3959	79	17	1	1	NUM
app01-3959	79	18	:	:	PUNCT
app01-3959	79	19	ve(ζ	ve(ζ	X
app01-3959	79	20	)	)	PUNCT
app01-3959	79	21	=	=	PUNCT
app01-3959	80	1	∞∑	∞∑	NUM
app01-3959	80	2	β=1	β=1	SYM
app01-3959	80	3	φβ	φβ	NOUN
app01-3959	80	4	,	,	PUNCT
app01-3959	80	5	we(ζ	we(ζ	X
app01-3959	80	6	)	)	PUNCT
app01-3959	80	7	=	=	PUNCT
app01-3959	81	1	∞∑	∞∑	PROPN
app01-3959	81	2	δ=1	δ=1	PROPN
app01-3959	81	3	ce	ce	PROPN
app01-3959	81	4	δφδ	δφδ	PROPN
app01-3959	81	5	.	.	PUNCT
app01-3959	82	1	(	(	PUNCT
app01-3959	82	2	11	11	NUM
app01-3959	82	3	)	)	PUNCT
app01-3959	82	4	the	the	DET
app01-3959	82	5	general	general	ADJ
app01-3959	82	6	element	element	NOUN
app01-3959	82	7	function	function	NOUN
app01-3959	82	8	of	of	ADP
app01-3959	82	9	this	this	DET
app01-3959	82	10	method	method	NOUN
app01-3959	82	11	is	be	AUX
app01-3959	82	12	derived	derive	VERB
app01-3959	82	13	by	by	ADP
app01-3959	82	14	inserting	insert	VERB
app01-3959	82	15	eq	eq	ADP
app01-3959	82	16	.	.	PUNCT
app01-3959	83	1	(	(	PUNCT
app01-3959	83	2	11	11	NUM
app01-3959	83	3	)	)	PUNCT
app01-3959	83	4	in	in	ADP
app01-3959	83	5	eq	eq	ADP
app01-3959	83	6	.	.	PUNCT
app01-3959	84	1	(	(	PUNCT
app01-3959	84	2	10	10	NUM
app01-3959	84	3	)	)	PUNCT
app01-3959	84	4	,	,	PUNCT
app01-3959	84	5	evaluated	evaluate	VERB
app01-3959	84	6	on	on	ADP
app01-3959	84	7	the	the	DET
app01-3959	84	8	domain	domain	NOUN
app01-3959	84	9	ζ	ζ	NOUN
app01-3959	84	10	:	:	PUNCT
app01-3959	85	1	1∫	1∫	NUM
app01-3959	85	2	0	0	NUM
app01-3959	86	1	∞∑	∞∑	NUM
app01-3959	86	2	δ=1	δ=1	PROPN
app01-3959	86	3	∞∑	∞∑	NUM
app01-3959	86	4	β=1	β=1	PUNCT
app01-3959	86	5	(	(	PUNCT
app01-3959	86	6	sce	sce	PROPN
app01-3959	86	7	δ	δ	PROPN
app01-3959	86	8	d2φδ	d2φδ	VERB
app01-3959	86	9	dζ2	dζ2	PROPN
app01-3959	86	10	d2φβ	d2φβ	SYM
app01-3959	86	11	dζ2	dζ2	PROPN
app01-3959	87	1	+	+	CCONJ
app01-3959	87	2	kce	kce	PROPN
app01-3959	87	3	δ	δ	PROPN
app01-3959	87	4	d3φδ	d3φδ	NOUN
app01-3959	87	5	dζ3	dζ3	VERB
app01-3959	87	6	d3φβ	d3φβ	VERB
app01-3959	87	7	dζ3	dζ3	NOUN
app01-3959	87	8	)	)	PUNCT
app01-3959	87	9	dζ	dζ	PROPN
app01-3959	87	10	=	=	PROPN
app01-3959	87	11	0	0	PROPN
app01-3959	87	12	.	.	PUNCT
app01-3959	88	1	(	(	PUNCT
app01-3959	88	2	12	12	NUM
app01-3959	88	3	)	)	PUNCT
app01-3959	88	4	34	34	NUM
app01-3959	88	5	vol	vol	NOUN
app01-3959	88	6	.	.	PUNCT
app01-3959	89	1	7/2017	7/2017	NUM
app01-3959	89	2	c1	c1	NOUN
app01-3959	89	3	-	-	PUNCT
app01-3959	89	4	continuous	continuous	ADJ
app01-3959	89	5	solutions	solution	NOUN
app01-3959	89	6	in	in	ADP
app01-3959	89	7	second	second	ADJ
app01-3959	89	8	gradient	gradient	NOUN
app01-3959	89	9	elasticity	elasticity	NOUN
app01-3959	89	10	3.2	3.2	NUM
app01-3959	89	11	.	.	PUNCT
app01-3959	90	1	hermite	hermite	ADJ
app01-3959	90	2	elements	element	NOUN
app01-3959	90	3	for	for	ADP
app01-3959	90	4	global	global	ADJ
app01-3959	90	5	c1	c1	PROPN
app01-3959	90	6	–	–	PUNCT
app01-3959	90	7	continuity	continuity	NOUN
app01-3959	90	8	in	in	ADP
app01-3959	90	9	order	order	NOUN
app01-3959	90	10	to	to	PART
app01-3959	90	11	solve	solve	VERB
app01-3959	90	12	the	the	DET
app01-3959	90	13	present	present	ADJ
app01-3959	90	14	weak	weak	ADJ
app01-3959	90	15	form	form	NOUN
app01-3959	90	16	of	of	ADP
app01-3959	90	17	the	the	DET
app01-3959	90	18	problem	problem	NOUN
app01-3959	90	19	,	,	PUNCT
app01-3959	90	20	the	the	DET
app01-3959	90	21	base	base	NOUN
app01-3959	90	22	functions	function	NOUN
app01-3959	90	23	need	need	VERB
app01-3959	90	24	to	to	PART
app01-3959	90	25	be	be	AUX
app01-3959	90	26	differentiable	differentiable	ADJ
app01-3959	90	27	three	three	NUM
app01-3959	90	28	times	time	NOUN
app01-3959	90	29	at	at	ADP
app01-3959	90	30	least	least	ADJ
app01-3959	90	31	.	.	PUNCT
app01-3959	91	1	in	in	ADP
app01-3959	91	2	order	order	NOUN
app01-3959	91	3	to	to	PART
app01-3959	91	4	guarantee	guarantee	VERB
app01-3959	91	5	that	that	SCONJ
app01-3959	91	6	information	information	NOUN
app01-3959	91	7	of	of	ADP
app01-3959	91	8	second	second	ADJ
app01-3959	91	9	gradients	gradient	NOUN
app01-3959	91	10	of	of	ADP
app01-3959	91	11	the	the	DET
app01-3959	91	12	trial	trial	NOUN
app01-3959	91	13	function	function	NOUN
app01-3959	91	14	w(x	w(x	NOUN
app01-3959	91	15	)	)	PUNCT
app01-3959	91	16	is	be	AUX
app01-3959	91	17	included	include	VERB
app01-3959	91	18	,	,	PUNCT
app01-3959	91	19	we	we	PRON
app01-3959	91	20	ask	ask	VERB
app01-3959	91	21	for	for	ADP
app01-3959	91	22	global	global	ADJ
app01-3959	91	23	continuity	continuity	NOUN
app01-3959	91	24	of	of	ADP
app01-3959	91	25	the	the	DET
app01-3959	91	26	first	first	ADJ
app01-3959	91	27	derivative	derivative	NOUN
app01-3959	91	28	of	of	ADP
app01-3959	91	29	w(x	w(x	NOUN
app01-3959	91	30	)	)	PUNCT
app01-3959	91	31	,	,	PUNCT
app01-3959	91	32	which	which	PRON
app01-3959	91	33	is	be	AUX
app01-3959	91	34	called	call	VERB
app01-3959	91	35	c1	c1	NOUN
app01-3959	91	36	–	–	PUNCT
app01-3959	91	37	continuity	continuity	NOUN
app01-3959	91	38	of	of	ADP
app01-3959	91	39	the	the	DET
app01-3959	91	40	solution	solution	NOUN
app01-3959	91	41	.	.	PUNCT
app01-3959	92	1	therefore	therefore	ADV
app01-3959	92	2	,	,	PUNCT
app01-3959	92	3	we	we	PRON
app01-3959	92	4	choose	choose	VERB
app01-3959	92	5	a	a	DET
app01-3959	92	6	linear	linear	ADJ
app01-3959	92	7	combination	combination	NOUN
app01-3959	92	8	of	of	ADP
app01-3959	92	9	four	four	NUM
app01-3959	92	10	different	different	ADJ
app01-3959	92	11	hermite	hermite	ADJ
app01-3959	92	12	polynomials	polynomial	NOUN
app01-3959	92	13	as	as	SCONJ
app01-3959	92	14	follows	follow	VERB
app01-3959	92	15	:	:	PUNCT
app01-3959	92	16	h1	h1	PROPN
app01-3959	92	17	=	=	ADJ
app01-3959	92	18	2ζ3	2ζ3	NUM
app01-3959	92	19	−	−	ADP
app01-3959	92	20	3ζ2	3ζ2	NUM
app01-3959	93	1	+	+	CCONJ
app01-3959	93	2	1	1	NUM
app01-3959	93	3	,	,	PUNCT
app01-3959	93	4	h2	h2	NOUN
app01-3959	93	5	=	=	SYM
app01-3959	93	6	ζ3	ζ3	NOUN
app01-3959	93	7	−	−	NOUN
app01-3959	93	8	2ζ2	2ζ2	NUM
app01-3959	93	9	+	+	CCONJ
app01-3959	93	10	ζ	ζ	NOUN
app01-3959	93	11	h3	h3	NOUN
app01-3959	93	12	=	=	PUNCT
app01-3959	93	13	−2ζ3	−2ζ3	PROPN
app01-3959	93	14	+	+	NUM
app01-3959	93	15	3ζ2	3ζ2	NUM
app01-3959	93	16	,	,	PUNCT
app01-3959	93	17	h4	h4	PROPN
app01-3959	93	18	=	=	SYM
app01-3959	93	19	ζ3	ζ3	NOUN
app01-3959	93	20	−	−	NOUN
app01-3959	93	21	ζ2	ζ2	NOUN
app01-3959	93	22	,	,	PUNCT
app01-3959	93	23	(	(	PUNCT
app01-3959	93	24	13	13	X
app01-3959	93	25	)	)	PUNCT
app01-3959	93	26	h1	h1	VERB
app01-3959	93	27	h2	h2	PROPN
app01-3959	93	28	h3	h3	NOUN
app01-3959	93	29	h4	h4	PROPN
app01-3959	93	30	0	0	NUM
app01-3959	93	31	≤	≤	NUM
app01-3959	93	32	ζ	ζ	NOUN
app01-3959	93	33	≤	≤	NUM
app01-3959	93	34	1	1	NUM
app01-3959	93	35	figure	figure	NOUN
app01-3959	93	36	3	3	NUM
app01-3959	93	37	.	.	NOUN
app01-3959	93	38	four	four	NUM
app01-3959	93	39	hermite	hermite	ADJ
app01-3959	93	40	polynoms	polynom	NOUN
app01-3959	93	41	per	per	ADP
app01-3959	93	42	element	element	NOUN
app01-3959	93	43	which	which	PRON
app01-3959	93	44	allow	allow	VERB
app01-3959	93	45	to	to	PART
app01-3959	93	46	influence	influence	VERB
app01-3959	93	47	the	the	DET
app01-3959	93	48	first	first	ADJ
app01-3959	93	49	derivative	derivative	NOUN
app01-3959	93	50	at	at	ADP
app01-3959	93	51	each	each	DET
app01-3959	93	52	boundary	boundary	NOUN
app01-3959	93	53	of	of	ADP
app01-3959	93	54	the	the	DET
app01-3959	93	55	element	element	NOUN
app01-3959	93	56	independently	independently	ADV
app01-3959	93	57	.	.	PUNCT
app01-3959	94	1	the	the	DET
app01-3959	94	2	unit	unit	NOUN
app01-3959	94	3	element	element	NOUN
app01-3959	94	4	now	now	ADV
app01-3959	94	5	is	be	AUX
app01-3959	94	6	a	a	DET
app01-3959	94	7	linear	linear	ADJ
app01-3959	94	8	combination	combination	NOUN
app01-3959	94	9	of	of	ADP
app01-3959	94	10	the	the	DET
app01-3959	94	11	four	four	NUM
app01-3959	94	12	hermite	hermite	ADJ
app01-3959	94	13	polynomials	polynomial	NOUN
app01-3959	94	14	:	:	PUNCT
app01-3959	94	15	ve(ζ	ve(ζ	X
app01-3959	94	16	)	)	PUNCT
app01-3959	94	17	=	=	SYM
app01-3959	94	18	4∑	4∑	NUM
app01-3959	94	19	β=1	β=1	NOUN
app01-3959	94	20	hβ	hβ	NOUN
app01-3959	94	21	,	,	PUNCT
app01-3959	94	22	we(ζ	we(ζ	X
app01-3959	94	23	)	)	PUNCT
app01-3959	95	1	=	=	SYM
app01-3959	95	2	4∑	4∑	PROPN
app01-3959	95	3	δ=1	δ=1	PROPN
app01-3959	95	4	ce	ce	PROPN
app01-3959	95	5	δhδ	δhδ	NOUN
app01-3959	95	6	(	(	PUNCT
app01-3959	95	7	14	14	NUM
app01-3959	95	8	)	)	PUNCT
app01-3959	95	9	where	where	SCONJ
app01-3959	95	10	ce	ce	PROPN
app01-3959	95	11	δ	δ	PROPN
app01-3959	95	12	are	be	AUX
app01-3959	95	13	four	four	NUM
app01-3959	95	14	constants	constant	NOUN
app01-3959	95	15	per	per	ADP
app01-3959	95	16	element	element	NOUN
app01-3959	95	17	.	.	PUNCT
app01-3959	96	1	3.3	3.3	NUM
app01-3959	96	2	.	.	PUNCT
app01-3959	96	3	structure	structure	NOUN
app01-3959	96	4	of	of	ADP
app01-3959	96	5	the	the	DET
app01-3959	96	6	element	element	NOUN
app01-3959	96	7	stiffnessand	stiffnessand	NOUN
app01-3959	96	8	system	system	NOUN
app01-3959	96	9	matrix	matrix	NOUN
app01-3959	96	10	by	by	ADP
app01-3959	96	11	using	use	VERB
app01-3959	96	12	hermite	hermite	ADJ
app01-3959	96	13	elements	element	NOUN
app01-3959	96	14	as	as	ADP
app01-3959	96	15	base	base	NOUN
app01-3959	96	16	functions	function	NOUN
app01-3959	96	17	eq	eq	ADJ
app01-3959	96	18	.	.	PUNCT
app01-3959	97	1	(	(	PUNCT
app01-3959	97	2	12	12	NUM
app01-3959	97	3	)	)	PUNCT
app01-3959	97	4	can	can	AUX
app01-3959	97	5	be	be	AUX
app01-3959	97	6	written	write	VERB
app01-3959	97	7	in	in	ADP
app01-3959	97	8	the	the	DET
app01-3959	97	9	following	following	ADJ
app01-3959	97	10	manner	manner	NOUN
