id	sid	tid	token	lemma	pos
fumecheng-2176	1	1	plane	plane	NOUN
fumecheng-2176	1	2	thermoelastic	thermoelastic	ADJ
fumecheng-2176	1	3	waves	wave	NOUN
fumecheng-2176	1	4	in	in	ADP
fumecheng-2176	1	5	infinite	infinite	ADJ
fumecheng-2176	1	6	half	half	ADJ
fumecheng-2176	1	7	-	-	PUNCT
fumecheng-2176	1	8	space	space	NOUN
fumecheng-2176	1	9	caused	cause	VERB
fumecheng-2176	1	10	facta	facta	PROPN
fumecheng-2176	1	11	universitatis	universitatis	PROPN
fumecheng-2176	1	12	series	series	NOUN
fumecheng-2176	1	13	:	:	PUNCT
fumecheng-2176	1	14	mechanical	mechanical	ADJ
fumecheng-2176	1	15	engineering	engineering	NOUN
fumecheng-2176	1	16	vol	vol	NOUN
fumecheng-2176	1	17	.	.	PUNCT
fumecheng-2176	2	1	14	14	NUM
fumecheng-2176	2	2	,	,	PUNCT
fumecheng-2176	2	3	no	no	DET
fumecheng-2176	2	4	3	3	NUM
fumecheng-2176	2	5	,	,	PUNCT
fumecheng-2176	2	6	2016	2016	NUM
fumecheng-2176	2	7	,	,	PUNCT
fumecheng-2176	2	8	pp	pp	ADJ
fumecheng-2176	2	9	.	.	PUNCT
fumecheng-2176	3	1	241	241	NUM
fumecheng-2176	3	2	249	249	NUM
fumecheng-2176	3	3	doi	doi	NOUN
fumecheng-2176	3	4	:	:	PUNCT
fumecheng-2176	3	5	10.22190	10.22190	NUM
fumecheng-2176	3	6	/	/	SYM
fumecheng-2176	3	7	fume1603241l	fume1603241l	ADJ
fumecheng-2176	3	8	original	original	ADJ
fumecheng-2176	3	9	scientific	scientific	ADJ
fumecheng-2176	3	10	paper	paper	NOUN
fumecheng-2176	3	11	indentation	indentation	NUM
fumecheng-2176	3	12	of	of	ADP
fumecheng-2176	3	13	flat	flat	ADV
fumecheng-2176	3	14	-	-	PUNCT
fumecheng-2176	3	15	ended	end	VERB
fumecheng-2176	3	16	and	and	CCONJ
fumecheng-2176	3	17	tapered	tapered	ADJ
fumecheng-2176	3	18	indenters	indenter	NOUN
fumecheng-2176	3	19	with	with	ADP
fumecheng-2176	3	20	polygonal	polygonal	ADJ
fumecheng-2176	3	21	cross	cross	ADJ
fumecheng-2176	3	22	-	-	ADJ
fumecheng-2176	3	23	sections	sections	ADJ
fumecheng-2176	3	24	udc	udc	NOUN
fumecheng-2176	3	25	539.3	539.3	NUM
fumecheng-2176	3	26	qiang	qiang	PROPN
fumecheng-2176	3	27	li	li	PROPN
fumecheng-2176	3	28	,	,	PUNCT
fumecheng-2176	3	29	valentin	valentin	PROPN
fumecheng-2176	3	30	l.	l.	PROPN
fumecheng-2176	3	31	popov	popov	PROPN
fumecheng-2176	3	32	department	department	PROPN
fumecheng-2176	3	33	of	of	ADP
fumecheng-2176	3	34	system	system	NOUN
fumecheng-2176	3	35	dynamics	dynamic	NOUN
fumecheng-2176	3	36	and	and	CCONJ
fumecheng-2176	3	37	the	the	DET
fumecheng-2176	3	38	physics	physics	NOUN
fumecheng-2176	3	39	of	of	ADP
fumecheng-2176	3	40	friction	friction	NOUN
fumecheng-2176	3	41	,	,	PUNCT
fumecheng-2176	3	42	tu	tu	PROPN
fumecheng-2176	3	43	berlin	berlin	PROPN
fumecheng-2176	3	44	,	,	PUNCT
fumecheng-2176	3	45	germany	germany	PROPN
fumecheng-2176	3	46	abstract	abstract	NOUN
fumecheng-2176	3	47	.	.	PUNCT
fumecheng-2176	4	1	using	use	VERB
fumecheng-2176	4	2	the	the	DET
fumecheng-2176	4	3	boundary	boundary	ADJ
fumecheng-2176	4	4	element	element	NOUN
fumecheng-2176	4	5	method	method	NOUN
fumecheng-2176	4	6	,	,	PUNCT
fumecheng-2176	4	7	we	we	PRON
fumecheng-2176	4	8	numerically	numerically	ADV
fumecheng-2176	4	9	study	study	VERB
fumecheng-2176	4	10	the	the	DET
fumecheng-2176	4	11	indentation	indentation	NOUN
fumecheng-2176	4	12	of	of	ADP
fumecheng-2176	4	13	prismatic	prismatic	ADJ
fumecheng-2176	4	14	and	and	CCONJ
fumecheng-2176	4	15	tapered	tapered	ADJ
fumecheng-2176	4	16	indenters	indenter	NOUN
fumecheng-2176	4	17	with	with	ADP
fumecheng-2176	4	18	polygonal	polygonal	ADJ
fumecheng-2176	4	19	cross	cross	NOUN
fumecheng-2176	4	20	-	-	NOUN
fumecheng-2176	4	21	sections	section	NOUN
fumecheng-2176	4	22	.	.	PUNCT
fumecheng-2176	5	1	the	the	DET
fumecheng-2176	5	2	contact	contact	NOUN
fumecheng-2176	5	3	stiffness	stiffness	NOUN
fumecheng-2176	5	4	of	of	ADP
fumecheng-2176	5	5	punches	punch	NOUN
fumecheng-2176	5	6	with	with	ADP
fumecheng-2176	5	7	flat	flat	ADJ
fumecheng-2176	5	8	bases	basis	NOUN
fumecheng-2176	5	9	in	in	ADP
fumecheng-2176	5	10	the	the	DET
fumecheng-2176	5	11	form	form	NOUN
fumecheng-2176	5	12	of	of	ADP
fumecheng-2176	5	13	a	a	DET
fumecheng-2176	5	14	triangle	triangle	NOUN
fumecheng-2176	5	15	and	and	CCONJ
fumecheng-2176	5	16	a	a	DET
fumecheng-2176	5	17	square	square	NOUN
fumecheng-2176	5	18	as	as	ADV
fumecheng-2176	5	19	well	well	ADV
fumecheng-2176	5	20	as	as	ADP
fumecheng-2176	5	21	a	a	DET
fumecheng-2176	5	22	number	number	NOUN
fumecheng-2176	5	23	of	of	ADP
fumecheng-2176	5	24	higher	high	ADJ
fumecheng-2176	5	25	-	-	PUNCT
fumecheng-2176	5	26	order	order	NOUN
fumecheng-2176	5	27	polygons	polygon	NOUN
fumecheng-2176	5	28	is	be	AUX
fumecheng-2176	5	29	determined	determine	VERB
fumecheng-2176	5	30	.	.	PUNCT
fumecheng-2176	6	1	in	in	ADP
fumecheng-2176	6	2	particular	particular	ADJ
fumecheng-2176	6	3	,	,	PUNCT
fumecheng-2176	6	4	the	the	DET
fumecheng-2176	6	5	classical	classical	ADJ
fumecheng-2176	6	6	results	result	NOUN
fumecheng-2176	6	7	of	of	ADP
fumecheng-2176	6	8	king	king	NOUN
fumecheng-2176	6	9	(	(	PUNCT
fumecheng-2176	6	10	1987	1987	NUM
fumecheng-2176	6	11	)	)	PUNCT
fumecheng-2176	6	12	for	for	ADP
fumecheng-2176	6	13	indenters	indenter	NOUN
fumecheng-2176	6	14	with	with	ADP
fumecheng-2176	6	15	triangle	triangle	NOUN
fumecheng-2176	6	16	and	and	CCONJ
fumecheng-2176	6	17	square	square	ADJ
fumecheng-2176	6	18	base	base	NOUN
fumecheng-2176	6	19	shapes	shape	NOUN
fumecheng-2176	6	20	are	be	AUX
fumecheng-2176	6	21	revised	revise	VERB
fumecheng-2176	6	22	and	and	CCONJ
fumecheng-2176	6	23	more	more	ADV
fumecheng-2176	6	24	precise	precise	ADJ
fumecheng-2176	6	25	numerical	numerical	ADJ
fumecheng-2176	6	26	results	result	NOUN
fumecheng-2176	6	27	are	be	AUX
fumecheng-2176	6	28	provided	provide	VERB
fumecheng-2176	6	29	.	.	PUNCT
fumecheng-2176	7	1	for	for	ADP
fumecheng-2176	7	2	tapered	tapered	ADJ
fumecheng-2176	7	3	indenters	indenter	NOUN
fumecheng-2176	7	4	,	,	PUNCT
fumecheng-2176	7	5	the	the	DET
fumecheng-2176	7	6	equivalent	equivalent	NOUN
fumecheng-2176	7	7	transformed	transform	VERB
fumecheng-2176	7	8	profile	profile	NOUN
fumecheng-2176	7	9	used	use	VERB
fumecheng-2176	7	10	in	in	ADP
fumecheng-2176	7	11	the	the	DET
fumecheng-2176	7	12	method	method	NOUN
fumecheng-2176	7	13	of	of	ADP
fumecheng-2176	7	14	dimensionality	dimensionality	NOUN
fumecheng-2176	7	15	reduction	reduction	NOUN
fumecheng-2176	7	16	(	(	PUNCT
fumecheng-2176	7	17	mdr	mdr	NOUN
fumecheng-2176	7	18	)	)	PUNCT
fumecheng-2176	7	19	is	be	AUX
fumecheng-2176	7	20	determined	determine	VERB
fumecheng-2176	7	21	.	.	PUNCT
fumecheng-2176	8	1	it	it	PRON
fumecheng-2176	8	2	is	be	AUX
fumecheng-2176	8	3	shown	show	VERB
fumecheng-2176	8	4	that	that	SCONJ
fumecheng-2176	8	5	the	the	DET
fumecheng-2176	8	6	mdr	mdr	PROPN
fumecheng-2176	8	7	-	-	PUNCT
fumecheng-2176	8	8	transformed	transform	VERB
fumecheng-2176	8	9	profile	profile	NOUN
fumecheng-2176	8	10	of	of	ADP
fumecheng-2176	8	11	polygon	polygon	NOUN
fumecheng-2176	8	12	-	-	PUNCT
fumecheng-2176	8	13	based	base	VERB
fumecheng-2176	8	14	indenters	indenter	NOUN
fumecheng-2176	8	15	with	with	ADP
fumecheng-2176	8	16	power	power	NOUN
fumecheng-2176	8	17	function	function	NOUN
fumecheng-2176	8	18	side	side	NOUN
fumecheng-2176	8	19	is	be	AUX
fumecheng-2176	8	20	given	give	VERB
fumecheng-2176	8	21	by	by	ADP
fumecheng-2176	8	22	the	the	DET
fumecheng-2176	8	23	power	power	NOUN
fumecheng-2176	8	24	function	function	NOUN
fumecheng-2176	8	25	with	with	ADP
fumecheng-2176	8	26	the	the	DET
fumecheng-2176	8	27	same	same	ADJ
fumecheng-2176	8	28	power	power	NOUN
fumecheng-2176	8	29	;	;	PUNCT
fumecheng-2176	8	30	it	it	PRON
fumecheng-2176	8	31	differs	differ	VERB
fumecheng-2176	8	32	from	from	ADP
fumecheng-2176	8	33	the	the	DET
fumecheng-2176	8	34	3d	3d	PROPN
fumecheng-2176	8	35	profile	profile	NOUN
fumecheng-2176	8	36	only	only	ADV
fumecheng-2176	8	37	by	by	ADP
fumecheng-2176	8	38	a	a	DET
fumecheng-2176	8	39	constant	constant	ADJ
fumecheng-2176	8	40	coefficient	coefficient	NOUN
fumecheng-2176	8	41	.	.	PUNCT
fumecheng-2176	9	1	these	these	DET
fumecheng-2176	9	2	coefficients	coefficient	NOUN
fumecheng-2176	9	3	are	be	AUX
fumecheng-2176	9	4	listed	list	VERB
fumecheng-2176	9	5	in	in	ADP
fumecheng-2176	9	6	the	the	DET
fumecheng-2176	9	7	paper	paper	NOUN
fumecheng-2176	9	8	for	for	ADP
fumecheng-2176	9	9	various	various	ADJ
fumecheng-2176	9	10	types	type	NOUN
fumecheng-2176	9	11	of	of	ADP
fumecheng-2176	9	12	indenters	indenter	NOUN
fumecheng-2176	9	13	,	,	PUNCT
fumecheng-2176	9	14	in	in	ADP
fumecheng-2176	9	15	particular	particular	ADJ
fumecheng-2176	9	16	for	for	ADP
fumecheng-2176	9	17	pyramidal	pyramidal	ADJ
fumecheng-2176	9	18	and	and	CCONJ
fumecheng-2176	9	19	paraboloid	paraboloid	ADJ
fumecheng-2176	9	20	ones	one	NOUN
fumecheng-2176	9	21	.	.	PUNCT
fumecheng-2176	10	1	the	the	DET
fumecheng-2176	10	2	determined	determined	ADJ
fumecheng-2176	10	3	mdr	mdr	PROPN
fumecheng-2176	10	4	-	-	ADJ
fumecheng-2176	10	5	transformed	transform	VERB
fumecheng-2176	10	6	profiles	profile	NOUN
fumecheng-2176	10	7	can	can	AUX
fumecheng-2176	10	8	be	be	AUX
fumecheng-2176	10	9	used	use	VERB
fumecheng-2176	10	10	for	for	ADP
fumecheng-2176	10	11	study	study	NOUN
fumecheng-2176	10	12	of	of	ADP
fumecheng-2176	10	13	other	other	ADJ
fumecheng-2176	10	14	contact	contact	NOUN
fumecheng-2176	10	15	problems	problem	NOUN
fumecheng-2176	10	16	such	such	ADJ
fumecheng-2176	10	17	as	as	ADP
fumecheng-2176	10	18	tangential	tangential	ADJ
fumecheng-2176	10	19	contact	contact	NOUN
fumecheng-2176	10	20	,	,	PUNCT
fumecheng-2176	10	21	normal	normal	ADJ
fumecheng-2176	10	22	contact	contact	NOUN
fumecheng-2176	10	23	with	with	ADP
fumecheng-2176	10	24	elastomers	elastomer	NOUN
fumecheng-2176	10	25	,	,	PUNCT
fumecheng-2176	10	26	and	and	CCONJ
fumecheng-2176	10	27	,	,	PUNCT
fumecheng-2176	10	28	in	in	ADP
fumecheng-2176	10	29	an	an	DET
fumecheng-2176	10	30	approximate	approximate	ADJ
fumecheng-2176	10	31	way	way	NOUN
fumecheng-2176	10	32	,	,	PUNCT
fumecheng-2176	10	33	to	to	PART
fumecheng-2176	10	34	adhesive	adhesive	ADJ
fumecheng-2176	10	35	contacts	contact	NOUN
fumecheng-2176	10	36	.	.	PUNCT
fumecheng-2176	11	1	key	key	ADJ
fumecheng-2176	11	2	words	word	NOUN
fumecheng-2176	11	3	:	:	PUNCT
fumecheng-2176	11	4	indentation	indentation	NOUN
fumecheng-2176	11	5	,	,	PUNCT
fumecheng-2176	11	6	contact	contact	NOUN
fumecheng-2176	11	7	stiffness	stiffness	NOUN
fumecheng-2176	11	8	,	,	PUNCT
fumecheng-2176	11	9	polygonal	polygonal	ADJ
fumecheng-2176	11	10	indenter	indenter	NOUN
fumecheng-2176	11	11	,	,	PUNCT
fumecheng-2176	11	12	boundary	boundary	ADJ
fumecheng-2176	11	13	element	element	NOUN
fumecheng-2176	11	14	method	method	NOUN
fumecheng-2176	11	15	,	,	PUNCT
fumecheng-2176	11	16	mdr	mdr	PROPN
fumecheng-2176	11	17	transformed	transform	VERB
fumecheng-2176	11	18	profile	profile	NOUN
fumecheng-2176	11	19	1	1	NUM
fumecheng-2176	11	20	.	.	PUNCT
fumecheng-2176	12	1	introduction	introduction	NOUN
fumecheng-2176	12	2	indentation	indentation	NOUN
fumecheng-2176	12	3	test	test	NOUN
fumecheng-2176	12	4	is	be	AUX
fumecheng-2176	12	5	a	a	DET
fumecheng-2176	12	6	very	very	ADV
fumecheng-2176	12	7	common	common	ADJ
fumecheng-2176	12	8	way	way	NOUN
fumecheng-2176	12	9	of	of	ADP
fumecheng-2176	12	10	probing	probe	VERB
fumecheng-2176	12	11	mechanical	mechanical	ADJ
fumecheng-2176	12	12	properties	property	NOUN
fumecheng-2176	12	13	of	of	ADP
fumecheng-2176	12	14	materials	material	NOUN
fumecheng-2176	12	15	such	such	ADJ
fumecheng-2176	12	16	as	as	ADP
fumecheng-2176	12	17	hardness	hardness	NOUN
fumecheng-2176	12	18	,	,	PUNCT
fumecheng-2176	12	19	contact	contact	NOUN
fumecheng-2176	12	20	stiffness	stiffness	NOUN
fumecheng-2176	12	21	,	,	PUNCT
fumecheng-2176	12	22	elastic	elastic	ADJ
fumecheng-2176	12	23	modulus	modulus	NOUN
fumecheng-2176	12	24	and	and	CCONJ
fumecheng-2176	12	25	strain	strain	NOUN
fumecheng-2176	12	26	-	-	PUNCT
fumecheng-2176	12	27	stress	stress	NOUN
fumecheng-2176	12	28	relation	relation	NOUN
fumecheng-2176	12	29	[	[	X
fumecheng-2176	12	30	1	1	NUM
fumecheng-2176	12	31	-	-	SYM
fumecheng-2176	12	32	3	3	NUM
fumecheng-2176	12	33	]	]	PUNCT
fumecheng-2176	12	34	.	.	PUNCT
fumecheng-2176	13	1	there	there	PRON
fumecheng-2176	13	2	is	be	VERB
fumecheng-2176	13	3	a	a	DET
fumecheng-2176	13	4	variety	variety	NOUN
fumecheng-2176	13	5	of	of	ADP
fumecheng-2176	13	6	indenter	indenter	NOUN
fumecheng-2176	13	7	geometries	geometries	PROPN
fumecheng-2176	13	8	used	use	VERB
fumecheng-2176	13	9	in	in	ADP
fumecheng-2176	13	10	macroand	macroand	NOUN
fumecheng-2176	13	11	microindentation	microindentation	NOUN
fumecheng-2176	13	12	;	;	PUNCT
fumecheng-2176	13	13	the	the	DET
fumecheng-2176	13	14	most	most	ADV
fumecheng-2176	13	15	popular	popular	ADJ
fumecheng-2176	13	16	are	be	AUX
fumecheng-2176	13	17	spherical	spherical	ADJ
fumecheng-2176	13	18	and	and	CCONJ
fumecheng-2176	13	19	pyramidal	pyramidal	ADJ
fumecheng-2176	13	20	indenters	indenter	NOUN
fumecheng-2176	13	21	(	(	PUNCT
fumecheng-2176	13	22	e.g.	e.g.	ADV
fumecheng-2176	13	23	for	for	ADP
fumecheng-2176	13	24	the	the	DET
fumecheng-2176	13	25	vickers	vickers	PROPN
fumecheng-2176	13	26	hardness	hardness	PROPN
fumecheng-2176	13	27	test	test	NOUN
fumecheng-2176	13	28	and	and	CCONJ
fumecheng-2176	13	29	brinell	brinell	VERB
fumecheng-2176	13	30	hardness	hardness	ADJ
fumecheng-2176	13	31	test	test	NOUN
fumecheng-2176	13	32	)	)	PUNCT
fumecheng-2176	14	1	[	[	X
fumecheng-2176	14	2	4	4	NUM
fumecheng-2176	14	3	]	]	PUNCT
fumecheng-2176	14	4	.	.	PUNCT
fumecheng-2176	15	1	the	the	DET
fumecheng-2176	15	2	contact	contact	NOUN
fumecheng-2176	15	3	stiffness	stiffness	NOUN
fumecheng-2176	15	4	of	of	ADP
fumecheng-2176	15	5	indenters	indenter	NOUN
fumecheng-2176	15	6	with	with	ADP
fumecheng-2176	15	7	regular	regular	ADJ
fumecheng-2176	15	8	geometries	geometry	NOUN
fumecheng-2176	15	9	is	be	AUX
fumecheng-2176	15	10	also	also	ADV
fumecheng-2176	15	11	important	important	ADJ
fumecheng-2176	15	12	for	for	ADP
fumecheng-2176	15	13	the	the	DET
fumecheng-2176	15	14	foundation	foundation	NOUN
fumecheng-2176	15	15	design	design	NOUN
fumecheng-2176	15	16	[	[	X
fumecheng-2176	15	17	5	5	NUM
fumecheng-2176	15	18	]	]	PUNCT
fumecheng-2176	15	19	.	.	PUNCT
fumecheng-2176	16	1	the	the	DET
fumecheng-2176	16	2	analytical	analytical	ADJ
fumecheng-2176	16	3	solution	solution	NOUN
fumecheng-2176	16	4	for	for	ADP
fumecheng-2176	16	5	contact	contact	NOUN
fumecheng-2176	16	6	between	between	ADP
fumecheng-2176	16	7	a	a	DET
fumecheng-2176	16	8	rigid	rigid	ADJ
fumecheng-2176	16	9	cylindrical	cylindrical	ADJ
fumecheng-2176	16	10	flat	flat	ADJ
fumecheng-2176	16	11	punch	punch	NOUN
fumecheng-2176	16	12	and	and	CCONJ
fumecheng-2176	16	13	an	an	DET
fumecheng-2176	16	14	elastic	elastic	ADJ
fumecheng-2176	16	15	half	half	NOUN
fumecheng-2176	16	16	space	space	NOUN
fumecheng-2176	16	17	was	be	AUX
fumecheng-2176	16	18	given	give	VERB
fumecheng-2176	16	19	by	by	ADP
fumecheng-2176	16	20	galin	galin	PROPN
fumecheng-2176	16	21	in	in	ADP
fumecheng-2176	16	22	1953	1953	NUM
fumecheng-2176	16	23	(	(	PUNCT
fumecheng-2176	16	24	english	english	ADJ
fumecheng-2176	16	25	translation	translation	NOUN
fumecheng-2176	16	26	see	see	VERB
fumecheng-2176	16	27	[	[	X
fumecheng-2176	16	28	6	6	NUM
fumecheng-2176	16	29	]	]	NUM
fumecheng-2176	16	30	)	)	PUNCT
fumecheng-2176	16	31	.	.	PUNCT
fumecheng-2176	17	1	his	his	PRON
fumecheng-2176	17	2	results	result	NOUN
fumecheng-2176	17	3	were	be	AUX
fumecheng-2176	17	4	later	later	ADV
fumecheng-2176	17	5	published	publish	VERB
fumecheng-2176	17	6	by	by	ADP
fumecheng-2176	17	7	sneddon	sneddon	PROPN
fumecheng-2176	17	8	and	and	CCONJ
fumecheng-2176	17	9	,	,	PUNCT
fumecheng-2176	17	10	in	in	ADP
fumecheng-2176	17	11	this	this	DET
fumecheng-2176	17	12	way	way	NOUN
fumecheng-2176	17	13	,	,	PUNCT
fumecheng-2176	17	14	made	make	VERB
fumecheng-2176	17	15	public	public	ADJ
fumecheng-2176	17	16	to	to	ADP
fumecheng-2176	17	17	the	the	DET
fumecheng-2176	17	18	western	western	ADJ
fumecheng-2176	17	19	world	world	NOUN
fumecheng-2176	18	1	[	[	X
fumecheng-2176	18	2	7	7	NUM
fumecheng-2176	18	3	]	]	PUNCT
fumecheng-2176	18	4	.	.	PUNCT
fumecheng-2176	19	1	based	base	VERB
fumecheng-2176	19	2	on	on	ADP
fumecheng-2176	19	3	this	this	PRON
fumecheng-2176	19	4	received	receive	VERB
fumecheng-2176	19	5	september	september	PROPN
fumecheng-2176	19	6	10	10	NUM
fumecheng-2176	19	7	,	,	PUNCT
fumecheng-2176	19	8	2016	2016	NUM
fumecheng-2176	19	9	/	/	SYM
fumecheng-2176	19	10	accepted	accept	VERB
fumecheng-2176	19	11	november	november	PROPN
fumecheng-2176	19	12	04	04	NUM
fumecheng-2176	19	13	,	,	PUNCT
fumecheng-2176	19	14	2016	2016	NUM
fumecheng-2176	19	15	corresponding	correspond	VERB
fumecheng-2176	19	16	author	author	NOUN
fumecheng-2176	19	17	:	:	PUNCT
fumecheng-2176	19	18	qiang	qiang	PROPN
fumecheng-2176	19	19	li	li	PROPN
fumecheng-2176	19	20	institute	institute	PROPN
fumecheng-2176	19	21	of	of	ADP
fumecheng-2176	19	22	mechanics	mechanic	NOUN
fumecheng-2176	19	23	,	,	PUNCT
fumecheng-2176	19	24	berlin	berlin	PROPN
fumecheng-2176	19	25	institute	institute	PROPN
fumecheng-2176	19	26	of	of	ADP
fumecheng-2176	19	27	technology	technology	PROPN
fumecheng-2176	19	28	,	,	PUNCT
fumecheng-2176	19	29	strasse	strasse	PROPN
fumecheng-2176	19	30	des	des	PROPN
fumecheng-2176	19	31	17	17	NUM
fumecheng-2176	19	32	.	.	PUNCT
fumecheng-2176	20	1	juni	juni	PROPN
fumecheng-2176	20	2	135	135	NUM
fumecheng-2176	20	3	,	,	PUNCT
fumecheng-2176	20	4	10623	10623	NUM
fumecheng-2176	20	5	berlin	berlin	PROPN
fumecheng-2176	20	6	,	,	PUNCT
fumecheng-2176	20	7	germany	germany	PROPN
fumecheng-2176	20	8	e	e	PROPN
fumecheng-2176	20	9	-	-	NOUN
fumecheng-2176	20	10	mail	mail	NOUN
fumecheng-2176	20	11	:	:	PUNCT
fumecheng-2176	20	12	qiang.li@tu-berlin.de	qiang.li@tu-berlin.de	NUM
fumecheng-2176	20	13	242	242	NUM
fumecheng-2176	20	14	q.	q.	PROPN
fumecheng-2176	20	15	li	li	PROPN
fumecheng-2176	20	16	,	,	PUNCT
fumecheng-2176	20	17	v.l	v.l	PROPN
fumecheng-2176	20	18	.	.	PROPN
fumecheng-2176	20	19	popov	popov	PROPN
fumecheng-2176	20	20	solution	solution	NOUN
fumecheng-2176	20	21	,	,	PUNCT
fumecheng-2176	20	22	oliver	oliver	PROPN
fumecheng-2176	20	23	and	and	CCONJ
fumecheng-2176	20	24	pharr	pharr	PROPN
