id	sid	tid	token	lemma	pos
app01-6375	1	1	acta	acta	PROPN
app01-6375	1	2	polytechnica	polytechnica	PROPN
app01-6375	1	3	ctu	ctu	PROPN
app01-6375	1	4	proceedings	proceeding	NOUN
app01-6375	1	5	doi:10.14311	doi:10.14311	NOUN
app01-6375	1	6	/	/	SYM
app01-6375	1	7	app.2020.26.0024	app.2020.26.0024	PROPN
app01-6375	1	8	acta	acta	PROPN
app01-6375	1	9	polytechnica	polytechnica	PROPN
app01-6375	1	10	ctu	ctu	NOUN
app01-6375	1	11	proceedings	proceeding	NOUN
app01-6375	1	12	26:24–29	26:24–29	NUM
app01-6375	1	13	,	,	PUNCT
app01-6375	1	14	2020	2020	NUM
app01-6375	1	15	©	©	PROPN
app01-6375	1	16	czech	czech	PROPN
app01-6375	1	17	technical	technical	PROPN
app01-6375	1	18	university	university	PROPN
app01-6375	1	19	in	in	ADP
app01-6375	1	20	prague	prague	PROPN
app01-6375	1	21	,	,	PUNCT
app01-6375	1	22	2020	2020	NUM
app01-6375	1	23	available	available	ADJ
app01-6375	1	24	online	online	ADV
app01-6375	1	25	at	at	ADP
app01-6375	1	26	https://ojs.cvut.cz/ojs/index.php/app	https://ojs.cvut.cz/ojs/index.php/app	NOUN
app01-6375	1	27	on	on	ADP
app01-6375	1	28	evaluation	evaluation	NOUN
app01-6375	1	29	of	of	ADP
app01-6375	1	30	the	the	DET
app01-6375	1	31	three	three	NUM
app01-6375	1	32	-	-	PUNCT
app01-6375	1	33	dimensional	dimensional	ADJ
app01-6375	1	34	isogeometric	isogeometric	ADJ
app01-6375	1	35	beam	beam	NOUN
app01-6375	1	36	element	element	NOUN
app01-6375	1	37	edita	edita	PROPN
app01-6375	1	38	dvořáková∗	dvořáková∗	PROPN
app01-6375	1	39	,	,	PUNCT
app01-6375	1	40	bořek	bořek	NOUN
app01-6375	1	41	patzák	patzák	VERB
app01-6375	1	42	czech	czech	PROPN
app01-6375	1	43	technical	technical	PROPN
app01-6375	1	44	university	university	PROPN
app01-6375	1	45	in	in	ADP
app01-6375	1	46	prague	prague	PROPN
app01-6375	1	47	,	,	PUNCT
app01-6375	1	48	faculty	faculty	NOUN
app01-6375	1	49	of	of	ADP
app01-6375	1	50	civil	civil	ADJ
app01-6375	1	51	engineering	engineering	NOUN
app01-6375	1	52	,	,	PUNCT
app01-6375	1	53	department	department	NOUN
app01-6375	1	54	of	of	ADP
app01-6375	1	55	mechanics	mechanic	NOUN
app01-6375	1	56	,	,	PUNCT
app01-6375	1	57	thákurova	thákurova	X
app01-6375	1	58	7	7	NUM
app01-6375	1	59	,	,	PUNCT
app01-6375	1	60	166	166	NUM
app01-6375	1	61	29	29	NUM
app01-6375	1	62	prague	prague	NOUN
app01-6375	1	63	6	6	NUM
app01-6375	1	64	,	,	PUNCT
app01-6375	1	65	czech	czech	PROPN
app01-6375	1	66	republic	republic	NOUN
app01-6375	1	67	∗	∗	NOUN
app01-6375	1	68	corresponding	correspond	VERB
app01-6375	1	69	author	author	NOUN
app01-6375	1	70	:	:	PUNCT
app01-6375	1	71	edita.dvorakova@fsv.cvut.cz	edita.dvorakova@fsv.cvut.cz	NOUN
app01-6375	1	72	abstract	abstract	NOUN
app01-6375	1	73	.	.	PUNCT
app01-6375	2	1	the	the	DET
app01-6375	2	2	exact	exact	ADJ
app01-6375	2	3	description	description	NOUN
app01-6375	2	4	of	of	ADP
app01-6375	2	5	the	the	DET
app01-6375	2	6	arbitrarily	arbitrarily	ADV
app01-6375	2	7	curved	curved	ADJ
app01-6375	2	8	geometries	geometry	NOUN
app01-6375	2	9	,	,	PUNCT
app01-6375	2	10	including	include	VERB
app01-6375	2	11	conic	conic	ADJ
app01-6375	2	12	sections	section	NOUN
app01-6375	2	13	,	,	PUNCT
app01-6375	2	14	is	be	AUX
app01-6375	2	15	an	an	DET
app01-6375	2	16	undeniable	undeniable	ADJ
app01-6375	2	17	advantage	advantage	NOUN
app01-6375	2	18	of	of	ADP
app01-6375	2	19	isogeometric	isogeometric	ADJ
app01-6375	2	20	analysis	analysis	NOUN
app01-6375	2	21	(	(	PUNCT
app01-6375	2	22	iga	iga	PROPN
app01-6375	2	23	)	)	PUNCT
app01-6375	2	24	over	over	ADP
app01-6375	2	25	standard	standard	ADJ
app01-6375	2	26	finite	finite	PROPN
app01-6375	2	27	element	element	NOUN
app01-6375	2	28	method	method	NOUN
app01-6375	2	29	(	(	PUNCT
app01-6375	2	30	fem	fem	PROPN
app01-6375	2	31	)	)	PUNCT
app01-6375	2	32	.	.	PUNCT
app01-6375	3	1	with	with	ADP
app01-6375	3	2	b	b	NOUN
app01-6375	3	3	-	-	PUNCT
app01-6375	3	4	spline	spline	ADJ
app01-6375	3	5	/	/	SYM
app01-6375	3	6	nurbs	nurbs	NOUN
app01-6375	3	7	approximation	approximation	NOUN
app01-6375	3	8	functions	function	NOUN
app01-6375	3	9	used	use	VERB
app01-6375	3	10	for	for	ADP
app01-6375	3	11	both	both	PRON
app01-6375	3	12	geometry	geometry	NOUN
app01-6375	3	13	and	and	CCONJ
app01-6375	3	14	unknown	unknown	ADJ
app01-6375	3	15	approximations	approximation	NOUN
app01-6375	3	16	,	,	PUNCT
app01-6375	3	17	iga	iga	PROPN
app01-6375	3	18	is	be	AUX
app01-6375	3	19	able	able	ADJ
app01-6375	3	20	to	to	PART
app01-6375	3	21	exactly	exactly	ADV
app01-6375	3	22	describe	describe	VERB
app01-6375	3	23	beams	beam	NOUN
app01-6375	3	24	of	of	ADP
app01-6375	3	25	various	various	ADJ
app01-6375	3	26	shapes	shape	NOUN
app01-6375	3	27	and	and	CCONJ
app01-6375	3	28	thus	thus	ADV
app01-6375	3	29	eliminate	eliminate	VERB
app01-6375	3	30	the	the	DET
app01-6375	3	31	geometry	geometry	NOUN
app01-6375	3	32	approximation	approximation	NOUN
app01-6375	3	33	errors	error	NOUN
app01-6375	3	34	.	.	PUNCT
app01-6375	4	1	moreover	moreover	ADV
app01-6375	4	2	,	,	PUNCT
app01-6375	4	3	naturally	naturally	ADV
app01-6375	4	4	higher	high	ADJ
app01-6375	4	5	continuity	continuity	NOUN
app01-6375	4	6	than	than	ADP
app01-6375	4	7	standard	standard	ADJ
app01-6375	4	8	c0	c0	NOUN
app01-6375	4	9	can	can	AUX
app01-6375	4	10	be	be	AUX
app01-6375	4	11	provided	provide	VERB
app01-6375	4	12	along	along	ADP
app01-6375	4	13	the	the	DET
app01-6375	4	14	entire	entire	ADJ
app01-6375	4	15	computational	computational	ADJ
app01-6375	4	16	domain	domain	NOUN
app01-6375	4	17	.	.	PUNCT
app01-6375	5	1	this	this	DET
app01-6375	5	2	paper	paper	NOUN
app01-6375	5	3	evaluates	evaluate	VERB
app01-6375	5	4	the	the	DET
app01-6375	5	5	performance	performance	NOUN
app01-6375	5	6	of	of	ADP
app01-6375	5	7	the	the	DET
app01-6375	5	8	nonlinear	nonlinear	ADJ
app01-6375	5	9	spatial	spatial	ADJ
app01-6375	5	10	bernoulli	bernoulli	PROPN
app01-6375	5	11	beam	beam	NOUN
app01-6375	5	12	adapted	adapt	VERB
app01-6375	5	13	from	from	ADP
app01-6375	5	14	formulation	formulation	NOUN
app01-6375	5	15	of	of	ADP
app01-6375	5	16	bauer	bauer	PROPN
app01-6375	5	17	et	et	PROPN
app01-6375	5	18	al	al	PROPN
app01-6375	5	19	.	.	PUNCT
app01-6375	6	1	[	[	X
app01-6375	6	2	1	1	NUM
app01-6375	6	3	]	]	PUNCT
app01-6375	6	4	.	.	PUNCT
app01-6375	7	1	the	the	DET
app01-6375	7	2	element	element	NOUN
app01-6375	7	3	formulation	formulation	NOUN
app01-6375	7	4	is	be	AUX
app01-6375	7	5	presented	present	VERB
app01-6375	7	6	and	and	CCONJ
app01-6375	7	7	the	the	DET
app01-6375	7	8	comparison	comparison	NOUN
app01-6375	7	9	with	with	ADP
app01-6375	7	10	standard	standard	ADJ
app01-6375	7	11	fem	fem	NOUN
app01-6375	7	12	straight	straight	ADJ
app01-6375	7	13	beam	beam	NOUN
app01-6375	7	14	element	element	NOUN
app01-6375	7	15	and	and	CCONJ
app01-6375	7	16	fully	fully	ADV
app01-6375	7	17	three	three	NUM
app01-6375	7	18	-	-	PUNCT
app01-6375	7	19	dimensional	dimensional	ADJ
app01-6375	7	20	analysis	analysis	NOUN
app01-6375	7	21	is	be	AUX
app01-6375	7	22	provided	provide	VERB
app01-6375	7	23	.	.	PUNCT
app01-6375	8	1	although	although	SCONJ
app01-6375	8	2	the	the	DET
app01-6375	8	3	element	element	NOUN
app01-6375	8	4	is	be	AUX
app01-6375	8	5	capable	capable	ADJ
app01-6375	8	6	of	of	ADP
app01-6375	8	7	geometrically	geometrically	ADV
app01-6375	8	8	nonlinear	nonlinear	ADJ
app01-6375	8	9	analysis	analysis	NOUN
app01-6375	8	10	,	,	PUNCT
app01-6375	8	11	only	only	ADV
app01-6375	8	12	geometrically	geometrically	ADV
app01-6375	8	13	linear	linear	ADJ
app01-6375	8	14	cases	case	NOUN
app01-6375	8	15	are	be	AUX
app01-6375	8	16	evaluated	evaluate	VERB
app01-6375	8	17	for	for	ADP
app01-6375	8	18	the	the	DET
app01-6375	8	19	purposes	purpose	NOUN
app01-6375	8	20	of	of	ADP
app01-6375	8	21	this	this	DET
app01-6375	8	22	study	study	NOUN
app01-6375	8	23	.	.	PUNCT
app01-6375	9	1	keywords	keyword	NOUN
app01-6375	9	2	:	:	PUNCT
app01-6375	9	3	bernoulli	bernoulli	PROPN
app01-6375	9	4	theory	theory	NOUN
app01-6375	9	5	,	,	PUNCT
app01-6375	9	6	curved	curved	ADJ
app01-6375	9	7	beam	beam	NOUN
app01-6375	9	8	element	element	NOUN
app01-6375	9	9	,	,	PUNCT
app01-6375	9	10	isogeometric	isogeometric	ADJ
app01-6375	9	11	analysis	analysis	NOUN
app01-6375	9	12	,	,	PUNCT
app01-6375	9	13	nurbs	nurb	NOUN
app01-6375	9	14	.	.	NOUN
app01-6375	9	15	1	1	X
app01-6375	9	16	.	.	X
app01-6375	9	17	introduction	introduction	NOUN
app01-6375	9	18	the	the	DET
app01-6375	9	19	desire	desire	NOUN
app01-6375	9	20	for	for	ADP
app01-6375	9	21	the	the	DET
app01-6375	9	22	automatic	automatic	ADJ
app01-6375	9	23	connection	connection	NOUN
app01-6375	9	24	between	between	ADP
app01-6375	9	25	computer	computer	NOUN
app01-6375	9	26	-	-	PUNCT
app01-6375	9	27	aided	aid	VERB
app01-6375	9	28	design	design	NOUN
app01-6375	9	29	(	(	PUNCT
app01-6375	9	30	cad	cad	NOUN
app01-6375	9	31	)	)	PUNCT
app01-6375	9	32	and	and	CCONJ
app01-6375	9	33	finite	finite	ADJ
app01-6375	9	34	element	element	NOUN
app01-6375	9	35	analysis	analysis	NOUN
app01-6375	9	36	(	(	PUNCT
app01-6375	9	37	fea	fea	NOUN