app01-3959	97	11	:	:	PUNCT
app01-3959	97	12	1∫	1∫	NUM
app01-3959	97	13	0	0	NUM
app01-3959	97	14	4∑	4∑	NUM
app01-3959	97	15	δ=1	δ=1	PROPN
app01-3959	97	16	4∑	4∑	NOUN
app01-3959	97	17	β=1	β=1	PUNCT
app01-3959	97	18	(	(	PUNCT
app01-3959	97	19	sce	sce	PROPN
app01-3959	97	20	δ	δ	PROPN
app01-3959	97	21	d2hδ	d2hδ	PROPN
app01-3959	97	22	dζ2	dζ2	PROPN
app01-3959	97	23	d2hβ	d2hβ	PUNCT
app01-3959	97	24	dζ2	dζ2	PROPN
app01-3959	97	25	+	+	CCONJ
app01-3959	97	26	kce	kce	PROPN
app01-3959	97	27	δ	δ	PROPN
app01-3959	97	28	d3hδ	d3hδ	NOUN
app01-3959	97	29	dζ3	dζ3	VERB
app01-3959	97	30	d3hβ	d3hβ	VERB
app01-3959	97	31	dζ3	dζ3	NOUN
app01-3959	97	32	)	)	PUNCT
app01-3959	97	33	dζ=0	dζ=0	PROPN
app01-3959	97	34	.	.	PUNCT
app01-3959	98	1	(	(	PUNCT
app01-3959	98	2	15	15	NUM
app01-3959	98	3	)	)	PUNCT
app01-3959	98	4	the	the	DET
app01-3959	98	5	element	element	ADJ
app01-3959	98	6	stiffness	stiffness	NOUN
app01-3959	98	7	matrix	matrix	NOUN
app01-3959	98	8	ke	ke	NOUN
app01-3959	98	9	reads	read	VERB
app01-3959	98	10	:	:	PUNCT
app01-3959	98	11	ke	ke	NOUN
app01-3959	98	12	δβ	δβ	NOUN
app01-3959	98	13	=	=	PUNCT
app01-3959	99	1	1∫	1∫	NUM
app01-3959	99	2	0	0	NUM
app01-3959	100	1	(	(	PUNCT
app01-3959	100	2	s	s	X
app01-3959	100	3	d2hδ	d2hδ	NOUN
app01-3959	100	4	dζ2	dζ2	PROPN
app01-3959	100	5	d2hβ	d2hβ	PUNCT
app01-3959	100	6	dζ2	dζ2	PROPN
app01-3959	101	1	+	+	PROPN
app01-3959	101	2	k	k	PROPN
app01-3959	101	3	d3hδ	d3hδ	NOUN
app01-3959	101	4	dζ3	dζ3	VERB
app01-3959	101	5	d3hβ	d3hβ	VERB
app01-3959	101	6	dζ3	dζ3	NOUN
app01-3959	101	7	)	)	PUNCT
app01-3959	101	8	dζ	dζ	PROPN
app01-3959	101	9	=	=	SYM
app01-3959	101	10			NOUN
app01-3959	101	11	ke	ke	NOUN
app01-3959	101	12	11	11	NUM
app01-3959	101	13	ke	ke	NOUN
app01-3959	101	14	12	12	NUM
app01-3959	101	15	ke	ke	NOUN
app01-3959	101	16	13	13	NUM
app01-3959	101	17	ke	ke	NOUN
app01-3959	101	18	14	14	NUM
app01-3959	101	19	ke	ke	NOUN
app01-3959	101	20	22	22	NUM
app01-3959	101	21	ke	ke	NOUN
app01-3959	101	22	23	23	NUM
app01-3959	101	23	ke	ke	NOUN
app01-3959	101	24	24	24	NUM
app01-3959	101	25	sym	sym	NOUN
app01-3959	101	26	.	.	PUNCT
app01-3959	102	1	ke	ke	PROPN
app01-3959	102	2	33	33	NUM
app01-3959	103	1	ke	ke	NOUN
app01-3959	103	2	34	34	NUM
app01-3959	103	3	ke	ke	NOUN
app01-3959	103	4	44	44	NUM
app01-3959	103	5			NOUN
app01-3959	103	6	=	=	SYM
app01-3959	103	7	const	const	NOUN
app01-3959	103	8	.	.	PUNCT
app01-3959	104	1	(	(	PUNCT
app01-3959	104	2	16	16	NUM
app01-3959	104	3	)	)	PUNCT
app01-3959	104	4	and	and	CCONJ
app01-3959	104	5	is	be	AUX
app01-3959	104	6	a	a	DET
app01-3959	104	7	symmetric	symmetric	ADJ
app01-3959	104	8	4×	4×	NOUN
app01-3959	104	9	4	4	NUM
app01-3959	104	10	matrix	matrix	NOUN
app01-3959	104	11	with	with	ADP
app01-3959	104	12	constant	constant	ADJ
app01-3959	104	13	components	component	NOUN
app01-3959	104	14	that	that	PRON
app01-3959	104	15	depend	depend	VERB
app01-3959	104	16	on	on	ADP
app01-3959	104	17	the	the	DET
app01-3959	104	18	material	material	NOUN
app01-3959	104	19	data	datum	NOUN
app01-3959	104	20	,	,	PUNCT
app01-3959	104	21	beam	beam	NOUN
app01-3959	104	22	geometry	geometry	NOUN
app01-3959	104	23	,	,	PUNCT
app01-3959	104	24	and	and	CCONJ
app01-3959	104	25	on	on	ADP
app01-3959	104	26	the	the	DET
app01-3959	104	27	length	length	NOUN
app01-3959	104	28	of	of	ADP
app01-3959	104	29	the	the	DET
app01-3959	104	30	element	element	NOUN
app01-3959	104	31	.	.	PUNCT
app01-3959	105	1	in	in	ADP
app01-3959	105	2	this	this	DET
app01-3959	105	3	approach	approach	NOUN
app01-3959	105	4	we	we	PRON
app01-3959	105	5	choose	choose	VERB
app01-3959	105	6	equidistantly	equidistantly	ADV
app01-3959	105	7	distributed	distribute	VERB
app01-3959	105	8	elements	element	NOUN
app01-3959	105	9	.	.	PUNCT
app01-3959	106	1	by	by	ADP
app01-3959	106	2	special	special	ADJ
app01-3959	106	3	assembling	assembling	NOUN
app01-3959	106	4	of	of	ADP
app01-3959	106	5	the	the	DET
app01-3959	106	6	system	system	NOUN
app01-3959	106	7	matrix	matrix	NOUN
app01-3959	106	8	it	it	PRON
app01-3959	106	9	is	be	AUX
app01-3959	106	10	now	now	ADV
app01-3959	106	11	possible	possible	ADJ
app01-3959	106	12	to	to	PART
app01-3959	106	13	connect	connect	VERB
app01-3959	106	14	the	the	DET
app01-3959	106	15	boundary	boundary	ADJ
app01-3959	106	16	values	value	NOUN
app01-3959	106	17	of	of	ADP
app01-3959	106	18	an	an	DET
app01-3959	106	19	element	element	NOUN
app01-3959	106	20	to	to	ADP
app01-3959	106	21	its	its	PRON
app01-3959	106	22	neighbors	neighbor	NOUN
app01-3959	106	23	and	and	CCONJ
app01-3959	106	24	,	,	PUNCT
app01-3959	106	25	in	in	ADP
app01-3959	106	26	addition	addition	NOUN
app01-3959	106	27	,	,	PUNCT
app01-3959	106	28	to	to	PART
app01-3959	106	29	bring	bring	VERB
app01-3959	106	30	together	together	ADV
app01-3959	106	31	the	the	DET
app01-3959	106	32	first	first	ADJ
app01-3959	106	33	derivatives	derivative	NOUN
app01-3959	106	34	in	in	ADP
app01-3959	106	35	between	between	ADP
app01-3959	106	36	.	.	PUNCT
app01-3959	107	1	this	this	PRON
app01-3959	107	2	will	will	AUX
app01-3959	107	3	be	be	AUX
app01-3959	107	4	achieved	achieve	VERB
app01-3959	107	5	by	by	ADP
app01-3959	107	6	the	the	DET
app01-3959	107	7	following	follow	VERB
app01-3959	107	8	structure	structure	NOUN
app01-3959	107	9	of	of	ADP
app01-3959	107	10	the	the	DET
app01-3959	107	11	system	system	NOUN
app01-3959	107	12	matrix	matrix	NOUN
app01-3959	107	13	k	k	NOUN
app01-3959	107	14	:	:	PUNCT
app01-3959	107	15	k	k	X
app01-3959	107	16	=	=	SYM
app01-3959	107	17			NOUN
app01-3959	107	18	k1	k1	PROPN
app01-3959	107	19	δβ	δβ	NOUN
app01-3959	107	20	+	+	CCONJ
app01-3959	107	21	k2	k2	ADJ
app01-3959	107	22	δβ	δβ	NOUN
app01-3959	107	23	+	+	CCONJ
app01-3959	107	24	k3	k3	VERB
app01-3959	107	25	δβ	δβ	NOUN
app01-3959	107	26	+	+	CCONJ
app01-3959	108	1	k	k	PROPN
app01-3959	108	2	·	·	PUNCT
app01-3959	108	3	·	·	PUNCT
app01-3959	108	4	·	·	SYM
app01-3959	108	5	δβ	δβ	NOUN
app01-3959	109	1	+	+	CCONJ
app01-3959	109	2	kn	kn	PROPN
app01-3959	109	3	δβ	δβ	NOUN
app01-3959	109	4			PROPN
app01-3959	109	5	.	.	PUNCT
app01-3959	110	1	(	(	PUNCT
app01-3959	110	2	17	17	NUM
app01-3959	110	3	)	)	PUNCT
app01-3959	110	4	due	due	ADP
app01-3959	110	5	to	to	ADP
app01-3959	110	6	the	the	DET
app01-3959	110	7	summation	summation	NOUN
app01-3959	110	8	of	of	ADP
app01-3959	110	9	the	the	DET
app01-3959	110	10	last	last	ADJ
app01-3959	110	11	entries	entry	NOUN
app01-3959	110	12	,	,	PUNCT
app01-3959	110	13	the	the	DET
app01-3959	110	14	specific	specific	ADJ
app01-3959	110	15	components	component	NOUN
app01-3959	110	16	of	of	ADP
app01-3959	110	17	neighboring	neighboring	NOUN
app01-3959	110	18	elements	element	NOUN
app01-3959	110	19	are	be	AUX
app01-3959	110	20	treated	treat	VERB
app01-3959	110	21	as	as	ADP
app01-3959	110	22	equivalent	equivalent	ADJ
app01-3959	110	23	.	.	PUNCT
app01-3959	111	1	this	this	PRON
app01-3959	111	2	refers	refer	VERB
app01-3959	111	3	to	to	ADP
app01-3959	111	4	both	both	PRON
app01-3959	111	5	,	,	PUNCT
app01-3959	111	6	the	the	DET
app01-3959	111	7	components	component	NOUN
app01-3959	111	8	that	that	PRON
app01-3959	111	9	represent	represent	VERB
app01-3959	111	10	direct	direct	ADJ
app01-3959	111	11	node	node	ADJ
app01-3959	111	12	values	value	NOUN
app01-3959	111	13	as	as	ADV
app01-3959	111	14	well	well	ADV
app01-3959	111	15	as	as	ADP
app01-3959	111	16	to	to	ADP
app01-3959	111	17	the	the	DET
app01-3959	111	18	corresponding	corresponding	ADJ
app01-3959	111	19	derivatives	derivative	NOUN
app01-3959	111	20	.	.	PUNCT
app01-3959	112	1	the	the	DET
app01-3959	112	2	solution	solution	NOUN
app01-3959	112	3	of	of	ADP
app01-3959	112	4	the	the	DET
app01-3959	112	5	entire	entire	ADJ
app01-3959	112	6	beam	beam	NOUN
app01-3959	112	7	bending	bending	NOUN
app01-3959	112	8	problem	problem	NOUN
app01-3959	112	9	is	be	AUX
app01-3959	112	10	now	now	ADV
app01-3959	112	11	approximated	approximate	VERB
app01-3959	112	12	by	by	ADP
app01-3959	112	13	a	a	DET
app01-3959	112	14	linear	linear	ADJ
app01-3959	112	15	system	system	NOUN
app01-3959	112	16	of	of	ADP
app01-3959	112	17	equations	equation	NOUN
app01-3959	112	18	:	:	PUNCT
app01-3959	112	19	kc	kc	PROPN
app01-3959	112	20	=	=	PUNCT
app01-3959	112	21	f	f	PROPN
app01-3959	112	22	⇒	⇒	NOUN
app01-3959	113	1	k\f	k\f	X
app01-3959	113	2	=	=	PUNCT
app01-3959	113	3	c	c	X
app01-3959	113	4	,	,	PUNCT
app01-3959	113	5	(	(	PUNCT
app01-3959	113	6	18	18	NUM
app01-3959	113	7	)	)	PUNCT
app01-3959	113	8	where	where	SCONJ
app01-3959	113	9	c	c	NOUN
app01-3959	113	10	is	be	AUX
app01-3959	113	11	the	the	DET
app01-3959	113	12	vector	vector	NOUN
app01-3959	113	13	of	of	ADP
app01-3959	113	14	element	element	ADJ
app01-3959	113	15	coefficients	coefficient	NOUN
app01-3959	113	16	and	and	CCONJ
app01-3959	113	17	f	f	PROPN
app01-3959	113	18	is	be	AUX
app01-3959	113	19	a	a	DET
app01-3959	113	20	right	right	ADJ
app01-3959	113	21	hand	hand	NOUN
app01-3959	113	22	side	side	NOUN
app01-3959	113	23	,	,	PUNCT
app01-3959	113	24	in	in	ADP
app01-3959	113	25	which	which	PRON
app01-3959	113	26	the	the	DET
app01-3959	113	27	external	external	ADJ
app01-3959	113	28	force	force	NOUN
app01-3959	113	29	f	f	PROPN
app01-3959	113	30	is	be	AUX
app01-3959	113	31	implemented	implement	VERB
app01-3959	113	32	(	(	PUNCT
app01-3959	113	33	here	here	ADV
app01-3959	113	34	,	,	PUNCT
app01-3959	113	35	situated	situate	VERB
app01-3959	113	36	at	at	ADP
app01-3959	113	37	the	the	DET
app01-3959	113	38	very	very	ADV
app01-3959	113	39	last	last	ADJ
app01-3959	113	40	node	node	NOUN
app01-3959	113	41	n	n	CCONJ
app01-3959	113	42	)	)	PUNCT
app01-3959	113	43	.	.	PUNCT