fumecheng-2176	20	25	proposed	propose	VERB
fumecheng-2176	20	26	an	an	DET
fumecheng-2176	20	27	analysis	analysis	NOUN
fumecheng-2176	20	28	method	method	NOUN
fumecheng-2176	20	29	to	to	PART
fumecheng-2176	20	30	determine	determine	VERB
fumecheng-2176	20	31	the	the	DET
fumecheng-2176	20	32	hardness	hardness	ADJ
fumecheng-2176	20	33	and	and	CCONJ
fumecheng-2176	20	34	elastic	elastic	ADJ
fumecheng-2176	20	35	modulus	modulus	NOUN
fumecheng-2176	20	36	from	from	ADP
fumecheng-2176	20	37	the	the	DET
fumecheng-2176	20	38	load	load	NOUN
fumecheng-2176	20	39	-	-	PUNCT
fumecheng-2176	20	40	displacement	displacement	ADJ
fumecheng-2176	20	41	curves	curve	NOUN
fumecheng-2176	20	42	of	of	ADP
fumecheng-2176	20	43	indentation	indentation	NOUN
fumecheng-2176	20	44	test	test	NOUN
fumecheng-2176	21	1	[	[	X
fumecheng-2176	21	2	8	8	NUM
fumecheng-2176	21	3	]	]	PUNCT
fumecheng-2176	21	4	.	.	PUNCT
fumecheng-2176	22	1	general	general	ADJ
fumecheng-2176	22	2	relations	relation	NOUN
fumecheng-2176	22	3	among	among	ADP
fumecheng-2176	22	4	contact	contact	NOUN
fumecheng-2176	22	5	stiffness	stiffness	NOUN
fumecheng-2176	22	6	,	,	PUNCT
fumecheng-2176	22	7	contact	contact	NOUN
fumecheng-2176	22	8	area	area	NOUN
fumecheng-2176	22	9	,	,	PUNCT
fumecheng-2176	22	10	and	and	CCONJ
fumecheng-2176	22	11	elastic	elastic	ADJ
fumecheng-2176	22	12	modulus	modulus	NOUN
fumecheng-2176	22	13	during	during	ADP
fumecheng-2176	22	14	indentation	indentation	NOUN
fumecheng-2176	22	15	have	have	AUX
fumecheng-2176	22	16	been	be	AUX
fumecheng-2176	22	17	analytically	analytically	ADV
fumecheng-2176	22	18	derived	derive	VERB
fumecheng-2176	22	19	only	only	ADV
fumecheng-2176	22	20	for	for	ADP
fumecheng-2176	22	21	axisymmetric	axisymmetric	ADJ
fumecheng-2176	22	22	indenters	indenter	NOUN
fumecheng-2176	22	23	.	.	PUNCT
fumecheng-2176	23	1	for	for	ADP
fumecheng-2176	23	2	a	a	DET
fumecheng-2176	23	3	non	non	ADJ
fumecheng-2176	23	4	-	-	ADJ
fumecheng-2176	23	5	axisymmetrical	axisymmetrical	ADJ
fumecheng-2176	23	6	geometry	geometry	NOUN
fumecheng-2176	23	7	,	,	PUNCT
fumecheng-2176	23	8	a	a	DET
fumecheng-2176	23	9	correction	correction	NOUN
fumecheng-2176	23	10	coefficient	coefficient	NOUN
fumecheng-2176	23	11	is	be	AUX
fumecheng-2176	23	12	needed	need	VERB
fumecheng-2176	23	13	[	[	PUNCT
fumecheng-2176	23	14	9	9	NUM
fumecheng-2176	23	15	]	]	PUNCT
fumecheng-2176	23	16	,	,	PUNCT
fumecheng-2176	23	17	which	which	PRON
fumecheng-2176	23	18	can	can	AUX
fumecheng-2176	23	19	be	be	AUX
fumecheng-2176	23	20	still	still	ADV
fumecheng-2176	23	21	found	find	VERB
fumecheng-2176	23	22	only	only	ADV
fumecheng-2176	23	23	numerically	numerically	ADV
fumecheng-2176	23	24	.	.	PUNCT
fumecheng-2176	24	1	in	in	ADP
fumecheng-2176	24	2	this	this	DET
fumecheng-2176	24	3	paper	paper	NOUN
fumecheng-2176	24	4	we	we	PRON
fumecheng-2176	24	5	numerically	numerically	ADV
fumecheng-2176	24	6	investigate	investigate	VERB
fumecheng-2176	24	7	the	the	DET
fumecheng-2176	24	8	indentation	indentation	NOUN
fumecheng-2176	24	9	of	of	ADP
fumecheng-2176	24	10	rigid	rigid	ADJ
fumecheng-2176	24	11	bodies	body	NOUN
fumecheng-2176	24	12	with	with	ADP
fumecheng-2176	24	13	various	various	ADJ
fumecheng-2176	24	14	geometries	geometry	NOUN
fumecheng-2176	24	15	:	:	PUNCT
fumecheng-2176	24	16	the	the	DET
fumecheng-2176	24	17	flat	flat	ADV
fumecheng-2176	24	18	-	-	PUNCT
fumecheng-2176	24	19	ended	end	VERB
fumecheng-2176	24	20	punches	punch	NOUN
fumecheng-2176	24	21	in	in	ADP
fumecheng-2176	24	22	section	section	NOUN
fumecheng-2176	24	23	2	2	NUM
fumecheng-2176	24	24	and	and	CCONJ
fumecheng-2176	24	25	tapered	tapered	ADJ
fumecheng-2176	24	26	indenters	indenter	NOUN
fumecheng-2176	24	27	in	in	ADP
fumecheng-2176	24	28	section	section	NOUN
fumecheng-2176	24	29	3	3	NUM
fumecheng-2176	24	30	.	.	PUNCT
fumecheng-2176	25	1	in	in	ADP
fumecheng-2176	25	2	both	both	DET
fumecheng-2176	25	3	cases	case	NOUN
fumecheng-2176	25	4	we	we	PRON
fumecheng-2176	25	5	consider	consider	VERB
fumecheng-2176	25	6	different	different	ADJ
fumecheng-2176	25	7	polygonal	polygonal	ADJ
fumecheng-2176	25	8	bases	basis	NOUN
fumecheng-2176	25	9	including	include	VERB
fumecheng-2176	25	10	triangle	triangle	NOUN
fumecheng-2176	25	11	and	and	CCONJ
fumecheng-2176	25	12	square	square	NOUN
fumecheng-2176	25	13	.	.	PUNCT
fumecheng-2176	26	1	note	note	VERB
fumecheng-2176	26	2	that	that	SCONJ
fumecheng-2176	26	3	the	the	DET
fumecheng-2176	26	4	assumption	assumption	NOUN
fumecheng-2176	26	5	of	of	ADP
fumecheng-2176	26	6	a	a	DET
fumecheng-2176	26	7	rigid	rigid	ADJ
fumecheng-2176	26	8	indenter	indenter	NOUN
fumecheng-2176	26	9	is	be	AUX
fumecheng-2176	26	10	no	no	DET
fumecheng-2176	26	11	restriction	restriction	NOUN
fumecheng-2176	26	12	as	as	ADP
fumecheng-2176	26	13	the	the	DET
fumecheng-2176	26	14	normal	normal	ADJ
fumecheng-2176	26	15	frictionless	frictionless	ADJ
fumecheng-2176	26	16	contact	contact	NOUN
fumecheng-2176	26	17	of	of	ADP
fumecheng-2176	26	18	two	two	NUM
fumecheng-2176	26	19	elastic	elastic	ADJ
fumecheng-2176	26	20	bodies	body	NOUN
fumecheng-2176	26	21	with	with	ADP
fumecheng-2176	26	22	elastic	elastic	ADJ
fumecheng-2176	26	23	moduli	moduli	NOUN
fumecheng-2176	26	24	e1	e1	PROPN
fumecheng-2176	26	25	and	and	CCONJ
fumecheng-2176	26	26	e2	e2	PROPN
fumecheng-2176	26	27	and	and	CCONJ
fumecheng-2176	26	28	poisson	poisson	NOUN
fumecheng-2176	26	29	numbers	number	NOUN
fumecheng-2176	26	30	ν1	ν1	NOUN
fumecheng-2176	26	31	and	and	CCONJ
fumecheng-2176	26	32	ν2	ν2	NOUN
fumecheng-2176	26	33	can	can	AUX
fumecheng-2176	26	34	always	always	ADV
fumecheng-2176	26	35	be	be	AUX
fumecheng-2176	26	36	reduced	reduce	VERB
fumecheng-2176	26	37	to	to	ADP
fumecheng-2176	26	38	the	the	DET
fumecheng-2176	26	39	contact	contact	NOUN
fumecheng-2176	26	40	of	of	ADP
fumecheng-2176	26	41	a	a	DET
fumecheng-2176	26	42	rigid	rigid	ADJ
fumecheng-2176	26	43	indenter	indenter	NOUN
fumecheng-2176	26	44	and	and	CCONJ
fumecheng-2176	26	45	an	an	DET
fumecheng-2176	26	46	elastic	elastic	ADJ
fumecheng-2176	26	47	medium	medium	NOUN
fumecheng-2176	26	48	with	with	ADP
fumecheng-2176	26	49	an	an	DET
fumecheng-2176	26	50	effective	effective	ADJ
fumecheng-2176	26	51	elastic	elastic	ADJ
fumecheng-2176	26	52	modulus	modulus	NOUN
fumecheng-2176	26	53	e	e	NOUN
fumecheng-2176	26	54	*	*	PUNCT
fumecheng-2176	26	55	determined	determine	VERB
fumecheng-2176	26	56	as	as	ADP
fumecheng-2176	26	57	[	[	X
fumecheng-2176	26	58	10	10	NUM
fumecheng-2176	26	59	]	]	SYM
fumecheng-2176	26	60	2	2	NUM
fumecheng-2176	26	61	2	2	NUM
fumecheng-2176	26	62	1	1	NUM
fumecheng-2176	26	63	2	2	NUM
fumecheng-2176	26	64	*	*	SYM
fumecheng-2176	26	65	1	1	NUM
fumecheng-2176	26	66	2	2	NUM
fumecheng-2176	26	67	1	1	NUM
fumecheng-2176	26	68	11	11	NUM
fumecheng-2176	26	69	e	e	NOUN
fumecheng-2176	26	70	ee	ee	ADP
fumecheng-2176	26	71			ADJ
fumecheng-2176	26	72			ADJ
fumecheng-2176	26	73			PROPN
fumecheng-2176	26	74			PROPN
fumecheng-2176	26	75			PUNCT
fumecheng-2176	26	76	.	.	PUNCT
fumecheng-2176	27	1	(	(	PUNCT
fumecheng-2176	27	2	1	1	X
fumecheng-2176	27	3	)	)	PUNCT
fumecheng-2176	27	4	in	in	ADP
fumecheng-2176	27	5	the	the	DET
fumecheng-2176	27	6	present	present	ADJ
fumecheng-2176	27	7	paper	paper	NOUN
fumecheng-2176	27	8	,	,	PUNCT
fumecheng-2176	27	9	the	the	DET
fumecheng-2176	27	10	indentation	indentation	NOUN
fumecheng-2176	27	11	test	test	NOUN
fumecheng-2176	27	12	is	be	AUX
fumecheng-2176	27	13	numerically	numerically	ADV
fumecheng-2176	27	14	simulated	simulate	VERB
fumecheng-2176	27	15	by	by	ADP
fumecheng-2176	27	16	the	the	DET
fumecheng-2176	27	17	high	high	ADJ
fumecheng-2176	27	18	resolution	resolution	NOUN
fumecheng-2176	27	19	boundary	boundary	ADJ
fumecheng-2176	27	20	element	element	NOUN
fumecheng-2176	27	21	method	method	NOUN
fumecheng-2176	27	22	(	(	PUNCT
fumecheng-2176	27	23	bem	bem	PROPN
fumecheng-2176	27	24	)	)	PUNCT
fumecheng-2176	27	25	,	,	PUNCT
fumecheng-2176	27	26	which	which	PRON
fumecheng-2176	27	27	has	have	AUX
fumecheng-2176	27	28	recently	recently	ADV
fumecheng-2176	27	29	been	be	AUX
fumecheng-2176	27	30	generalized	generalize	VERB
fumecheng-2176	27	31	to	to	ADP
fumecheng-2176	27	32	arbitrary	arbitrary	ADJ
fumecheng-2176	27	33	contact	contact	NOUN
fumecheng-2176	27	34	problems	problem	NOUN
fumecheng-2176	27	35	including	include	VERB
fumecheng-2176	27	36	tangential	tangential	ADJ
fumecheng-2176	27	37	contact	contact	NOUN
fumecheng-2176	27	38	and	and	CCONJ
fumecheng-2176	27	39	adhesive	adhesive	ADJ
fumecheng-2176	27	40	contact	contact	NOUN
fumecheng-2176	27	41	[	[	X
fumecheng-2176	27	42	11	11	NUM
fumecheng-2176	27	43	,	,	PUNCT
fumecheng-2176	27	44	12	12	NUM
fumecheng-2176	27	45	]	]	PUNCT
fumecheng-2176	27	46	.	.	PUNCT
fumecheng-2176	28	1	2	2	X
fumecheng-2176	28	2	.	.	X
fumecheng-2176	28	3	indentation	indentation	NOUN
fumecheng-2176	28	4	of	of	ADP
fumecheng-2176	28	5	prismatic	prismatic	ADJ
fumecheng-2176	28	6	indenters	indenter	NOUN
fumecheng-2176	28	7	with	with	ADP
fumecheng-2176	28	8	polygonal	polygonal	ADJ
fumecheng-2176	28	9	base	base	NOUN
fumecheng-2176	28	10	the	the	DET
fumecheng-2176	28	11	normal	normal	ADJ
fumecheng-2176	28	12	contact	contact	NOUN
fumecheng-2176	28	13	stiffness	stiffness	NOUN
fumecheng-2176	28	14	between	between	ADP
fumecheng-2176	28	15	a	a	DET
fumecheng-2176	28	16	rigid	rigid	ADJ
fumecheng-2176	28	17	flat	flat	ADJ
fumecheng-2176	28	18	cylinder	cylinder	NOUN
fumecheng-2176	28	19	and	and	CCONJ
fumecheng-2176	28	20	an	an	DET
fumecheng-2176	28	21	elastic	elastic	ADJ
fumecheng-2176	28	22	half	half	NOUN
fumecheng-2176	28	23	space	space	NOUN
fumecheng-2176	28	24	is	be	AUX
fumecheng-2176	28	25	given	give	VERB
fumecheng-2176	28	26	by	by	ADP
fumecheng-2176	28	27	k=2ae	k=2ae	NOUN
fumecheng-2176	28	28	*	*	PUNCT
fumecheng-2176	29	1	[	[	X
fumecheng-2176	29	2	7	7	NUM
fumecheng-2176	29	3	]	]	PUNCT
fumecheng-2176	29	4	,	,	PUNCT
fumecheng-2176	29	5	where	where	SCONJ
fumecheng-2176	29	6	a	a	PRON
fumecheng-2176	29	7	is	be	AUX
fumecheng-2176	29	8	the	the	DET
fumecheng-2176	29	9	radius	radius	NOUN
fumecheng-2176	29	10	of	of	ADP
fumecheng-2176	29	11	the	the	DET
fumecheng-2176	29	12	cylinder	cylinder	NOUN
fumecheng-2176	29	13	,	,	PUNCT
fumecheng-2176	29	14	and	and	CCONJ
fumecheng-2176	29	15	e	e	X
fumecheng-2176	29	16	*	*	PUNCT
fumecheng-2176	29	17	is	be	AUX
fumecheng-2176	29	18	the	the	DET
fumecheng-2176	29	19	effective	effective	ADJ
fumecheng-2176	29	20	elastic	elastic	ADJ
fumecheng-2176	29	21	modulus	modulus	NOUN
fumecheng-2176	29	22	,	,	PUNCT
fumecheng-2176	29	23	eq	eq	NOUN
fumecheng-2176	29	24	.	.	PUNCT
fumecheng-2176	30	1	(	(	PUNCT
fumecheng-2176	30	2	1	1	NUM
fumecheng-2176	30	3	)	)	PUNCT
fumecheng-2176	30	4	.	.	PUNCT
fumecheng-2176	31	1	in	in	ADP
fumecheng-2176	31	2	the	the	DET
fumecheng-2176	31	3	case	case	NOUN
fumecheng-2176	31	4	of	of	ADP
fumecheng-2176	31	5	a	a	DET
fumecheng-2176	31	6	prismatic	prismatic	ADJ
fumecheng-2176	31	7	indenter	indenter	NOUN
fumecheng-2176	31	8	with	with	ADP
fumecheng-2176	31	9	an	an	DET
fumecheng-2176	31	10	arbitrary	arbitrary	ADJ
fumecheng-2176	31	11	base	base	NOUN
fumecheng-2176	31	12	form	form	NOUN
fumecheng-2176	31	13	,	,	PUNCT
fumecheng-2176	31	14	the	the	DET
fumecheng-2176	31	15	normal	normal	ADJ
fumecheng-2176	31	16	contact	contact	NOUN
fumecheng-2176	31	17	stiffness	stiffness	NOUN
fumecheng-2176	31	18	is	be	AUX
fumecheng-2176	31	19	given	give	VERB
fumecheng-2176	31	20	by	by	ADP
fumecheng-2176	31	21	[	[	X
fumecheng-2176	31	22	5	5	NUM
fumecheng-2176	31	23	]	]	PUNCT
fumecheng-2176	31	24	:	:	PUNCT
fumecheng-2176	31	25	*	*	PUNCT
fumecheng-2176	31	26	2	2	NUM
fumecheng-2176	31	27	a	a	DET
fumecheng-2176	31	28	k	k	PROPN
fumecheng-2176	31	29	e	e	PROPN
fumecheng-2176	31	30			PROPN
fumecheng-2176	31	31			PROPN
fumecheng-2176	31	32			PROPN
fumecheng-2176	31	33	,	,	PUNCT
fumecheng-2176	31	34	(	(	PUNCT
fumecheng-2176	31	35	2	2	X
fumecheng-2176	31	36	)	)	PUNCT
fumecheng-2176	31	37	where	where	SCONJ
fumecheng-2176	31	38	a	a	PRON
fumecheng-2176	31	39	is	be	AUX
fumecheng-2176	31	40	the	the	DET
fumecheng-2176	31	41	contact	contact	NOUN
fumecheng-2176	31	42	area	area	NOUN
fumecheng-2176	31	43	of	of	ADP
fumecheng-2176	31	44	the	the	DET
fumecheng-2176	31	45	base	base	NOUN
fumecheng-2176	31	46	.	.	PUNCT
fumecheng-2176	32	1	obviously	obviously	ADV
fumecheng-2176	32	2	the	the	DET
fumecheng-2176	32	3	value	value	NOUN
fumecheng-2176	32	4	of	of	ADP
fumecheng-2176	32	5	β	β	PROPN
fumecheng-2176	32	6	is	be	AUX
fumecheng-2176	32	7	equal	equal	ADJ
fumecheng-2176	32	8	to	to	ADP
fumecheng-2176	32	9	1	1	NUM
fumecheng-2176	32	10	for	for	ADP
fumecheng-2176	32	11	the	the	DET
fumecheng-2176	32	12	flat	flat	ADV
fumecheng-2176	32	13	-	-	PUNCT
fumecheng-2176	32	14	ended	end	VERB
fumecheng-2176	32	15	cylinder	cylinder	NOUN
fumecheng-2176	32	16	.	.	PUNCT
fumecheng-2176	33	1	it	it	PRON
fumecheng-2176	33	2	was	be	AUX
fumecheng-2176	33	3	proven	prove	VERB
fumecheng-2176	33	4	that	that	SCONJ
fumecheng-2176	33	5	eq	eq	ADP
fumecheng-2176	33	6	.	.	PUNCT
fumecheng-2176	34	1	(	(	PUNCT
fumecheng-2176	34	2	2	2	X
fumecheng-2176	34	3	)	)	PUNCT
fumecheng-2176	34	4	is	be	AUX
fumecheng-2176	34	5	also	also	ADV
fumecheng-2176	34	6	valid	valid	ADJ
fumecheng-2176	34	7	for	for	ADP
fumecheng-2176	34	8	indenters	indenter	NOUN
fumecheng-2176	34	9	which	which	PRON
fumecheng-2176	34	10	have	have	VERB
fumecheng-2176	34	11	a	a	DET
fumecheng-2176	34	12	cross	cross	NOUN
fumecheng-2176	34	13	section	section	NOUN
fumecheng-2176	34	14	other	other	ADJ
fumecheng-2176	34	15	than	than	ADP
fumecheng-2176	34	16	a	a	DET
fumecheng-2176	34	17	circle	circle	NOUN
fumecheng-2176	35	1	[	[	X
fumecheng-2176	35	2	5	5	NUM
fumecheng-2176	35	3	]	]	PUNCT
fumecheng-2176	35	4	:	:	PUNCT
fumecheng-2176	35	5	β=1.034	β=1.034	PUNCT
fumecheng-2176	35	6	for	for	ADP
fumecheng-2176	35	7	triangle	triangle	NOUN
fumecheng-2176	35	8	and	and	CCONJ
fumecheng-2176	35	9	β=1.012	β=1.012	NUM
fumecheng-2176	35	10	for	for	ADP
fumecheng-2176	35	11	square	square	NOUN
fumecheng-2176	35	12	.	.	PUNCT
fumecheng-2176	36	1	these	these	DET
fumecheng-2176	36	2	results	result	NOUN
fumecheng-2176	36	3	were	be	AUX
fumecheng-2176	36	4	numerically	numerically	ADV
fumecheng-2176	36	5	obtained	obtain	VERB
fumecheng-2176	36	6	by	by	ADP
fumecheng-2176	36	7	king	king	NOUN
fumecheng-2176	36	8	in	in	ADP
fumecheng-2176	36	9	1987	1987	NUM
fumecheng-2176	36	10	.	.	PUNCT
fumecheng-2176	37	1	due	due	ADP
fumecheng-2176	37	2	to	to	ADP
fumecheng-2176	37	3	the	the	DET
fumecheng-2176	37	4	limitation	limitation	NOUN
fumecheng-2176	37	5	of	of	ADP
fumecheng-2176	37	6	computer	computer	NOUN
fumecheng-2176	37	7	technology	technology	NOUN
fumecheng-2176	37	8	at	at	ADP
fumecheng-2176	37	9	that	that	DET
fumecheng-2176	37	10	time	time	NOUN
fumecheng-2176	37	11	,	,	PUNCT
fumecheng-2176	37	12	king	king	NOUN
fumecheng-2176	37	13	used	use	VERB
fumecheng-2176	37	14	only	only	ADV
fumecheng-2176	37	15	200	200	NUM
fumecheng-2176	37	16	elements	element	NOUN
fumecheng-2176	37	17	for	for	ADP
fumecheng-2176	37	18	simulating	simulate	VERB
fumecheng-2176	37	19	a	a	DET
fumecheng-2176	37	20	triangle	triangle	NOUN
fumecheng-2176	37	21	indenter	indenter	NOUN
fumecheng-2176	37	22	,	,	PUNCT
fumecheng-2176	37	23	and	and	CCONJ
fumecheng-2176	37	24	the	the	DET
fumecheng-2176	37	25	fig	fig	NOUN
fumecheng-2176	37	26	.	.	PUNCT
fumecheng-2176	38	1	1	1	NUM
fumecheng-2176	38	2	prismatic	prismatic	ADJ
fumecheng-2176	38	3	indenters	indenter	NOUN
fumecheng-2176	38	4	with	with	ADP
fumecheng-2176	38	5	polygonal	polygonal	ADJ
fumecheng-2176	38	6	bases	basis	NOUN
fumecheng-2176	38	7	:	:	PUNCT
fumecheng-2176	38	8	m=3	m=3	PROPN
fumecheng-2176	38	9	(	(	PUNCT
fumecheng-2176	38	10	triangle	triangle	NOUN
fumecheng-2176	38	11	)	)	PUNCT
fumecheng-2176	38	12	,	,	PUNCT
fumecheng-2176	38	13	m=4	m=4	PROPN
fumecheng-2176	38	14	(	(	PUNCT
fumecheng-2176	38	15	square	square	NOUN
fumecheng-2176	38	16	)	)	PUNCT
fumecheng-2176	38	17	,	,	PUNCT
fumecheng-2176	38	18	m=5	m=5	PROPN
fumecheng-2176	38	19	(	(	PUNCT
fumecheng-2176	38	20	pentagon	pentagon	PROPN
fumecheng-2176	38	21	)	)	PUNCT
fumecheng-2176	38	22	and	and	CCONJ
fumecheng-2176	38	23	m=∞	m=∞	PROPN
fumecheng-2176	38	24	(	(	PUNCT
fumecheng-2176	38	25	circle	circle	NOUN
fumecheng-2176	38	26	)	)	PUNCT
fumecheng-2176	38	27	indentation	indentation	NOUN
fumecheng-2176	38	28	of	of	ADP
fumecheng-2176	38	29	flat	flat	ADV
fumecheng-2176	38	30	-	-	PUNCT
fumecheng-2176	38	31	ended	end	VERB
fumecheng-2176	38	32	and	and	CCONJ
fumecheng-2176	38	33	tapered	tapered	ADJ
fumecheng-2176	38	34	indenters	indenter	NOUN
fumecheng-2176	38	35	with	with	ADP
fumecheng-2176	38	36	polygonal	polygonal	ADJ
fumecheng-2176	38	37	cross	cross	NOUN
fumecheng-2176	38	38	-	-	NOUN
fumecheng-2176	38	39	sections	section	NOUN
fumecheng-2176	38	40	243	243	NUM
fumecheng-2176	38	41	triangular	triangular	NOUN
fumecheng-2176	38	42	area	area	NOUN
fumecheng-2176	38	43	looked	look	VERB
fumecheng-2176	38	44	quite	quite	ADV
fumecheng-2176	38	45	„	„	PUNCT
fumecheng-2176	38	46	rugged‟.	rugged‟.	PRON
fumecheng-2176	38	47	note	note	VERB
fumecheng-2176	38	48	that	that	SCONJ
fumecheng-2176	38	49	the	the	DET
fumecheng-2176	38	50	stiffness	stiffness	NOUN
fumecheng-2176	38	51	of	of	ADP
fumecheng-2176	38	52	a	a	DET
fumecheng-2176	38	53	flat	flat	ADJ
fumecheng-2176	38	54	punch	punch	NOUN
fumecheng-2176	38	55	and	and	CCONJ
fumecheng-2176	38	56	correspondingly	correspondingly	ADV
fumecheng-2176	38	57	factor	factor	NOUN
fumecheng-2176	38	58	β	β	NOUN
fumecheng-2176	38	59	are	be	AUX
fumecheng-2176	38	60	related	relate	VERB
fumecheng-2176	38	61	to	to	ADP
fumecheng-2176	38	62	the	the	DET
fumecheng-2176	38	63	so	so	ADV
fumecheng-2176	38	64	-	-	PUNCT
fumecheng-2176	38	65	called	call	VERB
fumecheng-2176	38	66	harmonic	harmonic	ADJ
fumecheng-2176	38	67	capacity	capacity	NOUN
fumecheng-2176	38	68	of	of	ADP
fumecheng-2176	38	69	the	the	DET
fumecheng-2176	38	70	base	base	NOUN
fumecheng-2176	38	71	form	form	NOUN
fumecheng-2176	38	72	of	of	ADP
fumecheng-2176	38	73	the	the	DET
fumecheng-2176	38	74	punch	punch	NOUN