app01-6375	9	38	)	)	PUNCT
app01-6375	9	39	has	have	AUX
app01-6375	9	40	been	be	AUX
app01-6375	9	41	the	the	DET
app01-6375	9	42	crucial	crucial	ADJ
app01-6375	9	43	impulse	impulse	NOUN
app01-6375	9	44	for	for	ADP
app01-6375	9	45	the	the	DET
app01-6375	9	46	development	development	NOUN
app01-6375	9	47	of	of	ADP
app01-6375	9	48	isogeometric	isogeometric	ADJ
app01-6375	9	49	analysis	analysis	NOUN
app01-6375	9	50	[	[	X
app01-6375	9	51	2	2	NUM
app01-6375	9	52	]	]	PUNCT
app01-6375	9	53	.	.	PUNCT
app01-6375	10	1	the	the	DET
app01-6375	10	2	idea	idea	NOUN
app01-6375	10	3	of	of	ADP
app01-6375	10	4	iga	iga	PROPN
app01-6375	10	5	is	be	AUX
app01-6375	10	6	to	to	PART
app01-6375	10	7	use	use	VERB
app01-6375	10	8	the	the	DET
app01-6375	10	9	basis	basis	NOUN
app01-6375	10	10	functions	function	NOUN
app01-6375	10	11	used	use	VERB
app01-6375	10	12	for	for	ADP
app01-6375	10	13	the	the	DET
app01-6375	10	14	geometry	geometry	NOUN
app01-6375	10	15	description	description	NOUN
app01-6375	10	16	in	in	ADP
app01-6375	10	17	cad	cad	PROPN
app01-6375	10	18	also	also	ADV
app01-6375	10	19	as	as	ADP
app01-6375	10	20	the	the	DET
app01-6375	10	21	approximation	approximation	NOUN
app01-6375	10	22	functions	function	NOUN
app01-6375	10	23	for	for	ADP
app01-6375	10	24	the	the	DET
app01-6375	10	25	analysis	analysis	NOUN
app01-6375	10	26	.	.	PUNCT
app01-6375	11	1	this	this	DET
app01-6375	11	2	results	result	VERB
app01-6375	11	3	in	in	ADP
app01-6375	11	4	the	the	DET
app01-6375	11	5	possibility	possibility	NOUN
app01-6375	11	6	of	of	ADP
app01-6375	11	7	only	only	ADV
app01-6375	11	8	one	one	NUM
app01-6375	11	9	model	model	NOUN
app01-6375	11	10	shared	share	VERB
app01-6375	11	11	between	between	ADP
app01-6375	11	12	the	the	DET
app01-6375	11	13	design	design	NOUN
app01-6375	11	14	and	and	CCONJ
app01-6375	11	15	analysis	analysis	NOUN
app01-6375	11	16	.	.	PUNCT
app01-6375	12	1	isogeometric	isogeometric	ADJ
app01-6375	12	2	approach	approach	NOUN
app01-6375	12	3	introduces	introduce	NOUN
app01-6375	12	4	into	into	ADP
app01-6375	12	5	the	the	DET
app01-6375	12	6	analysis	analysis	NOUN
app01-6375	12	7	some	some	DET
app01-6375	12	8	other	other	ADJ
app01-6375	12	9	very	very	ADV
app01-6375	12	10	important	important	ADJ
app01-6375	12	11	features	feature	NOUN
app01-6375	12	12	.	.	PUNCT
app01-6375	13	1	one	one	NUM
app01-6375	13	2	of	of	ADP
app01-6375	13	3	them	they	PRON
app01-6375	13	4	is	be	AUX
app01-6375	13	5	a	a	DET
app01-6375	13	6	possibility	possibility	NOUN
app01-6375	13	7	to	to	AUX
app01-6375	13	8	exactly	exactly	ADV
app01-6375	13	9	model	model	VERB
app01-6375	13	10	arbitrarily	arbitrarily	ADV
app01-6375	13	11	curved	curve	VERB
app01-6375	13	12	geometries	geometry	NOUN
app01-6375	13	13	,	,	PUNCT
app01-6375	13	14	including	include	VERB
app01-6375	13	15	a	a	DET
app01-6375	13	16	conic	conic	ADJ
app01-6375	13	17	sections	section	NOUN
app01-6375	13	18	which	which	PRON
app01-6375	13	19	can	can	AUX
app01-6375	13	20	be	be	AUX
app01-6375	13	21	only	only	ADV
app01-6375	13	22	approximated	approximate	VERB
app01-6375	13	23	by	by	ADP
app01-6375	13	24	standard	standard	ADJ
app01-6375	13	25	polynomial	polynomial	ADJ
app01-6375	13	26	basis	basis	NOUN
app01-6375	13	27	functions	function	NOUN
app01-6375	13	28	.	.	PUNCT
app01-6375	14	1	this	this	PRON
app01-6375	14	2	makes	make	VERB
app01-6375	14	3	it	it	PRON
app01-6375	14	4	very	very	ADV
app01-6375	14	5	convenient	convenient	ADJ
app01-6375	14	6	for	for	ADP
app01-6375	14	7	the	the	DET
app01-6375	14	8	use	use	NOUN
app01-6375	14	9	in	in	ADP
app01-6375	14	10	the	the	DET
app01-6375	14	11	analysis	analysis	NOUN
app01-6375	14	12	of	of	ADP
app01-6375	14	13	curved	curved	ADJ
app01-6375	14	14	beams	beam	NOUN
app01-6375	14	15	.	.	PUNCT
app01-6375	15	1	the	the	DET
app01-6375	15	2	focus	focus	NOUN
app01-6375	15	3	of	of	ADP
app01-6375	15	4	this	this	DET
app01-6375	15	5	paper	paper	NOUN
app01-6375	15	6	is	be	AUX
app01-6375	15	7	placed	place	VERB
app01-6375	15	8	on	on	ADP
app01-6375	15	9	the	the	DET
app01-6375	15	10	geometrically	geometrically	ADV
app01-6375	15	11	nonlinear	nonlinear	ADJ
app01-6375	15	12	three	three	NUM
app01-6375	15	13	-	-	PUNCT
app01-6375	15	14	dimensional	dimensional	ADJ
app01-6375	15	15	bernoulli	bernoulli	NOUN
app01-6375	15	16	beam	beam	NOUN
app01-6375	15	17	[	[	X
app01-6375	15	18	1	1	NUM
app01-6375	15	19	,	,	PUNCT
app01-6375	15	20	3	3	NUM
app01-6375	15	21	]	]	PUNCT
app01-6375	15	22	.	.	PUNCT
app01-6375	16	1	the	the	DET
app01-6375	16	2	beam	beam	NOUN
app01-6375	16	3	formulation	formulation	NOUN
app01-6375	16	4	is	be	AUX
app01-6375	16	5	briefly	briefly	ADV
app01-6375	16	6	introduced	introduce	VERB
app01-6375	16	7	and	and	CCONJ
app01-6375	16	8	the	the	DET
app01-6375	16	9	performance	performance	NOUN
app01-6375	16	10	over	over	ADP
app01-6375	16	11	standard	standard	ADJ
app01-6375	16	12	fem	fem	NOUN
app01-6375	16	13	approaches	approach	NOUN
app01-6375	16	14	is	be	AUX
app01-6375	16	15	evaluated	evaluate	VERB
app01-6375	16	16	.	.	PUNCT
app01-6375	17	1	2	2	X
app01-6375	17	2	.	.	X
app01-6375	17	3	nurbs	nurb	NOUN
app01-6375	17	4	-	-	PUNCT
app01-6375	17	5	based	base	VERB
app01-6375	17	6	analysis	analysis	NOUN
app01-6375	17	7	the	the	DET
app01-6375	17	8	most	most	ADV
app01-6375	17	9	wide	wide	ADJ
app01-6375	17	10	-	-	PUNCT
app01-6375	17	11	spread	spread	ADJ
app01-6375	17	12	technology	technology	NOUN
app01-6375	17	13	in	in	ADP
app01-6375	17	14	cad	cad	PROPN
app01-6375	17	15	industry	industry	NOUN
app01-6375	17	16	are	be	AUX
app01-6375	17	17	nurbs	nurb	NOUN
app01-6375	17	18	(	(	PUNCT
app01-6375	17	19	non	non	ADJ
app01-6375	17	20	-	-	ADJ
app01-6375	17	21	uniform	uniform	ADJ
app01-6375	17	22	rational	rational	ADJ
app01-6375	17	23	b	b	NOUN
app01-6375	17	24	-	-	PUNCT
app01-6375	17	25	splines	spline	NOUN
app01-6375	17	26	)	)	PUNCT
app01-6375	17	27	.	.	PUNCT
app01-6375	18	1	the	the	DET
app01-6375	18	2	nurbs	nurbs	NOUN
app01-6375	18	3	curve	curve	NOUN
app01-6375	18	4	is	be	AUX
app01-6375	18	5	obtained	obtain	VERB
app01-6375	18	6	by	by	ADP
app01-6375	18	7	linear	linear	ADJ
app01-6375	18	8	combination	combination	NOUN
app01-6375	18	9	of	of	ADP
app01-6375	18	10	cartesian	cartesian	ADJ
app01-6375	18	11	coordinates	coordinate	NOUN
app01-6375	18	12	of	of	ADP
app01-6375	18	13	the	the	DET
app01-6375	18	14	control	control	NOUN
app01-6375	18	15	points	point	VERB
app01-6375	18	16	p	p	NOUN
app01-6375	18	17	and	and	CCONJ
app01-6375	18	18	nurbs	nurbs	NOUN
app01-6375	18	19	functions	function	NOUN
app01-6375	18	20	rpi	rpi	ADJ
app01-6375	18	21	c(ξ	c(ξ	NOUN
app01-6375	18	22	)	)	PUNCT
app01-6375	19	1	=	=	SYM
app01-6375	20	1	n∑	n∑	NOUN
app01-6375	20	2	i=1	i=1	PROPN
app01-6375	21	1	rpi	rpi	PROPN
app01-6375	21	2	(	(	PUNCT
app01-6375	21	3	ξ)pi	ξ)pi	PROPN
app01-6375	21	4	.	.	PUNCT
app01-6375	22	1	(	(	PUNCT
app01-6375	22	2	1	1	X
app01-6375	22	3	)	)	PUNCT
app01-6375	22	4	each	each	DET
app01-6375	22	5	nurbs	nurb	NOUN
app01-6375	22	6	function	function	NOUN
app01-6375	22	7	is	be	AUX
app01-6375	22	8	generated	generate	VERB
app01-6375	22	9	by	by	ADP
app01-6375	22	10	weighting	weight	VERB
app01-6375	22	11	bspline	bspline	NOUN
app01-6375	22	12	functions	function	NOUN
app01-6375	22	13	np	np	INTJ
app01-6375	22	14	i	i	PRON
app01-6375	22	15	with	with	ADP
app01-6375	22	16	a	a	DET
app01-6375	22	17	given	give	VERB
app01-6375	22	18	weight	weight	NOUN
app01-6375	22	19	wi	wi	PROPN
app01-6375	22	20	associated	associate	VERB
app01-6375	22	21	with	with	ADP
app01-6375	22	22	control	control	NOUN
app01-6375	22	23	point	point	NOUN
app01-6375	22	24	pi	pi	NOUN
app01-6375	22	25	rpi	rpi	NOUN
app01-6375	22	26	(	(	PUNCT
app01-6375	22	27	ξ	ξ	NOUN
app01-6375	22	28	)	)	PUNCT
app01-6375	22	29	=	=	SYM
app01-6375	22	30	ni	ni	PROPN
app01-6375	22	31	,	,	PUNCT
app01-6375	22	32	p(ξ)wi∑n	p(ξ)wi∑n	PROPN
app01-6375	22	33	j=1nj	j=1nj	NOUN
app01-6375	22	34	,	,	PUNCT
app01-6375	22	35	p(ξ)wj	p(ξ)wj	PROPN
app01-6375	22	36	.	.	PUNCT
app01-6375	23	1	(	(	PUNCT
app01-6375	23	2	2	2	X
app01-6375	23	3	)	)	PUNCT
app01-6375	23	4	b	b	NOUN
app01-6375	23	5	-	-	PUNCT
app01-6375	23	6	spline	spline	NOUN
app01-6375	23	7	functions	function	NOUN
app01-6375	23	8	form	form	VERB
app01-6375	23	9	a	a	DET
app01-6375	23	10	special	special	ADJ
app01-6375	23	11	subset	subset	NOUN
app01-6375	23	12	of	of	ADP
app01-6375	23	13	nurbs	nurbs	NOUN
app01-6375	23	14	functions	function	NOUN
app01-6375	23	15	(	(	PUNCT
app01-6375	23	16	corresponding	correspond	VERB
app01-6375	23	17	to	to	AUX
app01-6375	23	18	constant	constant	ADJ
app01-6375	23	19	wi	wi	PROPN
app01-6375	23	20	)	)	PUNCT
app01-6375	23	21	and	and	CCONJ
app01-6375	23	22	are	be	AUX
app01-6375	23	23	derived	derive	VERB
app01-6375	23	24	recursively	recursively	ADV
app01-6375	23	25	starting	start	VERB
app01-6375	23	26	with	with	ADP
app01-6375	23	27	a	a	DET
app01-6375	23	28	piecewise	piecewise	NOUN
app01-6375	23	29	constant	constant	ADJ
app01-6375	23	30	functions	function	NOUN