app01-3959	114	1	the	the	DET
app01-3959	114	2	system	system	NOUN
app01-3959	114	3	is	be	AUX
app01-3959	114	4	solved	solve	VERB
app01-3959	114	5	using	use	VERB
app01-3959	114	6	the	the	DET
app01-3959	114	7	”	"	PUNCT
app01-3959	114	8	backslash	backslash	NOUN
app01-3959	114	9	”	"	PUNCT
app01-3959	114	10	operator	operator	NOUN
app01-3959	114	11	of	of	ADP
app01-3959	114	12	the	the	DET
app01-3959	114	13	commercial	commercial	ADJ
app01-3959	114	14	program	program	NOUN
app01-3959	114	15	matlab	matlab	PROPN
app01-3959	114	16	(	(	PUNCT
app01-3959	114	17	lu	lu	NOUN
app01-3959	114	18	decomposition	decomposition	NOUN
app01-3959	114	19	,	,	PUNCT
app01-3959	114	20	etc	etc	X
app01-3959	114	21	.	.	X
app01-3959	114	22	)	)	PUNCT
app01-3959	114	23	.	.	PUNCT
app01-3959	115	1	4	4	X
app01-3959	115	2	.	.	X
app01-3959	115	3	numerical	numerical	ADJ
app01-3959	115	4	example	example	NOUN
app01-3959	115	5	as	as	ADP
app01-3959	115	6	an	an	DET
app01-3959	115	7	example	example	NOUN
app01-3959	115	8	we	we	PRON
app01-3959	115	9	study	study	VERB
app01-3959	115	10	bending	bending	NOUN
app01-3959	115	11	of	of	ADP
app01-3959	115	12	a	a	DET
app01-3959	115	13	cantilever	cantilever	NOUN
app01-3959	115	14	beam	beam	NOUN
app01-3959	115	15	,	,	PUNCT
app01-3959	115	16	fixed	fix	VERB
app01-3959	115	17	at	at	ADP
app01-3959	115	18	the	the	DET
app01-3959	115	19	left	left	ADJ
app01-3959	115	20	hand	hand	NOUN
app01-3959	115	21	side	side	NOUN
app01-3959	115	22	and	and	CCONJ
app01-3959	115	23	loaded	load	VERB
app01-3959	115	24	with	with	ADP
app01-3959	115	25	a	a	DET
app01-3959	115	26	single	single	ADJ
app01-3959	115	27	force	force	NOUN
app01-3959	115	28	at	at	ADP
app01-3959	115	29	the	the	DET
app01-3959	115	30	free	free	ADJ
app01-3959	115	31	end	end	NOUN
app01-3959	115	32	,	,	PUNCT
app01-3959	115	33	as	as	SCONJ
app01-3959	115	34	presented	present	VERB
app01-3959	115	35	in	in	ADP
app01-3959	115	36	fig	fig	NOUN
app01-3959	115	37	.	.	PUNCT
app01-3959	116	1	2	2	NUM
app01-3959	116	2	.	.	PUNCT
app01-3959	117	1	material	material	NOUN
app01-3959	117	2	and	and	CCONJ
app01-3959	117	3	geometry	geometry	NOUN
app01-3959	117	4	data	datum	NOUN
app01-3959	117	5	is	be	AUX
app01-3959	117	6	given	give	VERB
app01-3959	117	7	in	in	ADP
app01-3959	117	8	tab	tab	NOUN
app01-3959	117	9	.	.	PUNCT
app01-3959	118	1	1	1	NUM
app01-3959	118	2	.	.	PUNCT
app01-3959	119	1	the	the	DET
app01-3959	119	2	material	material	NOUN
app01-3959	119	3	length	length	NOUN
app01-3959	119	4	scale	scale	NOUN
app01-3959	119	5	parameter	parameter	NOUN
app01-3959	119	6	`	`	PUNCT
app01-3959	119	7	is	be	AUX
app01-3959	119	8	chosen	choose	VERB
app01-3959	119	9	according	accord	VERB
app01-3959	119	10	to	to	ADP
app01-3959	119	11	a	a	DET
app01-3959	119	12	literature	literature	NOUN
app01-3959	119	13	value	value	NOUN
app01-3959	119	14	[	[	X
app01-3959	119	15	3	3	NUM
app01-3959	119	16	]	]	PUNCT
app01-3959	119	17	and	and	CCONJ
app01-3959	119	18	to	to	ADP
app01-3959	119	19	measurements	measurement	NOUN
app01-3959	119	20	performed	perform	VERB
app01-3959	119	21	by	by	ADP
app01-3959	119	22	the	the	DET
app01-3959	119	23	authors	author	NOUN
app01-3959	119	24	with	with	ADP
app01-3959	119	25	an	an	DET
app01-3959	119	26	atomic	atomic	ADJ
app01-3959	119	27	force	force	NOUN
app01-3959	119	28	microscope	microscope	NOUN
app01-3959	120	1	[	[	X
app01-3959	120	2	16	16	NUM
app01-3959	120	3	,	,	PUNCT
app01-3959	120	4	17	17	NUM
app01-3959	120	5	]	]	PUNCT
app01-3959	120	6	.	.	PUNCT
app01-3959	121	1	t	t	PROPN
app01-3959	121	2	w	w	PROPN
app01-3959	121	3	l	l	PROPN
app01-3959	121	4	e	e	X
app01-3959	121	5	`	`	PUNCT
app01-3959	121	6	0	0	X
app01-3959	121	7	=	=	PUNCT
app01-3959	121	8	`	`	PUNCT
app01-3959	121	9	1	1	X
app01-3959	121	10	=	=	SYM
app01-3959	121	11	`	`	PUNCT
app01-3959	121	12	2	2	NUM
app01-3959	121	13	f	f	NOUN
app01-3959	121	14	100	100	NUM
app01-3959	121	15	µm	µm	PART
app01-3959	121	16	2	2	NUM
app01-3959	121	17	t	t	NOUN
app01-3959	121	18	20	20	NUM
app01-3959	121	19	t	t	NOUN
app01-3959	121	20	1.44gpa	1.44gpa	NUM
app01-3959	121	21	17.6	17.6	NUM
app01-3959	121	22	µm	µm	ADP
app01-3959	121	23	1µn	1µn	ADJ
app01-3959	121	24	table	table	NOUN
app01-3959	121	25	1	1	NUM
app01-3959	121	26	.	.	PUNCT
app01-3959	121	27	dimensions	dimension	NOUN
app01-3959	121	28	,	,	PUNCT
app01-3959	121	29	loads	load	NOUN
app01-3959	121	30	and	and	CCONJ
app01-3959	121	31	material	material	NOUN
app01-3959	121	32	parameters	parameter	NOUN
app01-3959	121	33	the	the	DET
app01-3959	121	34	boundary	boundary	ADJ
app01-3959	121	35	condition	condition	NOUN
app01-3959	121	36	for	for	ADP
app01-3959	121	37	the	the	DET
app01-3959	121	38	fixation	fixation	NOUN
app01-3959	121	39	has	have	AUX
app01-3959	121	40	been	be	AUX
app01-3959	121	41	implemented	implement	VERB
app01-3959	121	42	by	by	ADP
app01-3959	121	43	canceling	cancel	VERB
app01-3959	121	44	the	the	DET
app01-3959	121	45	first	first	ADJ
app01-3959	121	46	and	and	CCONJ
app01-3959	121	47	second	second	ADJ
app01-3959	121	48	row	row	NOUN
app01-3959	121	49	and	and	CCONJ
app01-3959	121	50	column	column	NOUN
app01-3959	121	51	of	of	ADP
app01-3959	121	52	the	the	DET
app01-3959	121	53	system	system	NOUN
app01-3959	121	54	matrix	matrix	NOUN
app01-3959	121	55	eq	eq	ADP
app01-3959	121	56	.	.	PUNCT
app01-3959	122	1	(	(	PUNCT
app01-3959	122	2	17	17	NUM
app01-3959	122	3	)	)	PUNCT
app01-3959	122	4	,	,	PUNCT
app01-3959	122	5	since	since	SCONJ
app01-3959	122	6	,	,	PUNCT
app01-3959	122	7	regarding	regard	VERB
app01-3959	122	8	the	the	DET
app01-3959	122	9	first	first	ADJ
app01-3959	122	10	node	node	NOUN
app01-3959	122	11	of	of	ADP
app01-3959	122	12	the	the	DET
app01-3959	122	13	first	first	ADJ
app01-3959	122	14	element	element	NOUN
app01-3959	122	15	,	,	PUNCT
app01-3959	122	16	the	the	DET
app01-3959	122	17	current	current	ADJ
app01-3959	122	18	values	value	NOUN
app01-3959	122	19	of	of	ADP
app01-3959	122	20	deflection	deflection	NOUN
app01-3959	122	21	and	and	CCONJ
app01-3959	122	22	the	the	DET
app01-3959	122	23	derivative	derivative	NOUN
app01-3959	122	24	of	of	ADP
app01-3959	122	25	the	the	DET
app01-3959	122	26	deflection	deflection	NOUN
app01-3959	122	27	line	line	NOUN
app01-3959	122	28	are	be	AUX
app01-3959	122	29	equal	equal	ADJ
app01-3959	122	30	to	to	ADP
app01-3959	122	31	zero	zero	NUM
app01-3959	122	32	.	.	PUNCT
app01-3959	123	1	35	35	NUM
app01-3959	123	2	christian	christian	PROPN
app01-3959	123	3	liebold	liebold	PROPN
app01-3959	123	4	,	,	PUNCT
app01-3959	123	5	wolfgang	wolfgang	PROPN
app01-3959	123	6	h.	h.	PROPN
app01-3959	123	7	müller	müller	PROPN
app01-3959	123	8	acta	acta	PROPN
app01-3959	123	9	polytechnica	polytechnica	PROPN
app01-3959	123	10	ctu	ctu	NOUN
app01-3959	123	11	proceedings	proceeding	NOUN
app01-3959	124	1	er	er	INTJ
app01-3959	124	2	r	r	NOUN
app01-3959	124	3	×10−5	×10−5	PROPN
app01-3959	124	4	0	0	NUM
app01-3959	124	5	5	5	NUM
app01-3959	124	6	10	10	NUM
app01-3959	124	7	15	15	NUM
app01-3959	124	8	20	20	NUM
app01-3959	124	9	0	0	NUM
app01-3959	124	10	40	40	NUM
app01-3959	124	11	80	80	NUM
app01-3959	124	12	120	120	NUM
app01-3959	124	13	160	160	NUM
app01-3959	124	14	number	number	NOUN
app01-3959	124	15	of	of	ADP
app01-3959	124	16	elements	element	NOUN
app01-3959	124	17	n	n	PRON
app01-3959	124	18	figure	figure	VERB
app01-3959	124	19	4	4	NUM
app01-3959	124	20	.	.	PUNCT
app01-3959	124	21	convergence	convergence	VERB
app01-3959	124	22	the	the	DET
app01-3959	124	23	test	test	NOUN
app01-3959	124	24	for	for	ADP
app01-3959	124	25	convergence	convergence	NOUN
app01-3959	124	26	with	with	ADP
app01-3959	124	27	respect	respect	NOUN
app01-3959	124	28	to	to	ADP
app01-3959	124	29	higher	high	ADJ
app01-3959	124	30	numbers	number	NOUN
app01-3959	124	31	of	of	ADP
app01-3959	124	32	elements	element	NOUN
app01-3959	124	33	n	n	PRON
app01-3959	124	34	yield	yield	VERB
app01-3959	124	35	positive	positive	ADJ
app01-3959	124	36	results	result	NOUN
app01-3959	124	37	(	(	PUNCT
app01-3959	124	38	cf	cf	NOUN
app01-3959	124	39	.	.	PUNCT
app01-3959	124	40	fig	fig	NOUN
app01-3959	124	41	.	.	PUNCT
app01-3959	125	1	4	4	NUM
app01-3959	125	2	)	)	PUNCT
app01-3959	125	3	.	.	PUNCT
app01-3959	126	1	the	the	DET
app01-3959	126	2	relative	relative	ADJ
app01-3959	126	3	error	error	NOUN
app01-3959	126	4	of	of	ADP
app01-3959	126	5	tip	tip	NOUN
app01-3959	126	6	deflections	deflection	NOUN
app01-3959	126	7	err=	err=	ADP
app01-3959	126	8	wn	wn	PROPN
app01-3959	126	9	/	/	SYM
app01-3959	126	10	w1−1	w1−1	X
app01-3959	126	11	per	per	ADP
app01-3959	126	12	increase	increase	NOUN
app01-3959	126	13	of	of	ADP
app01-3959	126	14	elements	element	NOUN
app01-3959	126	15	achieves	achieve	VERB
app01-3959	126	16	values	value	NOUN
app01-3959	126	17	below	below	ADP
app01-3959	126	18	0.001h	0.001h	NOUN
app01-3959	126	19	.	.	PUNCT
app01-3959	127	1	lkmberlin	lkmberlin	PROPN
app01-3959	127	2	university	university	PROPN
app01-3959	127	3	of	of	ADP
app01-3959	127	4	technology	technology	PROPN
app01-3959	127	5	faculty	faculty	NOUN
app01-3959	127	6	v	v	NOUN
app01-3959	127	7	–	–	PUNCT
app01-3959	127	8	mechanical	mechanical	ADJ
app01-3959	127	9	engineering	engineering	NOUN
app01-3959	127	10	and	and	CCONJ
app01-3959	127	11	transport	transport	PROPN
app01-3959	127	12	systems	systems	PROPN
app01-3959	127	13	institute	institute	PROPN
app01-3959	127	14	of	of	ADP
app01-3959	127	15	mechanics	mechanic	NOUN
app01-3959	127	16	chair	chair	NOUN
app01-3959	127	17	of	of	ADP
app01-3959	127	18	continuum	continuum	ADJ
app01-3959	127	19	mechanics	mechanic	NOUN
app01-3959	127	20	and	and	CCONJ