fumecheng-2176	38	75	.	.	PUNCT
fumecheng-2176	39	1	this	this	DET
fumecheng-2176	39	2	analogy	analogy	NOUN
fumecheng-2176	39	3	was	be	AUX
fumecheng-2176	39	4	discussed	discuss	VERB
fumecheng-2176	39	5	by	by	ADP
fumecheng-2176	39	6	argatov	argatov	NOUN
fumecheng-2176	39	7	(	(	PUNCT
fumecheng-2176	39	8	2010	2010	NUM
fumecheng-2176	39	9	)	)	PUNCT
fumecheng-2176	40	1	[	[	X
fumecheng-2176	40	2	13	13	NUM
fumecheng-2176	40	3	]	]	PUNCT
fumecheng-2176	40	4	.	.	PUNCT
fumecheng-2176	41	1	below	below	ADV
fumecheng-2176	41	2	we	we	PRON
fumecheng-2176	41	3	repeat	repeat	VERB
fumecheng-2176	41	4	the	the	DET
fumecheng-2176	41	5	calculations	calculation	NOUN
fumecheng-2176	41	6	of	of	ADP
fumecheng-2176	41	7	king	king	NOUN
fumecheng-2176	41	8	using	use	VERB
fumecheng-2176	41	9	the	the	DET
fumecheng-2176	41	10	current	current	ADJ
fumecheng-2176	41	11	high	high	ADJ
fumecheng-2176	41	12	-	-	PUNCT
fumecheng-2176	41	13	resolution	resolution	NOUN
fumecheng-2176	41	14	bem	bem	NOUN
fumecheng-2176	41	15	and	and	CCONJ
fumecheng-2176	41	16	provide	provide	VERB
fumecheng-2176	41	17	corrected	correct	VERB
fumecheng-2176	41	18	values	value	NOUN
fumecheng-2176	41	19	.	.	PUNCT
fumecheng-2176	42	1	using	use	VERB
fumecheng-2176	42	2	the	the	DET
fumecheng-2176	42	3	boundary	boundary	ADJ
fumecheng-2176	42	4	element	element	NOUN
fumecheng-2176	42	5	method	method	NOUN
fumecheng-2176	42	6	we	we	PRON
fumecheng-2176	42	7	have	have	AUX
fumecheng-2176	42	8	numerically	numerically	ADV
fumecheng-2176	42	9	carried	carry	VERB
fumecheng-2176	42	10	out	out	ADP
fumecheng-2176	42	11	the	the	DET
fumecheng-2176	42	12	indentation	indentation	NOUN
fumecheng-2176	42	13	test	test	NOUN
fumecheng-2176	42	14	for	for	ADP
fumecheng-2176	42	15	different	different	ADJ
fumecheng-2176	42	16	shapes	shape	NOUN
fumecheng-2176	42	17	of	of	ADP
fumecheng-2176	42	18	cross	cross	NOUN
fumecheng-2176	42	19	section	section	NOUN
fumecheng-2176	42	20	of	of	ADP
fumecheng-2176	42	21	indenters	indenter	NOUN
fumecheng-2176	42	22	:	:	PUNCT
fumecheng-2176	42	23	from	from	ADP
fumecheng-2176	42	24	triangle	triangle	NOUN
fumecheng-2176	42	25	(	(	PUNCT
fumecheng-2176	42	26	m=3	m=3	PROPN
fumecheng-2176	42	27	)	)	PUNCT
fumecheng-2176	42	28	,	,	PUNCT
fumecheng-2176	42	29	square	square	NOUN
fumecheng-2176	42	30	(	(	PUNCT
fumecheng-2176	42	31	m=4	m=4	NOUN
fumecheng-2176	42	32	)	)	PUNCT
fumecheng-2176	42	33	,	,	PUNCT
fumecheng-2176	42	34	pentagon	pentagon	PROPN
fumecheng-2176	42	35	(	(	PUNCT
fumecheng-2176	42	36	m=5	m=5	NOUN
fumecheng-2176	42	37	)	)	PUNCT
fumecheng-2176	42	38	to	to	PART
fumecheng-2176	42	39	circle	circle	VERB
fumecheng-2176	42	40	(	(	PUNCT
fumecheng-2176	42	41	m=∞	m=∞	PROPN
fumecheng-2176	42	42	)	)	PUNCT
fumecheng-2176	42	43	as	as	SCONJ
fumecheng-2176	42	44	shown	show	VERB
fumecheng-2176	42	45	in	in	ADP
fumecheng-2176	42	46	fig.1	fig.1	PROPN
fumecheng-2176	42	47	.	.	PUNCT
fumecheng-2176	43	1	in	in	ADP
fumecheng-2176	43	2	the	the	DET
fumecheng-2176	43	3	simulation	simulation	NOUN
fumecheng-2176	43	4	,	,	PUNCT
fumecheng-2176	43	5	the	the	DET
fumecheng-2176	43	6	whole	whole	ADJ
fumecheng-2176	43	7	area	area	NOUN
fumecheng-2176	43	8	was	be	AUX
fumecheng-2176	43	9	divided	divide	VERB
fumecheng-2176	43	10	into	into	ADP
fumecheng-2176	43	11	1024x1024	1024x1024	NUM
fumecheng-2176	43	12	elements	element	NOUN
fumecheng-2176	43	13	where	where	SCONJ
fumecheng-2176	43	14	at	at	ADV
fumecheng-2176	43	15	least	least	ADV
fumecheng-2176	43	16	200000	200000	NUM
fumecheng-2176	43	17	elements	element	NOUN
fumecheng-2176	43	18	were	be	AUX
fumecheng-2176	43	19	in	in	ADP
fumecheng-2176	43	20	the	the	DET
fumecheng-2176	43	21	contact	contact	NOUN
fumecheng-2176	43	22	area	area	NOUN
fumecheng-2176	43	23	.	.	PUNCT
fumecheng-2176	44	1	it	it	PRON
fumecheng-2176	44	2	is	be	AUX
fumecheng-2176	44	3	at	at	ADP
fumecheng-2176	44	4	least	least	ADJ
fumecheng-2176	44	5	1000	1000	NUM
fumecheng-2176	44	6	times	time	NOUN
fumecheng-2176	44	7	more	more	ADJ
fumecheng-2176	44	8	than	than	ADP
fumecheng-2176	44	9	in	in	ADP
fumecheng-2176	44	10	the	the	DET
fumecheng-2176	44	11	king‟s	king‟s	NOUN
fumecheng-2176	44	12	simulations	simulation	NOUN
fumecheng-2176	44	13	;	;	PUNCT
fumecheng-2176	44	14	therefore	therefore	ADV
fumecheng-2176	44	15	,	,	PUNCT
fumecheng-2176	44	16	a	a	DET
fumecheng-2176	44	17	much	much	ADV
fumecheng-2176	44	18	more	more	ADV
fumecheng-2176	44	19	precise	precise	ADJ
fumecheng-2176	44	20	result	result	NOUN
fumecheng-2176	44	21	could	could	AUX
fumecheng-2176	44	22	be	be	AUX
fumecheng-2176	44	23	obtained	obtain	VERB
fumecheng-2176	44	24	.	.	PUNCT
fumecheng-2176	45	1	the	the	DET
fumecheng-2176	45	2	values	value	NOUN
fumecheng-2176	45	3	of	of	ADP
fumecheng-2176	45	4	coefficient	coefficient	NOUN
fumecheng-2176	45	5	β	β	PROPN
fumecheng-2176	45	6	for	for	ADP
fumecheng-2176	45	7	different	different	ADJ
fumecheng-2176	45	8	m	m	VERB
fumecheng-2176	45	9	are	be	AUX
fumecheng-2176	45	10	presented	present	VERB
fumecheng-2176	45	11	in	in	ADP
fumecheng-2176	45	12	fig.2	fig.2	PROPN
fumecheng-2176	45	13	and	and	CCONJ
fumecheng-2176	45	14	table1	table1	PROPN
fumecheng-2176	45	15	.	.	PUNCT
fumecheng-2176	46	1	for	for	ADP
fumecheng-2176	46	2	the	the	DET
fumecheng-2176	46	3	two	two	NUM
fumecheng-2176	46	4	most	most	ADV
fumecheng-2176	46	5	popular	popular	ADJ
fumecheng-2176	46	6	indenter	indenter	NOUN
fumecheng-2176	46	7	shapes	shape	NOUN
fumecheng-2176	46	8	,	,	PUNCT
fumecheng-2176	46	9	the	the	DET
fumecheng-2176	46	10	values	value	NOUN
fumecheng-2176	46	11	are	be	AUX
fumecheng-2176	46	12	:	:	PUNCT
fumecheng-2176	46	13	1.061	1.061	NUM
fumecheng-2176	46	14	,	,	PUNCT
fumecheng-2176	46	15	for	for	ADP
fumecheng-2176	46	16	triangle	triangle	NOUN
fumecheng-2176	46	17	,	,	PUNCT
fumecheng-2176	46	18	1.021	1.021	NUM
fumecheng-2176	46	19	,	,	PUNCT
fumecheng-2176	46	20	for	for	ADP
fumecheng-2176	46	21	square	square	NOUN
fumecheng-2176	46	22	,	,	PUNCT
fumecheng-2176	47	1			PROPN
fumecheng-2176	47	2			PROPN
fumecheng-2176	48	1			NUM
fumecheng-2176	49	1			NOUN
fumecheng-2176	49	2	(	(	PUNCT
fumecheng-2176	49	3	3	3	NUM
fumecheng-2176	49	4	)	)	PUNCT
fumecheng-2176	49	5	which	which	PRON
fumecheng-2176	49	6	is	be	AUX
fumecheng-2176	49	7	larger	large	ADJ
fumecheng-2176	49	8	than	than	ADP
fumecheng-2176	49	9	the	the	DET
fumecheng-2176	49	10	values	value	NOUN
fumecheng-2176	49	11	reported	report	VERB
fumecheng-2176	49	12	by	by	ADP
fumecheng-2176	49	13	king	king	NOUN
fumecheng-2176	50	1	[	[	X
fumecheng-2176	50	2	5	5	NUM
fumecheng-2176	50	3	]	]	PUNCT
fumecheng-2176	50	4	.	.	PUNCT
fumecheng-2176	51	1	it	it	PRON
fumecheng-2176	51	2	can	can	AUX
fumecheng-2176	51	3	be	be	AUX
fumecheng-2176	51	4	seen	see	VERB
fumecheng-2176	51	5	that	that	SCONJ
fumecheng-2176	51	6	with	with	ADP
fumecheng-2176	51	7	the	the	DET
fumecheng-2176	51	8	same	same	ADJ
fumecheng-2176	51	9	area	area	NOUN
fumecheng-2176	51	10	of	of	ADP
fumecheng-2176	51	11	cross	cross	NOUN
fumecheng-2176	51	12	section	section	NOUN
fumecheng-2176	51	13	,	,	PUNCT
fumecheng-2176	51	14	the	the	DET
fumecheng-2176	51	15	stiffness	stiffness	NOUN
fumecheng-2176	51	16	of	of	ADP
fumecheng-2176	51	17	triangular	triangular	NOUN
fumecheng-2176	51	18	indenter	indenter	NOUN
fumecheng-2176	51	19	is	be	AUX
fumecheng-2176	51	20	for	for	ADP
fumecheng-2176	51	21	6	6	NUM
fumecheng-2176	51	22	%	%	NOUN
fumecheng-2176	51	23	larger	large	ADJ
fumecheng-2176	51	24	than	than	ADP
fumecheng-2176	51	25	that	that	PRON
fumecheng-2176	51	26	of	of	ADP
fumecheng-2176	51	27	a	a	DET
fumecheng-2176	51	28	flat	flat	ADJ
fumecheng-2176	51	29	cylinder	cylinder	NOUN
fumecheng-2176	51	30	.	.	PUNCT
fumecheng-2176	52	1	fig	fig	NOUN
fumecheng-2176	52	2	.	.	PUNCT
fumecheng-2176	53	1	2	2	NUM
fumecheng-2176	53	2	factor	factor	NOUN
fumecheng-2176	53	3	β	β	NOUN
fumecheng-2176	53	4	for	for	ADP
fumecheng-2176	53	5	different	different	ADJ
fumecheng-2176	53	6	polygonal	polygonal	ADJ
fumecheng-2176	53	7	indenters	indenter	NOUN
fumecheng-2176	53	8	.	.	PUNCT
fumecheng-2176	54	1	the	the	DET
fumecheng-2176	54	2	two	two	NUM
fumecheng-2176	54	3	stars	star	NOUN
fumecheng-2176	54	4	indicate	indicate	VERB
fumecheng-2176	54	5	the	the	DET
fumecheng-2176	54	6	results	result	NOUN
fumecheng-2176	54	7	obtained	obtain	VERB
fumecheng-2176	54	8	numerically	numerically	ADV
fumecheng-2176	54	9	by	by	ADP
fumecheng-2176	54	10	king	king	NOUN
fumecheng-2176	54	11	in	in	ADP
fumecheng-2176	54	12	1987	1987	NUM
fumecheng-2176	54	13	[	[	X
fumecheng-2176	54	14	5	5	NUM
fumecheng-2176	54	15	]	]	SYM
fumecheng-2176	54	16	table	table	NOUN
fumecheng-2176	54	17	1	1	NUM
fumecheng-2176	54	18	values	value	NOUN
fumecheng-2176	54	19	of	of	ADP
fumecheng-2176	54	20	constant	constant	ADJ
fumecheng-2176	54	21	β	β	NOUN
fumecheng-2176	54	22	m	m	VERB
fumecheng-2176	54	23	polygon	polygon	NOUN
fumecheng-2176	54	24	3	3	NUM
fumecheng-2176	54	25	(	(	PUNCT
fumecheng-2176	54	26	triangle	triangle	NOUN
fumecheng-2176	54	27	)	)	PUNCT
fumecheng-2176	54	28	4	4	NUM
fumecheng-2176	54	29	(	(	PUNCT
fumecheng-2176	54	30	square	square	ADJ
fumecheng-2176	54	31	)	)	PUNCT
fumecheng-2176	54	32	5	5	NUM
fumecheng-2176	54	33	6	6	NUM
fumecheng-2176	54	34	7	7	NUM
fumecheng-2176	54	35	8	8	NUM
fumecheng-2176	54	36	∞	∞	NUM
fumecheng-2176	54	37	(	(	PUNCT
fumecheng-2176	54	38	cylinder	cylinder	NOUN
fumecheng-2176	54	39	)	)	PUNCT
fumecheng-2176	54	40	β	β	NOUN
fumecheng-2176	54	41	1.061	1.061	NUM
fumecheng-2176	54	42	1.021	1.021	NUM
fumecheng-2176	54	43	1.010	1.010	NUM
fumecheng-2176	54	44	1.005	1.005	NUM
fumecheng-2176	54	45	1.003	1.003	NUM
fumecheng-2176	54	46	1.002	1.002	NUM
fumecheng-2176	54	47	1.000	1.000	NUM
fumecheng-2176	54	48	244	244	NUM
fumecheng-2176	54	49	q.	q.	PROPN
fumecheng-2176	54	50	li	li	PROPN
fumecheng-2176	54	51	,	,	PUNCT
fumecheng-2176	54	52	v.l	v.l	PROPN
fumecheng-2176	54	53	.	.	PROPN
fumecheng-2176	54	54	popov	popov	PROPN
fumecheng-2176	54	55	3	3	NUM
fumecheng-2176	54	56	.	.	PUNCT
fumecheng-2176	55	1	indentation	indentation	NOUN
fumecheng-2176	55	2	of	of	ADP
fumecheng-2176	55	3	tapered	tapered	ADJ
fumecheng-2176	55	4	indenters	indenter	NOUN
fumecheng-2176	55	5	with	with	ADP
fumecheng-2176	55	6	polygonal	polygonal	ADJ
fumecheng-2176	55	7	base	base	NOUN
fumecheng-2176	55	8	and	and	CCONJ
fumecheng-2176	55	9	power	power	NOUN
fumecheng-2176	55	10	function	function	NOUN
fumecheng-2176	55	11	side	side	NOUN
fumecheng-2176	55	12	surface	surface	NOUN
fumecheng-2176	55	13	now	now	ADV
fumecheng-2176	55	14	we	we	PRON
fumecheng-2176	55	15	consider	consider	VERB
fumecheng-2176	55	16	the	the	DET
fumecheng-2176	55	17	tapered	tapered	ADJ
fumecheng-2176	55	18	indenters	indenter	NOUN
fumecheng-2176	55	19	which	which	PRON
fumecheng-2176	55	20	have	have	VERB
fumecheng-2176	55	21	a	a	DET
fumecheng-2176	55	22	regular	regular	ADJ
fumecheng-2176	55	23	polygonal	polygonal	ADJ
fumecheng-2176	55	24	base	base	NOUN
fumecheng-2176	55	25	,	,	PUNCT
fumecheng-2176	55	26	as	as	SCONJ
fumecheng-2176	55	27	shown	show	VERB
fumecheng-2176	55	28	in	in	ADP
fumecheng-2176	55	29	fig	fig	NOUN
fumecheng-2176	55	30	.	.	PUNCT
fumecheng-2176	56	1	3	3	X
fumecheng-2176	56	2	.	.	X
fumecheng-2176	56	3	we	we	PRON
fumecheng-2176	56	4	begin	begin	VERB
fumecheng-2176	56	5	with	with	ADP
fumecheng-2176	56	6	the	the	DET
fumecheng-2176	56	7	most	most	ADV
fumecheng-2176	56	8	common	common	ADJ
fumecheng-2176	56	9	type	type	NOUN
fumecheng-2176	56	10	–	–	PUNCT
fumecheng-2176	56	11	a	a	DET
fumecheng-2176	56	12	pyramid	pyramid	NOUN
fumecheng-2176	56	13	,	,	PUNCT
fumecheng-2176	56	14	and	and	CCONJ
fumecheng-2176	56	15	then	then	ADV
fumecheng-2176	56	16	extend	extend	VERB
fumecheng-2176	56	17	it	it	PRON
fumecheng-2176	56	18	to	to	ADP
fumecheng-2176	56	19	indenters	indenter	NOUN
fumecheng-2176	56	20	whose	whose	DET
fumecheng-2176	56	21	side	side	NOUN
fumecheng-2176	56	22	profile	profile	NOUN
fumecheng-2176	56	23	is	be	AUX
fumecheng-2176	56	24	an	an	DET
fumecheng-2176	56	25	arbitrary	arbitrary	ADJ
fumecheng-2176	56	26	power	power	NOUN
fumecheng-2176	56	27	function	function	NOUN
fumecheng-2176	56	28	.	.	PUNCT
fumecheng-2176	57	1	3.1	3.1	NUM
fumecheng-2176	57	2	.	.	PUNCT
fumecheng-2176	57	3	pyramidal	pyramidal	ADJ
fumecheng-2176	57	4	indenters	indenter	NOUN
fumecheng-2176	57	5	for	for	ADP
fumecheng-2176	57	6	the	the	DET
fumecheng-2176	57	7	contact	contact	NOUN
fumecheng-2176	57	8	between	between	ADP
fumecheng-2176	57	9	a	a	DET
fumecheng-2176	57	10	rigid	rigid	ADJ
fumecheng-2176	57	11	cone	cone	NOUN
fumecheng-2176	57	12	with	with	ADP
fumecheng-2176	57	13	profile	profile	NOUN
fumecheng-2176	57	14	f	f	X
fumecheng-2176	57	15	(	(	PUNCT
fumecheng-2176	57	16	r	r	NOUN
fumecheng-2176	57	17	)	)	PUNCT
fumecheng-2176	57	18	=	=	NOUN
fumecheng-2176	57	19	tanθ·r	tanθ·r	PROPN
fumecheng-2176	57	20	and	and	CCONJ
fumecheng-2176	57	21	an	an	DET
fumecheng-2176	57	22	elastic	elastic	ADJ
fumecheng-2176	57	23	half	half	NOUN
fumecheng-2176	57	24	space	space	NOUN
fumecheng-2176	57	25	with	with	ADP
fumecheng-2176	57	26	effective	effective	ADJ
fumecheng-2176	57	27	elastic	elastic	ADJ
fumecheng-2176	57	28	module	module	NOUN
fumecheng-2176	57	29	e	e	NOUN
fumecheng-2176	57	30	*	*	PUNCT
fumecheng-2176	57	31	,	,	PUNCT
fumecheng-2176	57	32	the	the	DET
fumecheng-2176	57	33	dependence	dependence	NOUN
fumecheng-2176	57	34	of	of	ADP
fumecheng-2176	57	35	normal	normal	ADJ
fumecheng-2176	57	36	force	force	NOUN
fumecheng-2176	57	37	on	on	ADP
fumecheng-2176	57	38	indentation	indentation	NOUN
fumecheng-2176	57	39	depth	depth	NOUN
fumecheng-2176	57	40	was	be	AUX
fumecheng-2176	57	41	analytically	analytically	ADV
fumecheng-2176	57	42	found	find	VERB
fumecheng-2176	57	43	by	by	ADP
fumecheng-2176	57	44	galin	galin	PROPN
fumecheng-2176	58	1	[	[	X
fumecheng-2176	58	2	6	6	NUM
fumecheng-2176	58	3	]	]	PUNCT
fumecheng-2176	58	4	(	(	PUNCT
fumecheng-2176	58	5	see	see	VERB
fumecheng-2176	58	6	also	also	ADV
fumecheng-2176	58	7	sneddon	sneddon	PROPN
fumecheng-2176	59	1	[	[	X
fumecheng-2176	59	2	7	7	NUM
fumecheng-2176	59	3	]	]	PUNCT
fumecheng-2176	59	4	):	):	PUNCT
fumecheng-2176	59	5	*	*	PUNCT
fumecheng-2176	59	6	22	22	NUM
fumecheng-2176	59	7	tan	tan	PROPN
fumecheng-2176	59	8	n	n	NOUN
fumecheng-2176	59	9	e	e	X
fumecheng-2176	59	10	f	f	PROPN
fumecheng-2176	59	11	d	d	X
fumecheng-2176	59	12			PROPN
fumecheng-2176	59	13			X
fumecheng-2176	59	14			NUM
fumecheng-2176	59	15	,	,	PUNCT
fumecheng-2176	59	16	(	(	PUNCT
fumecheng-2176	59	17	4	4	X
fumecheng-2176	59	18	)	)	PUNCT
fumecheng-2176	59	19	where	where	SCONJ
fumecheng-2176	59	20	d	d	NOUN
fumecheng-2176	59	21	is	be	AUX
fumecheng-2176	59	22	indentation	indentation	NOUN
fumecheng-2176	59	23	depth	depth	NOUN
fumecheng-2176	59	24	and	and	CCONJ
fumecheng-2176	59	25	θ	θ	NOUN
fumecheng-2176	59	26	is	be	AUX
fumecheng-2176	59	27	defined	define	VERB
fumecheng-2176	59	28	in	in	ADP
fumecheng-2176	59	29	fig	fig	NOUN
fumecheng-2176	59	30	.	.	PUNCT
fumecheng-2176	60	1	3(c	3(c	NUM
fumecheng-2176	60	2	)	)	PUNCT
fumecheng-2176	60	3	.	.	PUNCT
fumecheng-2176	61	1	this	this	DET
fumecheng-2176	61	2	solution	solution	NOUN
fumecheng-2176	61	3	can	can	AUX
fumecheng-2176	61	4	be	be	AUX
fumecheng-2176	61	5	easily	easily	ADV
fumecheng-2176	61	6	reproduced	reproduce	VERB
fumecheng-2176	61	7	using	use	VERB
fumecheng-2176	61	8	the	the	DET
fumecheng-2176	61	9	method	method	NOUN
fumecheng-2176	61	10	of	of	ADP
fumecheng-2176	61	11	dimensionality	dimensionality	NOUN
fumecheng-2176	61	12	reduction	reduction	NOUN
fumecheng-2176	61	13	(	(	PUNCT
fumecheng-2176	61	14	mdr	mdr	PROPN
fumecheng-2176	61	15	)	)	PUNCT
fumecheng-2176	61	16	.	.	PUNCT
fumecheng-2176	62	1	in	in	ADP
fumecheng-2176	62	2	the	the	DET
fumecheng-2176	62	3	framework	framework	NOUN
fumecheng-2176	62	4	of	of	ADP
fumecheng-2176	62	5	the	the	DET
fumecheng-2176	62	6	mdr	mdr	PROPN
fumecheng-2176	62	7	[	[	X
fumecheng-2176	62	8	14	14	NUM
fumecheng-2176	62	9	]	]	X
fumecheng-2176	62	10	,	,	PUNCT
fumecheng-2176	62	11	any	any	DET
fumecheng-2176	62	12	contact	contact	NOUN
fumecheng-2176	62	13	problem	problem	NOUN
fumecheng-2176	62	14	of	of	ADP
fumecheng-2176	62	15	an	an	DET
fumecheng-2176	62	16	axis	axis	ADJ
fumecheng-2176	62	17	-	-	PUNCT
fumecheng-2176	62	18	symmetrical	symmetrical	ADJ
fumecheng-2176	62	19	profile	profile	NOUN
fumecheng-2176	62	20	f(r	f(r	NOUN
fumecheng-2176	62	21	)	)	PUNCT
fumecheng-2176	62	22	with	with	ADP
fumecheng-2176	62	23	an	an	DET
fumecheng-2176	62	24	elastic	elastic	ADJ
fumecheng-2176	62	25	half	half	ADJ
fumecheng-2176	62	26	-	-	PUNCT
fumecheng-2176	62	27	space	space	NOUN
fumecheng-2176	62	28	can	can	AUX
fumecheng-2176	62	29	be	be	AUX
fumecheng-2176	62	30	mapped	map	VERB
fumecheng-2176	62	31	onto	onto	ADP
fumecheng-2176	62	32	a	a	DET
fumecheng-2176	62	33	contact	contact	NOUN
fumecheng-2176	62	34	of	of	ADP
fumecheng-2176	62	35	a	a	DET
fumecheng-2176	62	36	modified	modify	VERB
fumecheng-2176	62	37	(	(	PUNCT
fumecheng-2176	62	38	mdr	mdr	PROPN
fumecheng-2176	62	39	-	-	PUNCT
fumecheng-2176	62	40	transformed	transform	VERB
fumecheng-2176	62	41	)	)	PUNCT
fumecheng-2176	62	42	profile	profile	ADV
fumecheng-2176	62	43	g(x	g(x	NOUN
fumecheng-2176	62	44	):	):	PUNCT
fumecheng-2176	62	45	|	|	ADV
fumecheng-2176	62	46	|	|	ADV
fumecheng-2176	62	47	0	0	NUM
fumecheng-2176	62	48	2	2	NUM
fumecheng-2176	62	49	2	2	NUM
fumecheng-2176	62	50	(	(	PUNCT
fumecheng-2176	62	51	)	)	PUNCT
fumecheng-2176	62	52	(	(	PUNCT
fumecheng-2176	62	53	)	)	PUNCT
fumecheng-2176	63	1	|	|	ADV
fumecheng-2176	63	2	|	|	ADV
fumecheng-2176	63	3	d	d	NOUN
fumecheng-2176	63	4	x	x	X
fumecheng-2176	64	1	f	f	NOUN
fumecheng-2176	64	2	r	r	NOUN
fumecheng-2176	64	3	g	g	NOUN
fumecheng-2176	64	4	x	x	SYM
fumecheng-2176	64	5	x	x	PUNCT
fumecheng-2176	64	6	r	r	NOUN
fumecheng-2176	64	7	x	x	SYM
fumecheng-2176	64	8	r	r	NOUN
fumecheng-2176	64	9			CCONJ
fumecheng-2176	64	10			PROPN
fumecheng-2176	64	11			NOUN
fumecheng-2176	64	12			PUNCT
fumecheng-2176	64	13	,	,	PUNCT
fumecheng-2176	64	14	(	(	PUNCT
fumecheng-2176	64	15	5	5	X
fumecheng-2176	64	16	)	)	PUNCT
fumecheng-2176	64	17	with	with	ADP
fumecheng-2176	64	18	properly	properly	ADV