app01-6375	23	31	ni,0(ξ	ni,0(ξ	ADJ
app01-6375	23	32	)	)	PUNCT
app01-6375	23	33	=	=	PRON
app01-6375	23	34	{	{	PUNCT
app01-6375	23	35	1	1	NUM
app01-6375	23	36	if	if	SCONJ
app01-6375	23	37	ξi	ξi	NOUN
app01-6375	23	38	≤	≤	X
app01-6375	24	1	ξ	ξ	X
app01-6375	24	2	<	<	X
app01-6375	24	3	ξi+1	ξi+1	NUM
app01-6375	24	4	0	0	NUM
app01-6375	24	5	otherwise	otherwise	ADV
app01-6375	24	6	,	,	PUNCT
app01-6375	24	7	(	(	PUNCT
app01-6375	24	8	3	3	X
app01-6375	24	9	)	)	PUNCT
app01-6375	24	10	ni	ni	PROPN
app01-6375	24	11	,	,	PUNCT
app01-6375	24	12	p(ξ	p(ξ	NOUN
app01-6375	24	13	)	)	PUNCT
app01-6375	24	14	=	=	PUNCT
app01-6375	25	1	ξ	ξ	X
app01-6375	25	2	−	−	NOUN
app01-6375	25	3	ξi	ξi	NOUN
app01-6375	25	4	ξi+p	ξi+p	PROPN
app01-6375	25	5	−	−	PROPN
app01-6375	25	6	ξi	ξi	PROPN
app01-6375	25	7	ni	ni	PROPN
app01-6375	25	8	,	,	PUNCT
app01-6375	25	9	p−1(ξ	p−1(ξ	PROPN
app01-6375	25	10	)	)	PUNCT
app01-6375	26	1	+	+	NUM
app01-6375	26	2	ξi+p+1	ξi+p+1	NUM
app01-6375	26	3	−	−	NOUN
app01-6375	26	4	ξ	ξ	SYM
app01-6375	26	5	ξi+p+1	ξi+p+1	NUM
app01-6375	26	6	−	−	NOUN
app01-6375	26	7	ξi+1	ξi+1	NUM
app01-6375	26	8	ni+1,p−1(ξ	ni+1,p−1(ξ	NOUN
app01-6375	26	9	)	)	PUNCT
app01-6375	26	10	,	,	PUNCT
app01-6375	26	11	(	(	PUNCT
app01-6375	26	12	4	4	X
app01-6375	26	13	)	)	PUNCT
app01-6375	26	14	where	where	SCONJ
app01-6375	26	15	p	p	NOUN
app01-6375	26	16	is	be	AUX
app01-6375	26	17	the	the	DET
app01-6375	26	18	degree	degree	NOUN
app01-6375	26	19	of	of	ADP
app01-6375	26	20	the	the	DET
app01-6375	26	21	b	b	NOUN
app01-6375	26	22	-	-	PUNCT
app01-6375	26	23	spline	spline	NOUN
app01-6375	26	24	function	function	NOUN
app01-6375	26	25	,	,	PUNCT
app01-6375	26	26	ξi	ξi	PROPN
app01-6375	26	27	is	be	AUX
app01-6375	26	28	the	the	DET
app01-6375	26	29	coordinate	coordinate	NOUN
app01-6375	26	30	of	of	ADP
app01-6375	26	31	the	the	DET
app01-6375	26	32	ith	ith	NOUN
app01-6375	26	33	-	-	PUNCT
app01-6375	26	34	knot	knot	NOUN
app01-6375	26	35	and	and	CCONJ
app01-6375	26	36	ξ	ξ	PRON
app01-6375	26	37	∈	∈	PROPN
app01-6375	26	38	〈	〈	PROPN
app01-6375	26	39	0	0	NUM
app01-6375	26	40	,	,	PUNCT
app01-6375	26	41	1	1	NUM
app01-6375	26	42	〉	〉	PROPN
app01-6375	26	43	is	be	AUX
app01-6375	26	44	a	a	DET
app01-6375	26	45	parametric	parametric	ADJ
app01-6375	26	46	coordinate	coordinate	NOUN
app01-6375	26	47	.	.	PUNCT
app01-6375	27	1	the	the	DET
app01-6375	27	2	computational	computational	ADJ
app01-6375	27	3	domain	domain	NOUN
app01-6375	27	4	in	in	ADP
app01-6375	27	5	isogeometric	isogeometric	ADJ
app01-6375	27	6	analysis	analysis	NOUN
app01-6375	27	7	(	(	PUNCT
app01-6375	27	8	iga	iga	PROPN
app01-6375	27	9	)	)	PUNCT
app01-6375	27	10	is	be	AUX
app01-6375	27	11	firstly	firstly	ADV
app01-6375	27	12	divided	divide	VERB
app01-6375	27	13	into	into	ADP
app01-6375	27	14	patches	patch	NOUN
app01-6375	27	15	,	,	PUNCT
app01-6375	27	16	which	which	PRON
app01-6375	27	17	are	be	AUX
app01-6375	27	18	further	far	ADV
app01-6375	27	19	divided	divide	VERB
app01-6375	27	20	into	into	ADP
app01-6375	27	21	knotspans	knotspan	NOUN
app01-6375	27	22	(	(	PUNCT
app01-6375	27	23	often	often	ADV
app01-6375	27	24	referred	refer	VERB
app01-6375	27	25	to	to	ADP
app01-6375	27	26	as	as	ADP
app01-6375	27	27	elements	element	NOUN
app01-6375	27	28	in	in	ADP
app01-6375	27	29	iga	iga	PROPN
app01-6375	27	30	)	)	PUNCT
app01-6375	27	31	.	.	PUNCT
app01-6375	28	1	understanding	understanding	NOUN
app01-6375	28	2	of	of	ADP
app01-6375	28	3	knotspans	knotspan	NOUN
app01-6375	28	4	is	be	AUX
app01-6375	28	5	similar	similar	ADJ
app01-6375	28	6	to	to	ADP
app01-6375	28	7	elements	element	NOUN
app01-6375	28	8	in	in	ADP
app01-6375	28	9	standard	standard	ADJ
app01-6375	28	10	fem	fem	NOUN
app01-6375	28	11	,	,	PUNCT
app01-6375	28	12	nevertheless	nevertheless	ADV
app01-6375	28	13	higher	high	ADJ
app01-6375	28	14	continuity	continuity	NOUN
app01-6375	28	15	up	up	ADP
app01-6375	28	16	to	to	ADP
app01-6375	28	17	cp−1	cp−1	PROPN
app01-6375	28	18	between	between	ADP
app01-6375	28	19	knotspans	knotspan	NOUN
app01-6375	28	20	can	can	AUX
app01-6375	28	21	be	be	AUX
app01-6375	28	22	achieved	achieve	VERB
app01-6375	28	23	naturally	naturally	ADV
app01-6375	28	24	using	use	VERB
app01-6375	28	25	nurbs	nurb	NOUN
app01-6375	28	26	,	,	PUNCT
app01-6375	28	27	unlike	unlike	ADP
app01-6375	28	28	c0	c0	NOUN
app01-6375	28	29	in	in	ADP
app01-6375	28	30	standard	standard	ADJ
app01-6375	28	31	fem	fem	PROPN
app01-6375	28	32	.	.	PUNCT
app01-6375	29	1	moreover	moreover	ADV
app01-6375	29	2	,	,	PUNCT
app01-6375	29	3	the	the	DET
app01-6375	29	4	nurbs	nurbs	NOUN
app01-6375	29	5	basis	basis	NOUN
app01-6375	29	6	functions	function	NOUN
app01-6375	29	7	are	be	AUX
app01-6375	29	8	generally	generally	ADV
app01-6375	29	9	non	non	ADJ
app01-6375	29	10	-	-	NOUN
app01-6375	29	11	interpolatory	interpolatory	ADJ
app01-6375	29	12	.	.	PUNCT
app01-6375	30	1	in	in	ADP
app01-6375	30	2	the	the	DET
app01-6375	30	3	knots	knot	NOUN
app01-6375	30	4	(	(	PUNCT
app01-6375	30	5	points	point	NOUN
app01-6375	30	6	which	which	PRON
app01-6375	30	7	are	be	AUX
app01-6375	30	8	dividing	divide	VERB
app01-6375	30	9	patch	patch	NOUN
app01-6375	30	10	into	into	ADP
app01-6375	30	11	knotspans	knotspan	NOUN
app01-6375	30	12	)	)	PUNCT
app01-6375	30	13	,	,	PUNCT
app01-6375	30	14	the	the	DET
app01-6375	30	15	continuity	continuity	NOUN
app01-6375	30	16	can	can	AUX
app01-6375	30	17	be	be	AUX
app01-6375	30	18	locally	locally	ADV
app01-6375	30	19	decreased	decrease	VERB
app01-6375	30	20	up	up	ADP
app01-6375	30	21	to	to	ADP
app01-6375	30	22	c0	c0	NOUN
app01-6375	30	23	by	by	ADP
app01-6375	30	24	knot	knot	ADJ
app01-6375	30	25	multiplication	multiplication	NOUN
app01-6375	30	26	,	,	PUNCT
app01-6375	30	27	24	24	NUM
app01-6375	30	28	https://doi.org/10.14311/app.2020.26.0024	https://doi.org/10.14311/app.2020.26.0024	NOUN
app01-6375	30	29	https://ojs.cvut.cz/ojs/index.php/app	https://ojs.cvut.cz/ojs/index.php/app	NOUN
app01-6375	30	30	vol	vol	NOUN
app01-6375	30	31	.	.	PUNCT
app01-6375	31	1	26/2020	26/2020	NUM
app01-6375	31	2	on	on	ADP
app01-6375	31	3	evaluation	evaluation	NOUN
app01-6375	31	4	of	of	ADP
app01-6375	31	5	the	the	DET
app01-6375	31	6	three	three	NUM
app01-6375	31	7	-	-	PUNCT
app01-6375	31	8	dimensional	dimensional	ADJ
app01-6375	31	9	isogeometric	isogeometric	ADJ
app01-6375	31	10	beam	beam	NOUN
app01-6375	31	11	element	element	NOUN
app01-6375	31	12	n4,2	n4,2	NOUN
app01-6375	31	13	ξ	ξ	PROPN
app01-6375	31	14	knotspan	knotspan	NOUN
app01-6375	31	15	patch	patch	VERB
app01-6375	31	16	continuity	continuity	NOUN
app01-6375	31	17	:	:	PUNCT
app01-6375	32	1	c0	c0	PROPN
app01-6375	32	2	c0c1c∞	c0c1c∞	PROPN
app01-6375	32	3	c∞	c∞	PROPN
app01-6375	32	4	knotspan	knotspan	PROPN
app01-6375	32	5	p	p	NOUN
app01-6375	32	6	=	=	PROPN
app01-6375	32	7	2	2	NUM
app01-6375	32	8	,	,	PUNCT
app01-6375	32	9	ξ	ξ	X
app01-6375	32	10	=	=	PRON
app01-6375	32	11	{	{	PUNCT
app01-6375	32	12	0,0,0,0.5,1,1,1	0,0,0,0.5,1,1,1	NOUN
app01-6375	32	13	}	}	PUNCT
app01-6375	32	14	n1,2	n1,2	ADJ
app01-6375	32	15	n2,2	n2,2	PROPN
app01-6375	33	1	n3,2	n3,2	ADJ
app01-6375	33	2	knots	knot	NOUN
app01-6375	33	3	control	control	NOUN
app01-6375	33	4	points	point	NOUN
app01-6375	33	5	p1	p1	PROPN
app01-6375	33	6	p2	p2	NOUN
app01-6375	33	7	p4p3	p4p3	X
app01-6375	33	8	parametric	parametric	ADJ
app01-6375	33	9	space	space	NOUN
app01-6375	33	10	physical	physical	ADJ
app01-6375	33	11	space	space	NOUN
app01-6375	33	12	x	x	X
app01-6375	33	13	y	y	NOUN
app01-6375	33	14	figure	figure	NOUN
app01-6375	33	15	1	1	NUM
app01-6375	33	16	.	.	PUNCT
app01-6375	33	17	description	description	NOUN
app01-6375	33	18	of	of	ADP
app01-6375	33	19	b	b	NOUN
app01-6375	33	20	-	-	PUNCT
app01-6375	33	21	spline	spline	NOUN
app01-6375	33	22	(	(	PUNCT
app01-6375	33	23	nurbs	nurbs	PROPN
app01-6375	33	24	)	)	PUNCT
app01-6375	33	25	finite	finite	PROPN
app01-6375	33	26	element	element	NOUN
app01-6375	33	27	geometry	geometry	NOUN
app01-6375	33	28	.	.	PUNCT
app01-6375	34	1	the	the	DET
app01-6375	34	2	geometry	geometry	NOUN
app01-6375	34	3	is	be	AUX
app01-6375	34	4	modeled	model	VERB
app01-6375	34	5	by	by	ADP
app01-6375	34	6	one	one	NUM
app01-6375	34	7	patch	patch	NOUN
app01-6375	34	8	consisting	consist	VERB
app01-6375	34	9	of	of	ADP
app01-6375	34	10	two	two	NUM
app01-6375	34	11	knotspans	knotspan	NOUN
app01-6375	34	12	with	with	ADP
app01-6375	34	13	quadratic	quadratic	ADJ
app01-6375	34	14	nurbs	nurb	NOUN
app01-6375	34	15	approximation	approximation	NOUN
app01-6375	34	16	.	.	PUNCT
app01-6375	35	1	which	which	PRON
app01-6375	35	2	is	be	AUX
app01-6375	35	3	a	a	DET
app01-6375	35	4	standard	standard	ADJ
app01-6375	35	5	technique	technique	NOUN
app01-6375	35	6	in	in	ADP
app01-6375	35	7	nurbs	nurb	NOUN
app01-6375	35	8	technology	technology	NOUN
app01-6375	35	9	.	.	PUNCT
app01-6375	36	1	this	this	DET
app01-6375	36	2	procedure	procedure	NOUN
app01-6375	36	3	imposes	impose	VERB
app01-6375	36	4	the	the	DET
app01-6375	36	5	interpolatory	interpolatory	ADJ