app01-3959	127	21	materials	material	NOUN
app01-3959	127	22	theory	theory	NOUN
app01-3959	127	23	prof	prof	NOUN
app01-3959	127	24	.	.	PUNCT
app01-3959	128	1	dr	dr	PROPN
app01-3959	128	2	.	.	PROPN
app01-3959	128	3	rer	rer	PROPN
app01-3959	128	4	.	.	PUNCT
app01-3959	129	1	nat	nat	PROPN
app01-3959	129	2	.	.	PUNCT
app01-3959	130	1	w.	w.	PROPN
app01-3959	130	2	h.	h.	PROPN
app01-3959	130	3	müller	müller	PROPN
app01-3959	130	4	table	table	NOUN
app01-3959	130	5	:	:	PUNCT
app01-3959	130	6	dimensions	dimension	NOUN
app01-3959	130	7	,	,	PUNCT
app01-3959	130	8	loads	load	NOUN
app01-3959	130	9	and	and	CCONJ
app01-3959	130	10	material	material	NOUN
app01-3959	130	11	parameters	parameter	NOUN
app01-3959	130	12	𝑡	𝑡	PROPN
app01-3959	130	13	𝑊	𝑊	PROPN
app01-3959	130	14	𝐿	𝐿	NOUN
app01-3959	130	15	𝐸	𝐸	NOUN
app01-3959	131	1	ℓ0	ℓ0	NOUN
app01-3959	131	2	=	=	SYM
app01-3959	131	3	ℓ1	ℓ1	NOUN
app01-3959	131	4	=	=	SYM
app01-3959	131	5	ℓ2	ℓ2	NOUN
app01-3959	131	6	𝐹	𝐹	PROPN
app01-3959	131	7	100	100	NUM
app01-3959	131	8	µm	µm	ADP
app01-3959	131	9	2𝑡	2𝑡	NUM
app01-3959	131	10	20𝑡	20𝑡	NOUN
app01-3959	131	11	1.44	1.44	NUM
app01-3959	131	12	gpa	gpa	PROPN
app01-3959	131	13	17.6	17.6	NUM
app01-3959	131	14	µm	µm	ADP
app01-3959	131	15	1µn	1µn	ADJ
app01-3959	131	16	𝑤	𝑤	ADP
app01-3959	132	1	[	[	X
app01-3959	132	2	m	m	VERB
app01-3959	133	1	m	m	PRON
app01-3959	133	2	]	]	PUNCT
app01-3959	133	3	𝑥/𝐿	𝑥/𝐿	PROPN
app01-3959	133	4	d𝑤	d𝑤	VERB
app01-3959	133	5	d𝑥	d𝑥	PRON
app01-3959	133	6	𝑥/𝐿	𝑥/𝐿	PUNCT
app01-3959	134	1	d2𝑤	d2𝑤	ADJ
app01-3959	134	2	d𝑥2	d𝑥2	PROPN
app01-3959	135	1	𝑥/𝐿	𝑥/𝐿	NOUN
app01-3959	135	2	d3𝑤	d3𝑤	PROPN
app01-3959	135	3	d𝑥3	d𝑥3	NOUN
app01-3959	135	4	𝑥/𝐿	𝑥/𝐿	PROPN
app01-3959	136	1	dr.-ing	dr.-ing	NOUN
app01-3959	136	2	.	.	PUNCT
app01-3959	137	1	c.	c.	PROPN
app01-3959	137	2	liebold	liebold	PROPN
app01-3959	138	1	|	|	ADV
app01-3959	138	2	exnum	exnum	PROPN
app01-3959	138	3	2016	2016	NUM
app01-3959	138	4	,	,	PUNCT
app01-3959	138	5	liblice	liblice	VERB
app01-3959	138	6	|	|	ADV
app01-3959	138	7	1d	1d	NUM
app01-3959	138	8	example	example	NOUN
app01-3959	138	9	9/10	9/10	NUM
app01-3959	138	10	figure	figure	NOUN
app01-3959	138	11	5	5	NUM
app01-3959	138	12	.	.	PUNCT
app01-3959	138	13	deflection	deflection	NOUN
app01-3959	138	14	line	line	NOUN
app01-3959	138	15	the	the	DET
app01-3959	138	16	deflection	deflection	NOUN
app01-3959	138	17	line	line	NOUN
app01-3959	138	18	of	of	ADP
app01-3959	138	19	the	the	DET
app01-3959	138	20	beam	beam	NOUN
app01-3959	138	21	solution	solution	NOUN
app01-3959	138	22	is	be	AUX
app01-3959	138	23	presented	present	VERB
app01-3959	138	24	in	in	ADP
app01-3959	138	25	fig	fig	NOUN
app01-3959	138	26	.	.	PUNCT
app01-3959	139	1	5	5	NUM
app01-3959	139	2	.	.	PUNCT
app01-3959	140	1	five	five	NUM
app01-3959	140	2	elements	element	NOUN
app01-3959	140	3	are	be	AUX
app01-3959	140	4	shown	show	VERB
app01-3959	140	5	so	so	SCONJ
app01-3959	140	6	that	that	SCONJ
app01-3959	140	7	a	a	DET
app01-3959	140	8	closer	close	ADJ
app01-3959	140	9	look	look	NOUN
app01-3959	140	10	at	at	ADP
app01-3959	140	11	the	the	DET
app01-3959	140	12	solution	solution	NOUN
app01-3959	140	13	of	of	ADP
app01-3959	140	14	each	each	DET
app01-3959	140	15	element	element	NOUN
app01-3959	140	16	becomes	become	VERB
app01-3959	140	17	possible	possible	ADJ
app01-3959	140	18	,	,	PUNCT
app01-3959	140	19	which	which	PRON
app01-3959	140	20	consists	consist	VERB
app01-3959	140	21	of	of	ADP
app01-3959	140	22	reconstructed	reconstructed	ADJ
app01-3959	140	23	trial	trial	NOUN
app01-3959	140	24	functions	function	NOUN
app01-3959	140	25	,	,	PUNCT
app01-3959	140	26	cf	cf	NOUN
app01-3959	140	27	.	.	PUNCT
app01-3959	141	1	eq	eq	NOUN
app01-3959	141	2	.	.	PUNCT
app01-3959	142	1	(	(	PUNCT
app01-3959	142	2	14)2	14)2	X
app01-3959	142	3	.	.	PUNCT
app01-3959	143	1	figure	figure	VERB
app01-3959	143	2	6	6	NUM
app01-3959	143	3	presents	present	VERB
app01-3959	143	4	a	a	DET
app01-3959	143	5	plot	plot	NOUN
app01-3959	143	6	of	of	ADP
app01-3959	143	7	the	the	DET
app01-3959	143	8	first	first	ADJ
app01-3959	143	9	derivative	derivative	NOUN
app01-3959	143	10	of	of	ADP
app01-3959	143	11	the	the	DET
app01-3959	143	12	reconstructed	reconstructed	ADJ
app01-3959	143	13	trial	trial	NOUN
app01-3959	143	14	functions	function	NOUN
app01-3959	143	15	per	per	ADP
app01-3959	143	16	element	element	NOUN
app01-3959	143	17	and	and	CCONJ
app01-3959	143	18	clearly	clearly	ADV
app01-3959	143	19	demonstrates	demonstrate	VERB
app01-3959	143	20	continuity	continuity	NOUN
app01-3959	143	21	in	in	ADP
app01-3959	143	22	between	between	ADP
app01-3959	143	23	neighboring	neighboring	NOUN
app01-3959	143	24	elements	element	NOUN
app01-3959	143	25	and	and	CCONJ
app01-3959	143	26	therefore	therefore	ADV
app01-3959	143	27	c1	c1	PROPN
app01-3959	143	28	–	–	PUNCT
app01-3959	143	29	continuity	continuity	NOUN
app01-3959	143	30	.	.	PUNCT
app01-3959	144	1	lkmberlin	lkmberlin	PROPN
app01-3959	144	2	university	university	PROPN
app01-3959	144	3	of	of	ADP
app01-3959	144	4	technology	technology	PROPN
app01-3959	144	5	faculty	faculty	NOUN
app01-3959	144	6	v	v	NOUN
app01-3959	144	7	–	–	PUNCT
app01-3959	144	8	mechanical	mechanical	ADJ
app01-3959	144	9	engineering	engineering	NOUN
app01-3959	144	10	and	and	CCONJ
app01-3959	144	11	transport	transport	PROPN
app01-3959	144	12	systems	systems	PROPN
app01-3959	144	13	institute	institute	PROPN
app01-3959	144	14	of	of	ADP
app01-3959	144	15	mechanics	mechanic	NOUN
app01-3959	144	16	chair	chair	NOUN
app01-3959	144	17	of	of	ADP
app01-3959	144	18	continuum	continuum	ADJ
app01-3959	144	19	mechanics	mechanic	NOUN
app01-3959	144	20	and	and	CCONJ
app01-3959	144	21	materials	material	NOUN
app01-3959	144	22	theory	theory	NOUN
app01-3959	144	23	prof	prof	NOUN
app01-3959	144	24	.	.	PUNCT
app01-3959	145	1	dr	dr	PROPN
app01-3959	145	2	.	.	PROPN
app01-3959	145	3	rer	rer	PROPN
app01-3959	145	4	.	.	PUNCT
app01-3959	146	1	nat	nat	PROPN
app01-3959	146	2	.	.	PUNCT
app01-3959	147	1	w.	w.	PROPN
app01-3959	147	2	h.	h.	PROPN
app01-3959	147	3	müller	müller	PROPN
app01-3959	147	4	table	table	NOUN
app01-3959	147	5	:	:	PUNCT
app01-3959	147	6	dimensions	dimension	NOUN
app01-3959	147	7	,	,	PUNCT
app01-3959	147	8	loads	load	NOUN
app01-3959	147	9	and	and	CCONJ
app01-3959	147	10	material	material	NOUN
app01-3959	147	11	parameters	parameter	NOUN
app01-3959	147	12	𝑡	𝑡	PROPN
app01-3959	147	13	𝑊	𝑊	PROPN
app01-3959	147	14	𝐿	𝐿	NOUN
app01-3959	147	15	𝐸	𝐸	NOUN
app01-3959	148	1	ℓ0	ℓ0	NOUN
app01-3959	148	2	=	=	SYM
app01-3959	148	3	ℓ1	ℓ1	NOUN
app01-3959	148	4	=	=	SYM
app01-3959	148	5	ℓ2	ℓ2	NOUN
app01-3959	148	6	𝐹	𝐹	PROPN
app01-3959	148	7	100	100	NUM
app01-3959	148	8	µm	µm	ADP
app01-3959	148	9	2𝑡	2𝑡	NUM
app01-3959	148	10	20𝑡	20𝑡	NOUN
app01-3959	148	11	1.44	1.44	NUM
app01-3959	148	12	gpa	gpa	PROPN
app01-3959	148	13	17.6	17.6	NUM
app01-3959	148	14	µm	µm	ADP
app01-3959	148	15	1µn	1µn	ADJ
app01-3959	148	16	𝑤	𝑤	ADP
app01-3959	149	1	[	[	X
app01-3959	149	2	m	m	VERB
app01-3959	150	1	m	m	PRON
app01-3959	150	2	]	]	PUNCT
app01-3959	150	3	𝑥/𝐿	𝑥/𝐿	PROPN
app01-3959	150	4	d𝑤	d𝑤	VERB
app01-3959	150	5	d𝑥	d𝑥	PRON
app01-3959	150	6	𝑥/𝐿	𝑥/𝐿	PUNCT
app01-3959	151	1	d2𝑤	d2𝑤	ADJ
app01-3959	151	2	d𝑥2	d𝑥2	PROPN
app01-3959	152	1	𝑥/𝐿	𝑥/𝐿	NOUN
app01-3959	152	2	d3𝑤	d3𝑤	PROPN
app01-3959	152	3	d𝑥3	d𝑥3	NOUN
app01-3959	152	4	𝑥/𝐿	𝑥/𝐿	PROPN
app01-3959	153	1	dr.-ing	dr.-ing	NOUN
app01-3959	153	2	.	.	PUNCT
app01-3959	154	1	c.	c.	PROPN
app01-3959	154	2	liebold	liebold	PROPN
app01-3959	155	1	|	|	ADV
app01-3959	155	2	exnum	exnum	PROPN
app01-3959	155	3	2016	2016	NUM
app01-3959	155	4	,	,	PUNCT
app01-3959	155	5	liblice	liblice	VERB
app01-3959	155	6	|	|	ADV
app01-3959	155	7	1d	1d	NUM
app01-3959	155	8	example	example	NOUN
app01-3959	155	9	9/10figure	9/10figure	NUM
app01-3959	155	10	6	6	NUM
app01-3959	155	11	.	.	PUNCT
app01-3959	156	1	first	first	ADJ
app01-3959	156	2	derivative	derivative	NOUN
app01-3959	156	3	of	of	ADP
app01-3959	156	4	the	the	DET
app01-3959	156	5	solution	solution	NOUN
app01-3959	156	6	as	as	SCONJ
app01-3959	156	7	expected	expect	VERB
app01-3959	156	8	the	the	DET
app01-3959	156	9	global	global	ADJ
app01-3959	156	10	solution	solution	NOUN
app01-3959	156	11	is	be	AUX
app01-3959	156	12	not	not	PART
app01-3959	156	13	c2	c2	PROPN
app01-3959	156	14	–	–	PUNCT
app01-3959	156	15	continuous	continuous	ADJ
app01-3959	156	16	.	.	PUNCT
app01-3959	157	1	this	this	PRON
app01-3959	157	2	is	be	AUX
app01-3959	157	3	confirmed	confirm	VERB
app01-3959	157	4	by	by	ADP
app01-3959	157	5	the	the	DET
app01-3959	157	6	jumps	jump	NOUN
app01-3959	157	7	between	between	ADP
app01-3959	157	8	the	the	DET
app01-3959	157	9	elements	element	NOUN
app01-3959	157	10	in	in	ADP
app01-3959	157	11	their	their	PRON
app01-3959	157	12	second	second	ADJ
app01-3959	157	13	derivative	derivative	NOUN
app01-3959	157	14	in	in	ADP
app01-3959	157	15	fig	fig	NOUN
app01-3959	157	16	.	.	PUNCT
app01-3959	158	1	7	7	X
app01-3959	158	2	.	.	X
app01-3959	158	3	such	such	ADJ
app01-3959	158	4	jumps	jump	NOUN
app01-3959	158	5	are	be	AUX
app01-3959	158	6	also	also	ADV
app01-3959	158	7	present	present	ADJ
app01-3959	158	8	in	in	ADP
app01-3959	158	9	the	the	DET
app01-3959	158	10	third	third	ADJ
app01-3959	158	11	derivative	derivative	NOUN
app01-3959	158	12	in	in	ADP
app01-3959	158	13	fig	fig	NOUN
app01-3959	158	14	.	.	PUNCT
app01-3959	159	1	8	8	NUM
app01-3959	159	2	,	,	PUNCT
app01-3959	159	3	but	but	CCONJ
app01-3959	159	4	invisibly	invisibly	ADV
app01-3959	159	5	small	small	ADJ
app01-3959	159	6	.	.	PUNCT