fumecheng-2176	64	19	defined	define	VERB
fumecheng-2176	64	20	elastic	elastic	ADJ
fumecheng-2176	64	21	foundation	foundation	NOUN
fumecheng-2176	64	22	.	.	PUNCT
fumecheng-2176	65	1	for	for	ADP
fumecheng-2176	65	2	a	a	DET
fumecheng-2176	65	3	conical	conical	ADJ
fumecheng-2176	65	4	profile	profile	NOUN
fumecheng-2176	65	5	,	,	PUNCT
fumecheng-2176	65	6	f(r	f(r	X
fumecheng-2176	65	7	)	)	PUNCT
fumecheng-2176	65	8	=	=	SYM
fumecheng-2176	65	9	tanθ·r	tanθ·r	PROPN
fumecheng-2176	65	10	,	,	PUNCT
fumecheng-2176	65	11	the	the	DET
fumecheng-2176	65	12	substitution	substitution	NOUN
fumecheng-2176	65	13	in	in	ADP
fumecheng-2176	65	14	eq	eq	ADP
fumecheng-2176	65	15	.	.	PUNCT
fumecheng-2176	65	16	(	(	PUNCT
fumecheng-2176	65	17	5	5	NUM
fumecheng-2176	65	18	)	)	PUNCT
fumecheng-2176	65	19	and	and	CCONJ
fumecheng-2176	65	20	integration	integration	NOUN
fumecheng-2176	65	21	provides	provide	VERB
fumecheng-2176	65	22	the	the	DET
fumecheng-2176	65	23	mdr	mdr	PROPN
fumecheng-2176	65	24	-	-	ADJ
fumecheng-2176	65	25	transformed	transform	VERB
fumecheng-2176	65	26	profile	profile	NOUN
fumecheng-2176	65	27	:	:	PUNCT
fumecheng-2176	65	28	(	(	PUNCT
fumecheng-2176	65	29	)	)	PUNCT
fumecheng-2176	65	30	(	(	PUNCT
fumecheng-2176	65	31	/	/	SYM
fumecheng-2176	65	32	2	2	X
fumecheng-2176	65	33	)	)	PUNCT
fumecheng-2176	65	34	|	|	ADV
fumecheng-2176	65	35	|	|	ADV
fumecheng-2176	65	36	tang	tang	NOUN
fumecheng-2176	65	37	x	x	PROPN
fumecheng-2176	65	38	x	x	PROPN
fumecheng-2176	65	39			PROPN
fumecheng-2176	65	40			PROPN
fumecheng-2176	65	41			PROPN
fumecheng-2176	65	42	.	.	PUNCT
fumecheng-2176	66	1	(	(	PUNCT
fumecheng-2176	66	2	6	6	X
fumecheng-2176	66	3	)	)	PUNCT
fumecheng-2176	66	4	a	a	DET
fumecheng-2176	66	5	short	short	ADJ
fumecheng-2176	66	6	calculation	calculation	NOUN
fumecheng-2176	66	7	(	(	PUNCT
fumecheng-2176	66	8	see	see	VERB
fumecheng-2176	66	9	.	.	PUNCT
fumecheng-2176	67	1	e.g.	e.g.	ADV
fumecheng-2176	67	2	[	[	X
fumecheng-2176	67	3	14	14	NUM
fumecheng-2176	67	4	]	]	PUNCT
fumecheng-2176	67	5	)	)	PUNCT
fumecheng-2176	67	6	leads	lead	VERB
fumecheng-2176	67	7	to	to	ADP
fumecheng-2176	67	8	eq	eq	PROPN
fumecheng-2176	67	9	.	.	PUNCT
fumecheng-2176	68	1	(	(	PUNCT
fumecheng-2176	68	2	4	4	NUM
fumecheng-2176	68	3	)	)	PUNCT
fumecheng-2176	68	4	.	.	PUNCT
fumecheng-2176	69	1	fig	fig	NOUN
fumecheng-2176	69	2	.	.	PUNCT
fumecheng-2176	70	1	3	3	NUM
fumecheng-2176	70	2	pyramid	pyramid	NOUN
fumecheng-2176	70	3	indenters	indenter	NOUN
fumecheng-2176	70	4	for	for	ADP
fumecheng-2176	70	5	n=1	n=1	PROPN
fumecheng-2176	70	6	(	(	PUNCT
fumecheng-2176	70	7	a)-(c	a)-(c	PROPN
fumecheng-2176	70	8	)	)	PUNCT
fumecheng-2176	70	9	and	and	CCONJ
fumecheng-2176	70	10	parabolic	parabolic	ADJ
fumecheng-2176	70	11	indenters	indenter	NOUN
fumecheng-2176	70	12	for	for	ADP
fumecheng-2176	70	13	n=2	n=2	X
fumecheng-2176	70	14	(	(	PUNCT
fumecheng-2176	70	15	d)-(f	d)-(f	PROPN
fumecheng-2176	70	16	)	)	PUNCT
fumecheng-2176	70	17	with	with	ADP
fumecheng-2176	70	18	polygonal	polygonal	ADJ
fumecheng-2176	70	19	base	base	NOUN
fumecheng-2176	70	20	,	,	PUNCT
fumecheng-2176	70	21	m=3	m=3	PUNCT
fumecheng-2176	70	22	(	(	PUNCT
fumecheng-2176	70	23	triangle	triangle	NOUN
fumecheng-2176	70	24	)	)	PUNCT
fumecheng-2176	70	25	,	,	PUNCT
fumecheng-2176	70	26	m=4	m=4	PROPN
fumecheng-2176	70	27	(	(	PUNCT
fumecheng-2176	70	28	square),and	square),and	PROPN
fumecheng-2176	70	29	m=∞	m=∞	X
fumecheng-2176	70	30	(	(	PUNCT
fumecheng-2176	70	31	cycle	cycle	NOUN
fumecheng-2176	70	32	)	)	PUNCT
fumecheng-2176	70	33	indentation	indentation	NOUN
fumecheng-2176	70	34	of	of	ADP
fumecheng-2176	70	35	flat	flat	ADV
fumecheng-2176	70	36	-	-	PUNCT
fumecheng-2176	70	37	ended	end	VERB
fumecheng-2176	70	38	and	and	CCONJ
fumecheng-2176	70	39	tapered	tapered	ADJ
fumecheng-2176	70	40	indenters	indenter	NOUN
fumecheng-2176	70	41	with	with	ADP
fumecheng-2176	70	42	polygonal	polygonal	ADJ
fumecheng-2176	70	43	cross	cross	NOUN
fumecheng-2176	70	44	-	-	NOUN
fumecheng-2176	70	45	sections	section	NOUN
fumecheng-2176	70	46	245	245	NUM
fumecheng-2176	70	47	in	in	ADP
fumecheng-2176	70	48	[	[	X
fumecheng-2176	70	49	15	15	NUM
fumecheng-2176	70	50	]	]	PUNCT
fumecheng-2176	70	51	,	,	PUNCT
fumecheng-2176	70	52	it	it	PRON
fumecheng-2176	70	53	was	be	AUX
fumecheng-2176	70	54	shown	show	VERB
fumecheng-2176	70	55	that	that	SCONJ
fumecheng-2176	70	56	an	an	DET
fumecheng-2176	70	57	equivalent	equivalent	ADJ
fumecheng-2176	70	58	mdr	mdr	NOUN
fumecheng-2176	70	59	-	-	PUNCT
fumecheng-2176	70	60	transformed	transform	VERB
fumecheng-2176	70	61	profile	profile	NOUN
fumecheng-2176	70	62	does	do	AUX
fumecheng-2176	70	63	exist	exist	VERB
fumecheng-2176	70	64	not	not	PART
fumecheng-2176	70	65	only	only	ADV
fumecheng-2176	70	66	for	for	ADP
fumecheng-2176	70	67	axis	axis	ADJ
fumecheng-2176	70	68	-	-	PUNCT
fumecheng-2176	70	69	symmetrical	symmetrical	ADJ
fumecheng-2176	70	70	indenters	indenter	NOUN
fumecheng-2176	70	71	but	but	CCONJ
fumecheng-2176	70	72	also	also	ADV
fumecheng-2176	70	73	for	for	ADP
fumecheng-2176	70	74	indenters	indenter	NOUN
fumecheng-2176	70	75	of	of	ADP
fumecheng-2176	70	76	arbitrary	arbitrary	ADJ
fumecheng-2176	70	77	shape	shape	NOUN
fumecheng-2176	70	78	.	.	PUNCT
fumecheng-2176	71	1	as	as	SCONJ
fumecheng-2176	71	2	shown	show	VERB
fumecheng-2176	71	3	in	in	ADP
fumecheng-2176	71	4	[	[	X
fumecheng-2176	71	5	15	15	NUM
fumecheng-2176	71	6	]	]	PUNCT
fumecheng-2176	71	7	and	and	CCONJ
fumecheng-2176	71	8	[	[	X
fumecheng-2176	71	9	16	16	NUM
fumecheng-2176	71	10	]	]	X
fumecheng-2176	71	11	,	,	PUNCT
fumecheng-2176	71	12	for	for	ADP
fumecheng-2176	71	13	this	this	DET
fumecheng-2176	71	14	sake	sake	NOUN
fumecheng-2176	71	15	,	,	PUNCT
fumecheng-2176	71	16	quantity	quantity	NOUN
fumecheng-2176	71	17	l	l	NOUN
fumecheng-2176	71	18	=	=	NOUN
fumecheng-2176	71	19	k/(2e	k/(2e	NOUN
fumecheng-2176	71	20	*	*	PUNCT
fumecheng-2176	71	21	)	)	PUNCT
fumecheng-2176	71	22	(	(	PUNCT
fumecheng-2176	71	23	where	where	SCONJ
fumecheng-2176	71	24	k	k	NOUN
fumecheng-2176	71	25	=	=	NOUN
fumecheng-2176	71	26	dfn	dfn	NOUN
fumecheng-2176	71	27	/dd	/dd	NOUN
fumecheng-2176	71	28	is	be	AUX
fumecheng-2176	71	29	the	the	DET
fumecheng-2176	71	30	incremental	incremental	ADJ
fumecheng-2176	71	31	normal	normal	ADJ
fumecheng-2176	71	32	stiffness	stiffness	NOUN
fumecheng-2176	71	33	)	)	PUNCT
fumecheng-2176	71	34	should	should	AUX
fumecheng-2176	71	35	be	be	AUX
fumecheng-2176	71	36	determined	determine	VERB
fumecheng-2176	71	37	numerically	numerically	ADV
fumecheng-2176	71	38	as	as	ADP
fumecheng-2176	71	39	function	function	NOUN
fumecheng-2176	71	40	of	of	ADP
fumecheng-2176	71	41	indentation	indentation	NOUN
fumecheng-2176	71	42	depth	depth	NOUN
fumecheng-2176	71	43	d.	d.	NOUN
fumecheng-2176	71	44	inverse	inverse	NOUN
fumecheng-2176	71	45	function	function	NOUN
fumecheng-2176	71	46	d(l	d(l	ADV
fumecheng-2176	71	47	)	)	PUNCT
fumecheng-2176	71	48	is	be	AUX
fumecheng-2176	71	49	then	then	ADV
fumecheng-2176	71	50	exactly	exactly	ADV
fumecheng-2176	71	51	the	the	DET
fumecheng-2176	71	52	unknown	unknown	ADJ
fumecheng-2176	71	53	mdr	mdr	NOUN
fumecheng-2176	71	54	transformed	transform	VERB
fumecheng-2176	71	55	profile	profile	NOUN
fumecheng-2176	71	56	g(x	g(x	PROPN
fumecheng-2176	71	57	)	)	PUNCT
fumecheng-2176	71	58	.	.	PUNCT
fumecheng-2176	72	1	let	let	VERB
fumecheng-2176	72	2	us	we	PRON
fumecheng-2176	72	3	illustrate	illustrate	VERB
fumecheng-2176	72	4	this	this	DET
fumecheng-2176	72	5	simple	simple	ADJ
fumecheng-2176	72	6	procedure	procedure	NOUN
fumecheng-2176	72	7	on	on	ADP
fumecheng-2176	72	8	the	the	DET
fumecheng-2176	72	9	example	example	NOUN
fumecheng-2176	72	10	of	of	ADP
fumecheng-2176	72	11	conical	conical	PROPN
fumecheng-2176	72	12	indenter	indenter	PROPN
fumecheng-2176	72	13	.	.	PUNCT
fumecheng-2176	73	1	by	by	ADP
fumecheng-2176	73	2	differentiating	differentiate	VERB
fumecheng-2176	73	3	eq	eq	PROPN
fumecheng-2176	73	4	.	.	PUNCT
fumecheng-2176	73	5	(	(	PUNCT
fumecheng-2176	73	6	4	4	NUM
fumecheng-2176	73	7	)	)	PUNCT
fumecheng-2176	73	8	with	with	ADP
fumecheng-2176	73	9	respect	respect	NOUN
fumecheng-2176	73	10	of	of	ADP
fumecheng-2176	73	11	d	d	NOUN
fumecheng-2176	73	12	we	we	PRON
fumecheng-2176	73	13	get	get	VERB
fumecheng-2176	73	14	stiffness	stiffness	ADJ
fumecheng-2176	73	15	k=4e	k=4e	NOUN
fumecheng-2176	73	16	*	*	PUNCT
fumecheng-2176	73	17	d/(πtanθ	d/(πtanθ	PROPN
fumecheng-2176	73	18	)	)	PUNCT
fumecheng-2176	73	19	and	and	CCONJ
fumecheng-2176	73	20	length	length	NOUN
fumecheng-2176	73	21	l=2d/(πtanθ	l=2d/(πtanθ	PROPN
fumecheng-2176	73	22	)	)	PUNCT
fumecheng-2176	73	23	.	.	PUNCT
fumecheng-2176	74	1	inverse	inverse	NOUN
fumecheng-2176	74	2	relation	relation	NOUN
fumecheng-2176	74	3	d	d	PUNCT
fumecheng-2176	75	1	=	=	NOUN
fumecheng-2176	75	2	l(π/2)tanθ	l(π/2)tanθ	PROPN
fumecheng-2176	75	3	coincides	coincide	VERB
fumecheng-2176	75	4	exactly	exactly	ADV
fumecheng-2176	75	5	with	with	SCONJ
fumecheng-2176	75	6	the	the	DET
fumecheng-2176	75	7	mdr	mdr	PROPN
fumecheng-2176	75	8	transformed	transform	VERB
fumecheng-2176	75	9	profile	profile	NOUN
fumecheng-2176	75	10	(	(	PUNCT
fumecheng-2176	75	11	6	6	NUM
fumecheng-2176	75	12	)	)	PUNCT
fumecheng-2176	75	13	.	.	PUNCT
fumecheng-2176	76	1	this	this	DET
fumecheng-2176	76	2	procedure	procedure	NOUN
fumecheng-2176	76	3	is	be	AUX
fumecheng-2176	76	4	applicable	applicable	ADJ
fumecheng-2176	76	5	regardless	regardless	ADV
fumecheng-2176	76	6	of	of	ADP
fumecheng-2176	76	7	whether	whether	SCONJ
fumecheng-2176	76	8	dependence	dependence	NOUN
fumecheng-2176	76	9	fn(d	fn(d	NOUN
fumecheng-2176	76	10	)	)	PUNCT
fumecheng-2176	76	11	was	be	AUX
fumecheng-2176	76	12	obtained	obtain	VERB
fumecheng-2176	76	13	analytically	analytically	ADV
fumecheng-2176	76	14	,	,	PUNCT
fumecheng-2176	76	15	numerically	numerically	ADV
fumecheng-2176	76	16	or	or	CCONJ
fumecheng-2176	76	17	experimentally	experimentally	ADV
fumecheng-2176	76	18	.	.	PUNCT
fumecheng-2176	77	1	in	in	ADP
fumecheng-2176	77	2	the	the	DET
fumecheng-2176	77	3	following	following	NOUN
fumecheng-2176	77	4	,	,	PUNCT
fumecheng-2176	77	5	we	we	PRON
fumecheng-2176	77	6	determine	determine	VERB
fumecheng-2176	77	7	dependence	dependence	NOUN
fumecheng-2176	77	8	fn(d	fn(d	NUM
fumecheng-2176	77	9	)	)	PUNCT
fumecheng-2176	77	10	numerically	numerically	ADV
fumecheng-2176	77	11	and	and	CCONJ
fumecheng-2176	77	12	extract	extract	VERB
fumecheng-2176	77	13	from	from	ADP
fumecheng-2176	77	14	it	it	PRON
fumecheng-2176	77	15	the	the	DET
fumecheng-2176	77	16	mdr	mdr	PROPN
fumecheng-2176	77	17	-	-	ADJ
fumecheng-2176	77	18	transformed	transform	VERB
fumecheng-2176	77	19	profiles	profile	NOUN
fumecheng-2176	77	20	for	for	ADP
fumecheng-2176	77	21	a	a	DET
fumecheng-2176	77	22	number	number	NOUN
fumecheng-2176	77	23	of	of	ADP
fumecheng-2176	77	24	tapered	tapered	ADJ
fumecheng-2176	77	25	profiles	profile	NOUN
fumecheng-2176	77	26	with	with	ADP
fumecheng-2176	77	27	polygonal	polygonal	ADJ
fumecheng-2176	77	28	cross	cross	NOUN
fumecheng-2176	77	29	-	-	NOUN
fumecheng-2176	77	30	sections	section	NOUN
fumecheng-2176	77	31	(	(	PUNCT
fumecheng-2176	77	32	fig	fig	NOUN
fumecheng-2176	77	33	.	.	PUNCT
fumecheng-2176	78	1	3	3	NUM
fumecheng-2176	78	2	)	)	PUNCT
fumecheng-2176	78	3	.	.	PUNCT
fumecheng-2176	79	1	we	we	PRON
fumecheng-2176	79	2	start	start	VERB
fumecheng-2176	79	3	with	with	ADP
fumecheng-2176	79	4	consideration	consideration	NOUN
fumecheng-2176	79	5	of	of	ADP
fumecheng-2176	79	6	pyramidal	pyramidal	ADJ
fumecheng-2176	79	7	indenters	indenter	NOUN
fumecheng-2176	79	8	.	.	PUNCT
fumecheng-2176	80	1	as	as	SCONJ
fumecheng-2176	80	2	shown	show	VERB
fumecheng-2176	80	3	in	in	ADP
fumecheng-2176	80	4	fig	fig	NOUN
fumecheng-2176	80	5	.	.	PUNCT
fumecheng-2176	81	1	3(a)(b	3(a)(b	NUM
fumecheng-2176	81	2	)	)	PUNCT
fumecheng-2176	82	1	,	,	PUNCT
fumecheng-2176	82	2	the	the	DET
fumecheng-2176	82	3	bases	basis	NOUN
fumecheng-2176	82	4	of	of	ADP
fumecheng-2176	82	5	the	the	DET
fumecheng-2176	82	6	indenter	indenter	NOUN
fumecheng-2176	82	7	are	be	AUX
fumecheng-2176	82	8	regular	regular	ADJ
fumecheng-2176	82	9	polygons	polygon	NOUN
fumecheng-2176	82	10	.	.	PUNCT
fumecheng-2176	83	1	angle	angle	NOUN
fumecheng-2176	83	2	θ	θ	PROPN
fumecheng-2176	83	3	is	be	AUX
fumecheng-2176	83	4	defined	define	VERB
fumecheng-2176	83	5	as	as	ADP
fumecheng-2176	83	6	the	the	DET
fumecheng-2176	83	7	angle	angle	NOUN
fumecheng-2176	83	8	between	between	ADP
fumecheng-2176	83	9	the	the	DET
fumecheng-2176	83	10	ground	ground	NOUN
fumecheng-2176	83	11	plane	plane	NOUN
fumecheng-2176	83	12	and	and	CCONJ
fumecheng-2176	83	13	the	the	DET
fumecheng-2176	83	14	3d	3d	PROPN
fumecheng-2176	83	15	indenter	indenter	PROPN
fumecheng-2176	83	16	side	side	PROPN
fumecheng-2176	83	17	surface	surface	NOUN
fumecheng-2176	83	18	as	as	SCONJ
fumecheng-2176	83	19	shown	show	VERB
fumecheng-2176	83	20	in	in	ADP
fumecheng-2176	83	21	fig.3	fig.3	PROPN
fumecheng-2176	83	22	.	.	PUNCT
fumecheng-2176	84	1	in	in	ADP
fumecheng-2176	84	2	the	the	DET
fumecheng-2176	84	3	simulation	simulation	NOUN
fumecheng-2176	84	4	we	we	PRON
fumecheng-2176	84	5	calculated	calculate	VERB
fumecheng-2176	84	6	the	the	DET
fumecheng-2176	84	7	contacts	contact	NOUN
fumecheng-2176	84	8	of	of	ADP
fumecheng-2176	84	9	pyramid	pyramid	NOUN
fumecheng-2176	84	10	indenters	indenter	NOUN
fumecheng-2176	84	11	with	with	ADP
fumecheng-2176	84	12	different	different	ADJ
fumecheng-2176	84	13	polygonal	polygonal	ADJ
fumecheng-2176	84	14	bases	basis	NOUN
fumecheng-2176	84	15	varying	vary	VERB
fumecheng-2176	84	16	from	from	ADP
fumecheng-2176	84	17	m=3	m=3	PROPN
fumecheng-2176	84	18	to	to	ADP
fumecheng-2176	84	19	20	20	NUM
fumecheng-2176	84	20	,	,	PUNCT
fumecheng-2176	84	21	and	and	CCONJ
fumecheng-2176	84	22	for	for	ADP
fumecheng-2176	84	23	each	each	DET
fumecheng-2176	84	24	type	type	NOUN
fumecheng-2176	84	25	the	the	DET
fumecheng-2176	84	26	angle	angle	NOUN
fumecheng-2176	84	27	ranges	range	VERB
fumecheng-2176	84	28	from	from	ADP
fumecheng-2176	84	29	=π/64	=π/64	NOUN
fumecheng-2176	84	30	to	to	ADP
fumecheng-2176	84	31	31π/64	31π/64	NUM
fumecheng-2176	84	32	.	.	PUNCT
fumecheng-2176	85	1	all	all	DET
fumecheng-2176	85	2	the	the	DET
fumecheng-2176	85	3	simulation	simulation	NOUN
fumecheng-2176	85	4	results	result	NOUN
fumecheng-2176	85	5	show	show	VERB
fumecheng-2176	85	6	that	that	SCONJ
fumecheng-2176	85	7	the	the	DET
fumecheng-2176	85	8	one	one	NUM
fumecheng-2176	85	9	-	-	PUNCT
fumecheng-2176	85	10	dimensional	dimensional	ADJ
fumecheng-2176	85	11	profile	profile	NOUN
fumecheng-2176	85	12	is	be	AUX
fumecheng-2176	85	13	still	still	ADV
fumecheng-2176	85	14	a	a	DET
fumecheng-2176	85	15	linear	linear	ADJ
fumecheng-2176	85	16	function	function	NOUN
fumecheng-2176	85	17	which	which	PRON
fumecheng-2176	85	18	can	can	AUX
fumecheng-2176	85	19	be	be	AUX
fumecheng-2176	85	20	formulated	formulate	VERB
fumecheng-2176	85	21	as	as	ADP
fumecheng-2176	85	22	:	:	PUNCT
fumecheng-2176	85	23	1d	1d	NUM
fumecheng-2176	85	24	(	(	PUNCT
fumecheng-2176	85	25	)	)	PUNCT
fumecheng-2176	85	26	|	|	ADV
fumecheng-2176	85	27	|g	|g	VERB
fumecheng-2176	85	28	x	x	X
fumecheng-2176	85	29	c	c	NOUN
fumecheng-2176	85	30	x	x	PROPN
fumecheng-2176	86	1			NUM
fumecheng-2176	86	2	,	,	PUNCT
fumecheng-2176	86	3	(	(	PUNCT
fumecheng-2176	86	4	7	7	X
fumecheng-2176	86	5	)	)	PUNCT
fumecheng-2176	86	6	with	with	ADP
fumecheng-2176	86	7	c1d	c1d	PROPN
fumecheng-2176	86	8	:	:	PUNCT
fumecheng-2176	86	9	1d	1d	NUM
fumecheng-2176	86	10	tanc	tanc	NOUN
fumecheng-2176	86	11			PUNCT
fumecheng-2176	86	12			PROPN
fumecheng-2176	86	13			NUM
fumecheng-2176	86	14	,	,	PUNCT
fumecheng-2176	86	15	(	(	PUNCT
fumecheng-2176	86	16	8)	8)	NUM
fumecheng-2176	86	17	where	where	SCONJ
fumecheng-2176	86	18	α	α	PROPN
fumecheng-2176	86	19	is	be	AUX
fumecheng-2176	86	20	dependent	dependent	ADJ
fumecheng-2176	86	21	only	only	ADV
fumecheng-2176	86	22	on	on	ADP
fumecheng-2176	86	23	polygon	polygon	NOUN
fumecheng-2176	86	24	order	order	NOUN
fumecheng-2176	86	25	m.	m.	NOUN
fumecheng-2176	86	26	for	for	ADP
fumecheng-2176	86	27	the	the	DET
fumecheng-2176	86	28	sake	sake	NOUN
fumecheng-2176	86	29	of	of	ADP
fumecheng-2176	86	30	comparison	comparison	NOUN
fumecheng-2176	86	31	we	we	PRON
fumecheng-2176	86	32	can	can	AUX
fumecheng-2176	86	33	define	define	VERB
fumecheng-2176	86	34	a	a	DET
fumecheng-2176	86	35	fictive	fictive	ADJ
fumecheng-2176	86	36	rotationally	rotationally	ADV
fumecheng-2176	86	37	symmetric	symmetric	ADJ
fumecheng-2176	86	38	3d	3d	NUM
fumecheng-2176	86	39	profile	profile	NOUN
fumecheng-2176	86	40	with	with	ADP
fumecheng-2176	86	41	the	the	DET
fumecheng-2176	86	42	same	same	ADJ
fumecheng-2176	86	43	inclination	inclination	NOUN
fumecheng-2176	86	44	angle	angle	NOUN
fumecheng-2176	86	45	:	:	PUNCT
fumecheng-2176	86	46	3d	3d	NUM
fumecheng-2176	86	47	3d	3d	NOUN
fumecheng-2176	86	48	(	(	PUNCT
fumecheng-2176	86	49	)	)	PUNCT
fumecheng-2176	86	50	tanf	tanf	PROPN
fumecheng-2176	86	51	r	r	NOUN
fumecheng-2176	86	52	c	c	PROPN
fumecheng-2176	86	53	r	r	NOUN
fumecheng-2176	86	54	r	r	PRON
fumecheng-2176	86	55			PROPN
fumecheng-2176	86	56			PROPN
fumecheng-2176	86	57			PROPN
fumecheng-2176	86	58	.	.	PUNCT
fumecheng-2176	87	1	(	(	PUNCT
fumecheng-2176	87	2	9	9	NUM
fumecheng-2176	87	3	)	)	PUNCT
fumecheng-2176	87	4	then	then	ADV
fumecheng-2176	87	5	we	we	PRON
fumecheng-2176	87	6	can	can	AUX
fumecheng-2176	87	7	write	write	VERB
fumecheng-2176	87	8	α	α	PRON
fumecheng-2176	87	9	=	=	NOUN
fumecheng-2176	87	10	c1d	c1d	NOUN
fumecheng-2176	87	11	/	/	SYM
fumecheng-2176	87	12	c3d	c3d	NOUN
fumecheng-2176	87	13	.	.	PUNCT
fumecheng-2176	88	1	the	the	DET
fumecheng-2176	88	2	values	value	NOUN
fumecheng-2176	88	3	of	of	ADP
fumecheng-2176	88	4	α	α	NOUN
fumecheng-2176	88	5	for	for	ADP
fumecheng-2176	88	6	different	different	ADJ
fumecheng-2176	88	7	shapes	shape	NOUN
fumecheng-2176	88	8	of	of	ADP
fumecheng-2176	88	9	polygons	polygon	NOUN
fumecheng-2176	88	10	are	be	AUX
fumecheng-2176	88	11	shown	show	VERB
fumecheng-2176	88	12	in	in	ADP
fumecheng-2176	88	13	fig	fig	NOUN
fumecheng-2176	88	14	.	.	PUNCT