app01-6375	36	6	behavior	behavior	NOUN
app01-6375	36	7	of	of	ADP
app01-6375	36	8	the	the	DET
app01-6375	36	9	functions	function	NOUN
app01-6375	36	10	at	at	ADP
app01-6375	36	11	the	the	DET
app01-6375	36	12	particular	particular	ADJ
app01-6375	36	13	point	point	NOUN
app01-6375	36	14	.	.	PUNCT
app01-6375	37	1	for	for	ADP
app01-6375	37	2	better	well	ADJ
app01-6375	37	3	understanding	understanding	NOUN
app01-6375	37	4	of	of	ADP
app01-6375	37	5	nurbs	nurb	NOUN
app01-6375	37	6	see	see	VERB
app01-6375	37	7	fig	fig	NOUN
app01-6375	37	8	.	.	PUNCT
app01-6375	38	1	1	1	NUM
app01-6375	38	2	,	,	PUNCT
app01-6375	38	3	where	where	SCONJ
app01-6375	38	4	mapping	mapping	NOUN
app01-6375	38	5	between	between	ADP
app01-6375	38	6	real	real	ADJ
app01-6375	38	7	and	and	CCONJ
app01-6375	38	8	parametric	parametric	ADJ
app01-6375	38	9	geometry	geometry	NOUN
app01-6375	38	10	is	be	AUX
app01-6375	38	11	illustrated	illustrate	VERB
app01-6375	38	12	.	.	PUNCT
app01-6375	39	1	for	for	ADP
app01-6375	39	2	more	more	ADJ
app01-6375	39	3	information	information	NOUN
app01-6375	39	4	the	the	DET
app01-6375	39	5	reader	reader	NOUN
app01-6375	39	6	could	could	AUX
app01-6375	39	7	refer	refer	VERB
app01-6375	39	8	to	to	ADP
app01-6375	39	9	[	[	X
app01-6375	39	10	4	4	NUM
app01-6375	39	11	]	]	PUNCT
app01-6375	39	12	.	.	PUNCT
app01-6375	40	1	3	3	X
app01-6375	40	2	.	.	X
app01-6375	40	3	beam	beam	PROPN
app01-6375	40	4	element	element	NOUN
app01-6375	40	5	formulation	formulation	NOUN
app01-6375	40	6	the	the	DET
app01-6375	40	7	formulation	formulation	NOUN
app01-6375	40	8	of	of	ADP
app01-6375	40	9	the	the	DET
app01-6375	40	10	presented	present	VERB
app01-6375	40	11	three	three	NUM
app01-6375	40	12	-	-	PUNCT
app01-6375	40	13	dimensional	dimensional	ADJ
app01-6375	40	14	beam	beam	NOUN
app01-6375	40	15	element	element	NOUN
app01-6375	40	16	[	[	X
app01-6375	40	17	1	1	NUM
app01-6375	40	18	]	]	PUNCT
app01-6375	40	19	is	be	AUX
app01-6375	40	20	based	base	VERB
app01-6375	40	21	on	on	ADP
app01-6375	40	22	bernoulli	bernoulli	PROPN
app01-6375	40	23	beam	beam	PROPN
app01-6375	40	24	theory	theory	NOUN
app01-6375	40	25	and	and	CCONJ
app01-6375	40	26	accounts	account	NOUN
app01-6375	40	27	for	for	ADP
app01-6375	40	28	the	the	DET
app01-6375	40	29	geometrically	geometrically	ADV
app01-6375	40	30	nonlinear	nonlinear	ADJ
app01-6375	40	31	behaviour	behaviour	NOUN
app01-6375	40	32	.	.	PUNCT
app01-6375	41	1	bernoulli	bernoulli	PROPN
app01-6375	41	2	kinematics	kinematics	PROPN
app01-6375	41	3	assume	assume	VERB
app01-6375	41	4	that	that	SCONJ
app01-6375	41	5	the	the	DET
app01-6375	41	6	orthogonality	orthogonality	NOUN
app01-6375	41	7	of	of	ADP
app01-6375	41	8	the	the	DET
app01-6375	41	9	cross	cross	NOUN
app01-6375	41	10	-	-	NOUN
app01-6375	41	11	section	section	NOUN
app01-6375	41	12	to	to	ADP
app01-6375	41	13	the	the	DET
app01-6375	41	14	center	center	NOUN
app01-6375	41	15	line	line	NOUN
app01-6375	41	16	is	be	AUX
app01-6375	41	17	preserved	preserve	VERB
app01-6375	41	18	after	after	ADP
app01-6375	41	19	deformation	deformation	NOUN
app01-6375	41	20	and	and	CCONJ
app01-6375	41	21	that	that	SCONJ
app01-6375	41	22	the	the	DET
app01-6375	41	23	cross	cross	ADJ
app01-6375	41	24	-	-	ADJ
app01-6375	41	25	sectional	sectional	ADJ
app01-6375	41	26	dimensions	dimension	NOUN
app01-6375	41	27	remain	remain	VERB
app01-6375	41	28	unchanged	unchanged	ADJ
app01-6375	41	29	.	.	PUNCT
app01-6375	42	1	the	the	DET
app01-6375	42	2	element	element	NOUN
app01-6375	42	3	has	have	VERB
app01-6375	42	4	four	four	NUM
app01-6375	42	5	degrees	degree	NOUN
app01-6375	42	6	of	of	ADP
app01-6375	42	7	freedom	freedom	NOUN
app01-6375	42	8	in	in	ADP
app01-6375	42	9	each	each	DET
app01-6375	42	10	control	control	NOUN
app01-6375	42	11	point	point	NOUN
app01-6375	42	12	:	:	PUNCT
app01-6375	42	13	three	three	NUM
app01-6375	42	14	global	global	ADJ
app01-6375	42	15	displacements	displacement	NOUN
app01-6375	42	16	u	u	PROPN
app01-6375	42	17	,	,	PUNCT
app01-6375	42	18	v	v	NOUN
app01-6375	42	19	,	,	PUNCT
app01-6375	42	20	and	and	CCONJ
app01-6375	42	21	w	w	NOUN
app01-6375	42	22	and	and	CCONJ
app01-6375	42	23	additional	additional	ADJ
app01-6375	42	24	degree	degree	NOUN
app01-6375	42	25	of	of	ADP
app01-6375	42	26	freedom	freedom	NOUN
app01-6375	42	27	corresponding	correspond	VERB
app01-6375	42	28	to	to	PART
app01-6375	42	29	rotation	rotation	VERB
app01-6375	42	30	around	around	ADP
app01-6375	42	31	the	the	DET
app01-6375	42	32	center	center	NOUN
app01-6375	42	33	line	line	NOUN
app01-6375	42	34	ψ	ψ	NOUN
app01-6375	42	35	.	.	PUNCT
app01-6375	43	1	the	the	DET
app01-6375	43	2	rotational	rotational	ADJ
app01-6375	43	3	degree	degree	NOUN
app01-6375	43	4	of	of	ADP
app01-6375	43	5	freedom	freedom	NOUN
app01-6375	43	6	enables	enable	VERB
app01-6375	43	7	the	the	DET
app01-6375	43	8	element	element	NOUN
app01-6375	43	9	to	to	PART
app01-6375	43	10	develop	develop	VERB
app01-6375	43	11	a	a	DET
app01-6375	43	12	torsion	torsion	NOUN
app01-6375	43	13	(	(	PUNCT
app01-6375	43	14	warping	warp	VERB
app01-6375	43	15	effects	effect	NOUN
app01-6375	43	16	are	be	AUX
app01-6375	43	17	neglected	neglect	VERB
app01-6375	43	18	here	here	ADV
app01-6375	43	19	)	)	PUNCT
app01-6375	43	20	and	and	CCONJ
app01-6375	43	21	also	also	ADV
app01-6375	43	22	to	to	PART
app01-6375	43	23	model	model	VERB
app01-6375	43	24	initially	initially	ADV
app01-6375	43	25	twisted	twisted	ADJ
app01-6375	43	26	beams	beam	NOUN
app01-6375	43	27	.	.	PUNCT
app01-6375	44	1	3.1	3.1	NUM
app01-6375	44	2	.	.	PUNCT
app01-6375	44	3	geometric	geometric	ADJ
app01-6375	44	4	description	description	NOUN
app01-6375	44	5	in	in	ADP
app01-6375	44	6	the	the	DET
app01-6375	44	7	following	following	NOUN
app01-6375	44	8	,	,	PUNCT
app01-6375	44	9	the	the	DET
app01-6375	44	10	standard	standard	ADJ
app01-6375	44	11	notation	notation	NOUN
app01-6375	44	12	using	use	VERB
app01-6375	44	13	uppercase	uppercase	ADJ
app01-6375	44	14	and	and	CCONJ
app01-6375	44	15	lower	low	ADJ
app01-6375	44	16	-	-	PUNCT
app01-6375	44	17	case	case	NOUN
app01-6375	44	18	letters	letter	NOUN
app01-6375	44	19	for	for	ADP
app01-6375	44	20	the	the	DET
app01-6375	44	21	undeformed	undeformed	ADJ
app01-6375	44	22	and	and	CCONJ
app01-6375	44	23	deformed	deformed	ADJ
app01-6375	44	24	configuration	configuration	NOUN
app01-6375	44	25	,	,	PUNCT
app01-6375	44	26	respectively	respectively	ADV
app01-6375	44	27	,	,	PUNCT
app01-6375	44	28	is	be	AUX
app01-6375	44	29	adapted	adapt	VERB
app01-6375	44	30	.	.	PUNCT
app01-6375	45	1	the	the	DET
app01-6375	45	2	beam	beam	NOUN
app01-6375	45	3	formulation	formulation	NOUN
app01-6375	45	4	(	(	PUNCT
app01-6375	45	5	see	see	VERB
app01-6375	45	6	figure	figure	NOUN
app01-6375	45	7	2	2	NUM
app01-6375	45	8	)	)	PUNCT
app01-6375	45	9	starts	start	VERB
app01-6375	45	10	from	from	ADP
app01-6375	45	11	threedimensional	threedimensional	ADJ
app01-6375	45	12	approximation	approximation	NOUN
app01-6375	45	13	reduced	reduce	VERB
app01-6375	45	14	using	use	VERB
app01-6375	45	15	bernoulli	bernoulli	PROPN
app01-6375	45	16	kinematic	kinematic	ADJ
app01-6375	45	17	assumptions	assumption	NOUN
app01-6375	45	18	to	to	ADP
app01-6375	45	19	the	the	DET
app01-6375	45	20	displacements	displacement	NOUN
app01-6375	45	21	of	of	ADP
app01-6375	45	22	the	the	DET
app01-6375	45	23	center	center	NOUN
app01-6375	45	24	line	line	NOUN
app01-6375	45	25	,	,	PUNCT
app01-6375	45	26	which	which	PRON
app01-6375	45	27	is	be	AUX
app01-6375	45	28	given	give	VERB
app01-6375	45	29	by	by	ADP
app01-6375	45	30	the	the	DET
app01-6375	45	31	position	position	NOUN
app01-6375	45	32	vector	vector	NOUN
app01-6375	45	33	xc	xc	PROPN
app01-6375	45	34	(	(	PUNCT
app01-6375	45	35	xc	xc	PROPN
app01-6375	45	36	)	)	PUNCT
app01-6375	45	37	.	.	PUNCT
app01-6375	46	1	the	the	DET
app01-6375	46	2	position	position	NOUN
app01-6375	46	3	vector	vector	NOUN
app01-6375	46	4	of	of	ADP
app01-6375	46	5	the	the	DET
app01-6375	46	6	center	center	NOUN
app01-6375	46	7	line	line	NOUN
app01-6375	46	8	is	be	AUX
app01-6375	46	9	described	describe	VERB
app01-6375	46	10	as	as	ADP
app01-6375	46	11	a	a	DET
app01-6375	46	12	linear	linear	ADJ
app01-6375	46	13	combination	combination	NOUN
app01-6375	46	14	of	of	ADP
app01-6375	46	15	the	the	DET
app01-6375	46	16	control	control	NOUN
app01-6375	46	17	points	point	NOUN
app01-6375	46	18	coordinates	coordinate	NOUN
app01-6375	46	19	x̂i	x̂i	PROPN
app01-6375	46	20	and	and	CCONJ
app01-6375	46	21	the	the	DET
app01-6375	46	22	corresponding	corresponding	ADJ
app01-6375	46	23	basis	basis	NOUN
app01-6375	46	24	functions	function	NOUN
app01-6375	46	25	rpi	rpi	VERB
app01-6375	46	26	xc	xc	PUNCT
app01-6375	47	1	=	=	PUNCT
app01-6375	47	2	∑	∑	PROPN
app01-6375	47	3	i	i	PRON
app01-6375	47	4	rpi	rpi	VERB
app01-6375	47	5	x̂	x̂	PUNCT
app01-6375	48	1	i	i	PRON
app01-6375	48	2	,	,	PUNCT
app01-6375	48	3	(	(	PUNCT
app01-6375	48	4	5	5	NUM
app01-6375	48	5	)	)	PUNCT