app01-3959	160	1	lkmberlin	lkmberlin	PROPN
app01-3959	160	2	university	university	PROPN
app01-3959	160	3	of	of	ADP
app01-3959	160	4	technology	technology	PROPN
app01-3959	160	5	faculty	faculty	NOUN
app01-3959	160	6	v	v	NOUN
app01-3959	160	7	–	–	PUNCT
app01-3959	160	8	mechanical	mechanical	ADJ
app01-3959	160	9	engineering	engineering	NOUN
app01-3959	160	10	and	and	CCONJ
app01-3959	160	11	transport	transport	PROPN
app01-3959	160	12	systems	systems	PROPN
app01-3959	160	13	institute	institute	PROPN
app01-3959	160	14	of	of	ADP
app01-3959	160	15	mechanics	mechanic	NOUN
app01-3959	160	16	chair	chair	NOUN
app01-3959	160	17	of	of	ADP
app01-3959	160	18	continuum	continuum	ADJ
app01-3959	160	19	mechanics	mechanic	NOUN
app01-3959	160	20	and	and	CCONJ
app01-3959	160	21	materials	material	NOUN
app01-3959	160	22	theory	theory	NOUN
app01-3959	160	23	prof	prof	NOUN
app01-3959	160	24	.	.	PUNCT
app01-3959	161	1	dr	dr	PROPN
app01-3959	161	2	.	.	PROPN
app01-3959	161	3	rer	rer	PROPN
app01-3959	161	4	.	.	PUNCT
app01-3959	162	1	nat	nat	PROPN
app01-3959	162	2	.	.	PUNCT
app01-3959	163	1	w.	w.	PROPN
app01-3959	163	2	h.	h.	PROPN
app01-3959	163	3	müller	müller	PROPN
app01-3959	163	4	table	table	NOUN
app01-3959	163	5	:	:	PUNCT
app01-3959	163	6	dimensions	dimension	NOUN
app01-3959	163	7	,	,	PUNCT
app01-3959	163	8	loads	load	NOUN
app01-3959	163	9	and	and	CCONJ
app01-3959	163	10	material	material	NOUN
app01-3959	163	11	parameters	parameter	NOUN
app01-3959	163	12	𝑡	𝑡	PROPN
app01-3959	163	13	𝑊	𝑊	PROPN
app01-3959	163	14	𝐿	𝐿	NOUN
app01-3959	163	15	𝐸	𝐸	NOUN
app01-3959	164	1	ℓ0	ℓ0	NOUN
app01-3959	164	2	=	=	SYM
app01-3959	164	3	ℓ1	ℓ1	NOUN
app01-3959	164	4	=	=	SYM
app01-3959	164	5	ℓ2	ℓ2	NOUN
app01-3959	164	6	𝐹	𝐹	PROPN
app01-3959	164	7	100	100	NUM
app01-3959	164	8	µm	µm	ADP
app01-3959	164	9	2𝑡	2𝑡	NUM
app01-3959	164	10	20𝑡	20𝑡	NOUN
app01-3959	164	11	1.44	1.44	NUM
app01-3959	164	12	gpa	gpa	PROPN
app01-3959	164	13	17.6	17.6	NUM
app01-3959	164	14	µm	µm	ADP
app01-3959	164	15	1µn	1µn	ADJ
app01-3959	164	16	𝑤	𝑤	ADP
app01-3959	165	1	[	[	X
app01-3959	165	2	m	m	VERB
app01-3959	166	1	m	m	PRON
app01-3959	166	2	]	]	PUNCT
app01-3959	166	3	𝑥/𝐿	𝑥/𝐿	PROPN
app01-3959	166	4	d𝑤	d𝑤	VERB
app01-3959	166	5	d𝑥	d𝑥	PRON
app01-3959	166	6	𝑥/𝐿	𝑥/𝐿	PUNCT
app01-3959	167	1	d2𝑤	d2𝑤	ADJ
app01-3959	167	2	d𝑥2	d𝑥2	PROPN
app01-3959	168	1	𝑥/𝐿	𝑥/𝐿	NOUN
app01-3959	168	2	d3𝑤	d3𝑤	PROPN
app01-3959	168	3	d𝑥3	d𝑥3	NOUN
app01-3959	168	4	𝑥/𝐿	𝑥/𝐿	PROPN
app01-3959	169	1	dr.-ing	dr.-ing	NOUN
app01-3959	169	2	.	.	PUNCT
app01-3959	170	1	c.	c.	PROPN
app01-3959	170	2	liebold	liebold	PROPN
app01-3959	171	1	|	|	ADV
app01-3959	171	2	exnum	exnum	PROPN
app01-3959	171	3	2016	2016	NUM
app01-3959	171	4	,	,	PUNCT
app01-3959	171	5	liblice	liblice	VERB
app01-3959	171	6	|	|	ADV
app01-3959	171	7	1d	1d	NUM
app01-3959	171	8	example	example	NOUN
app01-3959	171	9	9/10	9/10	NUM
app01-3959	171	10	figure	figure	NOUN
app01-3959	171	11	7	7	NUM
app01-3959	171	12	.	.	PUNCT
app01-3959	171	13	second	second	ADJ
app01-3959	171	14	derivative	derivative	NOUN
app01-3959	171	15	of	of	ADP
app01-3959	171	16	the	the	DET
app01-3959	171	17	solution	solution	NOUN
app01-3959	171	18	lkmberlin	lkmberlin	PROPN
app01-3959	171	19	university	university	PROPN
app01-3959	171	20	of	of	ADP
app01-3959	171	21	technology	technology	PROPN
app01-3959	171	22	faculty	faculty	NOUN
app01-3959	171	23	v	v	NOUN
app01-3959	171	24	–	–	PUNCT
app01-3959	171	25	mechanical	mechanical	ADJ
app01-3959	171	26	engineering	engineering	NOUN
app01-3959	171	27	and	and	CCONJ
app01-3959	171	28	transport	transport	PROPN
app01-3959	171	29	systems	systems	PROPN
app01-3959	171	30	institute	institute	PROPN
app01-3959	171	31	of	of	ADP
app01-3959	171	32	mechanics	mechanic	NOUN
app01-3959	171	33	chair	chair	NOUN
app01-3959	171	34	of	of	ADP
app01-3959	171	35	continuum	continuum	ADJ
app01-3959	171	36	mechanics	mechanic	NOUN
app01-3959	171	37	and	and	CCONJ
app01-3959	171	38	materials	material	NOUN
app01-3959	171	39	theory	theory	NOUN
app01-3959	171	40	prof	prof	NOUN
app01-3959	171	41	.	.	PUNCT
app01-3959	172	1	dr	dr	PROPN
app01-3959	172	2	.	.	PROPN
app01-3959	172	3	rer	rer	PROPN
app01-3959	172	4	.	.	PUNCT
app01-3959	173	1	nat	nat	PROPN
app01-3959	173	2	.	.	PUNCT
app01-3959	174	1	w.	w.	PROPN
app01-3959	174	2	h.	h.	PROPN
app01-3959	174	3	müller	müller	PROPN
app01-3959	174	4	table	table	NOUN
app01-3959	174	5	:	:	PUNCT
app01-3959	174	6	dimensions	dimension	NOUN
app01-3959	174	7	,	,	PUNCT
app01-3959	174	8	loads	load	NOUN
app01-3959	174	9	and	and	CCONJ
app01-3959	174	10	material	material	NOUN
app01-3959	174	11	parameters	parameter	NOUN
app01-3959	174	12	𝑡	𝑡	PROPN
app01-3959	174	13	𝑊	𝑊	PROPN
app01-3959	174	14	𝐿	𝐿	NOUN
app01-3959	174	15	𝐸	𝐸	NOUN
app01-3959	175	1	ℓ0	ℓ0	NOUN
app01-3959	175	2	=	=	SYM
app01-3959	175	3	ℓ1	ℓ1	NOUN
app01-3959	175	4	=	=	SYM
app01-3959	175	5	ℓ2	ℓ2	NOUN
app01-3959	175	6	𝐹	𝐹	PROPN
app01-3959	175	7	100	100	NUM
app01-3959	175	8	µm	µm	ADP
app01-3959	175	9	2𝑡	2𝑡	NUM
app01-3959	175	10	20𝑡	20𝑡	NOUN
app01-3959	175	11	1.44	1.44	NUM
app01-3959	175	12	gpa	gpa	PROPN
app01-3959	175	13	17.6	17.6	NUM
app01-3959	175	14	µm	µm	ADP
app01-3959	175	15	1µn	1µn	ADJ
app01-3959	175	16	𝑤	𝑤	ADP
app01-3959	176	1	[	[	X
app01-3959	176	2	m	m	VERB
app01-3959	177	1	m	m	PRON
app01-3959	177	2	]	]	PUNCT
app01-3959	177	3	𝑥/𝐿	𝑥/𝐿	PROPN
app01-3959	177	4	d𝑤	d𝑤	VERB
app01-3959	177	5	d𝑥	d𝑥	PRON
app01-3959	177	6	𝑥/𝐿	𝑥/𝐿	PUNCT
app01-3959	178	1	d2𝑤	d2𝑤	ADJ
app01-3959	178	2	d𝑥2	d𝑥2	PROPN
app01-3959	179	1	𝑥/𝐿	𝑥/𝐿	NOUN
app01-3959	179	2	d3𝑤	d3𝑤	PROPN
app01-3959	179	3	d𝑥3	d𝑥3	NOUN
app01-3959	179	4	𝑥/𝐿	𝑥/𝐿	PROPN
app01-3959	180	1	dr.-ing	dr.-ing	NOUN
app01-3959	180	2	.	.	PUNCT
app01-3959	181	1	c.	c.	PROPN
app01-3959	181	2	liebold	liebold	PROPN
app01-3959	182	1	|	|	ADV
app01-3959	182	2	exnum	exnum	PROPN
app01-3959	182	3	2016	2016	NUM
app01-3959	182	4	,	,	PUNCT
app01-3959	182	5	liblice	liblice	VERB
app01-3959	182	6	|	|	ADV
app01-3959	182	7	1d	1d	NUM
app01-3959	182	8	example	example	NOUN
app01-3959	182	9	9/10figure	9/10figure	NUM
app01-3959	182	10	8	8	NUM
app01-3959	182	11	.	.	PUNCT
app01-3959	183	1	third	third	ADJ
app01-3959	183	2	derivative	derivative	NOUN
app01-3959	183	3	of	of	ADP
app01-3959	183	4	the	the	DET
app01-3959	183	5	solution	solution	NOUN
app01-3959	183	6	e	e	NOUN
app01-3959	183	7	∗	∗	X
app01-3959	183	8	[	[	X
app01-3959	183	9	g	g	X
app01-3959	183	10	pa	pa	PROPN
app01-3959	183	11	]	]	PUNCT
app01-3959	184	1	thickness	thickness	PROPN
app01-3959	184	2	t	t	PROPN
app01-3959	184	3	[	[	X
app01-3959	184	4	mm	mm	X
app01-3959	184	5	]	]	X
app01-3959	184	6	figure	figure	NOUN
app01-3959	184	7	9	9	NUM
app01-3959	184	8	.	.	NOUN
app01-3959	184	9	size	size	NOUN
app01-3959	184	10	effect	effect	NOUN
app01-3959	184	11	for	for	ADP
app01-3959	184	12	decreasing	decrease	VERB
app01-3959	184	13	thicknesses	thickness	NOUN
app01-3959	184	14	the	the	DET
app01-3959	184	15	sensitivity	sensitivity	NOUN
app01-3959	184	16	of	of	ADP
app01-3959	184	17	the	the	DET
app01-3959	184	18	implemented	implement	VERB
app01-3959	184	19	numerical	numerical	ADJ
app01-3959	184	20	model	model	NOUN
app01-3959	184	21	of	of	ADP
app01-3959	184	22	the	the	DET
app01-3959	184	23	modified	modify	VERB
app01-3959	184	24	second	second	ADJ
app01-3959	184	25	gradient	gradient	NOUN
app01-3959	184	26	continuum	continuum	NOUN
app01-3959	184	27	was	be	AUX
app01-3959	184	28	tested	test	VERB
app01-3959	184	29	for	for	ADP
app01-3959	184	30	incorporation	incorporation	NOUN
app01-3959	184	31	of	of	ADP
app01-3959	184	32	size	size	NOUN
app01-3959	184	33	effect	effect	NOUN
app01-3959	184	34	by	by	ADP
app01-3959	184	35	decreasing	decrease	VERB
app01-3959	184	36	the	the	DET
app01-3959	184	37	thickness	thickness	NOUN
app01-3959	184	38	values	value	NOUN
app01-3959	184	39	,	,	PUNCT
app01-3959	184	40	while	while	SCONJ
app01-3959	184	41	all	all	DET
app01-3959	184	42	other	other	ADJ
app01-3959	184	43	dimensions	dimension	NOUN
app01-3959	184	44	were	be	AUX
app01-3959	184	45	scaled	scale	VERB
app01-3959	184	46	in	in	ADP
app01-3959	184	47	parallel	parallel	NOUN
app01-3959	184	48	according	accord	VERB
app01-3959	184	49	to	to	ADP
app01-3959	184	50	tab	tab	NOUN
app01-3959	184	51	.	.	PUNCT
app01-3959	185	1	1	1	NUM
app01-3959	185	2	.	.	PUNCT
app01-3959	186	1	the	the	DET
app01-3959	186	2	solution	solution	NOUN
app01-3959	186	3	of	of	ADP
app01-3959	186	4	the	the	DET
app01-3959	186	5	tip	tip	NOUN
app01-3959	186	6	deflection	deflection	NOUN
app01-3959	186	7	was	be	AUX
app01-3959	186	8	used	use	VERB
app01-3959	186	9	in	in	ADP
app01-3959	186	10	a	a	DET
app01-3959	186	11	calculation	calculation	NOUN
app01-3959	186	12	of	of	ADP
app01-3959	186	13	an	an	DET
app01-3959	186	14	equivalent	equivalent	ADJ
app01-3959	186	15	young	young	ADJ
app01-3959	186	16	’s	’s	PART
app01-3959	186	17	modulus	modulus	NOUN
app01-3959	186	18	,	,	PUNCT
app01-3959	186	19	e∗	e∗	PROPN
app01-3959	186	20	,	,	PUNCT
app01-3959	186	21	with	with	ADP
app01-3959	186	22	a	a	DET
app01-3959	186	23	euler	euler	ADJ
app01-3959	186	24	-	-	PUNCT
app01-3959	186	25	bernoulli	bernoulli	NOUN
app01-3959	186	26	analytical	analytical	ADJ
app01-3959	186	27	beam	beam	NOUN
app01-3959	186	28	model	model	NOUN
app01-3959	186	29	of	of	ADP
app01-3959	186	30	the	the	DET
app01-3959	186	31	conventional	conventional	ADJ
app01-3959	186	32	cauchy	cauchy	ADJ
app01-3959	186	33	continuum	continuum	PROPN
app01-3959	186	34	.	.	PUNCT
app01-3959	187	1	as	as	SCONJ
app01-3959	187	2	plotted	plot	VERB
app01-3959	187	3	in	in	ADP
app01-3959	187	4	fig	fig	NOUN