fumecheng-2176	89	1	4(a	4(a	NUM
fumecheng-2176	89	2	)	)	PUNCT
fumecheng-2176	90	1	and	and	CCONJ
fumecheng-2176	90	2	table	table	NOUN
fumecheng-2176	90	3	2	2	NUM
fumecheng-2176	90	4	.	.	X
fumecheng-2176	91	1	for	for	ADP
fumecheng-2176	91	2	a	a	DET
fumecheng-2176	91	3	larger	large	ADJ
fumecheng-2176	91	4	m	m	NOUN
fumecheng-2176	91	5	,	,	PUNCT
fumecheng-2176	91	6	the	the	DET
fumecheng-2176	91	7	shape	shape	NOUN
fumecheng-2176	91	8	of	of	ADP
fumecheng-2176	91	9	the	the	DET
fumecheng-2176	91	10	pyramid	pyramid	NOUN
fumecheng-2176	91	11	indenter	indenter	NOUN
fumecheng-2176	91	12	is	be	AUX
fumecheng-2176	91	13	close	close	ADJ
fumecheng-2176	91	14	to	to	ADP
fumecheng-2176	91	15	a	a	DET
fumecheng-2176	91	16	cone	cone	NOUN
fumecheng-2176	91	17	,	,	PUNCT
fumecheng-2176	91	18	the	the	DET
fumecheng-2176	91	19	value	value	NOUN
fumecheng-2176	91	20	of	of	ADP
fumecheng-2176	91	21	α	α	NOUN
fumecheng-2176	91	22	is	be	AUX
fumecheng-2176	91	23	almost	almost	ADV
fumecheng-2176	91	24	equal	equal	ADJ
fumecheng-2176	91	25	to	to	ADP
fumecheng-2176	91	26	π/2	π/2	NUM
fumecheng-2176	91	27	.	.	PUNCT
fumecheng-2176	92	1	fig	fig	NOUN
fumecheng-2176	92	2	.	.	PUNCT
fumecheng-2176	93	1	4	4	NUM
fumecheng-2176	93	2	coefficient	coefficient	NOUN
fumecheng-2176	93	3	of	of	ADP
fumecheng-2176	93	4	α	α	NOUN
fumecheng-2176	93	5	for	for	ADP
fumecheng-2176	93	6	pyramidal	pyramidal	ADJ
fumecheng-2176	93	7	indenter	indenter	NOUN
fumecheng-2176	93	8	n=1	n=1	PROPN
fumecheng-2176	93	9	(	(	PUNCT
fumecheng-2176	93	10	a	a	NOUN
fumecheng-2176	93	11	)	)	PUNCT
fumecheng-2176	93	12	and	and	CCONJ
fumecheng-2176	93	13	parabolic	parabolic	ADJ
fumecheng-2176	93	14	indenter	indenter	NOUN
fumecheng-2176	93	15	n=2	n=2	X
fumecheng-2176	93	16	(	(	PUNCT
fumecheng-2176	93	17	b	b	NOUN
fumecheng-2176	93	18	)	)	PUNCT
fumecheng-2176	93	19	with	with	ADP
fumecheng-2176	93	20	different	different	ADJ
fumecheng-2176	93	21	polygonal	polygonal	ADJ
fumecheng-2176	93	22	bases	basis	NOUN
fumecheng-2176	93	23	246	246	NUM
fumecheng-2176	93	24	q.	q.	PROPN
fumecheng-2176	93	25	li	li	PROPN
fumecheng-2176	93	26	,	,	PUNCT
fumecheng-2176	93	27	v.l	v.l	PROPN
fumecheng-2176	93	28	.	.	PROPN
fumecheng-2176	93	29	popov	popov	PROPN
fumecheng-2176	93	30	table	table	NOUN
fumecheng-2176	93	31	2	2	NUM
fumecheng-2176	93	32	values	value	NOUN
fumecheng-2176	93	33	of	of	ADP
fumecheng-2176	93	34	coefficient	coefficient	NOUN
fumecheng-2176	93	35	α	α	PROPN
fumecheng-2176	93	36	m	m	VERB
fumecheng-2176	93	37	polygon	polygon	NOUN
fumecheng-2176	93	38	3	3	NUM
fumecheng-2176	93	39	triangle	triangle	NOUN
fumecheng-2176	93	40	4	4	NUM
fumecheng-2176	93	41	square	square	ADJ
fumecheng-2176	93	42	5	5	NUM
fumecheng-2176	93	43	6	6	NUM
fumecheng-2176	93	44	7	7	NUM
fumecheng-2176	93	45	10	10	NUM
fumecheng-2176	93	46	20	20	NUM
fumecheng-2176	93	47	30	30	NUM
fumecheng-2176	93	48	∞	∞	NUM
fumecheng-2176	93	49	cycle	cycle	NOUN
fumecheng-2176	93	50	α	α	PROPN
fumecheng-2176	93	51	(	(	PUNCT
fumecheng-2176	93	52	n=1	n=1	PROPN
fumecheng-2176	93	53	)	)	PUNCT
fumecheng-2176	93	54	pyramid	pyramid	NOUN
fumecheng-2176	93	55	1.133	1.133	NUM
fumecheng-2176	93	56	1.356	1.356	NUM
fumecheng-2176	93	57	1.422	1.422	NUM
fumecheng-2176	93	58	1.485	1.485	NUM
fumecheng-2176	93	59	1.510	1.510	NUM
fumecheng-2176	93	60	1.542	1.542	NUM
fumecheng-2176	93	61	1.564	1.564	NUM
fumecheng-2176	93	62	1.568	1.568	NUM
fumecheng-2176	93	63	π/2	π/2	NUM
fumecheng-2176	93	64	α	α	PROPN
fumecheng-2176	93	65	(	(	PUNCT
fumecheng-2176	93	66	n=2	n=2	NOUN
fumecheng-2176	93	67	)	)	PUNCT
fumecheng-2176	93	68	paraboloid	paraboloid	NOUN
fumecheng-2176	93	69	1.052	1.052	NUM
fumecheng-2176	93	70	1.493	1.493	NUM
fumecheng-2176	93	71	1.690	1.690	NUM
fumecheng-2176	93	72	1.791	1.791	NUM
fumecheng-2176	93	73	1.848	1.848	NUM
fumecheng-2176	93	74	1.928	1.928	NUM
fumecheng-2176	93	75	1.981	1.981	NUM
fumecheng-2176	93	76	1.993	1.993	NUM
fumecheng-2176	93	77	2	2	NUM
fumecheng-2176	93	78	3.2	3.2	NUM
fumecheng-2176	93	79	.	.	PUNCT
fumecheng-2176	94	1	indenters	indenter	NOUN
fumecheng-2176	94	2	with	with	ADP
fumecheng-2176	94	3	arbitrary	arbitrary	ADJ
fumecheng-2176	94	4	power	power	NOUN
fumecheng-2176	94	5	function	function	NOUN
fumecheng-2176	94	6	geometry	geometry	NOUN
fumecheng-2176	94	7	let	let	VERB
fumecheng-2176	94	8	us	we	PRON
fumecheng-2176	94	9	now	now	ADV
fumecheng-2176	94	10	consider	consider	VERB
fumecheng-2176	94	11	the	the	DET
fumecheng-2176	94	12	case	case	NOUN
fumecheng-2176	94	13	when	when	SCONJ
fumecheng-2176	94	14	the	the	DET
fumecheng-2176	94	15	side	side	NOUN
fumecheng-2176	94	16	surface	surface	NOUN
fumecheng-2176	94	17	of	of	ADP
fumecheng-2176	94	18	the	the	DET
fumecheng-2176	94	19	indenter	indenter	NOUN
fumecheng-2176	94	20	is	be	AUX
fumecheng-2176	94	21	not	not	PART
fumecheng-2176	94	22	flat	flat	ADJ
fumecheng-2176	94	23	but	but	CCONJ
fumecheng-2176	94	24	is	be	AUX
fumecheng-2176	94	25	given	give	VERB
fumecheng-2176	94	26	by	by	ADP
fumecheng-2176	94	27	a	a	DET
fumecheng-2176	94	28	power	power	NOUN
fumecheng-2176	94	29	function	function	NOUN
fumecheng-2176	94	30	.	.	PUNCT
fumecheng-2176	95	1	an	an	DET
fumecheng-2176	95	2	example	example	NOUN
fumecheng-2176	95	3	of	of	ADP
fumecheng-2176	95	4	parabolic	parabolic	ADJ
fumecheng-2176	95	5	indenter	indenter	NOUN
fumecheng-2176	95	6	(	(	PUNCT
fumecheng-2176	95	7	shape	shape	VERB
fumecheng-2176	95	8	with	with	ADP
fumecheng-2176	95	9	power	power	NOUN
fumecheng-2176	95	10	2	2	NUM
fumecheng-2176	95	11	)	)	PUNCT
fumecheng-2176	95	12	is	be	AUX
fumecheng-2176	95	13	shown	show	VERB
fumecheng-2176	95	14	in	in	ADP
fumecheng-2176	95	15	fig	fig	NOUN
fumecheng-2176	95	16	.	.	PUNCT
fumecheng-2176	96	1	3(d)-(f	3(d)-(f	NUM
fumecheng-2176	96	2	)	)	PUNCT
fumecheng-2176	96	3	.	.	PUNCT
fumecheng-2176	97	1	we	we	PRON
fumecheng-2176	97	2	first	first	ADV
fumecheng-2176	97	3	remember	remember	VERB
fumecheng-2176	97	4	the	the	DET
fumecheng-2176	97	5	corresponding	corresponding	ADJ
fumecheng-2176	97	6	solution	solution	NOUN
fumecheng-2176	97	7	for	for	ADP
fumecheng-2176	97	8	an	an	DET
fumecheng-2176	97	9	axisymmetric	axisymmetric	ADJ
fumecheng-2176	97	10	indenter	indenter	NOUN
fumecheng-2176	97	11	with	with	ADP
fumecheng-2176	97	12	an	an	DET
fumecheng-2176	97	13	arbitrary	arbitrary	ADJ
fumecheng-2176	97	14	power	power	NOUN
fumecheng-2176	97	15	function	function	NOUN
fumecheng-2176	97	16	shape	shape	NOUN
fumecheng-2176	97	17	f(r	f(r	NOUN
fumecheng-2176	97	18	)	)	PUNCT
fumecheng-2176	98	1	=	=	NOUN
fumecheng-2176	98	2	cn·r	cn·r	NUM
fumecheng-2176	98	3	n	n	NOUN
fumecheng-2176	98	4	.	.	PUNCT
fumecheng-2176	99	1	according	accord	VERB
fumecheng-2176	99	2	to	to	ADP
fumecheng-2176	99	3	eq	eq	PROPN
fumecheng-2176	99	4	.	.	PUNCT
fumecheng-2176	100	1	(	(	PUNCT
fumecheng-2176	100	2	5	5	X
fumecheng-2176	100	3	)	)	PUNCT
fumecheng-2176	100	4	its	its	PRON
fumecheng-2176	100	5	one	one	NUM
fumecheng-2176	100	6	-	-	PUNCT
fumecheng-2176	100	7	dimensional	dimensional	ADJ
fumecheng-2176	100	8	mdr	mdr	NOUN
fumecheng-2176	100	9	-	-	PUNCT
fumecheng-2176	100	10	transformed	transform	VERB
fumecheng-2176	100	11	profile	profile	NOUN
fumecheng-2176	100	12	is	be	AUX
fumecheng-2176	100	13	given	give	VERB
fumecheng-2176	100	14	by	by	ADP
fumecheng-2176	100	15	:	:	PUNCT
fumecheng-2176	100	16	(	(	PUNCT
fumecheng-2176	100	17	)	)	PUNCT
fumecheng-2176	100	18	|	|	ADV
fumecheng-2176	100	19	|nn	|nn	PUNCT
fumecheng-2176	100	20	ng	ng	PROPN
fumecheng-2176	100	21	x	x	SYM
fumecheng-2176	100	22	c	c	NOUN
fumecheng-2176	100	23	x	x	VERB
fumecheng-2176	100	24			PROPN
fumecheng-2176	100	25	,	,	PUNCT
fumecheng-2176	100	26	(	(	PUNCT
fumecheng-2176	100	27	10	10	NUM
fumecheng-2176	100	28	)	)	PUNCT
fumecheng-2176	100	29	where	where	SCONJ
fumecheng-2176	100	30	:	:	PUNCT
fumecheng-2176	100	31	(	(	PUNCT
fumecheng-2176	100	32	2	2	X
fumecheng-2176	100	33	)	)	SYM
fumecheng-2176	100	34	2	2	NUM
fumecheng-2176	100	35	(	(	PUNCT
fumecheng-2176	100	36	2	2	NUM
fumecheng-2176	100	37	1	1	NUM
fumecheng-2176	100	38	2	2	NUM
fumecheng-2176	100	39	)	)	PUNCT
fumecheng-2176	100	40	n	n	CCONJ
fumecheng-2176	100	41	n	n	CCONJ
fumecheng-2176	100	42	n	n	CCONJ
fumecheng-2176	100	43	n	n	PRON
fumecheng-2176	100	44			NOUN
fumecheng-2176	100	45			PUNCT
fumecheng-2176	100	46			PUNCT
fumecheng-2176	100	47			ADJ
fumecheng-2176	100	48			PROPN
fumecheng-2176	100	49			NUM
fumecheng-2176	100	50			NOUN
fumecheng-2176	100	51	,	,	PUNCT
fumecheng-2176	100	52	(	(	PUNCT
fumecheng-2176	100	53	11	11	NUM
fumecheng-2176	100	54	)	)	PUNCT
fumecheng-2176	100	55	and	and	CCONJ
fumecheng-2176	100	56	γ(n	γ(n	NUM
fumecheng-2176	100	57	)	)	PUNCT
fumecheng-2176	100	58	is	be	AUX
fumecheng-2176	100	59	gamma	gamma	NOUN
fumecheng-2176	100	60	function	function	NOUN
fumecheng-2176	100	61	.	.	PUNCT
fumecheng-2176	101	1	in	in	ADP
fumecheng-2176	101	2	particular	particular	ADJ
fumecheng-2176	101	3	,	,	PUNCT
fumecheng-2176	101	4	for	for	ADP
fumecheng-2176	101	5	the	the	DET
fumecheng-2176	101	6	cone	cone	NOUN
fumecheng-2176	101	7	(	(	PUNCT
fumecheng-2176	101	8	n=1	n=1	PROPN
fumecheng-2176	101	9	)	)	PUNCT
fumecheng-2176	101	10	κ1=	κ1=	PROPN
fumecheng-2176	101	11	π/2	π/2	NUM
fumecheng-2176	101	12	and	and	CCONJ
fumecheng-2176	101	13	for	for	ADP
fumecheng-2176	101	14	a	a	DET
fumecheng-2176	101	15	paraboloid	paraboloid	ADJ
fumecheng-2176	101	16	(	(	PUNCT
fumecheng-2176	101	17	n=2	n=2	NOUN
fumecheng-2176	101	18	)	)	PUNCT
fumecheng-2176	101	19	κ2=2	κ2=2	PROPN
fumecheng-2176	101	20	,	,	PUNCT
fumecheng-2176	101	21	corresponding	correspond	VERB
fumecheng-2176	101	22	to	to	ADP
fumecheng-2176	101	23	α	α	NOUN
fumecheng-2176	101	24	=	=	NOUN
fumecheng-2176	101	25	c1d	c1d	NOUN
fumecheng-2176	101	26	/	/	SYM
fumecheng-2176	101	27	c3d	c3d	NOUN
fumecheng-2176	101	28	for	for	ADP
fumecheng-2176	101	29	m=∞	m=∞	NOUN
fumecheng-2176	101	30	as	as	SCONJ
fumecheng-2176	101	31	shown	show	VERB
fumecheng-2176	101	32	in	in	ADP
fumecheng-2176	101	33	fig	fig	NOUN
fumecheng-2176	101	34	.	.	PUNCT
fumecheng-2176	101	35	4	4	NUM
fumecheng-2176	101	36	and	and	CCONJ
fumecheng-2176	101	37	table	table	NOUN
fumecheng-2176	101	38	2	2	NUM
fumecheng-2176	101	39	.	.	PUNCT
fumecheng-2176	102	1	as	as	ADP
fumecheng-2176	102	2	in	in	ADP
fumecheng-2176	102	3	the	the	DET
fumecheng-2176	102	4	previous	previous	ADJ
fumecheng-2176	102	5	section	section	NOUN
fumecheng-2176	102	6	,	,	PUNCT
fumecheng-2176	102	7	we	we	PRON
fumecheng-2176	102	8	define	define	VERB
fumecheng-2176	102	9	an	an	DET
fumecheng-2176	102	10	axis	axis	ADJ
fumecheng-2176	102	11	-	-	PUNCT
fumecheng-2176	102	12	symmetrical	symmetrical	ADJ
fumecheng-2176	102	13	shape	shape	NOUN
fumecheng-2176	102	14	with	with	ADP
fumecheng-2176	102	15	the	the	DET
fumecheng-2176	102	16	same	same	ADJ
fumecheng-2176	102	17	power	power	NOUN
fumecheng-2176	102	18	-	-	PUNCT
fumecheng-2176	102	19	law	law	NOUN
fumecheng-2176	102	20	shape	shape	NOUN
fumecheng-2176	102	21	as	as	SCONJ
fumecheng-2176	102	22	shown	show	VERB
fumecheng-2176	102	23	in	in	ADP
fumecheng-2176	102	24	detail	detail	NOUN
fumecheng-2176	102	25	in	in	ADP
fumecheng-2176	102	26	fig	fig	NOUN
fumecheng-2176	102	27	.	.	PUNCT
fumecheng-2176	103	1	3	3	X
fumecheng-2176	103	2	.	.	PUNCT
fumecheng-2176	103	3	to	to	PART
fumecheng-2176	103	4	underline	underline	VERB
fumecheng-2176	103	5	that	that	SCONJ
fumecheng-2176	103	6	we	we	PRON
fumecheng-2176	103	7	have	have	VERB
fumecheng-2176	103	8	to	to	PART
fumecheng-2176	103	9	do	do	VERB
fumecheng-2176	103	10	with	with	ADP
fumecheng-2176	103	11	a	a	DET
fumecheng-2176	103	12	three	three	NUM
fumecheng-2176	103	13	-	-	PUNCT
fumecheng-2176	103	14	dimensional	dimensional	ADJ
fumecheng-2176	103	15	body	body	NOUN
fumecheng-2176	103	16	which	which	PRON
fumecheng-2176	103	17	is	be	AUX
fumecheng-2176	103	18	in	in	ADP
fumecheng-2176	103	19	contact	contact	NOUN
fumecheng-2176	103	20	with	with	ADP
fumecheng-2176	103	21	a	a	DET
fumecheng-2176	103	22	three	three	NUM
fumecheng-2176	103	23	-	-	PUNCT
fumecheng-2176	103	24	dimensional	dimensional	ADJ
fumecheng-2176	103	25	half	half	ADJ
fumecheng-2176	103	26	-	-	PUNCT
fumecheng-2176	103	27	space	space	NOUN
fumecheng-2176	103	28	,	,	PUNCT
fumecheng-2176	103	29	we	we	PRON
fumecheng-2176	103	30	denote	denote	VERB
fumecheng-2176	103	31	the	the	DET
fumecheng-2176	103	32	corresponding	corresponding	ADJ
fumecheng-2176	103	33	reference	reference	NOUN
fumecheng-2176	103	34	shape	shape	NOUN
fumecheng-2176	103	35	as	as	ADP
fumecheng-2176	103	36	3	3	NUM
fumecheng-2176	103	37	3	3	NUM
fumecheng-2176	103	38	(	(	PUNCT
fumecheng-2176	103	39	)	)	PUNCT
fumecheng-2176	103	40	n	n	PROPN
fumecheng-2176	104	1	d	d	NOUN
fumecheng-2176	104	2	df	df	NOUN
fumecheng-2176	104	3	r	r	NOUN
fumecheng-2176	104	4	c	c	X
fumecheng-2176	104	5	r	r	VERB
fumecheng-2176	104	6			PROPN
fumecheng-2176	104	7	.	.	PUNCT
fumecheng-2176	105	1	(	(	PUNCT
fumecheng-2176	105	2	12	12	NUM
fumecheng-2176	105	3	)	)	PUNCT
fumecheng-2176	105	4	this	this	DET
fumecheng-2176	105	5	shape	shape	NOUN
fumecheng-2176	105	6	coincides	coincide	VERB
fumecheng-2176	105	7	with	with	ADP
fumecheng-2176	105	8	the	the	DET
fumecheng-2176	105	9	vertical	vertical	ADJ
fumecheng-2176	105	10	section	section	NOUN
fumecheng-2176	105	11	of	of	ADP
fumecheng-2176	105	12	the	the	DET
fumecheng-2176	105	13	polygonal	polygonal	ADJ
fumecheng-2176	105	14	indenters	indenter	NOUN
fumecheng-2176	105	15	(	(	PUNCT
fumecheng-2176	105	16	shown	show	VERB
fumecheng-2176	105	17	by	by	ADP
fumecheng-2176	105	18	dashed	dash	VERB
fumecheng-2176	105	19	lines	line	NOUN
fumecheng-2176	105	20	in	in	ADP
fumecheng-2176	105	21	fig	fig	NOUN
fumecheng-2176	105	22	.	.	PUNCT
fumecheng-2176	106	1	3	3	NUM
fumecheng-2176	106	2	)	)	PUNCT
fumecheng-2176	106	3	.	.	PUNCT
fumecheng-2176	107	1	the	the	DET
fumecheng-2176	107	2	numerical	numerical	ADJ
fumecheng-2176	107	3	indentation	indentation	NOUN
fumecheng-2176	107	4	tests	test	NOUN
fumecheng-2176	107	5	were	be	AUX
fumecheng-2176	107	6	carried	carry	VERB
fumecheng-2176	107	7	out	out	ADP
fumecheng-2176	107	8	for	for	ADP
fumecheng-2176	107	9	different	different	ADJ
fumecheng-2176	107	10	indenters	indenter	NOUN
fumecheng-2176	107	11	with	with	ADP
fumecheng-2176	107	12	power	power	NOUN
fumecheng-2176	107	13	function	function	NOUN
fumecheng-2176	107	14	n	n	CCONJ
fumecheng-2176	107	15	from	from	ADP
fumecheng-2176	107	16	1	1	NUM
fumecheng-2176	107	17	to	to	PART
fumecheng-2176	107	18	20	20	NUM
fumecheng-2176	107	19	and	and	CCONJ
fumecheng-2176	107	20	the	the	DET
fumecheng-2176	107	21	polygonal	polygonal	ADJ
fumecheng-2176	107	22	base	base	NOUN
fumecheng-2176	107	23	parameter	parameter	NOUN
fumecheng-2176	107	24	m	m	VERB
fumecheng-2176	107	25	from	from	ADP
fumecheng-2176	107	26	3	3	NUM
fumecheng-2176	107	27	to	to	ADP
fumecheng-2176	107	28	30	30	NUM
fumecheng-2176	107	29	.	.	PUNCT
fumecheng-2176	108	1	the	the	DET
fumecheng-2176	108	2	results	result	NOUN
fumecheng-2176	108	3	show	show	VERB
fumecheng-2176	108	4	that	that	SCONJ
fumecheng-2176	108	5	the	the	DET
fumecheng-2176	108	6	1d	1d	NUM
fumecheng-2176	108	7	profile	profile	NOUN
fumecheng-2176	108	8	for	for	ADP
fumecheng-2176	108	9	an	an	DET
fumecheng-2176	108	10	arbitrary	arbitrary	ADJ
fumecheng-2176	108	11	power	power	NOUN
fumecheng-2176	108	12	function	function	NOUN
fumecheng-2176	108	13	is	be	AUX
fumecheng-2176	108	14	still	still	ADV
fumecheng-2176	108	15	a	a	DET
fumecheng-2176	108	16	power	power	NOUN
fumecheng-2176	108	17	function	function	NOUN
fumecheng-2176	108	18	with	with	ADP
fumecheng-2176	108	19	the	the	DET
fumecheng-2176	108	20	same	same	ADJ
fumecheng-2176	108	21	power	power	NOUN
fumecheng-2176	108	22	.	.	PUNCT
fumecheng-2176	109	1	coefficient	coefficient	NOUN
fumecheng-2176	109	2	α	α	NOUN
fumecheng-2176	109	3	=	=	SYM
fumecheng-2176	109	4	c1d	c1d	NOUN
fumecheng-2176	109	5	/	/	SYM
fumecheng-2176	109	6	c3d	c3d	NOUN
fumecheng-2176	109	7	for	for	ADP
fumecheng-2176	109	8	the	the	DET
fumecheng-2176	109	9	same	same	ADJ
fumecheng-2176	109	10	type	type	NOUN
fumecheng-2176	109	11	of	of	ADP
fumecheng-2176	109	12	indenter	indenter	NOUN
fumecheng-2176	109	13	(	(	PUNCT
fumecheng-2176	109	14	fixed	fix	VERB
fumecheng-2176	109	15	n	n	PROPN
fumecheng-2176	109	16	and	and	CCONJ
fumecheng-2176	109	17	m	m	NOUN
fumecheng-2176	109	18	)	)	PUNCT
fumecheng-2176	109	19	is	be	AUX
fumecheng-2176	109	20	constant	constant	ADJ
fumecheng-2176	109	21	(	(	PUNCT
fumecheng-2176	109	22	independent	independent	ADJ
fumecheng-2176	109	23	of	of	ADP
fumecheng-2176	109	24	coefficient	coefficient	NOUN
fumecheng-2176	109	25	c3d	c3d	NOUN
fumecheng-2176	109	26	)	)	PUNCT
fumecheng-2176	109	27	.	.	PUNCT
fumecheng-2176	110	1	an	an	DET
fumecheng-2176	110	2	example	example	NOUN
fumecheng-2176	110	3	of	of	ADP
fumecheng-2176	110	4	parabolic	parabolic	ADJ
fumecheng-2176	110	5	indenter	indenter	NOUN
fumecheng-2176	110	6	(	(	PUNCT
fumecheng-2176	110	7	n=2	n=2	ADV
fumecheng-2176	110	8	)	)	PUNCT
fumecheng-2176	110	9	is	be	AUX
fumecheng-2176	110	10	shown	show	VERB
fumecheng-2176	110	11	in	in	ADP
fumecheng-2176	110	12	fig	fig	NOUN
fumecheng-2176	110	13	.	.	PUNCT
fumecheng-2176	111	1	4	4	NUM
fumecheng-2176	111	2	(	(	PUNCT
fumecheng-2176	111	3	b	b	NOUN
fumecheng-2176	111	4	)	)	PUNCT
fumecheng-2176	111	5	,	,	PUNCT
fumecheng-2176	111	6	where	where	SCONJ
fumecheng-2176	111	7	the	the	DET
fumecheng-2176	111	8	values	value	NOUN
fumecheng-2176	111	9	of	of	ADP
fumecheng-2176	111	10	α	α	NOUN
fumecheng-2176	111	11	for	for	ADP
fumecheng-2176	111	12	triangle	triangle	NOUN
fumecheng-2176	111	13	,	,	PUNCT
fumecheng-2176	111	14	square	square	ADJ
fumecheng-2176	111	15	and	and	CCONJ
fumecheng-2176	111	16	further	further	ADJ
fumecheng-2176	111	17	polygonal	polygonal	ADJ
fumecheng-2176	111	18	based	base	VERB
fumecheng-2176	111	19	profile	profile	NOUN
fumecheng-2176	111	20	are	be	AUX
fumecheng-2176	111	21	presented	present	VERB
fumecheng-2176	111	22	.	.	PUNCT
fumecheng-2176	112	1	in	in	ADP
fumecheng-2176	112	2	the	the	DET
fumecheng-2176	112	3	limiting	limit	VERB
fumecheng-2176	112	4	case	case	NOUN
fumecheng-2176	112	5	the	the	DET
fumecheng-2176	112	6	indenter	indenter	NOUN