app01-6375	48	6	xc	xc	NOUN
app01-6375	49	1	=	=	PUNCT
app01-6375	49	2	∑	∑	PROPN
app01-6375	49	3	i	i	PRON
app01-6375	49	4	rpi	rpi	VERB
app01-6375	49	5	x̂	x̂	PROPN
app01-6375	49	6	i.	i.	PROPN
app01-6375	49	7	(	(	PUNCT
app01-6375	49	8	6	6	NUM
app01-6375	49	9	)	)	PUNCT
app01-6375	49	10	deformed	deform	VERB
app01-6375	49	11	position	position	NOUN
app01-6375	49	12	vector	vector	NOUN
app01-6375	49	13	is	be	AUX
app01-6375	49	14	given	give	VERB
app01-6375	49	15	as	as	ADP
app01-6375	49	16	x̂i	x̂i	PROPN
app01-6375	49	17	=	=	SYM
app01-6375	49	18	x̂i	x̂i	PROPN
app01-6375	50	1	+	+	NUM
app01-6375	50	2	ûi	ûi	PROPN
app01-6375	50	3	,	,	PUNCT
app01-6375	50	4	(	(	PUNCT
app01-6375	50	5	7	7	X
app01-6375	50	6	)	)	PUNCT
app01-6375	50	7	where	where	SCONJ
app01-6375	50	8	ûi	ûi	PROPN
app01-6375	50	9	is	be	AUX
app01-6375	50	10	a	a	DET
app01-6375	50	11	vector	vector	NOUN
app01-6375	50	12	of	of	ADP
app01-6375	50	13	global	global	ADJ
app01-6375	50	14	degrees	degree	NOUN
app01-6375	50	15	of	of	ADP
app01-6375	50	16	freedom	freedom	NOUN
app01-6375	50	17	(	(	PUNCT
app01-6375	50	18	u	u	NOUN
app01-6375	50	19	,	,	PUNCT
app01-6375	50	20	v	v	NOUN
app01-6375	50	21	,	,	PUNCT
app01-6375	50	22	w	w	NOUN
app01-6375	50	23	)	)	PUNCT
app01-6375	50	24	.	.	PUNCT
app01-6375	51	1	additionally	additionally	ADV
app01-6375	51	2	to	to	ADP
app01-6375	51	3	the	the	DET
app01-6375	51	4	center	center	ADJ
app01-6375	51	5	line	line	NOUN
app01-6375	51	6	,	,	PUNCT
app01-6375	51	7	the	the	DET
app01-6375	51	8	cross	cross	ADJ
app01-6375	51	9	-	-	ADJ
app01-6375	51	10	section	section	ADJ
app01-6375	51	11	orientation	orientation	NOUN
app01-6375	51	12	is	be	AUX
app01-6375	51	13	described	describe	VERB
app01-6375	51	14	by	by	ADP
app01-6375	51	15	a	a	DET
app01-6375	51	16	moving	move	VERB
app01-6375	51	17	trihedral	trihedral	NOUN
app01-6375	51	18	given	give	VERB
app01-6375	51	19	by	by	ADP
app01-6375	51	20	the	the	DET
app01-6375	51	21	base	base	NOUN
app01-6375	51	22	vectors	vector	NOUN
app01-6375	51	23	ai	ai	VERB
app01-6375	51	24	(	(	PUNCT
app01-6375	51	25	ai	ai	VERB
app01-6375	51	26	)	)	PUNCT
app01-6375	51	27	with	with	ADP
app01-6375	51	28	i	i	PROPN
app01-6375	51	29	∈	∈	PROPN
app01-6375	51	30	{	{	PUNCT
app01-6375	51	31	1	1	NUM
app01-6375	51	32	,	,	PUNCT
app01-6375	51	33	2	2	NUM
app01-6375	51	34	,	,	PUNCT
app01-6375	51	35	3	3	NUM
app01-6375	51	36	}	}	PUNCT
app01-6375	51	37	.	.	PUNCT
app01-6375	52	1	a	a	DET
app01-6375	52	2	position	position	NOUN
app01-6375	52	3	vector	vector	NOUN
app01-6375	52	4	of	of	ADP
app01-6375	52	5	an	an	DET
app01-6375	52	6	arbitrary	arbitrary	ADJ
app01-6375	52	7	point	point	NOUN
app01-6375	52	8	of	of	ADP
app01-6375	52	9	a	a	DET
app01-6375	52	10	beam	beam	NOUN
app01-6375	52	11	continuum	continuum	NOUN
app01-6375	52	12	given	give	VERB
app01-6375	52	13	by	by	ADP
app01-6375	52	14	coordinates	coordinate	NOUN
app01-6375	52	15	x	x	SYM
app01-6375	52	16	(	(	PUNCT
app01-6375	52	17	x	x	X
app01-6375	52	18	)	)	PUNCT
app01-6375	52	19	can	can	AUX
app01-6375	52	20	be	be	AUX
app01-6375	52	21	expressed	express	VERB
app01-6375	52	22	as	as	ADP
app01-6375	52	23	x(θ1	x(θ1	PROPN
app01-6375	52	24	,	,	PUNCT
app01-6375	52	25	θ2	θ2	PROPN
app01-6375	52	26	,	,	PUNCT
app01-6375	52	27	θ3	θ3	PROPN
app01-6375	52	28	)	)	PUNCT
app01-6375	52	29	=	=	PUNCT
app01-6375	53	1	xc(θ1	xc(θ1	NUM
app01-6375	53	2	)	)	PUNCT
app01-6375	54	1	+	+	CCONJ
app01-6375	54	2	θ2a2(θ1	θ2a2(θ1	X
app01-6375	54	3	)	)	PUNCT
app01-6375	55	1	+	+	CCONJ
app01-6375	55	2	θ3a3(θ1	θ3a3(θ1	X
app01-6375	55	3	)	)	PUNCT
app01-6375	55	4	,	,	PUNCT
app01-6375	55	5	(	(	PUNCT
app01-6375	55	6	8)	8)	NUM
app01-6375	55	7	x(θ1	x(θ1	PROPN
app01-6375	55	8	,	,	PUNCT
app01-6375	55	9	θ2	θ2	PROPN
app01-6375	55	10	,	,	PUNCT
app01-6375	55	11	θ3	θ3	PROPN
app01-6375	55	12	)	)	PUNCT
app01-6375	55	13	=	=	PUNCT
app01-6375	55	14	xc(θ1	xc(θ1	NUM
app01-6375	55	15	)	)	PUNCT
app01-6375	56	1	+	+	CCONJ
app01-6375	56	2	θ2a2(θ1	θ2a2(θ1	X
app01-6375	56	3	)	)	PUNCT
app01-6375	57	1	+	+	CCONJ
app01-6375	57	2	θ3a3(θ1	θ3a3(θ1	X
app01-6375	57	3	)	)	PUNCT
app01-6375	57	4	,	,	PUNCT
app01-6375	57	5	(	(	PUNCT
app01-6375	57	6	9	9	X
app01-6375	57	7	)	)	PUNCT
app01-6375	57	8	where	where	SCONJ
app01-6375	57	9	θi	θi	X
app01-6375	57	10	are	be	AUX
app01-6375	57	11	the	the	DET
app01-6375	57	12	convective	convective	ADJ
app01-6375	57	13	contravariant	contravariant	ADJ
app01-6375	57	14	coordinates	coordinate	NOUN
app01-6375	57	15	.	.	PUNCT
app01-6375	58	1	the	the	DET
app01-6375	58	2	first	first	ADJ
app01-6375	58	3	components	component	NOUN
app01-6375	58	4	of	of	ADP
app01-6375	58	5	a	a	DET
app01-6375	58	6	moving	move	VERB
app01-6375	58	7	trihedral	trihedral	ADJ
app01-6375	58	8	a1	a1	NOUN
app01-6375	58	9	and	and	CCONJ
app01-6375	58	10	a1	a1	NOUN
app01-6375	58	11	are	be	AUX
app01-6375	58	12	aligned	align	VERB
app01-6375	58	13	with	with	ADP
app01-6375	58	14	a	a	DET
app01-6375	58	15	normalized	normalize	VERB
app01-6375	58	16	tangents	tangent	NOUN
app01-6375	58	17	t	t	PROPN
app01-6375	58	18	and	and	CCONJ
app01-6375	58	19	t	t	PROPN
app01-6375	58	20	,	,	PUNCT
app01-6375	58	21	respectively	respectively	ADV
app01-6375	58	22	,	,	PUNCT
app01-6375	58	23	and	and	CCONJ
app01-6375	58	24	are	be	AUX
app01-6375	58	25	computed	compute	VERB
app01-6375	58	26	as	as	ADP
app01-6375	58	27	a1	a1	NOUN
app01-6375	58	28	=	=	NOUN
app01-6375	58	29	∑	∑	PUNCT
app01-6375	59	1	i	i	PRON
app01-6375	59	2	rpi,1x̂	rpi,1x̂	PROPN
app01-6375	60	1	i	i	PRON
app01-6375	60	2	,	,	PUNCT
app01-6375	60	3	(	(	PUNCT
app01-6375	60	4	10	10	NUM
app01-6375	60	5	)	)	PUNCT
app01-6375	60	6	a1	a1	NOUN
app01-6375	60	7	=	=	NOUN
app01-6375	60	8	∑	∑	PUNCT
app01-6375	60	9	i	i	PRON
app01-6375	60	10	rpi,1x̂	rpi,1x̂	PROPN
app01-6375	60	11	i	i	PRON
app01-6375	60	12	,	,	PUNCT
app01-6375	60	13	(	(	PUNCT
app01-6375	60	14	11	11	NUM
app01-6375	60	15	)	)	PUNCT
app01-6375	60	16	where	where	SCONJ
app01-6375	60	17	(	(	PUNCT
app01-6375	60	18	·	·	PUNCT
app01-6375	60	19	)	)	PUNCT
app01-6375	60	20	,	,	PUNCT
app01-6375	60	21	i	i	PRON
app01-6375	60	22	denotes	denote	VERB
app01-6375	60	23	the	the	DET
app01-6375	60	24	derivative	derivative	NOUN
app01-6375	60	25	with	with	ADP
app01-6375	60	26	respect	respect	NOUN
app01-6375	60	27	to	to	ADP
app01-6375	60	28	the	the	DET
app01-6375	60	29	coordinate	coordinate	NOUN
app01-6375	60	30	θi	θi	PROPN
app01-6375	60	31	.	.	PUNCT
app01-6375	61	1	the	the	DET
app01-6375	61	2	remaining	remain	VERB
app01-6375	61	3	components	component	NOUN
app01-6375	61	4	aα	aα	NOUN
app01-6375	61	5	with	with	ADP
app01-6375	61	6	α	α	PROPN
app01-6375	61	7	∈	∈	PROPN
app01-6375	61	8	{	{	PUNCT
app01-6375	61	9	2	2	NUM
app01-6375	61	10	,	,	PUNCT
app01-6375	61	11	3	3	NUM
app01-6375	61	12	}	}	PUNCT
app01-6375	61	13	are	be	AUX
app01-6375	61	14	orthogonal	orthogonal	ADJ
app01-6375	61	15	to	to	ADP
app01-6375	61	16	the	the	DET
app01-6375	61	17	tangent	tangent	NOUN
app01-6375	61	18	of	of	ADP
app01-6375	61	19	the	the	DET
app01-6375	61	20	center	center	NOUN
app01-6375	61	21	line	line	NOUN
app01-6375	61	22	(	(	PUNCT
app01-6375	61	23	resp	resp	NOUN
app01-6375	61	24	.	.	PUNCT
app01-6375	62	1	a1	a1	NOUN
app01-6375	62	2	)	)	PUNCT
app01-6375	62	3	and	and	CCONJ
app01-6375	62	4	are	be	AUX
app01-6375	62	5	described	describe	VERB
app01-6375	62	6	by	by	ADP
app01-6375	62	7	the	the	DET
app01-6375	62	8	reference	reference	NOUN
app01-6375	62	9	trihedral	trihedral	NOUN
app01-6375	62	10	,	,	PUNCT
app01-6375	62	11	given	give	VERB
app01-6375	62	12	by	by	ADP
app01-6375	62	13	a0	a0	PROPN
app01-6375	62	14	α	α	PROPN
app01-6375	62	15	,	,	PUNCT
app01-6375	62	16	t0	t0	PROPN
app01-6375	62	17	,	,	PUNCT
app01-6375	62	18	as	as	ADP
app01-6375	62	19	aα	aα	NOUN
app01-6375	62	20	=	=	PUNCT
app01-6375	62	21	r̄t(ψ)λ(t0,t)a0	r̄t(ψ)λ(t0,t)a0	VERB
app01-6375	62	22	α	α	NOUN
app01-6375	62	23	,	,	PUNCT
app01-6375	62	24	(	(	PUNCT
app01-6375	62	25	12	12	NUM
app01-6375	62	26	)	)	PUNCT
app01-6375	62	27	where	where	SCONJ
app01-6375	62	28	ψ	ψ	NOUN
app01-6375	62	29	is	be	AUX
app01-6375	62	30	a	a	DET
app01-6375	62	31	initial	initial	ADJ
app01-6375	62	32	rotation	rotation	NOUN
app01-6375	62	33	about	about	ADP
app01-6375	62	34	a	a	DET
app01-6375	62	35	tangent	tangent	NOUN
app01-6375	62	36	of	of	ADP
app01-6375	62	37	a	a	DET
app01-6375	62	38	beam	beam	NOUN
app01-6375	62	39	,	,	PUNCT
app01-6375	62	40	and	and	CCONJ
app01-6375	63	1	λ	λ	PROPN
app01-6375	63	2	and	and	CCONJ
app01-6375	63	3	r̄t	r̄t	PROPN
app01-6375	63	4	are	be	AUX
app01-6375	63	5	the	the	DET
app01-6375	63	6	two	two	NUM
app01-6375	63	7	key	key	ADJ
app01-6375	63	8	operations	operation	NOUN
app01-6375	63	9	used	use	VERB
app01-6375	63	10	25	25	NUM
app01-6375	63	11	edita	edita	PROPN
app01-6375	63	12	dvořáková	dvořáková	PROPN
app01-6375	63	13	,	,	PUNCT
app01-6375	63	14	bořek	bořek	PROPN
app01-6375	63	15	patzák	patzák	VERB
app01-6375	63	16	acta	acta	PROPN
app01-6375	63	17	polytechnica	polytechnica	PROPN
app01-6375	63	18	ctu	ctu	PROPN