app01-3959	187	5	.	.	PUNCT
app01-3959	188	1	9	9	NUM
app01-3959	188	2	,	,	PUNCT
app01-3959	188	3	a	a	DET
app01-3959	188	4	size	size	NOUN
app01-3959	188	5	effect	effect	NOUN
app01-3959	188	6	is	be	AUX
app01-3959	188	7	clearly	clearly	ADV
app01-3959	188	8	present	present	ADJ
app01-3959	188	9	.	.	PUNCT
app01-3959	189	1	for	for	ADP
app01-3959	189	2	small	small	ADJ
app01-3959	189	3	thicknesses	thickness	NOUN
app01-3959	189	4	the	the	DET
app01-3959	189	5	equivalent	equivalent	ADJ
app01-3959	189	6	young	young	ADJ
app01-3959	189	7	’s	’s	PART
app01-3959	189	8	modulus	modulus	NOUN
app01-3959	189	9	is	be	AUX
app01-3959	189	10	calculated	calculate	VERB
app01-3959	189	11	to	to	PART
app01-3959	189	12	be	be	AUX
app01-3959	189	13	about	about	ADV
app01-3959	189	14	three	three	NUM
app01-3959	189	15	times	time	NOUN
app01-3959	189	16	larger	large	ADJ
app01-3959	189	17	than	than	ADP
app01-3959	189	18	the	the	DET
app01-3959	189	19	usual	usual	ADJ
app01-3959	189	20	one	one	NOUN
app01-3959	189	21	.	.	PUNCT
app01-3959	190	1	36	36	NUM
app01-3959	190	2	vol	vol	NOUN
app01-3959	190	3	.	.	PUNCT
app01-3959	191	1	7/2017	7/2017	NUM
app01-3959	191	2	c1	c1	NOUN
app01-3959	191	3	-	-	PUNCT
app01-3959	191	4	continuous	continuous	ADJ
app01-3959	191	5	solutions	solution	NOUN
app01-3959	191	6	in	in	ADP
app01-3959	191	7	second	second	ADJ
app01-3959	191	8	gradient	gradient	NOUN
app01-3959	191	9	elasticity	elasticity	NOUN
app01-3959	191	10	5	5	NUM
app01-3959	191	11	.	.	PUNCT
app01-3959	192	1	conclusions	conclusion	NOUN
app01-3959	192	2	based	base	VERB
app01-3959	192	3	on	on	ADP
app01-3959	192	4	a	a	DET
app01-3959	192	5	modified	modify	VERB
app01-3959	192	6	strain	strain	NOUN
app01-3959	192	7	gradient	gradient	NOUN
app01-3959	192	8	theory	theory	NOUN
app01-3959	192	9	for	for	ADP
app01-3959	192	10	linear	linear	ADJ
app01-3959	192	11	isotropic	isotropic	NOUN
app01-3959	192	12	materials	material	NOUN
app01-3959	192	13	we	we	PRON
app01-3959	192	14	have	have	AUX
app01-3959	192	15	evaluated	evaluate	VERB
app01-3959	192	16	the	the	DET
app01-3959	192	17	eulerbernoulli	eulerbernoulli	PROPN
app01-3959	192	18	beam	beam	PROPN
app01-3959	192	19	assumptions	assumption	NOUN
app01-3959	192	20	to	to	PART
app01-3959	192	21	derive	derive	VERB
app01-3959	192	22	the	the	DET
app01-3959	192	23	ordinary	ordinary	ADJ
app01-3959	192	24	differential	differential	ADJ
app01-3959	192	25	equation	equation	NOUN
app01-3959	192	26	of	of	ADP
app01-3959	192	27	the	the	DET
app01-3959	192	28	problem	problem	NOUN
app01-3959	192	29	.	.	PUNCT
app01-3959	193	1	the	the	DET
app01-3959	193	2	weak	weak	ADJ
app01-3959	193	3	form	form	NOUN
app01-3959	193	4	was	be	AUX
app01-3959	193	5	derived	derive	VERB
app01-3959	193	6	using	use	VERB
app01-3959	193	7	test	test	NOUN
app01-3959	193	8	functions	function	NOUN
app01-3959	193	9	.	.	PUNCT
app01-3959	194	1	third	third	ADJ
app01-3959	194	2	order	order	NOUN
app01-3959	194	3	hermite	hermite	ADJ
app01-3959	194	4	polynomials	polynomial	NOUN
app01-3959	194	5	have	have	AUX
app01-3959	194	6	been	be	AUX
app01-3959	194	7	summed	sum	VERB
app01-3959	194	8	up	up	ADP
app01-3959	194	9	for	for	ADP
app01-3959	194	10	an	an	DET
app01-3959	194	11	element	element	ADJ
app01-3959	194	12	formulation	formulation	NOUN
app01-3959	194	13	:	:	PUNCT
app01-3959	194	14	these	these	PRON
app01-3959	194	15	are	be	AUX
app01-3959	194	16	able	able	ADJ
app01-3959	194	17	to	to	PART
app01-3959	194	18	access	access	VERB
app01-3959	194	19	and	and	CCONJ
app01-3959	194	20	influence	influence	NOUN
app01-3959	194	21	first	first	ADJ
app01-3959	194	22	derivatives	derivative	NOUN
app01-3959	194	23	between	between	ADP
app01-3959	194	24	the	the	DET
app01-3959	194	25	elements	element	NOUN
app01-3959	194	26	.	.	PUNCT
app01-3959	195	1	the	the	DET
app01-3959	195	2	element	element	ADJ
app01-3959	195	3	stiffness	stiffness	NOUN
app01-3959	195	4	and	and	CCONJ
app01-3959	195	5	system	system	NOUN
app01-3959	195	6	matrix	matrix	NOUN
app01-3959	195	7	have	have	AUX
app01-3959	195	8	been	be	AUX
app01-3959	195	9	formulated	formulate	VERB
app01-3959	195	10	for	for	ADP
app01-3959	195	11	the	the	DET
app01-3959	195	12	problem	problem	NOUN
app01-3959	195	13	of	of	ADP
app01-3959	195	14	a	a	DET
app01-3959	195	15	cantilever	cantilever	NOUN
app01-3959	195	16	beam	beam	NOUN
app01-3959	195	17	.	.	PUNCT
app01-3959	196	1	the	the	DET
app01-3959	196	2	resulting	result	VERB
app01-3959	196	3	system	system	NOUN
app01-3959	196	4	of	of	ADP
app01-3959	196	5	linear	linear	PROPN
app01-3959	196	6	equations	equation	NOUN
app01-3959	196	7	was	be	AUX
app01-3959	196	8	solved	solve	VERB
app01-3959	196	9	numerically	numerically	ADV
app01-3959	196	10	to	to	PART
app01-3959	196	11	determine	determine	VERB
app01-3959	196	12	the	the	DET
app01-3959	196	13	coefficients	coefficient	NOUN
app01-3959	196	14	of	of	ADP
app01-3959	196	15	the	the	DET
app01-3959	196	16	trial	trial	NOUN
app01-3959	196	17	functions	function	NOUN
app01-3959	196	18	for	for	ADP
app01-3959	196	19	each	each	DET
app01-3959	196	20	element	element	NOUN
app01-3959	196	21	.	.	PUNCT
app01-3959	197	1	the	the	DET
app01-3959	197	2	global	global	ADJ
app01-3959	197	3	solution	solution	NOUN
app01-3959	197	4	was	be	AUX
app01-3959	197	5	reconstructed	reconstruct	VERB
app01-3959	197	6	element	element	ADJ
app01-3959	197	7	-	-	ADJ
app01-3959	197	8	wise	wise	ADJ
app01-3959	197	9	and	and	CCONJ
app01-3959	197	10	first	first	ADJ
app01-3959	197	11	,	,	PUNCT
app01-3959	197	12	second	second	ADJ
app01-3959	197	13	and	and	CCONJ
app01-3959	197	14	third	third	ADJ
app01-3959	197	15	order	order	NOUN
app01-3959	197	16	derivatives	derivative	NOUN
app01-3959	197	17	have	have	AUX
app01-3959	197	18	been	be	AUX
app01-3959	197	19	calculated	calculate	VERB
app01-3959	197	20	.	.	PUNCT
app01-3959	198	1	it	it	PRON
app01-3959	198	2	was	be	AUX
app01-3959	198	3	demonstrated	demonstrate	VERB
app01-3959	198	4	,	,	PUNCT
app01-3959	198	5	that	that	SCONJ
app01-3959	198	6	this	this	DET
app01-3959	198	7	procedure	procedure	NOUN
app01-3959	198	8	guarantees	guarantee	VERB
app01-3959	198	9	c1	c1	NOUN
app01-3959	198	10	–	–	PUNCT
app01-3959	198	11	continuity	continuity	NOUN
app01-3959	198	12	of	of	ADP
app01-3959	198	13	the	the	DET
app01-3959	198	14	solution	solution	NOUN
app01-3959	198	15	.	.	PUNCT
app01-3959	199	1	this	this	PRON
app01-3959	199	2	is	be	AUX
app01-3959	199	3	considered	consider	VERB
app01-3959	199	4	to	to	PART
app01-3959	199	5	be	be	AUX
app01-3959	199	6	an	an	DET
app01-3959	199	7	important	important	ADJ
app01-3959	199	8	quality	quality	NOUN
app01-3959	199	9	in	in	ADP
app01-3959	199	10	second	second	ADJ
app01-3959	199	11	gradient	gradient	NOUN
app01-3959	199	12	theories	theory	NOUN
app01-3959	199	13	.	.	PUNCT
app01-3959	200	1	furthermore	furthermore	ADV
app01-3959	200	2	,	,	PUNCT
app01-3959	200	3	the	the	DET
app01-3959	200	4	size	size	NOUN
app01-3959	200	5	effect	effect	NOUN
app01-3959	200	6	,	,	PUNCT
app01-3959	200	7	measured	measure	VERB
app01-3959	200	8	by	by	ADP
app01-3959	200	9	the	the	DET
app01-3959	200	10	authors	author	NOUN
app01-3959	200	11	in	in	ADP
app01-3959	200	12	previous	previous	ADJ
app01-3959	200	13	work	work	NOUN
app01-3959	200	14	,	,	PUNCT
app01-3959	200	15	could	could	AUX
app01-3959	200	16	be	be	AUX
app01-3959	200	17	reproduced	reproduce	VERB
app01-3959	200	18	by	by	ADP
app01-3959	200	19	using	use	VERB
app01-3959	200	20	similar	similar	ADJ
app01-3959	200	21	material	material	NOUN
app01-3959	200	22	as	as	ADV
app01-3959	200	23	well	well	ADV
app01-3959	200	24	as	as	ADP
app01-3959	200	25	geometry	geometry	NOUN
app01-3959	200	26	data	datum	NOUN
app01-3959	200	27	.	.	PUNCT
app01-3959	201	1	this	this	PRON
app01-3959	201	2	provides	provide	VERB
app01-3959	201	3	the	the	DET
app01-3959	201	4	impetus	impetus	NOUN
app01-3959	201	5	for	for	ADP
app01-3959	201	6	the	the	DET
app01-3959	201	7	development	development	NOUN
app01-3959	201	8	of	of	ADP
app01-3959	201	9	a	a	DET
app01-3959	201	10	three	three	NUM
app01-3959	201	11	dimensional	dimensional	ADJ
app01-3959	201	12	finite	finite	ADJ
app01-3959	201	13	element	element	NOUN
app01-3959	201	14	formulation	formulation	NOUN
app01-3959	201	15	of	of	ADP
app01-3959	201	16	a	a	DET
app01-3959	201	17	strain	strain	NOUN
app01-3959	201	18	gradient	gradient	NOUN
app01-3959	201	19	continuum	continuum	ADJ
app01-3959	201	20	on	on	ADP
app01-3959	201	21	the	the	DET
app01-3959	201	22	basis	basis	NOUN
app01-3959	201	23	of	of	ADP
app01-3959	201	24	hermite	hermite	ADJ
app01-3959	201	25	elements	element	NOUN
app01-3959	201	26	.	.	PUNCT
app01-3959	202	1	references	reference	NOUN
app01-3959	202	2	[	[	X
app01-3959	202	3	1	1	NUM
app01-3959	202	4	]	]	PUNCT
app01-3959	202	5	w.	w.	PROPN
app01-3959	202	6	j.	j.	PROPN
app01-3959	202	7	poole	poole	PROPN
app01-3959	202	8	,	,	PUNCT
app01-3959	202	9	m.	m.	PROPN
app01-3959	202	10	f.	f.	PROPN
app01-3959	202	11	ashby	ashby	PROPN
app01-3959	202	12	,	,	PUNCT
app01-3959	202	13	n.	n.	PROPN
app01-3959	202	14	a.	a.	NOUN
app01-3959	202	15	fleck	fleck	PROPN
app01-3959	202	16	.	.	PUNCT
app01-3959	203	1	micro	micro	NOUN
app01-3959	203	2	-	-	NOUN
app01-3959	203	3	hardness	hardness	NOUN
app01-3959	203	4	of	of	ADP
app01-3959	203	5	annealed	annealed	ADJ
app01-3959	203	6	and	and	CCONJ
app01-3959	203	7	work	work	NOUN
app01-3959	203	8	-	-	PUNCT
app01-3959	203	9	hardened	harden	VERB
app01-3959	203	10	copper	copper	NOUN
app01-3959	203	11	polycrystals	polycrystal	NOUN
app01-3959	203	12	.	.	PUNCT
app01-3959	204	1	scripta	scripta	PROPN
app01-3959	204	2	materialia	materialia	PROPN