fumecheng-2176	112	7	is	be	AUX
fumecheng-2176	112	8	a	a	DET
fumecheng-2176	112	9	spherical	spherical	ADJ
fumecheng-2176	112	10	cylinder	cylinder	NOUN
fumecheng-2176	112	11	,	,	PUNCT
fumecheng-2176	112	12	and	and	CCONJ
fumecheng-2176	112	13	α=2	α=2	PROPN
fumecheng-2176	112	14	corresponding	correspond	VERB
fumecheng-2176	112	15	to	to	ADP
fumecheng-2176	112	16	κ2=2	κ2=2	PROPN
fumecheng-2176	112	17	is	be	AUX
fumecheng-2176	112	18	well	well	ADV
fumecheng-2176	112	19	-	-	PUNCT
fumecheng-2176	112	20	known	know	VERB
fumecheng-2176	112	21	from	from	ADP
fumecheng-2176	112	22	the	the	DET
fumecheng-2176	112	23	mdr	mdr	PROPN
fumecheng-2176	112	24	theory	theory	NOUN
fumecheng-2176	112	25	[	[	X
fumecheng-2176	112	26	14	14	NUM
fumecheng-2176	112	27	]	]	PUNCT
fumecheng-2176	112	28	.	.	PUNCT
fumecheng-2176	113	1	if	if	SCONJ
fumecheng-2176	113	2	we	we	PRON
fumecheng-2176	113	3	use	use	VERB
fumecheng-2176	113	4	the	the	DET
fumecheng-2176	113	5	following	follow	VERB
fumecheng-2176	113	6	parameter	parameter	NOUN
fumecheng-2176	113	7	instead	instead	ADV
fumecheng-2176	113	8	of	of	ADP
fumecheng-2176	113	9	α	α	PROPN
fumecheng-2176	113	10	1	1	NUM
fumecheng-2176	113	11	3	3	NUM
fumecheng-2176	113	12	d	d	NOUN
fumecheng-2176	113	13	n	n	PROPN
fumecheng-2176	113	14	d	d	NOUN
fumecheng-2176	113	15	c	c	NOUN
fumecheng-2176	113	16	c	c	NOUN
fumecheng-2176	113	17			NOUN
fumecheng-2176	113	18			VERB
fumecheng-2176	113	19			PRON
fumecheng-2176	113	20	,	,	PUNCT
fumecheng-2176	113	21	(	(	PUNCT
fumecheng-2176	113	22	13	13	NUM
fumecheng-2176	113	23	)	)	PUNCT
fumecheng-2176	113	24	then	then	ADV
fumecheng-2176	113	25	in	in	ADP
fumecheng-2176	113	26	the	the	DET
fumecheng-2176	113	27	limiting	limit	VERB
fumecheng-2176	113	28	case	case	NOUN
fumecheng-2176	113	29	m=∞	m=∞	NOUN
fumecheng-2176	113	30	,	,	PUNCT
fumecheng-2176	113	31	value	value	NOUN
fumecheng-2176	113	32	ξ	ξ	PROPN
fumecheng-2176	113	33	for	for	ADP
fumecheng-2176	113	34	any	any	DET
fumecheng-2176	113	35	power	power	NOUN
fumecheng-2176	113	36	function	function	NOUN
fumecheng-2176	113	37	n	n	PRON
fumecheng-2176	113	38	will	will	AUX
fumecheng-2176	113	39	be	be	AUX
fumecheng-2176	113	40	equal	equal	ADJ
fumecheng-2176	113	41	to	to	ADP
fumecheng-2176	113	42	1	1	NUM
fumecheng-2176	113	43	,	,	PUNCT
fumecheng-2176	113	44	ξm=∞=1	ξm=∞=1	NOUN
fumecheng-2176	113	45	.	.	PUNCT
fumecheng-2176	114	1	some	some	DET
fumecheng-2176	114	2	values	value	NOUN
fumecheng-2176	114	3	of	of	ADP
fumecheng-2176	114	4	ξ	ξ	PROPN
fumecheng-2176	114	5	,	,	PUNCT
fumecheng-2176	114	6	in	in	ADP
fumecheng-2176	114	7	particular	particular	ADJ
fumecheng-2176	114	8	for	for	ADP
fumecheng-2176	114	9	pyramid	pyramid	NOUN
fumecheng-2176	114	10	and	and	CCONJ
fumecheng-2176	114	11	parabolic	parabolic	ADJ
fumecheng-2176	114	12	indenter	indenter	NOUN
fumecheng-2176	114	13	with	with	ADP
fumecheng-2176	114	14	triangle	triangle	NOUN
fumecheng-2176	114	15	and	and	CCONJ
fumecheng-2176	114	16	square	square	ADJ
fumecheng-2176	114	17	base	base	NOUN
fumecheng-2176	114	18	are	be	AUX
fumecheng-2176	114	19	shown	show	VERB
fumecheng-2176	114	20	in	in	ADP
fumecheng-2176	114	21	fig	fig	NOUN
fumecheng-2176	114	22	.	.	PUNCT
fumecheng-2176	115	1	5	5	NUM
fumecheng-2176	115	2	and	and	CCONJ
fumecheng-2176	115	3	table	table	NOUN
fumecheng-2176	115	4	3	3	NUM
fumecheng-2176	115	5	.	.	PUNCT
fumecheng-2176	115	6	indentation	indentation	NOUN
fumecheng-2176	115	7	of	of	ADP
fumecheng-2176	115	8	flat	flat	ADV
fumecheng-2176	115	9	-	-	PUNCT
fumecheng-2176	115	10	ended	end	VERB
fumecheng-2176	115	11	and	and	CCONJ
fumecheng-2176	115	12	tapered	tapered	ADJ
fumecheng-2176	115	13	indenters	indenter	NOUN
fumecheng-2176	115	14	with	with	ADP
fumecheng-2176	115	15	polygonal	polygonal	ADJ
fumecheng-2176	115	16	cross	cross	ADJ
fumecheng-2176	115	17	-	-	ADJ
fumecheng-2176	115	18	sections	section	NOUN
fumecheng-2176	115	19	247	247	NUM
fumecheng-2176	115	20	fig	fig	NOUN
fumecheng-2176	115	21	.	.	PUNCT
fumecheng-2176	116	1	5	5	NUM
fumecheng-2176	116	2	coefficient	coefficient	NOUN
fumecheng-2176	116	3	of	of	ADP
fumecheng-2176	116	4	ξ	ξ	PROPN
fumecheng-2176	116	5	for	for	ADP
fumecheng-2176	116	6	indenters	indenter	NOUN
fumecheng-2176	116	7	with	with	ADP
fumecheng-2176	116	8	power	power	NOUN
fumecheng-2176	116	9	function	function	NOUN
fumecheng-2176	116	10	profile	profile	NOUN
fumecheng-2176	116	11	table	table	NOUN
fumecheng-2176	116	12	3	3	NUM
fumecheng-2176	116	13	values	value	NOUN
fumecheng-2176	116	14	of	of	ADP
fumecheng-2176	116	15	coefficient	coefficient	NOUN
fumecheng-2176	116	16			NOUN
fumecheng-2176	116	17	n	n	CCONJ
fumecheng-2176	116	18	m	m	VERB
fumecheng-2176	116	19	3	3	NUM
fumecheng-2176	116	20	(	(	PUNCT
fumecheng-2176	116	21	triangle	triangle	NOUN
fumecheng-2176	116	22	)	)	PUNCT
fumecheng-2176	116	23	4	4	NUM
fumecheng-2176	116	24	(	(	PUNCT
fumecheng-2176	116	25	square	square	ADJ
fumecheng-2176	116	26	)	)	PUNCT
fumecheng-2176	116	27	5	5	NUM
fumecheng-2176	116	28	10	10	NUM
fumecheng-2176	116	29	20	20	NUM
fumecheng-2176	116	30	30	30	NUM
fumecheng-2176	116	31	1	1	NUM
fumecheng-2176	116	32	(	(	PUNCT
fumecheng-2176	116	33	pyramid	pyramid	NOUN
fumecheng-2176	116	34	)	)	PUNCT
fumecheng-2176	116	35	0.723	0.723	NUM
fumecheng-2176	116	36	0.866	0.866	NUM
fumecheng-2176	116	37	0.923	0.923	NUM
fumecheng-2176	116	38	0.986	0.986	NUM
fumecheng-2176	116	39	1.000	1.000	NUM
fumecheng-2176	116	40	1.000	1.000	NUM
fumecheng-2176	116	41	2	2	NUM
fumecheng-2176	116	42	(	(	PUNCT
fumecheng-2176	116	43	paraboloid	paraboloid	NOUN
fumecheng-2176	116	44	)	)	PUNCT
fumecheng-2176	116	45	0.526	0.526	NUM
fumecheng-2176	116	46	0.747	0.747	NUM
fumecheng-2176	116	47	0.845	0.845	NUM
fumecheng-2176	116	48	0.964	0.964	NUM
fumecheng-2176	116	49	0.991	0.991	NUM
fumecheng-2176	116	50	0.997	0.997	NUM
fumecheng-2176	116	51	3	3	NUM
fumecheng-2176	116	52	0.384	0.384	NUM
fumecheng-2176	116	53	0.648	0.648	NUM
fumecheng-2176	116	54	0.777	0.777	NUM
fumecheng-2176	116	55	0.947	0.947	NUM
fumecheng-2176	116	56	0.987	0.987	NUM
fumecheng-2176	116	57	0.994	0.994	NUM
fumecheng-2176	116	58	10	10	NUM
fumecheng-2176	116	59	0.043	0.043	NUM
fumecheng-2176	116	60	0.241	0.241	NUM
fumecheng-2176	116	61	0.058	0.058	NUM
fumecheng-2176	116	62	0.835	0.835	NUM
fumecheng-2176	116	63	0.957	0.957	NUM
fumecheng-2176	116	64	0.983	0.983	NUM
fumecheng-2176	116	65	20	20	NUM
fumecheng-2176	116	66	0.002	0.002	NUM
fumecheng-2176	116	67	0.058	0.058	NUM
fumecheng-2176	116	68	0.190	0.190	NUM
fumecheng-2176	116	69	0.695	0.695	NUM
fumecheng-2176	116	70	0.918	0.918	NUM
fumecheng-2176	116	71	0.964	0.964	NUM
fumecheng-2176	116	72	3.3	3.3	NUM
fumecheng-2176	116	73	.	.	PUNCT
fumecheng-2176	117	1	consideration	consideration	NOUN
fumecheng-2176	117	2	of	of	ADP
fumecheng-2176	117	3	indenters	indenter	NOUN
fumecheng-2176	117	4	with	with	ADP
fumecheng-2176	117	5	the	the	DET
fumecheng-2176	117	6	same	same	ADJ
fumecheng-2176	117	7	base	base	NOUN
fumecheng-2176	117	8	area	area	NOUN
fumecheng-2176	117	9	in	in	ADP
fumecheng-2176	117	10	section	section	NOUN
fumecheng-2176	117	11	2	2	NUM
fumecheng-2176	117	12	it	it	PRON
fumecheng-2176	117	13	is	be	AUX
fumecheng-2176	117	14	found	find	VERB
fumecheng-2176	117	15	that	that	SCONJ
fumecheng-2176	117	16	the	the	DET
fumecheng-2176	117	17	contact	contact	NOUN
fumecheng-2176	117	18	stiffnesses	stiffness	NOUN
fumecheng-2176	117	19	of	of	ADP
fumecheng-2176	117	20	triangular	triangular	NOUN
fumecheng-2176	117	21	,	,	PUNCT
fumecheng-2176	117	22	rectangular	rectangular	ADJ
fumecheng-2176	117	23	indenters	indenter	NOUN
fumecheng-2176	117	24	and	and	CCONJ
fumecheng-2176	117	25	flat	flat	ADJ
fumecheng-2176	117	26	cylinder	cylinder	NOUN
fumecheng-2176	117	27	with	with	ADP
fumecheng-2176	117	28	the	the	DET
fumecheng-2176	117	29	same	same	ADJ
fumecheng-2176	117	30	cross	cross	ADJ
fumecheng-2176	117	31	-	-	ADJ
fumecheng-2176	117	32	section	section	ADJ
fumecheng-2176	117	33	area	area	NOUN
fumecheng-2176	117	34	are	be	AUX
fumecheng-2176	117	35	almost	almost	ADV
fumecheng-2176	117	36	the	the	DET
fumecheng-2176	117	37	same	same	ADJ
fumecheng-2176	117	38	,	,	PUNCT
fumecheng-2176	117	39	and	and	CCONJ
fumecheng-2176	117	40	differ	differ	VERB
fumecheng-2176	117	41	at	at	ADP
fumecheng-2176	117	42	most	most	ADJ
fumecheng-2176	117	43	by	by	ADP
fumecheng-2176	117	44	6	6	NUM
fumecheng-2176	117	45	%	%	NOUN
fumecheng-2176	117	46	.	.	PUNCT
fumecheng-2176	118	1	it	it	PRON
fumecheng-2176	118	2	thus	thus	ADV
fumecheng-2176	118	3	appears	appear	VERB
fumecheng-2176	118	4	to	to	PART
fumecheng-2176	118	5	be	be	AUX
fumecheng-2176	118	6	sensible	sensible	ADJ
fumecheng-2176	118	7	to	to	PART
fumecheng-2176	118	8	try	try	VERB
fumecheng-2176	118	9	as	as	ADP
fumecheng-2176	118	10	“	"	PUNCT
fumecheng-2176	118	11	reference	reference	NOUN
fumecheng-2176	118	12	”	"	PUNCT
fumecheng-2176	118	13	indenters	indenter	VERB
fumecheng-2176	118	14	the	the	DET
fumecheng-2176	118	15	axisymmetrical	axisymmetrical	ADJ
fumecheng-2176	118	16	profiles	profile	NOUN
fumecheng-2176	118	17	with	with	ADP
fumecheng-2176	118	18	the	the	DET
fumecheng-2176	118	19	same	same	ADJ
fumecheng-2176	118	20	area	area	NOUN
fumecheng-2176	118	21	of	of	ADP
fumecheng-2176	118	22	cross	cross	NOUN
fumecheng-2176	118	23	-	-	NOUN
fumecheng-2176	118	24	section	section	NOUN
fumecheng-2176	118	25	.	.	PUNCT
fumecheng-2176	119	1	this	this	DET
fumecheng-2176	119	2	definition	definition	NOUN
fumecheng-2176	119	3	is	be	AUX
fumecheng-2176	119	4	slightly	slightly	ADV
fumecheng-2176	119	5	different	different	ADJ
fumecheng-2176	119	6	from	from	ADP
fumecheng-2176	119	7	the	the	DET
fumecheng-2176	119	8	definition	definition	NOUN
fumecheng-2176	119	9	in	in	ADP
fumecheng-2176	119	10	the	the	DET
fumecheng-2176	119	11	previous	previous	ADJ
fumecheng-2176	119	12	section	section	NOUN
fumecheng-2176	119	13	.	.	PUNCT
fumecheng-2176	120	1	for	for	ADP
fumecheng-2176	120	2	both	both	PRON
fumecheng-2176	120	3	initial	initial	ADJ
fumecheng-2176	120	4	polygonal	polygonal	ADJ
fumecheng-2176	120	5	profile	profile	NOUN
fumecheng-2176	120	6	and	and	CCONJ
fumecheng-2176	120	7	the	the	DET
fumecheng-2176	120	8	reference	reference	NOUN
fumecheng-2176	120	9	axisymmetrical	axisymmetrical	ADJ
fumecheng-2176	120	10	profile	profile	NOUN
fumecheng-2176	120	11	we	we	PRON
fumecheng-2176	120	12	carry	carry	VERB
fumecheng-2176	120	13	out	out	ADP
fumecheng-2176	120	14	the	the	DET
fumecheng-2176	120	15	mdr	mdr	PROPN
fumecheng-2176	120	16	transformation	transformation	NOUN
fumecheng-2176	120	17	and	and	CCONJ
fumecheng-2176	120	18	determine	determine	VERB
fumecheng-2176	120	19	the	the	DET
fumecheng-2176	120	20	equivalent	equivalent	ADJ
fumecheng-2176	120	21	1d	1d	NUM
fumecheng-2176	120	22	-	-	PUNCT
fumecheng-2176	120	23	mdr	mdr	NOUN
fumecheng-2176	120	24	profiles	profile	NOUN
fumecheng-2176	120	25	.	.	PUNCT
fumecheng-2176	121	1	let	let	VERB
fumecheng-2176	121	2	us	we	PRON
fumecheng-2176	121	3	explain	explain	VERB
fumecheng-2176	121	4	the	the	DET
fumecheng-2176	121	5	exact	exact	ADJ
fumecheng-2176	121	6	procedure	procedure	NOUN
fumecheng-2176	121	7	on	on	ADP
fumecheng-2176	121	8	the	the	DET
fumecheng-2176	121	9	example	example	NOUN
fumecheng-2176	121	10	of	of	ADP
fumecheng-2176	121	11	a	a	DET
fumecheng-2176	121	12	pyramid	pyramid	NOUN
fumecheng-2176	121	13	indenter	indenter	NOUN
fumecheng-2176	121	14	(	(	PUNCT
fumecheng-2176	121	15	n=1	n=1	PROPN
fumecheng-2176	121	16	)	)	PUNCT
fumecheng-2176	121	17	.	.	PUNCT
fumecheng-2176	122	1	first	first	ADV
fumecheng-2176	122	2	,	,	PUNCT
fumecheng-2176	122	3	we	we	PRON
fumecheng-2176	122	4	determine	determine	VERB
fumecheng-2176	122	5	the	the	DET
fumecheng-2176	122	6	area	area	NOUN
fumecheng-2176	122	7	of	of	ADP
fumecheng-2176	122	8	the	the	DET
fumecheng-2176	122	9	indenter	indenter	NOUN
fumecheng-2176	122	10	at	at	ADP
fumecheng-2176	122	11	different	different	ADJ
fumecheng-2176	122	12	height	height	NOUN
fumecheng-2176	122	13	and	and	CCONJ
fumecheng-2176	122	14	construct	construct	VERB
fumecheng-2176	122	15	a	a	DET
fumecheng-2176	122	16	cone	cone	NOUN
fumecheng-2176	122	17	with	with	ADP
fumecheng-2176	122	18	exactly	exactly	ADV
fumecheng-2176	122	19	the	the	DET
fumecheng-2176	122	20	same	same	ADJ
fumecheng-2176	122	21	cross	cross	ADJ
fumecheng-2176	122	22	-	-	ADJ
fumecheng-2176	122	23	section	section	ADJ
fumecheng-2176	122	24	areas	area	NOUN
fumecheng-2176	122	25	.	.	PUNCT
fumecheng-2176	123	1	then	then	ADV
fumecheng-2176	123	2	we	we	PRON
fumecheng-2176	123	3	carry	carry	VERB
fumecheng-2176	123	4	out	out	ADP
fumecheng-2176	123	5	the	the	DET
fumecheng-2176	123	6	three	three	NUM
fumecheng-2176	123	7	dimensional	dimensional	ADJ
fumecheng-2176	123	8	indentation	indentation	NOUN
fumecheng-2176	123	9	test	test	NOUN
fumecheng-2176	123	10	of	of	ADP
fumecheng-2176	123	11	the	the	DET
fumecheng-2176	123	12	polygonal	polygonal	ADJ
fumecheng-2176	123	13	indenter	indenter	NOUN
fumecheng-2176	123	14	by	by	ADP
fumecheng-2176	123	15	the	the	DET
fumecheng-2176	123	16	bem	bem	PROPN
fumecheng-2176	123	17	simulation	simulation	NOUN
fumecheng-2176	123	18	and	and	CCONJ
fumecheng-2176	123	19	extract	extract	VERB
fumecheng-2176	123	20	corresponding	correspond	VERB
fumecheng-2176	123	21	mdr	mdr	PROPN
fumecheng-2176	123	22	profile	profile	PROPN
fumecheng-2176	123	23	g(x)m	g(x)m	NOUN
fumecheng-2176	123	24	-	-	PUNCT
fumecheng-2176	123	25	poly	poly	ADJ
fumecheng-2176	123	26	and	and	CCONJ
fumecheng-2176	123	27	corresponding	corresponding	ADJ
fumecheng-2176	123	28	coefficient	coefficient	PROPN
fumecheng-2176	123	29	c1d	c1d	PROPN
fumecheng-2176	123	30	,	,	PUNCT
fumecheng-2176	123	31	m	m	NOUN
fumecheng-2176	123	32	-	-	NOUN
fumecheng-2176	123	33	poly	poly	ADJ
fumecheng-2176	123	34	as	as	SCONJ
fumecheng-2176	123	35	described	describe	VERB
fumecheng-2176	123	36	in	in	ADP
fumecheng-2176	123	37	section	section	NOUN
fumecheng-2176	123	38	3	3	NUM
fumecheng-2176	123	39	.	.	PUNCT
fumecheng-2176	124	1	for	for	ADP
fumecheng-2176	124	2	the	the	DET
fumecheng-2176	124	3	reference	reference	NOUN
fumecheng-2176	124	4	axisymmetrical	axisymmetrical	ADJ
fumecheng-2176	124	5	profile	profile	NOUN
fumecheng-2176	124	6	,	,	PUNCT
fumecheng-2176	124	7	the	the	DET
fumecheng-2176	124	8	corresponding	correspond	VERB
fumecheng-2176	124	9	mdr	mdr	PROPN
fumecheng-2176	124	10	transformed	transform	VERB
fumecheng-2176	124	11	profile	profile	NOUN
fumecheng-2176	124	12	and	and	CCONJ
fumecheng-2176	124	13	the	the	DET
fumecheng-2176	124	14	corresponding	corresponding	ADJ
fumecheng-2176	124	15	coefficient	coefficient	PROPN
fumecheng-2176	124	16	c1d	c1d	PROPN
fumecheng-2176	124	17	,	,	PUNCT
fumecheng-2176	124	18	m=∞	m=∞	PROPN
fumecheng-2176	124	19	are	be	AUX
fumecheng-2176	124	20	determined	determine	VERB
fumecheng-2176	124	21	by	by	ADP
fumecheng-2176	124	22	(	(	PUNCT
fumecheng-2176	124	23	5	5	NUM
fumecheng-2176	124	24	)	)	PUNCT
fumecheng-2176	124	25	.	.	PUNCT
fumecheng-2176	125	1	finally	finally	ADV
fumecheng-2176	125	2	we	we	PRON
fumecheng-2176	125	3	compare	compare	VERB
fumecheng-2176	125	4	this	this	DET
fumecheng-2176	125	5	c1d	c1d	PROPN
fumecheng-2176	125	6	,	,	PUNCT
fumecheng-2176	125	7	m	m	NOUN
fumecheng-2176	125	8	-	-	NOUN
fumecheng-2176	125	9	poly	poly	ADJ
fumecheng-2176	125	10	and	and	CCONJ
fumecheng-2176	125	11	the	the	DET
fumecheng-2176	125	12	coefficient	coefficient	NOUN
fumecheng-2176	125	13	of	of	ADP
fumecheng-2176	125	14	the	the	DET
fumecheng-2176	125	15	axisymmetric	axisymmetric	ADJ
fumecheng-2176	125	16	conical	conical	NOUN
fumecheng-2176	125	17	profile	profile	NOUN
fumecheng-2176	125	18	using	use	VERB
fumecheng-2176	125	19	the	the	DET
fumecheng-2176	125	20	ratio	ratio	NOUN
fumecheng-2176	125	21	1	1	NUM
fumecheng-2176	125	22	,	,	PUNCT
fumecheng-2176	125	23	-poly	-poly	PROPN
fumecheng-2176	125	24	1	1	NUM
fumecheng-2176	125	25	,	,	PUNCT
fumecheng-2176	125	26	d	d	PROPN
fumecheng-2176	125	27	m	m	VERB
fumecheng-2176	125	28	d	d	NOUN
fumecheng-2176	125	29	m	m	VERB
fumecheng-2176	125	30	c	c	NOUN
fumecheng-2176	125	31	c	c	NOUN
fumecheng-2176	125	32			NOUN
fumecheng-2176	125	33			PROPN
fumecheng-2176	125	34			PROPN
fumecheng-2176	125	35	.	.	PUNCT
fumecheng-2176	126	1	(	(	PUNCT
fumecheng-2176	126	2	14	14	NUM
fumecheng-2176	126	3	)	)	PUNCT
fumecheng-2176	126	4	248	248	NUM
fumecheng-2176	126	5	q.	q.	PROPN
fumecheng-2176	126	6	li	li	PROPN
fumecheng-2176	126	7	,	,	PUNCT
fumecheng-2176	126	8	v.l	v.l	PROPN
fumecheng-2176	126	9	.	.	PROPN
fumecheng-2176	126	10	popov	popov	PROPN
fumecheng-2176	126	11	in	in	ADP
fumecheng-2176	126	12	an	an	DET
fumecheng-2176	126	13	absolute	absolute	ADJ
fumecheng-2176	126	14	similar	similar	ADJ
fumecheng-2176	126	15	way	way	NOUN
fumecheng-2176	126	16	comparisons	comparison	NOUN
fumecheng-2176	126	17	were	be	AUX
fumecheng-2176	126	18	also	also	ADV
fumecheng-2176	126	19	carried	carry	VERB
fumecheng-2176	126	20	out	out	ADP
fumecheng-2176	126	21	for	for	ADP
fumecheng-2176	126	22	other	other	ADJ
fumecheng-2176	126	23	power	power	NOUN
fumecheng-2176	126	24	function	function	NOUN
fumecheng-2176	126	25	geometries	geometry	NOUN
fumecheng-2176	126	26	.	.	PUNCT
fumecheng-2176	127	1	the	the	DET
fumecheng-2176	127	2	results	result	NOUN
fumecheng-2176	127	3	are	be	AUX
fumecheng-2176	127	4	shown	show	VERB
fumecheng-2176	127	5	in	in	ADP
fumecheng-2176	127	6	fig.6	fig.6	PROPN
fumecheng-2176	127	7	and	and	CCONJ
fumecheng-2176	127	8	table	table	NOUN
fumecheng-2176	127	9	4	4	NUM
fumecheng-2176	127	10	.	.	PUNCT
fumecheng-2176	128	1	it	it	PRON
fumecheng-2176	128	2	can	can	AUX
fumecheng-2176	128	3	be	be	AUX
fumecheng-2176	128	4	seen	see	VERB
fumecheng-2176	128	5	that	that	SCONJ
fumecheng-2176	128	6	the	the	DET
fumecheng-2176	128	7	coefficient	coefficient	NOUN
fumecheng-2176	128	8	c1d	c1d	PROPN
fumecheng-2176	128	9	of	of	ADP
fumecheng-2176	128	10	pyramid	pyramid	PROPN
fumecheng-2176	128	11	indenter	indenter	PROPN
fumecheng-2176	128	12	is	be	AUX
fumecheng-2176	128	13	close	close	ADJ
fumecheng-2176	128	14	to	to	ADP
fumecheng-2176	128	15	that	that	PRON
fumecheng-2176	128	16	of	of	ADP