app01-6375	63	19	proceedings	proceeding	NOUN
app01-6375	63	20	a1(θ1	a1(θ1	NOUN
app01-6375	63	21	)	)	PUNCT
app01-6375	63	22	a2(θ1	a2(θ1	PROPN
app01-6375	63	23	)	)	PUNCT
app01-6375	63	24	a3(θ1	a3(θ1	NOUN
app01-6375	63	25	)	)	PUNCT
app01-6375	63	26	a1(θ1	a1(θ1	PROPN
app01-6375	63	27	)	)	PUNCT
app01-6375	63	28	a3(θ1	a3(θ1	PROPN
app01-6375	63	29	)	)	PUNCT
app01-6375	63	30	a2(θ1	a2(θ1	PROPN
app01-6375	63	31	)	)	PUNCT
app01-6375	63	32	u(θ1	u(θ1	PROPN
app01-6375	63	33	,	,	PUNCT
app01-6375	63	34	θ2	θ2	PROPN
app01-6375	63	35	,	,	PUNCT
app01-6375	63	36	θ3	θ3	PROPN
app01-6375	63	37	)	)	PUNCT
app01-6375	63	38	x(θ1	x(θ1	PROPN
app01-6375	63	39	,	,	PUNCT
app01-6375	63	40	θ2	θ2	PROPN
app01-6375	63	41	,	,	PUNCT
app01-6375	63	42	θ3	θ3	PROPN
app01-6375	63	43	)	)	PUNCT
app01-6375	63	44	xc(θ1	xc(θ1	PUNCT
app01-6375	63	45	)	)	PUNCT
app01-6375	64	1	xc(θ1	xc(θ1	X
app01-6375	64	2	)	)	PUNCT
app01-6375	65	1	x	x	PUNCT
app01-6375	65	2	y	y	PROPN
app01-6375	65	3	z	z	NOUN
app01-6375	65	4	figure	figure	NOUN
app01-6375	65	5	2	2	NUM
app01-6375	65	6	.	.	X
app01-6375	65	7	illustration	illustration	NOUN
app01-6375	65	8	of	of	ADP
app01-6375	65	9	the	the	DET
app01-6375	65	10	beam	beam	NOUN
app01-6375	65	11	in	in	ADP
app01-6375	65	12	its	its	PRON
app01-6375	65	13	undeformed	undeformed	ADJ
app01-6375	65	14	and	and	CCONJ
app01-6375	65	15	deformed	deformed	ADJ
app01-6375	65	16	configurations	configuration	NOUN
app01-6375	65	17	.	.	PUNCT
app01-6375	66	1	t0	t0	PROPN
app01-6375	66	2	t0	t0	PROPN
app01-6375	66	3	a0	a0	PROPN
app01-6375	66	4	2	2	NUM
app01-6375	66	5	a0	a0	PROPN
app01-6375	66	6	3	3	NUM
app01-6375	66	7	t	t	NOUN
app01-6375	66	8	λ(t0	λ(t0	PROPN
app01-6375	66	9	,	,	PUNCT
app01-6375	66	10	t	t	PROPN
app01-6375	66	11	)	)	PUNCT
app01-6375	66	12	λ(t0	λ(t0	PROPN
app01-6375	66	13	,	,	PUNCT
app01-6375	66	14	t	t	PROPN
app01-6375	66	15	)	)	PUNCT
app01-6375	66	16	λ(t0	λ(t0	PROPN
app01-6375	66	17	,	,	PUNCT
app01-6375	66	18	t	t	PROPN
app01-6375	66	19	)	)	PUNCT
app01-6375	66	20	a0	a0	PROPN
app01-6375	66	21	3	3	NUM
app01-6375	66	22	a0	a0	PROPN
app01-6375	66	23	3	3	NUM
app01-6375	66	24	λ(t0	λ(t0	PROPN
app01-6375	66	25	,	,	PUNCT
app01-6375	66	26	t	t	NOUN
app01-6375	66	27	)	)	PUNCT
app01-6375	66	28	a0	a0	PROPN
app01-6375	66	29	2	2	NUM
app01-6375	66	30	t0	t0	PROPN
app01-6375	66	31	a0	a0	PROPN
app01-6375	66	32	2	2	NUM
app01-6375	66	33	a0	a0	PROPN
app01-6375	66	34	3	3	NUM
app01-6375	66	35	t	t	NOUN
app01-6375	66	36	λ(t0	λ(t0	PROPN
app01-6375	66	37	,	,	PUNCT
app01-6375	66	38	t	t	PROPN
app01-6375	66	39	)	)	PUNCT
app01-6375	66	40	a0	a0	PROPN
app01-6375	66	41	3	3	NUM
app01-6375	66	42	λ(t0	λ(t0	PROPN
app01-6375	66	43	,	,	PUNCT
app01-6375	66	44	t	t	NOUN
app01-6375	66	45	)	)	PUNCT
app01-6375	66	46	a0	a0	PROPN
app01-6375	66	47	2	2	NUM
app01-6375	66	48	r̄t	r̄t	PROPN
app01-6375	66	49	(	(	PUNCT
app01-6375	66	50	ψ	ψ	NOUN
app01-6375	66	51	)	)	PUNCT
app01-6375	66	52	r̄t	r̄t	ADP
app01-6375	66	53	(	(	PUNCT
app01-6375	66	54	ψ	ψ	NOUN
app01-6375	66	55	)	)	PUNCT
app01-6375	66	56	a3	a3	NOUN
app01-6375	66	57	a2	a2	PROPN
app01-6375	66	58	figure	figure	NOUN
app01-6375	66	59	3	3	NUM
app01-6375	66	60	.	.	PUNCT
app01-6375	67	1	the	the	DET
app01-6375	67	2	λ(t0,t	λ(t0,t	NOUN
app01-6375	67	3	)	)	PUNCT
app01-6375	67	4	and	and	CCONJ
app01-6375	67	5	r̄t(ψ	r̄t(ψ	NOUN
app01-6375	67	6	)	)	PUNCT
app01-6375	67	7	operations	operation	NOUN
app01-6375	67	8	used	use	VERB
app01-6375	67	9	for	for	ADP
app01-6375	67	10	the	the	DET
app01-6375	67	11	alignment	alignment	NOUN
app01-6375	67	12	of	of	ADP
app01-6375	67	13	the	the	DET
app01-6375	67	14	cross	cross	NOUN
app01-6375	67	15	-	-	NOUN
app01-6375	67	16	section	section	NOUN
app01-6375	67	17	at	at	ADP
app01-6375	67	18	the	the	DET
app01-6375	67	19	current	current	ADJ
app01-6375	67	20	position	position	NOUN
app01-6375	67	21	.	.	PUNCT
app01-6375	68	1	for	for	ADP
app01-6375	68	2	the	the	DET
app01-6375	68	3	alignment	alignment	NOUN
app01-6375	68	4	of	of	ADP
app01-6375	68	5	a	a	DET
app01-6375	68	6	moving	move	VERB
app01-6375	68	7	trihedral	trihedral	ADJ
app01-6375	68	8	illustrated	illustrate	VERB
app01-6375	68	9	in	in	ADP
app01-6375	68	10	figure	figure	NOUN
app01-6375	68	11	3	3	NUM
app01-6375	68	12	.	.	PUNCT
app01-6375	69	1	while	while	SCONJ
app01-6375	69	2	the	the	DET
app01-6375	69	3	mapping	mapping	NOUN
app01-6375	69	4	matrix	matrix	NOUN
app01-6375	69	5	λ(t0,t	λ(t0,t	NOUN
app01-6375	69	6	)	)	PUNCT
app01-6375	69	7	aligns	align	VERB
app01-6375	69	8	the	the	DET
app01-6375	69	9	reference	reference	NOUN
app01-6375	69	10	trihedral	trihedral	NOUN
app01-6375	69	11	given	give	VERB
app01-6375	69	12	by	by	ADP
app01-6375	69	13	the	the	DET
app01-6375	69	14	tangent	tangent	ADJ
app01-6375	69	15	t0	t0	PROPN
app01-6375	69	16	to	to	ADP
app01-6375	69	17	the	the	DET
app01-6375	69	18	tangent	tangent	NOUN
app01-6375	69	19	t	t	PROPN
app01-6375	69	20	at	at	ADP
app01-6375	69	21	the	the	DET
app01-6375	69	22	current	current	ADJ
app01-6375	69	23	position	position	NOUN
app01-6375	69	24	,	,	PUNCT
app01-6375	69	25	the	the	DET
app01-6375	69	26	rotation	rotation	NOUN
app01-6375	69	27	matrix	matrix	NOUN
app01-6375	69	28	r̄t(ψ	r̄t(ψ	NOUN
app01-6375	69	29	)	)	PUNCT
app01-6375	69	30	rotates	rotate	VERB
app01-6375	69	31	the	the	DET
app01-6375	69	32	aligned	aligned	ADJ
app01-6375	69	33	reference	reference	NOUN
app01-6375	69	34	trihedral	trihedral	ADJ
app01-6375	69	35	about	about	ADP
app01-6375	69	36	t	t	NOUN
app01-6375	69	37	with	with	ADP
app01-6375	69	38	given	give	VERB
app01-6375	69	39	rotation	rotation	NOUN
app01-6375	69	40	ψ	ψ	NOUN
app01-6375	69	41	.	.	PUNCT
app01-6375	70	1	the	the	DET
app01-6375	70	2	rotation	rotation	NOUN
app01-6375	70	3	ψ	ψ	X
app01-6375	70	4	=	=	X
app01-6375	70	5	ψ(θ1	ψ(θ1	NOUN
app01-6375	70	6	)	)	PUNCT
app01-6375	70	7	is	be	AUX
app01-6375	70	8	calculated	calculate	VERB
app01-6375	70	9	using	use	VERB
app01-6375	70	10	basis	basis	NOUN
app01-6375	70	11	functions	function	NOUN
app01-6375	70	12	and	and	CCONJ
app01-6375	70	13	values	value	NOUN
app01-6375	70	14	ψ̂i	ψ̂i	PUNCT
app01-6375	70	15	assigned	assign	VERB
app01-6375	70	16	to	to	ADP
app01-6375	70	17	the	the	DET
app01-6375	70	18	control	control	NOUN
app01-6375	70	19	points	point	NOUN
app01-6375	70	20	.	.	PUNCT
app01-6375	71	1	the	the	DET
app01-6375	71	2	euler	euler	PROPN
app01-6375	71	3	-	-	PUNCT
app01-6375	71	4	rodriguez	rodriguez	NOUN
app01-6375	71	5	formula	formula	NOUN
app01-6375	71	6	[	[	X
app01-6375	71	7	5	5	NUM
app01-6375	71	8	]	]	PUNCT
app01-6375	71	9	is	be	AUX
app01-6375	71	10	used	use	VERB
app01-6375	71	11	to	to	PART
app01-6375	71	12	define	define	VERB
app01-6375	71	13	both	both	PRON
app01-6375	71	14	the	the	DET
app01-6375	71	15	mapping	mapping	NOUN
app01-6375	71	16	matrix	matrix	NOUN
app01-6375	71	17	λ	λ	PROPN
app01-6375	71	18	and	and	CCONJ
app01-6375	71	19	the	the	DET
app01-6375	71	20	rotation	rotation	NOUN
app01-6375	71	21	matrix	matrix	NOUN
app01-6375	71	22	rt	rt	PROPN
app01-6375	71	23	.	.	PUNCT
app01-6375	71	24	analogical	analogical	ADJ
app01-6375	71	25	procedures	procedure	NOUN
app01-6375	71	26	denoted	denote	VERB
app01-6375	71	27	as	as	ADP
app01-6375	71	28	λ(t	λ(t	PROPN
app01-6375	71	29	,	,	PUNCT
app01-6375	71	30	t	t	PROPN
app01-6375	71	31	)	)	PUNCT
app01-6375	71	32	and	and	CCONJ
app01-6375	71	33	r̄t(ψ	r̄t(ψ	NOUN
app01-6375	71	34	)	)	PUNCT
app01-6375	71	35	are	be	AUX
app01-6375	71	36	used	use	VERB
app01-6375	71	37	to	to	PART
app01-6375	71	38	align	align	VERB
app01-6375	71	39	the	the	DET
app01-6375	71	40	moving	move	VERB
app01-6375	71	41	trihedral	trihedral	NOUN
app01-6375	71	42	of	of	ADP
app01-6375	71	43	the	the	DET
app01-6375	71	44	undeformed	undeformed	ADJ
app01-6375	71	45	to	to	ADP
app01-6375	71	46	the	the	DET
app01-6375	71	47	deformed	deform	VERB
app01-6375	71	48	configuration	configuration	NOUN
app01-6375	71	49	.	.	PUNCT
app01-6375	72	1	the	the	DET
app01-6375	72	2	base	base	NOUN
app01-6375	72	3	vectors	vector	NOUN
app01-6375	72	4	aα	aα	NOUN
app01-6375	72	5	of	of	ADP
app01-6375	72	6	the	the	DET
app01-6375	72	7	deformed	deform	VERB
app01-6375	72	8	configuration	configuration	NOUN
app01-6375	72	9	are	be	AUX
app01-6375	72	10	given	give	VERB
app01-6375	72	11	as	as	ADP
app01-6375	72	12	aα	aα	NOUN
app01-6375	72	13	=	=	PUNCT
app01-6375	72	14	r̄t(ψ)λ(t	r̄t(ψ)λ(t	NOUN
app01-6375	72	15	,	,	PUNCT
app01-6375	72	16	t)aα	t)aα	VERB
app01-6375	72	17	,	,	PUNCT
app01-6375	72	18	(	(	PUNCT
app01-6375	72	19	13	13	NUM
app01-6375	72	20	)	)	PUNCT
app01-6375	72	21	where	where	SCONJ
app01-6375	72	22	ψ	ψ	NOUN
app01-6375	72	23	=	=	SYM
app01-6375	72	24	ψ(θi	ψ(θi	X
app01-6375	72	25	)	)	PUNCT
app01-6375	72	26	is	be	AUX
app01-6375	72	27	a	a	DET
app01-6375	72	28	rotational	rotational	ADJ
app01-6375	72	29	degree	degree	NOUN
app01-6375	72	30	of	of	ADP
app01-6375	72	31	freedom	freedom	NOUN
app01-6375	72	32	evaluated	evaluate	VERB
app01-6375	72	33	at	at	ADP
app01-6375	72	34	the	the	DET
app01-6375	72	35	current	current	ADJ