app01-3959	204	3	34(4):559–564	34(4):559–564	PROPN
app01-3959	204	4	,	,	PUNCT
app01-3959	204	5	1996	1996	NUM
app01-3959	204	6	.	.	PUNCT
app01-3959	205	1	[	[	X
app01-3959	205	2	2	2	NUM
app01-3959	205	3	]	]	PUNCT
app01-3959	205	4	x.	x.	NOUN
app01-3959	205	5	h.	h.	PROPN
app01-3959	205	6	guo	guo	PROPN
app01-3959	205	7	,	,	PUNCT
app01-3959	205	8	d.	d.	PROPN
app01-3959	205	9	n.	n.	PROPN
app01-3959	205	10	fang	fang	PROPN
app01-3959	205	11	,	,	PUNCT
app01-3959	205	12	x.	x.	PROPN
app01-3959	205	13	d.	d.	PROPN
app01-3959	205	14	li	li	PROPN
app01-3959	205	15	.	.	PROPN
app01-3959	205	16	measurement	measurement	PROPN
app01-3959	205	17	of	of	ADP
app01-3959	205	18	deformation	deformation	NOUN
app01-3959	205	19	of	of	ADP
app01-3959	205	20	pure	pure	ADJ
app01-3959	205	21	ni	ni	NOUN
app01-3959	205	22	foils	foil	NOUN
app01-3959	205	23	by	by	ADP
app01-3959	205	24	speckle	speckle	NOUN
app01-3959	205	25	pattern	pattern	NOUN
app01-3959	205	26	interferometry	interferometry	NOUN
app01-3959	205	27	.	.	PUNCT
app01-3959	206	1	mechanical	mechanical	ADJ
app01-3959	206	2	engineering	engineering	NOUN
app01-3959	206	3	27(2):21–25	27(2):21–25	NUM
app01-3959	206	4	,	,	PUNCT
app01-3959	206	5	2005	2005	NUM
app01-3959	206	6	.	.	PUNCT
app01-3959	207	1	[	[	X
app01-3959	207	2	3	3	X
app01-3959	207	3	]	]	X
app01-3959	207	4	d.	d.	PROPN
app01-3959	207	5	c.	c.	PROPN
app01-3959	207	6	c.	c.	PROPN
app01-3959	207	7	lam	lam	PROPN
app01-3959	207	8	,	,	PUNCT
app01-3959	207	9	f.	f.	PROPN
app01-3959	207	10	yang	yang	PROPN
app01-3959	207	11	,	,	PUNCT
app01-3959	207	12	c.	c.	PROPN
app01-3959	207	13	m.	m.	PROPN
app01-3959	207	14	chong	chong	PROPN
app01-3959	207	15	,	,	PUNCT
app01-3959	207	16	et	et	PROPN
app01-3959	207	17	al	al	PROPN
app01-3959	207	18	.	.	PUNCT
app01-3959	207	19	experiments	experiment	NOUN
app01-3959	207	20	and	and	CCONJ
app01-3959	207	21	theory	theory	NOUN
app01-3959	207	22	in	in	ADP
app01-3959	207	23	strain	strain	NOUN
app01-3959	207	24	gradient	gradient	ADJ
app01-3959	207	25	elasticity	elasticity	NOUN
app01-3959	207	26	.	.	PUNCT
app01-3959	208	1	j	j	PROPN
app01-3959	208	2	mech	mech	NOUN
app01-3959	208	3	phys	phy	NOUN
app01-3959	208	4	sol	sol	NOUN
app01-3959	208	5	51(8):1477–1508	51(8):1477–1508	NUM
app01-3959	208	6	,	,	PUNCT
app01-3959	208	7	2003	2003	NUM
app01-3959	208	8	.	.	PUNCT
app01-3959	209	1	[	[	X
app01-3959	209	2	4	4	NUM
app01-3959	209	3	]	]	PUNCT
app01-3959	209	4	a.	a.	PROPN
app01-3959	209	5	w.	w.	PROPN
app01-3959	209	6	mcfarland	mcfarland	PROPN
app01-3959	209	7	,	,	PUNCT
app01-3959	209	8	j.	j.	PROPN
app01-3959	209	9	s.	s.	PROPN
app01-3959	209	10	colton	colton	PROPN
app01-3959	209	11	.	.	PUNCT
app01-3959	210	1	role	role	NOUN
app01-3959	210	2	of	of	ADP
app01-3959	210	3	material	material	NOUN
app01-3959	210	4	microstructure	microstructure	NOUN
app01-3959	210	5	in	in	ADP
app01-3959	210	6	plate	plate	NOUN
app01-3959	210	7	stiffness	stiffness	NOUN
app01-3959	210	8	with	with	ADP
app01-3959	210	9	relevance	relevance	NOUN
app01-3959	210	10	to	to	ADP
app01-3959	210	11	microcantilever	microcantilever	NOUN
app01-3959	210	12	sensors	sensor	NOUN
app01-3959	210	13	.	.	PUNCT
app01-3959	211	1	journal	journal	NOUN
app01-3959	211	2	of	of	ADP
app01-3959	211	3	micromechanics	micromechanic	NOUN
app01-3959	211	4	and	and	CCONJ
app01-3959	211	5	microengineering	microengineere	VERB
app01-3959	211	6	15(5):1060–1067	15(5):1060–1067	NUM
app01-3959	211	7	,	,	PUNCT
app01-3959	211	8	2005	2005	NUM
app01-3959	211	9	.	.	PUNCT
app01-3959	212	1	[	[	X
app01-3959	212	2	5	5	X
app01-3959	212	3	]	]	PUNCT
app01-3959	212	4	s.	s.	PROPN
app01-3959	212	5	cuenot	cuenot	PROPN
app01-3959	212	6	,	,	PUNCT
app01-3959	212	7	c.	c.	PROPN
app01-3959	212	8	fretigny	fretigny	PROPN
app01-3959	212	9	,	,	PUNCT
app01-3959	212	10	s.	s.	PROPN
app01-3959	212	11	demoustier	demoustier	PROPN
app01-3959	212	12	-	-	PUNCT
app01-3959	212	13	champagne	champagne	PROPN
app01-3959	212	14	,	,	PUNCT
app01-3959	212	15	b.	b.	PROPN
app01-3959	212	16	nysten	nysten	PROPN
app01-3959	212	17	.	.	PUNCT
app01-3959	213	1	surface	surface	NOUN
app01-3959	213	2	tension	tension	NOUN
app01-3959	213	3	effect	effect	NOUN
app01-3959	213	4	on	on	ADP
app01-3959	213	5	the	the	DET
app01-3959	213	6	mechanical	mechanical	ADJ
app01-3959	213	7	properties	property	NOUN
app01-3959	213	8	of	of	ADP
app01-3959	213	9	nanomaterials	nanomaterial	NOUN
app01-3959	213	10	measured	measure	VERB
app01-3959	213	11	by	by	ADP
app01-3959	213	12	atomic	atomic	ADJ
app01-3959	213	13	force	force	NOUN
app01-3959	213	14	microscopy	microscopy	NOUN
app01-3959	213	15	.	.	PUNCT
app01-3959	214	1	physical	physical	ADJ
app01-3959	214	2	review	review	PROPN
app01-3959	214	3	b	b	PROPN
app01-3959	214	4	69:01–05	69:01–05	PROPN
app01-3959	214	5	,	,	PUNCT
app01-3959	214	6	2004	2004	NUM
app01-3959	214	7	.	.	PUNCT
app01-3959	215	1	[	[	X
app01-3959	215	2	6	6	NUM
app01-3959	215	3	]	]	PUNCT
app01-3959	215	4	x.-f	x.-f	NOUN
app01-3959	215	5	.	.	PUNCT
app01-3959	216	1	li	li	PROPN
app01-3959	216	2	,	,	PUNCT
app01-3959	216	3	b.-l	b.-l	PROPN
app01-3959	216	4	.	.	PUNCT
app01-3959	217	1	wang	wang	PROPN
app01-3959	217	2	,	,	PUNCT
app01-3959	217	3	k.	k.	PROPN
app01-3959	217	4	y.	y.	PROPN
app01-3959	217	5	lee	lee	PROPN
app01-3959	217	6	.	.	PROPN
app01-3959	218	1	size	size	PROPN
app01-3959	218	2	effect	effect	NOUN
app01-3959	218	3	in	in	ADP
app01-3959	218	4	the	the	DET
app01-3959	218	5	mechanical	mechanical	ADJ
app01-3959	218	6	response	response	NOUN
app01-3959	218	7	of	of	ADP
app01-3959	218	8	nanobeams	nanobeam	NOUN
app01-3959	218	9	.	.	PUNCT
app01-3959	219	1	j	j	PROPN
app01-3959	219	2	of	of	ADP
app01-3959	219	3	adv	adv	PROPN
app01-3959	219	4	research	research	NOUN
app01-3959	219	5	in	in	ADP
app01-3959	219	6	mech	mech	NOUN
app01-3959	219	7	eng	eng	PROPN
app01-3959	219	8	1(1):4–16	1(1):4–16	PROPN
app01-3959	219	9	,	,	PUNCT
app01-3959	219	10	2010	2010	NUM
app01-3959	219	11	.	.	PUNCT
app01-3959	220	1	[	[	X
app01-3959	220	2	7	7	X
app01-3959	220	3	]	]	X
app01-3959	220	4	r.	r.	NOUN
app01-3959	220	5	toupin	toupin	PROPN
app01-3959	220	6	.	.	PUNCT
app01-3959	221	1	elastic	elastic	ADJ
app01-3959	221	2	materials	material	NOUN
app01-3959	221	3	with	with	ADP
app01-3959	221	4	couple	couple	NOUN
app01-3959	221	5	-	-	PUNCT
app01-3959	221	6	stresses	stress	NOUN
app01-3959	221	7	.	.	PUNCT
app01-3959	222	1	arma	arma	PROPN
app01-3959	222	2	11:385–414	11:385–414	PROPN
app01-3959	222	3	,	,	PUNCT
app01-3959	222	4	1962	1962	NUM
app01-3959	222	5	.	.	PUNCT
app01-3959	223	1	[	[	X
app01-3959	223	2	8	8	NUM
app01-3959	223	3	]	]	PUNCT
app01-3959	223	4	r.	r.	PROPN
app01-3959	223	5	mindlin	mindlin	PROPN
app01-3959	223	6	.	.	PUNCT
app01-3959	224	1	effects	effect	NOUN
app01-3959	224	2	of	of	ADP
app01-3959	224	3	couple	couple	NOUN
app01-3959	224	4	-	-	PUNCT
app01-3959	224	5	stresses	stress	NOUN
app01-3959	224	6	in	in	ADP
app01-3959	224	7	linear	linear	PROPN
app01-3959	224	8	elasticity	elasticity	NOUN
app01-3959	224	9	.	.	PUNCT
app01-3959	225	1	arma	arma	PROPN
app01-3959	225	2	11:415–448	11:415–448	NUM
app01-3959	225	3	,	,	PUNCT
app01-3959	225	4	1962	1962	NUM
app01-3959	225	5	.	.	PUNCT
app01-3959	226	1	[	[	X
app01-3959	226	2	9	9	NUM
app01-3959	226	3	]	]	PUNCT
app01-3959	226	4	r.	r.	PROPN
app01-3959	226	5	d.	d.	PROPN
app01-3959	226	6	mindlin	mindlin	PROPN
app01-3959	226	7	,	,	PUNCT
app01-3959	226	8	n.	n.	PROPN
app01-3959	226	9	n.	n.	PROPN
app01-3959	226	10	eshel	eshel	PROPN
app01-3959	226	11	.	.	PUNCT
app01-3959	227	1	on	on	ADP
app01-3959	227	2	first	first	ADJ
app01-3959	227	3	strain	strain	NOUN
app01-3959	227	4	-	-	PUNCT
app01-3959	227	5	gradient	gradient	NOUN
app01-3959	227	6	theories	theory	NOUN
app01-3959	227	7	in	in	ADP
app01-3959	227	8	linear	linear	PROPN
app01-3959	227	9	elasticity	elasticity	NOUN
app01-3959	227	10	.	.	PUNCT
app01-3959	228	1	international	international	ADJ
app01-3959	228	2	journal	journal	PROPN
app01-3959	228	3	of	of	ADP
app01-3959	228	4	solids	solid	NOUN
app01-3959	228	5	and	and	CCONJ
app01-3959	228	6	structures	structure	NOUN
app01-3959	228	7	4:109–124	4:109–124	NUM
app01-3959	228	8	,	,	PUNCT
app01-3959	228	9	1968	1968	NUM
app01-3959	228	10	.	.	PUNCT
app01-3959	229	1	[	[	X
app01-3959	229	2	10	10	NUM
app01-3959	229	3	]	]	PUNCT
app01-3959	229	4	a.	a.	NOUN
app01-3959	229	5	eringen	eringen	PROPN
app01-3959	229	6	.	.	PUNCT
app01-3959	230	1	nonlocal	nonlocal	ADJ
app01-3959	230	2	continuum	continuum	ADJ
app01-3959	230	3	field	field	NOUN
app01-3959	230	4	theories	theory	NOUN
app01-3959	230	5	.	.	PUNCT
app01-3959	231	1	springer	springer	NOUN
app01-3959	231	2	-	-	PUNCT
app01-3959	231	3	verlag	verlag	PROPN
app01-3959	231	4	,	,	PUNCT
app01-3959	231	5	new	new	PROPN
app01-3959	231	6	york	york	PROPN
app01-3959	231	7	2010	2010	NUM
app01-3959	231	8	.	.	PUNCT
app01-3959	232	1	[	[	X
app01-3959	232	2	11	11	NUM
app01-3959	232	3	]	]	PUNCT
app01-3959	232	4	m.	m.	NOUN
app01-3959	232	5	lazar	lazar	PROPN
app01-3959	232	6	.	.	PUNCT
app01-3959	233	1	irreducible	irreducible	ADJ
app01-3959	233	2	decomposition	decomposition	NOUN
app01-3959	233	3	of	of	ADP
app01-3959	233	4	strain	strain	NOUN
app01-3959	233	5	gradient	gradient	ADJ
app01-3959	233	6	tensor	tensor	NOUN
app01-3959	233	7	in	in	ADP
app01-3959	233	8	isotropic	isotropic	ADJ
app01-3959	233	9	strain	strain	NOUN
app01-3959	233	10	gradient	gradient	NOUN
app01-3959	233	11	elasticity	elasticity	NOUN
app01-3959	233	12	.	.	PUNCT
app01-3959	234	1	zamm	zamm	PROPN
app01-3959	234	2	z	z	PROPN
app01-3959	234	3	angew	angew	PROPN
app01-3959	234	4	math	math	PROPN