fumecheng-2176	128	17	conical	conical	ADJ
fumecheng-2176	128	18	indenter	indenter	NOUN
fumecheng-2176	128	19	:	:	PUNCT
fumecheng-2176	128	20	it	it	PRON
fumecheng-2176	128	21	differs	differ	VERB
fumecheng-2176	128	22	by	by	ADP
fumecheng-2176	128	23	at	at	ADP
fumecheng-2176	128	24	most	most	ADV
fumecheng-2176	128	25	7	7	NUM
fumecheng-2176	128	26	%	%	NOUN
fumecheng-2176	128	27	in	in	ADP
fumecheng-2176	128	28	the	the	DET
fumecheng-2176	128	29	case	case	NOUN
fumecheng-2176	128	30	of	of	ADP
fumecheng-2176	128	31	triangular	triangular	NOUN
fumecheng-2176	128	32	base	base	NOUN
fumecheng-2176	128	33	(	(	PUNCT
fumecheng-2176	128	34	c1d	c1d	ADJ
fumecheng-2176	128	35	=	=	VERB
fumecheng-2176	128	36	0.927	0.927	NUM
fumecheng-2176	128	37	)	)	PUNCT
fumecheng-2176	128	38	.	.	PUNCT
fumecheng-2176	129	1	it	it	PRON
fumecheng-2176	129	2	is	be	AUX
fumecheng-2176	129	3	noted	note	VERB
fumecheng-2176	129	4	that	that	SCONJ
fumecheng-2176	129	5	coefficient	coefficient	NOUN
fumecheng-2176	129	6	c1d	c1d	ADJ
fumecheng-2176	129	7	can	can	AUX
fumecheng-2176	129	8	not	not	PART
fumecheng-2176	129	9	directly	directly	ADV
fumecheng-2176	129	10	reflect	reflect	VERB
fumecheng-2176	129	11	the	the	DET
fumecheng-2176	129	12	contact	contact	NOUN
fumecheng-2176	129	13	stiffness	stiffness	NOUN
fumecheng-2176	129	14	.	.	PUNCT
fumecheng-2176	130	1	take	take	VERB
fumecheng-2176	130	2	an	an	DET
fumecheng-2176	130	3	example	example	NOUN
fumecheng-2176	130	4	of	of	ADP
fumecheng-2176	130	5	triangular	triangular	NOUN
fumecheng-2176	130	6	indenter	indenter	NOUN
fumecheng-2176	130	7	with	with	ADP
fumecheng-2176	130	8	power	power	NOUN
fumecheng-2176	130	9	n=20	n=20	NOUN
fumecheng-2176	130	10	whose	whose	DET
fumecheng-2176	130	11	geometry	geometry	NOUN
fumecheng-2176	130	12	is	be	AUX
fumecheng-2176	130	13	close	close	ADJ
fumecheng-2176	130	14	to	to	ADP
fumecheng-2176	130	15	the	the	DET
fumecheng-2176	130	16	flat	flat	ADJ
fumecheng-2176	130	17	triangular	triangular	NOUN
fumecheng-2176	130	18	indenter	indenter	NOUN
fumecheng-2176	130	19	(	(	PUNCT
fumecheng-2176	130	20	fig.1a	fig.1a	NOUN
fumecheng-2176	130	21	)	)	PUNCT
fumecheng-2176	130	22	,	,	PUNCT
fumecheng-2176	130	23	its	its	PRON
fumecheng-2176	130	24	ζ	ζ	NOUN
fumecheng-2176	130	25	is	be	AUX
fumecheng-2176	130	26	very	very	ADV
fumecheng-2176	130	27	small	small	ADJ
fumecheng-2176	130	28	ζ	ζ	NOUN
fumecheng-2176	130	29	=	=	SYM
fumecheng-2176	130	30	0.295	0.295	NUM
fumecheng-2176	130	31	(	(	PUNCT
fumecheng-2176	130	32	m=3	m=3	PROPN
fumecheng-2176	130	33	,	,	PUNCT
fumecheng-2176	130	34	n=20	n=20	NOUN
fumecheng-2176	130	35	)	)	PUNCT
fumecheng-2176	130	36	,	,	PUNCT
fumecheng-2176	130	37	but	but	CCONJ
fumecheng-2176	130	38	the	the	DET
fumecheng-2176	130	39	contact	contact	NOUN
fumecheng-2176	130	40	stiffness	stiffness	NOUN
fumecheng-2176	130	41	at	at	ADP
fumecheng-2176	130	42	the	the	DET
fumecheng-2176	130	43	large	large	ADJ
fumecheng-2176	130	44	indentation	indentation	NOUN
fumecheng-2176	130	45	depth	depth	NOUN
fumecheng-2176	130	46	is	be	AUX
fumecheng-2176	130	47	the	the	DET
fumecheng-2176	130	48	same	same	ADJ
fumecheng-2176	130	49	to	to	ADP
fumecheng-2176	130	50	the	the	DET
fumecheng-2176	130	51	flat	flat	ADJ
fumecheng-2176	130	52	indenter	indenter	NOUN
fumecheng-2176	130	53	.	.	PUNCT
fumecheng-2176	131	1	fig	fig	NOUN
fumecheng-2176	131	2	.	.	PUNCT
fumecheng-2176	132	1	6	6	NUM
fumecheng-2176	132	2	comparison	comparison	NOUN
fumecheng-2176	132	3	of	of	ADP
fumecheng-2176	132	4	coefficient	coefficient	NOUN
fumecheng-2176	132	5	c1d	c1d	PROPN
fumecheng-2176	132	6	among	among	ADP
fumecheng-2176	132	7	different	different	ADJ
fumecheng-2176	132	8	indenters	indenter	NOUN
fumecheng-2176	132	9	with	with	ADP
fumecheng-2176	132	10	the	the	DET
fumecheng-2176	132	11	same	same	ADJ
fumecheng-2176	132	12	base	base	NOUN
fumecheng-2176	132	13	area	area	NOUN
fumecheng-2176	132	14	table	table	NOUN
fumecheng-2176	132	15	4	4	NUM
fumecheng-2176	132	16	coefficient	coefficient	NOUN
fumecheng-2176	132	17	ζ	ζ	NOUN
fumecheng-2176	132	18	for	for	ADP
fumecheng-2176	132	19	different	different	ADJ
fumecheng-2176	132	20	power	power	NOUN
fumecheng-2176	132	21	n	n	NOUN
fumecheng-2176	132	22	and	and	CCONJ
fumecheng-2176	132	23	polygon	polygon	PROPN
fumecheng-2176	132	24	m	m	PROPN
fumecheng-2176	132	25	n	n	VERB
fumecheng-2176	132	26	m	m	VERB
fumecheng-2176	132	27	3	3	NUM
fumecheng-2176	132	28	(	(	PUNCT
fumecheng-2176	132	29	triangle	triangle	NOUN
fumecheng-2176	132	30	)	)	PUNCT
fumecheng-2176	132	31	4	4	NUM
fumecheng-2176	132	32	(	(	PUNCT
fumecheng-2176	132	33	square	square	ADJ
fumecheng-2176	132	34	)	)	PUNCT
fumecheng-2176	132	35	5	5	NUM
fumecheng-2176	132	36	6	6	NUM
fumecheng-2176	132	37	10	10	NUM
fumecheng-2176	132	38	20	20	NUM
fumecheng-2176	132	39	1	1	NUM
fumecheng-2176	132	40	(	(	PUNCT
fumecheng-2176	132	41	pyramid	pyramid	NOUN
fumecheng-2176	132	42	)	)	PUNCT
fumecheng-2176	132	43	0.927	0.927	NUM
fumecheng-2176	132	44	0.974	0.974	NUM
fumecheng-2176	132	45	0.988	0.988	NUM
fumecheng-2176	132	46	0.994	0.994	NUM
fumecheng-2176	132	47	1.000	1.000	NUM
fumecheng-2176	132	48	1.000	1.000	NUM
fumecheng-2176	132	49	2	2	NUM
fumecheng-2176	132	50	(	(	PUNCT
fumecheng-2176	132	51	paraboloid	paraboloid	NOUN
fumecheng-2176	132	52	)	)	PUNCT
fumecheng-2176	132	53	0.870	0.870	NUM
fumecheng-2176	132	54	0.951	0.951	NUM
fumecheng-2176	132	55	0.977	0.977	NUM
fumecheng-2176	132	56	0.988	0.988	NUM
fumecheng-2176	132	57	0.997	0.997	NUM
fumecheng-2176	132	58	1.000	1.000	NUM
fumecheng-2176	132	59	3	3	NUM
fumecheng-2176	132	60	0.817	0.817	NUM
fumecheng-2176	132	61	0.931	0.931	NUM
fumecheng-2176	132	62	0.966	0.966	NUM
fumecheng-2176	132	63	0.981	0.981	NUM
fumecheng-2176	132	64	0.996	0.996	NUM
fumecheng-2176	132	65	1.000	1.000	NUM
fumecheng-2176	132	66	10	10	NUM
fumecheng-2176	132	67	0.536	0.536	NUM
fumecheng-2176	132	68	0.806	0.806	NUM
fumecheng-2176	132	69	0.820	0.820	NUM
fumecheng-2176	132	70	0.893	0.893	NUM
fumecheng-2176	132	71	0.990	0.990	NUM
fumecheng-2176	132	72	1.000	1.000	NUM
fumecheng-2176	132	73	20	20	NUM
fumecheng-2176	132	74	0.295	0.295	NUM
fumecheng-2176	132	75	0.651	0.651	NUM
fumecheng-2176	132	76	0.814	0.814	NUM
fumecheng-2176	132	77	0.889	0.889	NUM
fumecheng-2176	132	78	0.973	0.973	NUM
fumecheng-2176	132	79	0.997	0.997	NUM
fumecheng-2176	132	80	4	4	NUM
fumecheng-2176	132	81	.	.	PUNCT
fumecheng-2176	133	1	conclusion	conclusion	NOUN
fumecheng-2176	133	2	indentation	indentation	NOUN
fumecheng-2176	133	3	of	of	ADP
fumecheng-2176	133	4	flat	flat	ADV
fumecheng-2176	133	5	-	-	PUNCT
fumecheng-2176	133	6	ended	end	VERB
fumecheng-2176	133	7	and	and	CCONJ
fumecheng-2176	133	8	tapered	tapered	ADJ
fumecheng-2176	133	9	indenters	indenter	NOUN
fumecheng-2176	133	10	with	with	ADP
fumecheng-2176	133	11	polygonal	polygonal	ADJ
fumecheng-2176	133	12	base	base	NOUN
fumecheng-2176	133	13	was	be	AUX
fumecheng-2176	133	14	numerically	numerically	ADV
fumecheng-2176	133	15	simulated	simulate	VERB
fumecheng-2176	133	16	using	use	VERB
fumecheng-2176	133	17	the	the	DET
fumecheng-2176	133	18	boundary	boundary	ADJ
fumecheng-2176	133	19	element	element	NOUN
fumecheng-2176	133	20	method	method	NOUN
fumecheng-2176	133	21	.	.	PUNCT
fumecheng-2176	134	1	the	the	DET
fumecheng-2176	134	2	contact	contact	NOUN
fumecheng-2176	134	3	stiffnesses	stiffness	NOUN
fumecheng-2176	134	4	of	of	ADP
fumecheng-2176	134	5	prismatic	prismatic	ADJ
fumecheng-2176	134	6	punches	punch	NOUN
fumecheng-2176	134	7	with	with	ADP
fumecheng-2176	134	8	the	the	DET
fumecheng-2176	134	9	same	same	ADJ
fumecheng-2176	134	10	cross	cross	PROPN
fumecheng-2176	134	11	section	section	NOUN
fumecheng-2176	134	12	area	area	NOUN
fumecheng-2176	134	13	are	be	AUX
fumecheng-2176	134	14	almost	almost	ADV
fumecheng-2176	134	15	same	same	ADJ
fumecheng-2176	134	16	as	as	ADP
fumecheng-2176	134	17	the	the	DET
fumecheng-2176	134	18	cylindrical	cylindrical	ADJ
fumecheng-2176	134	19	indenter	indenter	NOUN
fumecheng-2176	134	20	,	,	PUNCT
fumecheng-2176	134	21	where	where	SCONJ
fumecheng-2176	134	22	the	the	DET
fumecheng-2176	134	23	triangular	triangular	NOUN
fumecheng-2176	134	24	punch	punch	NOUN
fumecheng-2176	134	25	differs	differ	VERB
fumecheng-2176	134	26	at	at	ADP
fumecheng-2176	134	27	most	most	ADJ
fumecheng-2176	134	28	by	by	ADP
fumecheng-2176	134	29	6	6	NUM
fumecheng-2176	134	30	%	%	NOUN
fumecheng-2176	134	31	.	.	PUNCT
fumecheng-2176	135	1	for	for	ADP
fumecheng-2176	135	2	pyramidal	pyramidal	ADJ
fumecheng-2176	135	3	indenter	indenter	NOUN
fumecheng-2176	135	4	and	and	CCONJ
fumecheng-2176	135	5	others	other	NOUN
fumecheng-2176	135	6	with	with	ADP
fumecheng-2176	135	7	power	power	NOUN
fumecheng-2176	135	8	function	function	NOUN
fumecheng-2176	135	9	side	side	NOUN
fumecheng-2176	135	10	,	,	PUNCT
fumecheng-2176	135	11	the	the	DET
fumecheng-2176	135	12	one	one	NUM
fumecheng-2176	135	13	dimensional	dimensional	ADJ
fumecheng-2176	135	14	mdr	mdr	NOUN
fumecheng-2176	135	15	transformed	transform	VERB
fumecheng-2176	135	16	profile	profile	NOUN
fumecheng-2176	135	17	was	be	AUX
fumecheng-2176	135	18	generated	generate	VERB
fumecheng-2176	135	19	based	base	VERB
fumecheng-2176	135	20	on	on	ADP
fumecheng-2176	135	21	the	the	DET
fumecheng-2176	135	22	three	three	NUM
fumecheng-2176	135	23	dimensional	dimensional	ADJ
fumecheng-2176	135	24	simulation	simulation	NOUN
fumecheng-2176	135	25	of	of	ADP
fumecheng-2176	135	26	indentation	indentation	NOUN
fumecheng-2176	135	27	.	.	PUNCT
fumecheng-2176	136	1	it	it	PRON
fumecheng-2176	136	2	is	be	AUX
fumecheng-2176	136	3	found	find	VERB
fumecheng-2176	136	4	that	that	SCONJ
fumecheng-2176	136	5	the	the	DET
fumecheng-2176	136	6	1d	1d	NUM
fumecheng-2176	136	7	profile	profile	NOUN
fumecheng-2176	136	8	is	be	AUX
fumecheng-2176	136	9	still	still	ADV
fumecheng-2176	136	10	a	a	DET
fumecheng-2176	136	11	power	power	NOUN
fumecheng-2176	136	12	function	function	NOUN
fumecheng-2176	136	13	with	with	ADP
fumecheng-2176	136	14	the	the	DET
fumecheng-2176	136	15	same	same	ADJ
fumecheng-2176	136	16	power	power	NOUN
fumecheng-2176	136	17	and	and	CCONJ
fumecheng-2176	136	18	it	it	PRON
fumecheng-2176	136	19	differs	differ	VERB
fumecheng-2176	136	20	only	only	ADV
fumecheng-2176	136	21	by	by	ADP
fumecheng-2176	136	22	a	a	DET
fumecheng-2176	136	23	constant	constant	ADJ
fumecheng-2176	136	24	factor	factor	NOUN
fumecheng-2176	136	25	.	.	PUNCT
fumecheng-2176	137	1	the	the	DET
fumecheng-2176	137	2	factor	factor	NOUN
fumecheng-2176	137	3	was	be	AUX
fumecheng-2176	137	4	numerically	numerically	ADV
fumecheng-2176	137	5	calculated	calculate	VERB
fumecheng-2176	137	6	for	for	ADP
fumecheng-2176	137	7	the	the	DET
fumecheng-2176	137	8	indenters	indenter	NOUN
fumecheng-2176	137	9	with	with	ADP
fumecheng-2176	137	10	different	different	ADJ
fumecheng-2176	137	11	power	power	NOUN
fumecheng-2176	137	12	function	function	NOUN
fumecheng-2176	137	13	side	side	NOUN
fumecheng-2176	137	14	and	and	CCONJ
fumecheng-2176	137	15	different	different	ADJ
fumecheng-2176	137	16	polygonal	polygonal	ADJ
fumecheng-2176	137	17	base	base	NOUN
fumecheng-2176	137	18	.	.	PUNCT
fumecheng-2176	138	1	the	the	DET
fumecheng-2176	138	2	generated	generate	VERB
fumecheng-2176	138	3	mdr	mdr	PROPN
fumecheng-2176	138	4	profiles	profile	NOUN
fumecheng-2176	138	5	can	can	AUX
fumecheng-2176	138	6	be	be	AUX
fumecheng-2176	138	7	used	use	VERB
fumecheng-2176	138	8	for	for	ADP
fumecheng-2176	138	9	the	the	DET
fumecheng-2176	138	10	further	further	ADJ
fumecheng-2176	138	11	contact	contact	NOUN
fumecheng-2176	138	12	problems	problem	NOUN
fumecheng-2176	138	13	,	,	PUNCT
fumecheng-2176	138	14	such	such	ADJ
fumecheng-2176	138	15	as	as	ADP
fumecheng-2176	138	16	tangential	tangential	ADJ
fumecheng-2176	138	17	contact	contact	NOUN
fumecheng-2176	138	18	or	or	CCONJ
fumecheng-2176	138	19	contact	contact	NOUN
fumecheng-2176	138	20	with	with	ADP
fumecheng-2176	138	21	linear	linear	ADJ
fumecheng-2176	138	22	viscoelastic	viscoelastic	ADJ
fumecheng-2176	138	23	bodies	body	NOUN
fumecheng-2176	138	24	.	.	PUNCT
fumecheng-2176	139	1	indentation	indentation	NOUN
fumecheng-2176	139	2	of	of	ADP
fumecheng-2176	139	3	flat	flat	ADV
fumecheng-2176	139	4	-	-	PUNCT
fumecheng-2176	139	5	ended	end	VERB
fumecheng-2176	139	6	and	and	CCONJ
fumecheng-2176	139	7	tapered	tapered	ADJ
fumecheng-2176	139	8	indenters	indenter	NOUN
fumecheng-2176	139	9	with	with	ADP
fumecheng-2176	139	10	polygonal	polygonal	ADJ
fumecheng-2176	139	11	cross	cross	NOUN
fumecheng-2176	139	12	-	-	NOUN
fumecheng-2176	139	13	sections	section	NOUN
fumecheng-2176	139	14	249	249	NUM
fumecheng-2176	139	15	references	reference	NOUN
fumecheng-2176	139	16	1	1	NUM
fumecheng-2176	139	17	.	.	PUNCT
fumecheng-2176	139	18	oliver	oliver	PROPN
fumecheng-2176	139	19	,	,	PUNCT
fumecheng-2176	139	20	w.c	w.c	AUX
fumecheng-2176	139	21	.	.	PROPN
fumecheng-2176	139	22	,	,	PUNCT
fumecheng-2176	139	23	pharr	pharr	PROPN
fumecheng-2176	139	24	,	,	PUNCT
fumecheng-2176	139	25	g.m	g.m	PROPN
fumecheng-2176	139	26	.	.	PROPN
fumecheng-2176	139	27	,	,	PUNCT
fumecheng-2176	139	28	2011	2011	NUM
fumecheng-2176	139	29	,	,	PUNCT
fumecheng-2176	139	30	measurement	measurement	NOUN
fumecheng-2176	139	31	of	of	ADP
fumecheng-2176	139	32	hardness	hardness	NOUN
fumecheng-2176	139	33	and	and	CCONJ
fumecheng-2176	139	34	elastic	elastic	ADJ
fumecheng-2176	139	35	modulus	modulus	NOUN
fumecheng-2176	139	36	by	by	ADP
fumecheng-2176	139	37	instrumented	instrumented	ADJ
fumecheng-2176	139	38	indentation	indentation	NOUN
fumecheng-2176	139	39	:	:	PUNCT
fumecheng-2176	139	40	advances	advance	NOUN
fumecheng-2176	139	41	in	in	ADP
fumecheng-2176	139	42	understanding	understanding	NOUN
fumecheng-2176	139	43	and	and	CCONJ
fumecheng-2176	139	44	refinements	refinement	NOUN
fumecheng-2176	139	45	to	to	ADP
fumecheng-2176	139	46	methodology	methodology	NOUN
fumecheng-2176	139	47	,	,	PUNCT
fumecheng-2176	139	48	journal	journal	NOUN
fumecheng-2176	139	49	of	of	ADP
fumecheng-2176	139	50	materials	material	NOUN
fumecheng-2176	139	51	research	research	NOUN
fumecheng-2176	139	52	,	,	PUNCT
fumecheng-2176	139	53	19(1	19(1	NUM
fumecheng-2176	139	54	)	)	PUNCT
fumecheng-2176	139	55	,	,	PUNCT
fumecheng-2176	139	56	pp	pp	PROPN
fumecheng-2176	139	57	.	.	PUNCT
fumecheng-2176	140	1	3–20	3–20	NUM
fumecheng-2176	140	2	.	.	PUNCT
fumecheng-2176	141	1	2	2	NUM
fumecheng-2176	141	2	.	.	X
fumecheng-2176	141	3	fischer	fischer	PROPN
fumecheng-2176	141	4	-	-	PUNCT
fumecheng-2176	141	5	cripps	cripps	PROPN
fumecheng-2176	141	6	,	,	PUNCT
fumecheng-2176	141	7	a.c	a.c	PROPN
fumecheng-2176	141	8	.	.	PROPN
fumecheng-2176	141	9	,	,	PUNCT
fumecheng-2176	141	10	2000	2000	NUM
fumecheng-2176	141	11	,	,	PUNCT
fumecheng-2176	141	12	a	a	DET
fumecheng-2176	141	13	review	review	NOUN
fumecheng-2176	141	14	of	of	ADP
fumecheng-2176	141	15	analysis	analysis	NOUN
fumecheng-2176	141	16	methods	method	NOUN
fumecheng-2176	141	17	for	for	ADP
fumecheng-2176	141	18	sub	sub	ADJ
fumecheng-2176	141	19	-	-	ADJ
fumecheng-2176	141	20	micron	micron	ADJ
fumecheng-2176	141	21	indentation	indentation	NOUN
fumecheng-2176	141	22	testing	testing	NOUN
fumecheng-2176	141	23	,	,	PUNCT
fumecheng-2176	141	24	vacuum	vacuum	PROPN
fumecheng-2176	141	25	,	,	PUNCT
fumecheng-2176	141	26	58(4	58(4	NUM
fumecheng-2176	141	27	)	)	PUNCT
fumecheng-2176	141	28	,	,	PUNCT
fumecheng-2176	141	29	pp.569	pp.569	PROPN
fumecheng-2176	141	30	-	-	PUNCT
fumecheng-2176	141	31	585	585	NUM
fumecheng-2176	141	32	.	.	NOUN
fumecheng-2176	142	1	3	3	NUM
fumecheng-2176	142	2	.	.	X
fumecheng-2176	142	3	hay	hay	PROPN
fumecheng-2176	142	4	,	,	PUNCT
fumecheng-2176	142	5	j.	j.	PROPN
fumecheng-2176	142	6	,	,	PUNCT
fumecheng-2176	142	7	agee	agee	PROPN
fumecheng-2176	142	8	,	,	PUNCT
fumecheng-2176	142	9	p.	p.	PROPN
fumecheng-2176	142	10	,	,	PUNCT
fumecheng-2176	142	11	herbert	herbert	PROPN
fumecheng-2176	142	12	,	,	PUNCT
fumecheng-2176	142	13	e.	e.	PROPN
fumecheng-2176	142	14	,	,	PUNCT
fumecheng-2176	142	15	2010	2010	NUM
fumecheng-2176	142	16	,	,	PUNCT
fumecheng-2176	142	17	continuous	continuous	ADJ
fumecheng-2176	142	18	stiffness	stiffness	NOUN
fumecheng-2176	142	19	measurement	measurement	NOUN
fumecheng-2176	142	20	during	during	ADP
fumecheng-2176	142	21	instrumented	instrumented	ADJ
fumecheng-2176	142	22	indentation	indentation	NOUN
fumecheng-2176	142	23	testing	testing	NOUN
fumecheng-2176	142	24	,	,	PUNCT
fumecheng-2176	142	25	experimental	experimental	ADJ
fumecheng-2176	142	26	techniques	technique	NOUN
fumecheng-2176	142	27	,	,	PUNCT
fumecheng-2176	142	28	34	34	NUM
fumecheng-2176	142	29	,	,	PUNCT
fumecheng-2176	142	30	pp	pp	ADJ
fumecheng-2176	142	31	.	.	PUNCT
fumecheng-2176	143	1	86–94	86–94	NUM
fumecheng-2176	143	2	.	.	PUNCT
fumecheng-2176	144	1	4	4	NUM
fumecheng-2176	144	2	.	.	X
fumecheng-2176	144	3	swadener	swadener	PROPN
fumecheng-2176	144	4	,	,	PUNCT
fumecheng-2176	144	5	j.g	j.g	PROPN
fumecheng-2176	144	6	.	.	PROPN
fumecheng-2176	144	7	,	,	PUNCT
fumecheng-2176	144	8	george	george	PROPN
fumecheng-2176	144	9	,	,	PUNCT
fumecheng-2176	144	10	e.p	e.p	PROPN
fumecheng-2176	144	11	.	.	PROPN
fumecheng-2176	144	12	,	,	PUNCT
fumecheng-2176	144	13	pharr	pharr	PROPN
fumecheng-2176	144	14	,	,	PUNCT
fumecheng-2176	144	15	g.m	g.m	PROPN
fumecheng-2176	144	16	.	.	PROPN
fumecheng-2176	144	17	,	,	PUNCT
fumecheng-2176	144	18	2002	2002	NUM
fumecheng-2176	144	19	,	,	PUNCT
fumecheng-2176	144	20	the	the	DET
fumecheng-2176	144	21	correlation	correlation	NOUN
fumecheng-2176	144	22	of	of	ADP
fumecheng-2176	144	23	the	the	DET
fumecheng-2176	144	24	indentation	indentation	NOUN
fumecheng-2176	144	25	size	size	NOUN
fumecheng-2176	144	26	effect	effect	NOUN
fumecheng-2176	144	27	measured	measure	VERB
fumecheng-2176	144	28	with	with	ADP
fumecheng-2176	144	29	indenters	indenter	NOUN
fumecheng-2176	144	30	of	of	ADP
fumecheng-2176	144	31	various	various	ADJ
fumecheng-2176	144	32	shapes	shape	NOUN
fumecheng-2176	144	33	,	,	PUNCT
fumecheng-2176	144	34	journal	journal	NOUN
fumecheng-2176	144	35	of	of	ADP
fumecheng-2176	144	36	the	the	DET
fumecheng-2176	144	37	mechanics	mechanic	NOUN