app01-6375	72	36	position	position	NOUN
app01-6375	72	37	θi	θi	PROPN
app01-6375	72	38	.	.	PUNCT
app01-6375	73	1	the	the	DET
app01-6375	73	2	base	base	NOUN
app01-6375	73	3	vectors	vector	NOUN
app01-6375	73	4	of	of	ADP
app01-6375	73	5	the	the	DET
app01-6375	73	6	undeformed	undeformed	ADJ
app01-6375	73	7	continuum	continuum	ADJ
app01-6375	73	8	gi	gi	NOUN
app01-6375	73	9	are	be	AUX
app01-6375	73	10	defined	define	VERB
app01-6375	73	11	as	as	ADP
app01-6375	73	12	gi	gi	NOUN
app01-6375	73	13	=	=	SYM
app01-6375	73	14	x	x	NOUN
app01-6375	73	15	,	,	PUNCT
app01-6375	73	16	i	i	PRON
app01-6375	73	17	leading	lead	VERB
app01-6375	73	18	to	to	ADP
app01-6375	73	19	g1(θ1	g1(θ1	PROPN
app01-6375	73	20	,	,	PUNCT
app01-6375	73	21	θ2	θ2	PROPN
app01-6375	73	22	,	,	PUNCT
app01-6375	73	23	θ3	θ3	PROPN
app01-6375	73	24	)	)	PUNCT
app01-6375	73	25	=	=	PUNCT
app01-6375	74	1	a1(θ1	a1(θ1	NOUN
app01-6375	74	2	)	)	PUNCT
app01-6375	74	3	+	+	NUM
app01-6375	74	4	θ2a2,1(θ1	θ2a2,1(θ1	X
app01-6375	74	5	)	)	PUNCT
app01-6375	75	1	+	+	X
app01-6375	76	1	θ3a3,1(θ1	θ3a3,1(θ1	NUM
app01-6375	76	2	)	)	PUNCT
app01-6375	77	1	,	,	PUNCT
app01-6375	77	2	g2(θ1	g2(θ1	NOUN
app01-6375	77	3	)	)	PUNCT
app01-6375	77	4	=	=	PUNCT
app01-6375	77	5	a2(θ1	a2(θ1	PROPN
app01-6375	77	6	)	)	PUNCT
app01-6375	77	7	,	,	PUNCT
app01-6375	77	8	(	(	PUNCT
app01-6375	77	9	14	14	X
app01-6375	77	10	)	)	PUNCT
app01-6375	77	11	g3(θ1	g3(θ1	NOUN
app01-6375	77	12	)	)	PUNCT
app01-6375	78	1	=	=	SYM
app01-6375	78	2	a3(θ1	a3(θ1	PROPN
app01-6375	78	3	)	)	PUNCT
app01-6375	78	4	with	with	ADP
app01-6375	78	5	analogical	analogical	ADJ
app01-6375	78	6	equations	equation	NOUN
app01-6375	78	7	for	for	ADP
app01-6375	78	8	the	the	DET
app01-6375	78	9	base	base	NOUN
app01-6375	78	10	vectors	vector	NOUN
app01-6375	78	11	gi	gi	NOUN
app01-6375	78	12	=	=	SYM
app01-6375	79	1	x	x	X
app01-6375	79	2	,	,	PUNCT
app01-6375	79	3	i	i	PRON
app01-6375	79	4	of	of	ADP
app01-6375	79	5	the	the	DET
app01-6375	79	6	undeformed	undeformed	ADJ
app01-6375	79	7	configuration	configuration	NOUN
app01-6375	79	8	.	.	PUNCT
app01-6375	80	1	in	in	ADP
app01-6375	80	2	the	the	DET
app01-6375	80	3	sequel	sequel	NOUN
app01-6375	80	4	,	,	PUNCT
app01-6375	80	5	dot	dot	NOUN
app01-6375	80	6	products	product	NOUN
app01-6375	80	7	gi	gi	X
app01-6375	80	8	·	·	PUNCT
app01-6375	80	9	gj	gj	PROPN
app01-6375	80	10	(	(	PUNCT
app01-6375	80	11	gi	gi	INTJ
app01-6375	80	12	·	·	PUNCT
app01-6375	80	13	gj	gj	NOUN
app01-6375	80	14	)	)	PUNCT
app01-6375	80	15	and	and	CCONJ
app01-6375	80	16	ai	ai	VERB
app01-6375	80	17	·	·	PUNCT
app01-6375	80	18	aj	aj	PROPN
app01-6375	80	19	(	(	PUNCT
app01-6375	80	20	ai	ai	PROPN
app01-6375	80	21	·	·	PUNCT
app01-6375	80	22	aj	aj	PROPN
app01-6375	80	23	)	)	PUNCT
app01-6375	80	24	are	be	AUX
app01-6375	80	25	denoted	denote	VERB
app01-6375	80	26	as	as	ADP
app01-6375	80	27	gij	gij	ADJ
app01-6375	80	28	(	(	PUNCT
app01-6375	80	29	gij	gij	NOUN
app01-6375	80	30	)	)	PUNCT
app01-6375	80	31	and	and	CCONJ
app01-6375	80	32	aij	aij	PROPN
app01-6375	80	33	(	(	PUNCT
app01-6375	80	34	aij	aij	PROPN
app01-6375	80	35	)	)	PUNCT
app01-6375	80	36	,	,	PUNCT
app01-6375	80	37	respectively	respectively	ADV
app01-6375	80	38	.	.	PUNCT
app01-6375	81	1	3.2	3.2	NUM
app01-6375	81	2	.	.	PUNCT
app01-6375	81	3	green	green	ADJ
app01-6375	81	4	-	-	PUNCT
app01-6375	81	5	lagrange	lagrange	NOUN
app01-6375	81	6	strain	strain	NOUN
app01-6375	81	7	tensor	tensor	NOUN
app01-6375	81	8	the	the	DET
app01-6375	81	9	green	green	ADJ
app01-6375	81	10	-	-	PUNCT
app01-6375	81	11	lagrange	lagrange	NOUN
app01-6375	81	12	strain	strain	NOUN
app01-6375	81	13	tensor	tensor	NOUN
app01-6375	81	14	e	e	NOUN
app01-6375	81	15	calculated	calculate	VERB
app01-6375	81	16	for	for	ADP
app01-6375	81	17	the	the	DET
app01-6375	81	18	curvilinear	curvilinear	ADJ
app01-6375	81	19	coordinate	coordinate	NOUN
app01-6375	81	20	system	system	NOUN
app01-6375	81	21	is	be	AUX
app01-6375	81	22	defined	define	VERB
app01-6375	81	23	as	as	ADP
app01-6375	81	24	eij	eij	PROPN
app01-6375	81	25	=	=	NOUN
app01-6375	81	26	1	1	NUM
app01-6375	81	27	2	2	NUM
app01-6375	81	28	(	(	PUNCT
app01-6375	81	29	gij	gij	NOUN
app01-6375	81	30	−gij	−gij	ADV
app01-6375	81	31	)	)	PUNCT
app01-6375	81	32	.	.	PUNCT
app01-6375	82	1	(	(	PUNCT
app01-6375	82	2	15	15	NUM
app01-6375	82	3	)	)	PUNCT
app01-6375	82	4	and	and	CCONJ
app01-6375	82	5	for	for	ADP
app01-6375	82	6	the	the	DET
app01-6375	82	7	orthogonal	orthogonal	ADJ
app01-6375	82	8	base	base	NOUN
app01-6375	82	9	vectors	vector	NOUN
app01-6375	82	10	,	,	PUNCT
app01-6375	82	11	the	the	DET
app01-6375	82	12	transformation	transformation	NOUN
app01-6375	82	13	to	to	ADP
app01-6375	82	14	the	the	DET
app01-6375	82	15	cartesian	cartesian	ADJ
app01-6375	82	16	coordinate	coordinate	NOUN
app01-6375	82	17	system	system	NOUN
app01-6375	82	18	denoted	denote	VERB
app01-6375	82	19	with	with	ADP
app01-6375	82	20	(	(	PUNCT
app01-6375	82	21	̃	̃	PROPN
app01-6375	82	22	·	·	PUNCT
app01-6375	82	23	)	)	PUNCT
app01-6375	82	24	is	be	AUX
app01-6375	82	25	given	give	VERB
app01-6375	82	26	by	by	ADP
app01-6375	82	27	ẽij	ẽij	PROPN
app01-6375	82	28	=	=	SYM
app01-6375	82	29	eij	eij	PROPN
app01-6375	82	30	‖gi‖2‖gj‖2	‖gi‖2‖gj‖2	NOUN
app01-6375	82	31	.	.	PUNCT
app01-6375	83	1	(	(	PUNCT
app01-6375	83	2	16	16	NUM
app01-6375	83	3	)	)	PUNCT
app01-6375	83	4	by	by	ADP
app01-6375	83	5	substituting	substitute	VERB
app01-6375	83	6	geometric	geometric	ADJ
app01-6375	83	7	relations	relation	NOUN
app01-6375	83	8	into	into	ADP
app01-6375	83	9	the	the	DET
app01-6375	83	10	strain	strain	NOUN
app01-6375	83	11	tensor	tensor	NOUN
app01-6375	83	12	,	,	PUNCT
app01-6375	83	13	the	the	DET
app01-6375	83	14	individual	individual	ADJ
app01-6375	83	15	components	component	NOUN
app01-6375	83	16	of	of	ADP
app01-6375	83	17	the	the	DET
app01-6375	83	18	tensor	tensor	NOUN
app01-6375	83	19	can	can	AUX
app01-6375	83	20	be	be	AUX
app01-6375	83	21	derived	derive	VERB
app01-6375	83	22	.	.	PUNCT
app01-6375	84	1	during	during	ADP
app01-6375	84	2	the	the	DET
app01-6375	84	3	derivation	derivation	NOUN
app01-6375	84	4	additional	additional	ADJ
app01-6375	84	5	simplifications	simplification	NOUN
app01-6375	84	6	are	be	AUX
app01-6375	84	7	made	make	VERB
app01-6375	84	8	assuming	assume	VERB
app01-6375	84	9	that	that	SCONJ
app01-6375	84	10	only	only	ADV
app01-6375	84	11	a	a	DET
app01-6375	84	12	slender	slender	ADJ
app01-6375	84	13	beam	beam	NOUN
app01-6375	84	14	is	be	AUX
app01-6375	84	15	considered	consider	VERB
app01-6375	84	16	(	(	PUNCT
app01-6375	84	17	b	b	NUM
app01-6375	84	18	,	,	PUNCT
app01-6375	84	19	h	h	NOUN
app01-6375	84	20	<	<	X
app01-6375	84	21	<	<	X
app01-6375	84	22	lwhere	lwhere	PROPN
app01-6375	84	23	b	b	PROPN
app01-6375	84	24	and	and	CCONJ
app01-6375	84	25	h	h	NOUN
app01-6375	84	26	are	be	AUX
app01-6375	84	27	cross	cross	ADJ
app01-6375	84	28	-	-	ADJ
app01-6375	84	29	sectional	sectional	ADJ
app01-6375	84	30	dimensions	dimension	NOUN
app01-6375	84	31	and	and	CCONJ
app01-6375	84	32	l	l	NOUN
app01-6375	84	33	is	be	AUX
app01-6375	84	34	a	a	DET
app01-6375	84	35	length	length	NOUN
app01-6375	84	36	of	of	ADP
app01-6375	84	37	the	the	DET
app01-6375	84	38	beam	beam	NOUN
app01-6375	84	39	)	)	PUNCT
app01-6375	84	40	resulting	result	VERB
app01-6375	84	41	in	in	ADP
app01-6375	84	42	the	the	DET
app01-6375	84	43	following	follow	VERB
app01-6375	84	44	equations	equation	NOUN
app01-6375	84	45	for	for	ADP
app01-6375	84	46	the	the	DET
app01-6375	84	47	diagonal	diagonal	ADJ
app01-6375	84	48	term	term	NOUN
app01-6375	84	49	e11	e11	X
app01-6375	84	50	e11	e11	NOUN
app01-6375	84	51	=	=	SYM
app01-6375	84	52	1	1	NUM
app01-6375	84	53	2(a11	2(a11	NUM
app01-6375	84	54	−a11)︸	−a11)︸	NOUN
app01-6375	84	55	︷︷	︷︷	PROPN
app01-6375	84	56	︸	︸	X
app01-6375	84	57	ε	ε	PROPN
app01-6375	84	58	+	+	PROPN
app01-6375	84	59	θ2	θ2	PROPN
app01-6375	84	60	a2,1	a2,1	PROPN
app01-6375	84	61	·	·	PUNCT
app01-6375	84	62	a1	a1	PROPN
app01-6375	84	63	−a2,1	−a2,1	PROPN
app01-6375	84	64	·	·	PROPN
app01-6375	84	65	a1︸	a1︸	PROPN
app01-6375	84	66	︷︷	︷︷	PROPN
app01-6375	84	67	︸	︸	ADP
app01-6375	84	68	κ21	κ21	PROPN
app01-6375	84	69	+	+	PROPN
app01-6375	84	70	θ3	θ3	PROPN
app01-6375	84	71	a3,1	a3,1	PROPN
app01-6375	84	72	·	·	PUNCT
app01-6375	84	73	a1	a1	PROPN
app01-6375	84	74	−a3,1	−a3,1	NUM
app01-6375	84	75	·	·	PUNCT
app01-6375	84	76	a1︸	a1︸	PROPN
app01-6375	84	77	︷︷	︷︷	PROPN
app01-6375	84	78	︸	︸	ADP
app01-6375	84	79	κ31	κ31	ADJ
app01-6375	84	80	.	.	PUNCT
app01-6375	85	1	(	(	PUNCT
app01-6375	85	2	17	17	NUM
app01-6375	85	3	)	)	PUNCT
app01-6375	85	4	the	the	DET
app01-6375	85	5	diagonal	diagonal	ADJ
app01-6375	85	6	terms	term	NOUN
app01-6375	85	7	eαα	eαα	ADJ
app01-6375	85	8	as	as	ADV
app01-6375	85	9	well	well	ADV
app01-6375	85	10	as	as	ADP
app01-6375	85	11	the	the	DET
app01-6375	85	12	shear	shear	NOUN
app01-6375	85	13	term	term	NOUN
app01-6375	85	14	e23	e23	NOUN
app01-6375	85	15	are	be	AUX
app01-6375	85	16	equal	equal	ADJ