app01-3959	234	5	mech	mech	PROPN
app01-3959	234	6	2016	2016	NUM
app01-3959	234	7	.	.	PUNCT
app01-3959	235	1	doi:10.1002	doi:10.1002	NOUN
app01-3959	235	2	/	/	SYM
app01-3959	235	3	zamm.201500278	zamm.201500278	PROPN
app01-3959	235	4	.	.	PUNCT
app01-3959	236	1	[	[	X
app01-3959	236	2	12	12	NUM
app01-3959	236	3	]	]	X
app01-3959	236	4	n.	n.	NOUN
app01-3959	236	5	a.	a.	NOUN
app01-3959	236	6	fleck	fleck	PROPN
app01-3959	236	7	,	,	PUNCT
app01-3959	236	8	j.	j.	PROPN
app01-3959	236	9	w.	w.	PROPN
app01-3959	236	10	hutchinson	hutchinson	PROPN
app01-3959	236	11	.	.	PROPN
app01-3959	236	12	strain	strain	PROPN
app01-3959	236	13	gradient	gradient	NOUN
app01-3959	236	14	plasticity	plasticity	NOUN
app01-3959	236	15	.	.	PUNCT
app01-3959	237	1	advances	advance	NOUN
app01-3959	237	2	in	in	ADP
app01-3959	237	3	applied	apply	VERB
app01-3959	237	4	mechanics	mechanic	NOUN
app01-3959	237	5	,	,	PUNCT
app01-3959	237	6	academic	academic	ADJ
app01-3959	237	7	press	press	NOUN
app01-3959	237	8	,	,	PUNCT
app01-3959	237	9	new	new	PROPN
app01-3959	237	10	york	york	PROPN
app01-3959	237	11	33:295–361	33:295–361	PROPN
app01-3959	237	12	,	,	PUNCT
app01-3959	237	13	1997	1997	NUM
app01-3959	237	14	.	.	PUNCT
app01-3959	238	1	[	[	X
app01-3959	238	2	13	13	NUM
app01-3959	238	3	]	]	X
app01-3959	238	4	c.	c.	PROPN
app01-3959	238	5	liebold	liebold	PROPN
app01-3959	238	6	,	,	PUNCT
app01-3959	238	7	w.	w.	PROPN
app01-3959	238	8	h.	h.	PROPN
app01-3959	238	9	müller	müller	PROPN
app01-3959	238	10	.	.	PUNCT
app01-3959	239	1	measuring	measure	VERB
app01-3959	239	2	material	material	NOUN
app01-3959	239	3	coefficients	coefficient	NOUN
app01-3959	239	4	of	of	ADP
app01-3959	239	5	higher	high	ADJ
app01-3959	239	6	gradient	gradient	NOUN
app01-3959	239	7	elasticity	elasticity	NOUN
app01-3959	239	8	by	by	ADP
app01-3959	239	9	using	use	VERB
app01-3959	239	10	afm	afm	PROPN
app01-3959	239	11	techniques	technique	NOUN
app01-3959	239	12	and	and	CCONJ
app01-3959	239	13	raman	raman	NOUN
app01-3959	239	14	-	-	PUNCT
app01-3959	239	15	spectroscopy	spectroscopy	NOUN
app01-3959	239	16	.	.	PUNCT
app01-3959	240	1	advanced	advanced	ADJ
app01-3959	240	2	structured	structured	ADJ
app01-3959	240	3	materials	material	NOUN
app01-3959	240	4	,	,	PUNCT
app01-3959	240	5	springer	springer	NOUN
app01-3959	240	6	berlin	berlin	PROPN
app01-3959	240	7	heidelberg	heidelberg	PROPN
app01-3959	240	8	22:255–271	22:255–271	PROPN
app01-3959	240	9	,	,	PUNCT
app01-3959	240	10	2013	2013	NUM
app01-3959	240	11	.	.	PUNCT
app01-3959	241	1	[	[	X
app01-3959	241	2	14	14	NUM
app01-3959	241	3	]	]	X
app01-3959	241	4	f.	f.	PROPN
app01-3959	241	5	yang	yang	PROPN
app01-3959	241	6	,	,	PUNCT
app01-3959	241	7	c.	c.	PROPN
app01-3959	241	8	m.	m.	PROPN
app01-3959	241	9	chong	chong	PROPN
app01-3959	241	10	,	,	PUNCT
app01-3959	241	11	d.	d.	PROPN
app01-3959	241	12	c.	c.	PROPN
app01-3959	241	13	c.	c.	PROPN
app01-3959	241	14	lam	lam	PROPN
app01-3959	241	15	,	,	PUNCT
app01-3959	241	16	p.	p.	PROPN
app01-3959	241	17	tong	tong	PROPN
app01-3959	241	18	.	.	PUNCT
app01-3959	242	1	couple	couple	NOUN
app01-3959	242	2	stress	stress	NOUN
app01-3959	242	3	based	base	VERB
app01-3959	242	4	strain	strain	NOUN
app01-3959	242	5	gradient	gradient	NOUN
app01-3959	242	6	theory	theory	NOUN
app01-3959	242	7	for	for	ADP
app01-3959	242	8	elasticity	elasticity	NOUN
app01-3959	242	9	.	.	PUNCT
app01-3959	243	1	international	international	ADJ
app01-3959	243	2	journal	journal	PROPN
app01-3959	243	3	of	of	ADP
app01-3959	243	4	solids	solid	NOUN
app01-3959	243	5	and	and	CCONJ
app01-3959	243	6	structures	structure	NOUN
app01-3959	243	7	39(10):2731–2743	39(10):2731–2743	NUM
app01-3959	243	8	,	,	PUNCT
app01-3959	243	9	2010	2010	NUM
app01-3959	243	10	.	.	PUNCT
app01-3959	244	1	[	[	X
app01-3959	244	2	15	15	NUM
app01-3959	244	3	]	]	X
app01-3959	244	4	s.	s.	PROPN
app01-3959	244	5	kong	kong	PROPN
app01-3959	244	6	,	,	PUNCT
app01-3959	244	7	s.	s.	PROPN
app01-3959	244	8	zhou	zhou	PROPN
app01-3959	244	9	,	,	PUNCT
app01-3959	244	10	z.	z.	PROPN
app01-3959	244	11	nie	nie	PROPN
app01-3959	244	12	,	,	PUNCT
app01-3959	244	13	k.	k.	PROPN
app01-3959	244	14	wang	wang	PROPN
app01-3959	244	15	.	.	PUNCT
app01-3959	245	1	static	static	ADJ
app01-3959	245	2	and	and	CCONJ
app01-3959	245	3	dynamic	dynamic	ADJ
app01-3959	245	4	analysis	analysis	NOUN
app01-3959	245	5	of	of	ADP
app01-3959	245	6	micro	micro	ADJ
app01-3959	245	7	beams	beam	NOUN
app01-3959	245	8	based	base	VERB
app01-3959	245	9	on	on	ADP
app01-3959	245	10	strain	strain	NOUN
app01-3959	245	11	gradient	gradient	ADJ
app01-3959	245	12	elasticity	elasticity	NOUN
app01-3959	245	13	theory	theory	NOUN
app01-3959	245	14	.	.	PUNCT
app01-3959	246	1	international	international	ADJ
app01-3959	246	2	journal	journal	PROPN
app01-3959	246	3	of	of	ADP
app01-3959	246	4	engineering	engineering	NOUN
app01-3959	246	5	science	science	NOUN
app01-3959	246	6	47:487–498	47:487–498	PROPN
app01-3959	246	7	,	,	PUNCT
app01-3959	246	8	2009	2009	NUM
app01-3959	246	9	.	.	PUNCT
app01-3959	247	1	[	[	X
app01-3959	247	2	16	16	NUM
app01-3959	247	3	]	]	X
app01-3959	247	4	c.	c.	PROPN
app01-3959	247	5	liebold	liebold	PROPN
app01-3959	247	6	,	,	PUNCT
app01-3959	247	7	w.	w.	PROPN
app01-3959	247	8	h.	h.	PROPN
app01-3959	247	9	müller	müller	PROPN
app01-3959	247	10	.	.	PUNCT
app01-3959	248	1	applications	application	NOUN
app01-3959	248	2	of	of	ADP
app01-3959	248	3	strain	strain	NOUN
app01-3959	248	4	gradient	gradient	NOUN
app01-3959	248	5	theories	theory	NOUN
app01-3959	248	6	to	to	ADP
app01-3959	248	7	the	the	DET
app01-3959	248	8	size	size	NOUN
app01-3959	248	9	effect	effect	NOUN
app01-3959	248	10	in	in	ADP
app01-3959	248	11	submicrostructures	submicrostructure	NOUN
app01-3959	248	12	incl	incl	NOUN
app01-3959	248	13	.	.	PUNCT
app01-3959	249	1	experimental	experimental	ADJ
app01-3959	249	2	analysis	analysis	NOUN
app01-3959	249	3	of	of	ADP
app01-3959	249	4	elastic	elastic	ADJ
app01-3959	249	5	material	material	NOUN
app01-3959	249	6	parameters	parameter	NOUN
app01-3959	249	7	.	.	PUNCT
app01-3959	250	1	bulletin	bulletin	NOUN
app01-3959	250	2	of	of	ADP
app01-3959	250	3	ticmi	ticmi	NOUN
app01-3959	250	4	19(1):45–55	19(1):45–55	NUM
app01-3959	250	5	,	,	PUNCT
app01-3959	250	6	2015	2015	NUM
app01-3959	250	7	.	.	PUNCT
app01-3959	251	1	[	[	X
app01-3959	251	2	17	17	NUM
app01-3959	251	3	]	]	X
app01-3959	251	4	c.	c.	PROPN
app01-3959	251	5	liebold	liebold	PROPN
app01-3959	251	6	,	,	PUNCT
app01-3959	251	7	w.	w.	PROPN
app01-3959	251	8	h.	h.	PROPN
app01-3959	251	9	müller	müller	PROPN
app01-3959	251	10	.	.	PUNCT
app01-3959	252	1	comparison	comparison	NOUN
app01-3959	252	2	of	of	ADP
app01-3959	252	3	gradient	gradient	ADJ
app01-3959	252	4	elasticity	elasticity	NOUN
app01-3959	252	5	models	model	NOUN
app01-3959	252	6	for	for	ADP
app01-3959	252	7	the	the	DET
app01-3959	252	8	bending	bending	NOUN
app01-3959	252	9	of	of	ADP
app01-3959	252	10	micromaterials	micromaterial	NOUN
app01-3959	252	11	.	.	PUNCT
app01-3959	253	1	elsevier	elsevier	NOUN
app01-3959	253	2	,	,	PUNCT
app01-3959	253	3	computational	computational	ADJ
app01-3959	253	4	materials	material	NOUN
app01-3959	253	5	science	science	NOUN
app01-3959	253	6	116:52–61	116:52–61	NUM
app01-3959	253	7	,	,	PUNCT
app01-3959	253	8	2016	2016	NUM
app01-3959	253	9	.	.	PUNCT
app01-3959	254	1	37	37	NUM
app01-3959	254	2	http://dx.doi.org/10.1002/zamm.201500278	http://dx.doi.org/10.1002/zamm.201500278	PROPN
app01-3959	254	3	acta	acta	PROPN
app01-3959	254	4	polytechnica	polytechnica	PROPN
app01-3959	254	5	ctu	ctu	NOUN
app01-3959	254	6	proceedings	proceeding	NOUN
app01-3959	254	7	7:33–37	7:33–37	NUM
app01-3959	254	8	,	,	PUNCT
app01-3959	254	9	2017	2017	NUM
app01-3959	254	10	1	1	NUM
app01-3959	254	11	introduction	introduction	NOUN
app01-3959	254	12	2	2	NUM
app01-3959	254	13	modified	modify	VERB
app01-3959	254	14	strain	strain	NOUN
app01-3959	254	15	gradient	gradient	NOUN
app01-3959	254	16	theory	theory	NOUN
app01-3959	254	17	2.1	2.1	NUM
app01-3959	254	18	strain	strain	NOUN
app01-3959	254	19	energy	energy	NOUN
app01-3959	254	20	function	function	NOUN
app01-3959	254	21	2.2	2.2	NUM
app01-3959	254	22	governing	governing	NOUN
app01-3959	254	23	euler	euler	NOUN
app01-3959	254	24	-	-	PUNCT
app01-3959	254	25	bernoulli	bernoulli	PROPN
app01-3959	254	26	differential	differential	ADJ
app01-3959	254	27	equation	equation	NOUN
app01-3959	254	28	3	3	NUM
app01-3959	254	29	finite	finite	PROPN
app01-3959	254	30	element	element	NOUN
app01-3959	254	31	implementation	implementation	NOUN
app01-3959	254	32	3.1	3.1	NUM
app01-3959	254	33	weak	weak	ADJ
app01-3959	254	34	form	form	NOUN
app01-3959	254	35	and	and	CCONJ
app01-3959	254	36	discretization	discretization	NOUN
app01-3959	254	37	3.2	3.2	NUM
app01-3959	254	38	hermite	hermite	ADJ
app01-3959	254	39	elements	element	NOUN
app01-3959	254	40	for	for	ADP
app01-3959	254	41	global	global	ADJ
app01-3959	254	42	c1	c1	PROPN
app01-3959	254	43	–	–	PUNCT
app01-3959	254	44	continuity	continuity	NOUN
app01-3959	254	45	3.3	3.3	NUM
app01-3959	254	46	structure	structure	NOUN
app01-3959	254	47	of	of	ADP
app01-3959	254	48	the	the	DET
app01-3959	254	49	element	element	NOUN
app01-3959	254	50	stiffnessand	stiffnessand	NOUN
app01-3959	254	51	system	system	NOUN
app01-3959	254	52	matrix	matrix	NOUN
app01-3959	254	53	4	4	NUM
app01-3959	254	54	numerical	numerical	ADJ
app01-3959	254	55	example	example	NOUN
app01-3959	254	56	5	5	NUM
app01-3959	254	57	conclusions	conclusion	NOUN
app01-3959	254	58	references	reference	NOUN