fumecheng-2176	144	38	and	and	CCONJ
fumecheng-2176	144	39	physics	physic	NOUN
fumecheng-2176	144	40	of	of	ADP
fumecheng-2176	144	41	solids	solid	NOUN
fumecheng-2176	144	42	,	,	PUNCT
fumecheng-2176	144	43	50(4	50(4	NUM
fumecheng-2176	144	44	)	)	PUNCT
fumecheng-2176	144	45	,	,	PUNCT
fumecheng-2176	144	46	pp	pp	ADP
fumecheng-2176	144	47	.	.	PUNCT
fumecheng-2176	145	1	681	681	NUM
fumecheng-2176	145	2	-	-	SYM
fumecheng-2176	145	3	694	694	NUM
fumecheng-2176	145	4	.	.	PUNCT
fumecheng-2176	146	1	5	5	NUM
fumecheng-2176	146	2	.	.	X
fumecheng-2176	146	3	king	king	PROPN
fumecheng-2176	146	4	,	,	PUNCT
fumecheng-2176	146	5	r.b	r.b	PROPN
fumecheng-2176	146	6	.	.	PROPN
fumecheng-2176	146	7	,	,	PUNCT
fumecheng-2176	146	8	1987	1987	NUM
fumecheng-2176	146	9	,	,	PUNCT
fumecheng-2176	146	10	elastic	elastic	ADJ
fumecheng-2176	146	11	analysis	analysis	NOUN
fumecheng-2176	146	12	of	of	ADP
fumecheng-2176	146	13	some	some	DET
fumecheng-2176	146	14	punch	punch	NOUN
fumecheng-2176	146	15	problems	problem	NOUN
fumecheng-2176	146	16	for	for	ADP
fumecheng-2176	146	17	a	a	DET
fumecheng-2176	146	18	layered	layered	ADJ
fumecheng-2176	146	19	medium	medium	NOUN
fumecheng-2176	146	20	,	,	PUNCT
fumecheng-2176	146	21	international	international	ADJ
fumecheng-2176	146	22	journal	journal	NOUN
fumecheng-2176	146	23	of	of	ADP
fumecheng-2176	146	24	solids	solid	NOUN
fumecheng-2176	146	25	and	and	CCONJ
fumecheng-2176	146	26	structures	structure	NOUN
fumecheng-2176	146	27	,	,	PUNCT
fumecheng-2176	146	28	23(12	23(12	NUM
fumecheng-2176	146	29	)	)	PUNCT
fumecheng-2176	146	30	,	,	PUNCT
fumecheng-2176	146	31	pp	pp	PROPN
fumecheng-2176	146	32	.	.	PUNCT
fumecheng-2176	147	1	1657	1657	NUM
fumecheng-2176	147	2	-	-	SYM
fumecheng-2176	147	3	1664	1664	NUM
fumecheng-2176	147	4	.	.	PUNCT
fumecheng-2176	148	1	6	6	NUM
fumecheng-2176	148	2	.	.	X
fumecheng-2176	148	3	galin	galin	PROPN
fumecheng-2176	148	4	,	,	PUNCT
fumecheng-2176	148	5	l.a	l.a	PROPN
fumecheng-2176	148	6	.	.	PROPN
fumecheng-2176	148	7	,	,	PUNCT
fumecheng-2176	148	8	1961	1961	NUM
fumecheng-2176	148	9	,	,	PUNCT
fumecheng-2176	148	10	contact	contact	NOUN
fumecheng-2176	148	11	problems	problem	NOUN
fumecheng-2176	148	12	in	in	ADP
fumecheng-2176	148	13	the	the	DET
fumecheng-2176	148	14	theory	theory	NOUN
fumecheng-2176	148	15	of	of	ADP
fumecheng-2176	148	16	elasticity	elasticity	NOUN
fumecheng-2176	148	17	,	,	PUNCT
fumecheng-2176	148	18	north	north	PROPN
fumecheng-2176	148	19	carolina	carolina	PROPN
fumecheng-2176	148	20	state	state	PROPN
fumecheng-2176	148	21	college	college	PROPN
fumecheng-2176	148	22	,	,	PUNCT
fumecheng-2176	148	23	usa	usa	PROPN
fumecheng-2176	148	24	7	7	NUM
fumecheng-2176	148	25	.	.	PUNCT
fumecheng-2176	148	26	sneddon	sneddon	PROPN
fumecheng-2176	148	27	,	,	PUNCT
fumecheng-2176	148	28	i.n	i.n	PROPN
fumecheng-2176	148	29	.	.	PROPN
fumecheng-2176	148	30	,	,	PUNCT
fumecheng-2176	148	31	1965	1965	NUM
fumecheng-2176	148	32	,	,	PUNCT
fumecheng-2176	148	33	the	the	DET
fumecheng-2176	148	34	relation	relation	NOUN
fumecheng-2176	148	35	between	between	ADP
fumecheng-2176	148	36	load	load	NOUN
fumecheng-2176	148	37	and	and	CCONJ
fumecheng-2176	148	38	penetration	penetration	NOUN
fumecheng-2176	148	39	in	in	ADP
fumecheng-2176	148	40	the	the	DET
fumecheng-2176	148	41	axisymmetric	axisymmetric	ADJ
fumecheng-2176	148	42	boussinesq	boussinesq	ADJ
fumecheng-2176	148	43	problem	problem	NOUN
fumecheng-2176	148	44	for	for	ADP
fumecheng-2176	148	45	a	a	DET
fumecheng-2176	148	46	punch	punch	NOUN
fumecheng-2176	148	47	of	of	ADP
fumecheng-2176	148	48	arbitrary	arbitrary	ADJ
fumecheng-2176	148	49	profile	profile	NOUN
fumecheng-2176	148	50	,	,	PUNCT
fumecheng-2176	148	51	international	international	ADJ
fumecheng-2176	148	52	journal	journal	NOUN
fumecheng-2176	148	53	of	of	ADP
fumecheng-2176	148	54	engineering	engineering	NOUN
fumecheng-2176	148	55	science	science	NOUN
fumecheng-2176	148	56	,	,	PUNCT
fumecheng-2176	148	57	23(12	23(12	NUM
fumecheng-2176	148	58	)	)	PUNCT
fumecheng-2176	148	59	,	,	PUNCT
fumecheng-2176	148	60	pp	pp	PROPN
fumecheng-2176	148	61	.	.	PUNCT
fumecheng-2176	148	62	1657	1657	NUM
fumecheng-2176	148	63	-	-	SYM
fumecheng-2176	148	64	1664	1664	NUM
fumecheng-2176	148	65	.	.	PUNCT
fumecheng-2176	149	1	8	8	NUM
fumecheng-2176	149	2	.	.	X
fumecheng-2176	149	3	oliver	oliver	PROPN
fumecheng-2176	149	4	,	,	PUNCT
fumecheng-2176	149	5	w.c	w.c	PROPN
fumecheng-2176	149	6	.	.	PROPN
fumecheng-2176	149	7	,	,	PUNCT
fumecheng-2176	149	8	pharr	pharr	PROPN
fumecheng-2176	149	9	,	,	PUNCT
fumecheng-2176	149	10	g.m	g.m	PROPN
fumecheng-2176	149	11	.	.	PROPN
fumecheng-2176	149	12	,	,	PUNCT
fumecheng-2176	149	13	1992	1992	NUM
fumecheng-2176	149	14	,	,	PUNCT
fumecheng-2176	149	15	an	an	DET
fumecheng-2176	149	16	improved	improved	ADJ
fumecheng-2176	149	17	technique	technique	NOUN
fumecheng-2176	149	18	for	for	ADP
fumecheng-2176	149	19	determining	determine	VERB
fumecheng-2176	149	20	hardness	hardness	ADJ
fumecheng-2176	149	21	and	and	CCONJ
fumecheng-2176	149	22	elastic	elastic	ADJ
fumecheng-2176	149	23	-	-	PUNCT
fumecheng-2176	149	24	modulus	modulus	NOUN
fumecheng-2176	149	25	using	use	VERB
fumecheng-2176	149	26	load	load	NOUN
fumecheng-2176	149	27	and	and	CCONJ
fumecheng-2176	149	28	displacement	displacement	ADJ
fumecheng-2176	149	29	sensing	sense	VERB
fumecheng-2176	149	30	indentation	indentation	NOUN
fumecheng-2176	149	31	experiments	experiment	NOUN
fumecheng-2176	149	32	,	,	PUNCT
fumecheng-2176	149	33	journal	journal	NOUN
fumecheng-2176	149	34	of	of	ADP
fumecheng-2176	149	35	materials	material	NOUN
fumecheng-2176	149	36	research	research	NOUN
fumecheng-2176	149	37	,	,	PUNCT
fumecheng-2176	149	38	7(6	7(6	NUM
fumecheng-2176	149	39	)	)	PUNCT
fumecheng-2176	149	40	,	,	PUNCT
fumecheng-2176	149	41	pp	pp	PROPN
fumecheng-2176	149	42	.	.	PUNCT
fumecheng-2176	150	1	1564	1564	NUM
fumecheng-2176	150	2	-	-	SYM
fumecheng-2176	150	3	1583	1583	NUM
fumecheng-2176	150	4	.	.	PUNCT
fumecheng-2176	151	1	9	9	X
fumecheng-2176	151	2	.	.	X
fumecheng-2176	151	3	pharr	pharr	PROPN
fumecheng-2176	151	4	,	,	PUNCT
fumecheng-2176	151	5	g.m	g.m	PROPN
fumecheng-2176	151	6	.	.	PROPN
fumecheng-2176	151	7	,	,	PUNCT
fumecheng-2176	151	8	oliver	oliver	PROPN
fumecheng-2176	151	9	,	,	PUNCT
fumecheng-2176	151	10	w.c	w.c	PROPN
fumecheng-2176	151	11	.	.	PROPN
fumecheng-2176	151	12	,	,	PUNCT
fumecheng-2176	151	13	brotzen	brotzen	PROPN
fumecheng-2176	151	14	,	,	PUNCT
fumecheng-2176	151	15	f.r	f.r	PROPN
fumecheng-2176	151	16	.	.	PROPN
fumecheng-2176	151	17	,	,	PUNCT
fumecheng-2176	151	18	2011	2011	NUM
fumecheng-2176	151	19	,	,	PUNCT
fumecheng-2176	151	20	on	on	ADP
fumecheng-2176	151	21	the	the	DET
fumecheng-2176	151	22	generality	generality	NOUN
fumecheng-2176	151	23	of	of	ADP
fumecheng-2176	151	24	the	the	DET
fumecheng-2176	151	25	relationship	relationship	NOUN
fumecheng-2176	151	26	among	among	ADP
fumecheng-2176	151	27	contact	contact	NOUN
fumecheng-2176	151	28	stiffness	stiffness	NOUN
fumecheng-2176	151	29	,	,	PUNCT
fumecheng-2176	151	30	contact	contact	NOUN
fumecheng-2176	151	31	area	area	NOUN
fumecheng-2176	151	32	,	,	PUNCT
fumecheng-2176	151	33	and	and	CCONJ
fumecheng-2176	151	34	elastic	elastic	ADJ
fumecheng-2176	151	35	modulus	modulus	NOUN
fumecheng-2176	151	36	during	during	ADP
fumecheng-2176	151	37	indentation	indentation	NOUN
fumecheng-2176	151	38	,	,	PUNCT
fumecheng-2176	151	39	journal	journal	NOUN
fumecheng-2176	151	40	of	of	ADP
fumecheng-2176	151	41	materials	material	NOUN
fumecheng-2176	151	42	research	research	NOUN
fumecheng-2176	151	43	,	,	PUNCT
fumecheng-2176	151	44	7(3	7(3	NUM
fumecheng-2176	151	45	)	)	PUNCT
fumecheng-2176	151	46	,	,	PUNCT
fumecheng-2176	151	47	pp	pp	ADJ
fumecheng-2176	151	48	.	.	PUNCT
fumecheng-2176	152	1	613–617	613–617	NUM
fumecheng-2176	152	2	.	.	PUNCT
fumecheng-2176	153	1	10	10	NUM
fumecheng-2176	153	2	.	.	PUNCT
fumecheng-2176	154	1	popov	popov	PROPN
fumecheng-2176	154	2	v.l	v.l	PROPN
fumecheng-2176	154	3	.	.	PROPN
fumecheng-2176	154	4	,	,	PUNCT
fumecheng-2176	154	5	2010	2010	NUM
fumecheng-2176	154	6	,	,	PUNCT
fumecheng-2176	154	7	contact	contact	NOUN
fumecheng-2176	154	8	mechanics	mechanic	NOUN
fumecheng-2176	154	9	and	and	CCONJ
fumecheng-2176	154	10	friction	friction	NOUN
fumecheng-2176	154	11	:	:	PUNCT
fumecheng-2176	154	12	physical	physical	ADJ
fumecheng-2176	154	13	principles	principle	NOUN
fumecheng-2176	154	14	and	and	CCONJ
fumecheng-2176	154	15	foundations	foundation	NOUN
fumecheng-2176	154	16	,	,	PUNCT
fumecheng-2176	154	17	springer	springer	NOUN
fumecheng-2176	154	18	,	,	PUNCT
fumecheng-2176	154	19	berlin	berlin	PROPN
fumecheng-2176	154	20	.	.	PUNCT
fumecheng-2176	155	1	11	11	NUM
fumecheng-2176	155	2	.	.	PUNCT
fumecheng-2176	156	1	pohrt	pohrt	PROPN
fumecheng-2176	156	2	,	,	PUNCT
fumecheng-2176	156	3	r.	r.	PROPN
fumecheng-2176	156	4	,	,	PUNCT
fumecheng-2176	156	5	li	li	PROPN
fumecheng-2176	156	6	,	,	PUNCT
fumecheng-2176	156	7	q.	q.	PROPN
fumecheng-2176	156	8	,	,	PUNCT
fumecheng-2176	156	9	2014	2014	NUM
fumecheng-2176	156	10	,	,	PUNCT
fumecheng-2176	156	11	complete	complete	ADJ
fumecheng-2176	156	12	boundary	boundary	ADJ
fumecheng-2176	156	13	element	element	NOUN
fumecheng-2176	156	14	formulation	formulation	NOUN
fumecheng-2176	156	15	for	for	ADP
fumecheng-2176	156	16	normal	normal	ADJ
fumecheng-2176	156	17	and	and	CCONJ
fumecheng-2176	156	18	tangential	tangential	ADJ
fumecheng-2176	156	19	contact	contact	NOUN
fumecheng-2176	156	20	problems	problem	NOUN
fumecheng-2176	156	21	,	,	PUNCT
fumecheng-2176	156	22	physical	physical	ADJ
fumecheng-2176	156	23	mesomechanics	mesomechanic	NOUN
fumecheng-2176	156	24	,	,	PUNCT
fumecheng-2176	156	25	17(4	17(4	NUM
fumecheng-2176	156	26	)	)	PUNCT
fumecheng-2176	156	27	,	,	PUNCT
fumecheng-2176	157	1	pp	pp	PROPN
fumecheng-2176	157	2	.	.	PUNCT
fumecheng-2176	158	1	334	334	NUM
fumecheng-2176	158	2	-	-	SYM
fumecheng-2176	158	3	340	340	NUM
fumecheng-2176	158	4	.	.	PUNCT
fumecheng-2176	159	1	12	12	NUM
fumecheng-2176	159	2	.	.	PUNCT
fumecheng-2176	160	1	pohrt	pohrt	PROPN
fumecheng-2176	160	2	,	,	PUNCT
fumecheng-2176	160	3	r.	r.	PROPN
fumecheng-2176	160	4	,	,	PUNCT
fumecheng-2176	160	5	popov	popov	PROPN
fumecheng-2176	160	6	,	,	PUNCT
fumecheng-2176	160	7	v.l	v.l	PROPN
fumecheng-2176	160	8	.	.	PROPN
fumecheng-2176	160	9	,	,	PUNCT
fumecheng-2176	160	10	2015	2015	NUM
fumecheng-2176	160	11	,	,	PUNCT
fumecheng-2176	160	12	adhesive	adhesive	ADJ
fumecheng-2176	160	13	contact	contact	NOUN
fumecheng-2176	160	14	simulation	simulation	NOUN
fumecheng-2176	160	15	of	of	ADP
fumecheng-2176	160	16	elastic	elastic	ADJ
fumecheng-2176	160	17	solids	solid	NOUN
fumecheng-2176	160	18	using	use	VERB
fumecheng-2176	160	19	local	local	ADJ
fumecheng-2176	160	20	mesh	mesh	NOUN
fumecheng-2176	160	21	-	-	PUNCT
fumecheng-2176	160	22	dependent	dependent	ADJ
fumecheng-2176	160	23	detachment	detachment	NOUN
fumecheng-2176	160	24	criterion	criterion	NOUN
fumecheng-2176	160	25	in	in	ADP
fumecheng-2176	160	26	boundary	boundary	ADJ
fumecheng-2176	160	27	elements	element	NOUN
fumecheng-2176	160	28	method	method	NOUN
fumecheng-2176	160	29	,	,	PUNCT
fumecheng-2176	160	30	facta	facta	PROPN
fumecheng-2176	160	31	universitatis	universitatis	PROPN
fumecheng-2176	160	32	series	series	NOUN
fumecheng-2176	160	33	:	:	PUNCT
fumecheng-2176	160	34	mechanical	mechanical	ADJ
fumecheng-2176	160	35	engineering	engineering	NOUN
fumecheng-2176	160	36	,	,	PUNCT
fumecheng-2176	160	37	13(1	13(1	NUM
fumecheng-2176	160	38	)	)	PUNCT
fumecheng-2176	160	39	,	,	PUNCT
fumecheng-2176	161	1	pp	pp	ADP
fumecheng-2176	161	2	.	.	PUNCT
fumecheng-2176	162	1	3	3	NUM
fumecheng-2176	162	2	-	-	SYM
fumecheng-2176	162	3	10	10	NUM
fumecheng-2176	162	4	13	13	NUM
fumecheng-2176	162	5	.	.	PUNCT
fumecheng-2176	163	1	argatov	argatov	PROPN
fumecheng-2176	163	2	,	,	PUNCT
fumecheng-2176	163	3	i.	i.	PROPN
fumecheng-2176	163	4	,	,	PUNCT
fumecheng-2176	163	5	2010	2010	NUM
fumecheng-2176	163	6	,	,	PUNCT
fumecheng-2176	163	7	frictionless	frictionless	NOUN
fumecheng-2176	163	8	and	and	CCONJ
fumecheng-2176	163	9	adhesive	adhesive	ADJ
fumecheng-2176	163	10	nanoindentation	nanoindentation	NOUN
fumecheng-2176	163	11	:	:	PUNCT
fumecheng-2176	163	12	asymptotic	asymptotic	ADJ
fumecheng-2176	163	13	modeling	modeling	NOUN
fumecheng-2176	163	14	of	of	ADP
fumecheng-2176	163	15	size	size	NOUN
fumecheng-2176	163	16	effects	effect	NOUN
fumecheng-2176	163	17	,	,	PUNCT
fumecheng-2176	163	18	mechanics	mechanic	NOUN
fumecheng-2176	163	19	of	of	ADP
fumecheng-2176	163	20	materials	material	NOUN
fumecheng-2176	163	21	,	,	PUNCT
fumecheng-2176	163	22	42(8	42(8	NUM
fumecheng-2176	163	23	)	)	PUNCT
fumecheng-2176	163	24	,	,	PUNCT
fumecheng-2176	163	25	pp	pp	ADP
fumecheng-2176	163	26	.	.	PUNCT
fumecheng-2176	164	1	807–815	807–815	NUM
fumecheng-2176	164	2	.	.	NOUN
fumecheng-2176	165	1	14	14	NUM
fumecheng-2176	165	2	.	.	PUNCT
fumecheng-2176	166	1	popov	popov	PROPN
fumecheng-2176	166	2	,	,	PUNCT
fumecheng-2176	166	3	v.l	v.l	PROPN
fumecheng-2176	166	4	.	.	PROPN
fumecheng-2176	166	5	,	,	PUNCT
fumecheng-2176	166	6	heß	heß	PROPN
fumecheng-2176	166	7	,	,	PUNCT
fumecheng-2176	166	8	m.	m.	NOUN
fumecheng-2176	166	9	,	,	PUNCT
fumecheng-2176	166	10	2015	2015	NUM
fumecheng-2176	166	11	,	,	PUNCT
fumecheng-2176	166	12	method	method	NOUN
fumecheng-2176	166	13	of	of	ADP
fumecheng-2176	166	14	dimensionality	dimensionality	NOUN
fumecheng-2176	166	15	reduction	reduction	NOUN
fumecheng-2176	166	16	in	in	ADP
fumecheng-2176	166	17	contact	contact	NOUN
fumecheng-2176	166	18	mechanics	mechanic	NOUN
fumecheng-2176	166	19	and	and	CCONJ
fumecheng-2176	166	20	friction	friction	NOUN
fumecheng-2176	166	21	,	,	PUNCT
fumecheng-2176	166	22	springer	springer	NOUN
fumecheng-2176	166	23	,	,	PUNCT
fumecheng-2176	166	24	berlin	berlin	PROPN
fumecheng-2176	166	25	.	.	PUNCT
fumecheng-2176	167	1	15	15	NUM
fumecheng-2176	167	2	.	.	PUNCT
fumecheng-2176	168	1	argatov	argatov	PROPN
fumecheng-2176	168	2	,	,	PUNCT
fumecheng-2176	168	3	i.	i.	PROPN
fumecheng-2176	168	4	,	,	PUNCT
fumecheng-2176	168	5	heß	heß	PROPN
fumecheng-2176	168	6	,	,	PUNCT
fumecheng-2176	168	7	m.	m.	NOUN
fumecheng-2176	168	8	,	,	PUNCT
fumecheng-2176	168	9	pohrt	pohrt	PROPN
fumecheng-2176	168	10	,	,	PUNCT
fumecheng-2176	168	11	r.	r.	PROPN
fumecheng-2176	168	12	,	,	PUNCT
fumecheng-2176	168	13	popov	popov	PROPN
fumecheng-2176	168	14	,	,	PUNCT
fumecheng-2176	168	15	v.l	v.l	PROPN
fumecheng-2176	168	16	.	.	PROPN
fumecheng-2176	168	17	,	,	PUNCT
fumecheng-2176	168	18	2016	2016	NUM
fumecheng-2176	168	19	,	,	PUNCT
fumecheng-2176	168	20	the	the	DET
fumecheng-2176	168	21	extension	extension	NOUN
fumecheng-2176	168	22	of	of	ADP
fumecheng-2176	168	23	the	the	DET
fumecheng-2176	168	24	method	method	NOUN
fumecheng-2176	168	25	of	of	ADP
fumecheng-2176	168	26	dimensionality	dimensionality	NOUN
fumecheng-2176	168	27	reduction	reduction	NOUN
fumecheng-2176	168	28	to	to	ADP
fumecheng-2176	168	29	non	non	ADJ
fumecheng-2176	168	30	-	-	ADJ
fumecheng-2176	168	31	compact	compact	ADJ
fumecheng-2176	168	32	and	and	CCONJ
fumecheng-2176	168	33	non	non	ADJ
fumecheng-2176	168	34	-	-	ADJ
fumecheng-2176	168	35	axisymmetric	axisymmetric	ADJ
fumecheng-2176	168	36	contact	contact	NOUN
fumecheng-2176	168	37	,	,	PUNCT
fumecheng-2176	168	38	journal	journal	NOUN
fumecheng-2176	168	39	of	of	ADP
fumecheng-2176	168	40	applied	apply	VERB
fumecheng-2176	168	41	mathematics	mathematic	NOUN
fumecheng-2176	168	42	and	and	CCONJ
fumecheng-2176	168	43	mechanics	mechanic	NOUN
fumecheng-2176	168	44	(	(	PUNCT
fumecheng-2176	168	45	zamm	zamm	PROPN
fumecheng-2176	168	46	)	)	PUNCT
fumecheng-2176	168	47	,	,	PUNCT
fumecheng-2176	168	48	96(10	96(10	NUM
fumecheng-2176	168	49	)	)	PUNCT
fumecheng-2176	168	50	,	,	PUNCT
fumecheng-2176	168	51	pp	pp	ADJ
fumecheng-2176	168	52	.	.	PUNCT
fumecheng-2176	169	1	1144	1144	NUM
fumecheng-2176	169	2	-	-	SYM
fumecheng-2176	169	3	1155	1155	NUM
fumecheng-2176	169	4	.	.	PUNCT
fumecheng-2176	170	1	16	16	NUM
fumecheng-2176	170	2	.	.	PUNCT
fumecheng-2176	171	1	popov	popov	PROPN
fumecheng-2176	171	2	,	,	PUNCT
fumecheng-2176	171	3	v.l	v.l	PROPN
fumecheng-2176	171	4	.	.	PROPN
fumecheng-2176	171	5	,	,	PUNCT
fumecheng-2176	171	6	pohrt	pohrt	PROPN
fumecheng-2176	171	7	,	,	PUNCT
fumecheng-2176	171	8	r.	r.	PROPN
fumecheng-2176	171	9	,	,	PUNCT
fumecheng-2176	171	10	heß	heß	PROPN
fumecheng-2176	171	11	,	,	PUNCT
fumecheng-2176	171	12	m.	m.	NOUN
fumecheng-2176	171	13	,	,	PUNCT
fumecheng-2176	171	14	2016	2016	NUM
fumecheng-2176	171	15	,	,	PUNCT
fumecheng-2176	171	16	general	general	ADJ
fumecheng-2176	171	17	procedure	procedure	NOUN
fumecheng-2176	171	18	for	for	ADP
fumecheng-2176	171	19	solution	solution	NOUN
fumecheng-2176	171	20	of	of	ADP
fumecheng-2176	171	21	contact	contact	NOUN
fumecheng-2176	171	22	problems	problem	NOUN
fumecheng-2176	171	23	under	under	ADP
fumecheng-2176	171	24	dynamic	dynamic	ADJ
fumecheng-2176	171	25	normal	normal	ADJ
fumecheng-2176	171	26	and	and	CCONJ
fumecheng-2176	171	27	tangential	tangential	ADJ
fumecheng-2176	171	28	loading	loading	NOUN
fumecheng-2176	171	29	based	base	VERB
fumecheng-2176	171	30	on	on	ADP
fumecheng-2176	171	31	the	the	DET
fumecheng-2176	171	32	known	know	VERB
fumecheng-2176	171	33	solution	solution	NOUN
fumecheng-2176	171	34	of	of	ADP
fumecheng-2176	171	35	normal	normal	ADJ
fumecheng-2176	171	36	contact	contact	NOUN
fumecheng-2176	171	37	problem	problem	NOUN
fumecheng-2176	171	38	,	,	PUNCT
fumecheng-2176	171	39	journal	journal	NOUN
fumecheng-2176	171	40	of	of	ADP
fumecheng-2176	171	41	strain	strain	ADJ
fumecheng-2176	171	42	analysis	analysis	NOUN
fumecheng-2176	171	43	for	for	ADP
fumecheng-2176	171	44	engineering	engineering	NOUN
fumecheng-2176	171	45	design	design	NOUN
fumecheng-2176	171	46	,	,	PUNCT
fumecheng-2176	171	47	51(4	51(4	NUM
fumecheng-2176	171	48	)	)	PUNCT
fumecheng-2176	171	49	,	,	PUNCT
fumecheng-2176	171	50	pp	pp	ADP
fumecheng-2176	171	51	.	.	PUNCT
fumecheng-2176	171	52	247	247	NUM
fumecheng-2176	171	53	-	-	SYM
fumecheng-2176	171	54	255	255	NUM
fumecheng-2176	171	55	.	.	PUNCT