app01-6375	85	17	to	to	ADP
app01-6375	85	18	zero	zero	NUM
app01-6375	85	19	.	.	PUNCT
app01-6375	86	1	this	this	DET
app01-6375	86	2	yields	yield	NOUN
app01-6375	86	3	from	from	ADP
app01-6375	86	4	the	the	DET
app01-6375	86	5	bernoulli	bernoulli	PROPN
app01-6375	86	6	assumptions	assumption	NOUN
app01-6375	86	7	(	(	PUNCT
app01-6375	86	8	undeformable	undeformable	ADJ
app01-6375	86	9	cross	cross	NOUN
app01-6375	86	10	–	–	NOUN
app01-6375	86	11	section	section	NOUN
app01-6375	86	12	)	)	PUNCT
app01-6375	86	13	.	.	PUNCT
app01-6375	87	1	for	for	ADP
app01-6375	87	2	the	the	DET
app01-6375	87	3	off	off	ADJ
app01-6375	87	4	-	-	PUNCT
app01-6375	87	5	diagonal	diagonal	ADJ
app01-6375	87	6	terms	term	NOUN
app01-6375	87	7	e12	e12	NOUN
app01-6375	87	8	,	,	PUNCT
app01-6375	87	9	e13	e13	PROPN
app01-6375	87	10	e1α	e1α	X
app01-6375	87	11	=	=	PUNCT
app01-6375	87	12	1	1	NUM
app01-6375	87	13	2θ	2θ	NUM
app01-6375	87	14	β	β	X
app01-6375	87	15	(	(	PUNCT
app01-6375	87	16	aβ,1	aβ,1	NOUN
app01-6375	87	17	·	·	PUNCT
app01-6375	87	18	aα	aα	NOUN
app01-6375	87	19	−	−	NOUN
app01-6375	87	20	(	(	PUNCT
app01-6375	87	21	aβ,1	aβ,1	PROPN
app01-6375	87	22	·	·	PUNCT
app01-6375	87	23	aα)︸	aα)︸	NOUN
app01-6375	87	24	︷︷	︷︷	PROPN
app01-6375	87	25	︸	︸	X
app01-6375	87	26	κβα	κβα	PROPN
app01-6375	87	27	,	,	PUNCT
app01-6375	87	28	(	(	PUNCT
app01-6375	87	29	18	18	NUM
app01-6375	87	30	)	)	PUNCT
app01-6375	87	31	where	where	SCONJ
app01-6375	87	32	(	(	PUNCT
app01-6375	87	33	α	α	NOUN
app01-6375	87	34	,	,	PUNCT
app01-6375	87	35	β	β	NOUN
app01-6375	87	36	)	)	PUNCT
app01-6375	87	37	∈	∈	NOUN
app01-6375	87	38	{	{	PUNCT
app01-6375	87	39	(	(	PUNCT
app01-6375	87	40	2	2	NUM
app01-6375	87	41	,	,	PUNCT
app01-6375	87	42	3	3	NUM
app01-6375	87	43	)	)	PUNCT
app01-6375	87	44	,	,	PUNCT
app01-6375	87	45	(	(	PUNCT
app01-6375	87	46	3	3	NUM
app01-6375	87	47	,	,	PUNCT
app01-6375	87	48	2	2	NUM
app01-6375	87	49	)	)	PUNCT
app01-6375	87	50	}	}	PUNCT
app01-6375	87	51	.	.	PUNCT
app01-6375	88	1	26	26	NUM
app01-6375	88	2	vol	vol	NOUN
app01-6375	88	3	.	.	PUNCT
app01-6375	88	4	26/2020	26/2020	NUM
app01-6375	88	5	on	on	ADP
app01-6375	88	6	evaluation	evaluation	NOUN
app01-6375	88	7	of	of	ADP
app01-6375	88	8	the	the	DET
app01-6375	88	9	three	three	NUM
app01-6375	88	10	-	-	PUNCT
app01-6375	88	11	dimensional	dimensional	ADJ
app01-6375	88	12	isogeometric	isogeometric	ADJ
app01-6375	88	13	beam	beam	NOUN
app01-6375	88	14	element	element	NOUN
app01-6375	88	15	3.3	3.3	NUM
app01-6375	88	16	.	.	PUNCT
app01-6375	89	1	constitutive	constitutive	ADJ
app01-6375	89	2	equations	equation	NOUN
app01-6375	89	3	the	the	DET
app01-6375	89	4	energetically	energetically	ADV
app01-6375	89	5	conjugated	conjugate	VERB
app01-6375	89	6	stress	stress	ADJ
app01-6375	89	7	tensor	tensor	NOUN
app01-6375	89	8	to	to	ADP
app01-6375	89	9	the	the	DET
app01-6375	89	10	green	green	ADJ
app01-6375	89	11	-	-	PUNCT
app01-6375	89	12	lagrange	lagrange	NOUN
app01-6375	89	13	strain	strain	NOUN
app01-6375	89	14	tensor	tensor	NOUN
app01-6375	89	15	is	be	AUX
app01-6375	89	16	the	the	DET
app01-6375	89	17	second	second	ADJ
app01-6375	89	18	piolakirchhoff	piolakirchhoff	NOUN
app01-6375	89	19	tensor	tensor	NOUN
app01-6375	89	20	s.	s.	PROPN
app01-6375	89	21	elastic	elastic	ADJ
app01-6375	89	22	isotropic	isotropic	NOUN
app01-6375	89	23	material	material	NOUN
app01-6375	89	24	is	be	AUX
app01-6375	89	25	considered	consider	VERB
app01-6375	89	26	within	within	ADP
app01-6375	89	27	this	this	DET
app01-6375	89	28	work	work	NOUN
app01-6375	89	29	and	and	CCONJ
app01-6375	89	30	st	st	PROPN
app01-6375	89	31	.	.	PROPN
app01-6375	89	32	venant	venant	PROPN
app01-6375	89	33	–	–	PUNCT
app01-6375	89	34	kirchhoff	kirchhoff	NOUN
app01-6375	89	35	material	material	NOUN
app01-6375	89	36	is	be	AUX
app01-6375	89	37	applied	apply	VERB
app01-6375	89	38	.	.	PUNCT
app01-6375	90	1	as	as	SCONJ
app01-6375	90	2	the	the	DET
app01-6375	90	3	beam	beam	NOUN
app01-6375	90	4	formulation	formulation	NOUN
app01-6375	90	5	is	be	AUX
app01-6375	90	6	reduced	reduce	VERB
app01-6375	90	7	to	to	ADP
app01-6375	90	8	the	the	DET
app01-6375	90	9	center	center	NOUN
app01-6375	90	10	line	line	NOUN
app01-6375	90	11	and	and	CCONJ
app01-6375	90	12	bernoulli	bernoulli	NOUN
app01-6375	90	13	theory	theory	NOUN
app01-6375	90	14	is	be	AUX
app01-6375	90	15	assumed	assume	VERB
app01-6375	90	16	,	,	PUNCT
app01-6375	90	17	the	the	DET
app01-6375	90	18	shear	shear	NOUN
app01-6375	90	19	forces	force	NOUN
app01-6375	90	20	s̃23	s̃23	NOUN
app01-6375	90	21	and	and	CCONJ
app01-6375	90	22	s̃32	s̃32	PROPN
app01-6375	90	23	and	and	CCONJ
app01-6375	90	24	normal	normal	ADJ
app01-6375	90	25	forces	force	NOUN
app01-6375	90	26	s̃22	s̃22	PUNCT
app01-6375	90	27	s̃33	s̃33	PRON
app01-6375	90	28	vanish	vanish	ADJ
app01-6375	90	29	and	and	CCONJ
app01-6375	90	30	the	the	DET
app01-6375	90	31	full	full	ADJ
app01-6375	90	32	constitutive	constitutive	ADJ
app01-6375	90	33	relation	relation	NOUN
app01-6375	90	34	can	can	AUX
app01-6375	90	35	be	be	AUX
app01-6375	90	36	reduced	reduce	VERB
app01-6375	90	37	to	to	PRON
app01-6375	90	38	s̃11	s̃11	NOUN
app01-6375	90	39	s̃12	s̃12	PUNCT
app01-6375	91	1	s̃13	s̃13	ADJ
app01-6375	91	2			NOUN
app01-6375	91	3	=	=	PUNCT
app01-6375	91	4			X
app01-6375	91	5	e	e	X
app01-6375	91	6	0	0	NUM
app01-6375	91	7	0	0	NUM
app01-6375	91	8	0	0	NUM
app01-6375	91	9	g	g	NOUN
app01-6375	91	10	0	0	NUM
app01-6375	91	11	0	0	NUM
app01-6375	91	12	0	0	NUM
app01-6375	91	13	g	g	NOUN
app01-6375	91	14			NOUN
app01-6375	91	15	︸	︸	ADP
app01-6375	91	16	︷︷	︷︷	NOUN
app01-6375	91	17	︸	︸	X
app01-6375	91	18	d	d	PART
app01-6375	91	19			PROPN
app01-6375	91	20	ẽ11	ẽ11	NOUN
app01-6375	91	21	ẽ12	ẽ12	NOUN
app01-6375	91	22	ẽ13	ẽ13	PROPN
app01-6375	91	23			NOUN
app01-6375	91	24	,	,	PUNCT
app01-6375	91	25	(	(	PUNCT
app01-6375	91	26	19	19	NUM
app01-6375	91	27	)	)	PUNCT
app01-6375	91	28	where	where	SCONJ
app01-6375	91	29	e	e	NOUN
app01-6375	91	30	is	be	AUX
app01-6375	91	31	young	young	ADJ
app01-6375	91	32	’s	’s	PART
app01-6375	91	33	modulus	modulus	NOUN
app01-6375	91	34	,	,	PUNCT
app01-6375	91	35	g	g	PROPN
app01-6375	91	36	is	be	AUX
app01-6375	91	37	the	the	DET
app01-6375	91	38	shear	shear	NOUN
app01-6375	91	39	modulus	modulus	NOUN
app01-6375	91	40	and	and	CCONJ
app01-6375	91	41	d	d	NOUN
app01-6375	91	42	is	be	AUX
app01-6375	91	43	a	a	DET
app01-6375	91	44	reduced	reduce	VERB
app01-6375	91	45	elasticity	elasticity	NOUN
app01-6375	91	46	matrix	matrix	NOUN
app01-6375	91	47	.	.	PUNCT
app01-6375	92	1	3.4	3.4	NUM
app01-6375	92	2	.	.	PUNCT
app01-6375	92	3	principle	principle	NOUN
app01-6375	92	4	of	of	ADP
app01-6375	92	5	virtual	virtual	ADJ
app01-6375	92	6	work	work	NOUN
app01-6375	92	7	the	the	DET
app01-6375	92	8	system	system	NOUN
app01-6375	92	9	is	be	AUX
app01-6375	92	10	in	in	ADP
app01-6375	92	11	equilibrium	equilibrium	NOUN
app01-6375	92	12	when	when	SCONJ
app01-6375	92	13	the	the	DET
app01-6375	92	14	overall	overall	ADJ
app01-6375	92	15	virtual	virtual	ADJ
app01-6375	92	16	work	work	NOUN
app01-6375	92	17	of	of	ADP
app01-6375	92	18	the	the	DET
app01-6375	92	19	system	system	NOUN
app01-6375	92	20	is	be	AUX
app01-6375	92	21	equal	equal	ADJ
app01-6375	92	22	to	to	ADP
app01-6375	92	23	zero	zero	NUM
app01-6375	92	24	δw	δw	NOUN
app01-6375	92	25	=	=	SYM
app01-6375	92	26	−δwint	−δwint	NOUN
app01-6375	93	1	+	+	CCONJ
app01-6375	93	2	δwext	δwext	NOUN
app01-6375	93	3	=	=	SYM
app01-6375	93	4	0	0	PROPN
app01-6375	93	5	.	.	PUNCT
app01-6375	94	1	(	(	PUNCT
app01-6375	94	2	20	20	NUM
app01-6375	94	3	)	)	PUNCT
app01-6375	94	4	the	the	DET
app01-6375	94	5	internal	internal	ADJ
app01-6375	94	6	end	end	NOUN
app01-6375	94	7	external	external	ADJ
app01-6375	94	8	virtual	virtual	ADJ
app01-6375	94	9	work	work	NOUN
app01-6375	94	10	of	of	ADP
app01-6375	94	11	the	the	DET
app01-6375	94	12	system	system	NOUN
app01-6375	94	13	is	be	AUX
app01-6375	94	14	given	give	VERB
app01-6375	94	15	by	by	ADP
app01-6375	94	16	δwint	δwint	NOUN
app01-6375	94	17	=	=	PUNCT
app01-6375	94	18	∫	∫	PROPN
app01-6375	94	19	ω	ω	PROPN
app01-6375	94	20	s	s	PART
app01-6375	94	21	:	:	PUNCT
app01-6375	94	22	δedx	δedx	PROPN
app01-6375	94	23	,	,	PUNCT
app01-6375	94	24	(	(	PUNCT
app01-6375	94	25	21	21	NUM
app01-6375	94	26	)	)	PUNCT
app01-6375	94	27	δwext	δwext	NOUN
app01-6375	94	28	=	=	SYM
app01-6375	94	29	∫	∫	PROPN
app01-6375	95	1	γn	γn	ADP
app01-6375	95	2	t	t	PROPN
app01-6375	95	3	:	:	PUNCT
app01-6375	95	4	δudx+	δudx+	X
app01-6375	95	5	∫	∫	PROPN
app01-6375	95	6	ω	ω	PROPN
app01-6375	95	7	ρ0b	ρ0b	NOUN
app01-6375	95	8	:	:	PUNCT
app01-6375	95	9	δudx	δudx	PROPN
app01-6375	95	10	,	,	PUNCT
app01-6375	95	11	(	(	PUNCT
app01-6375	95	12	22	22	NUM
app01-6375	95	13	)	)	PUNCT
app01-6375	95	14	where	where	SCONJ
app01-6375	95	15	ω	ω	NUM
app01-6375	95	16	and	and	CCONJ
app01-6375	95	17	γn	γn	NOUN
app01-6375	95	18	are	be	AUX
app01-6375	95	19	the	the	DET
app01-6375	95	20	domain	domain	NOUN
app01-6375	95	21	and	and	CCONJ
app01-6375	95	22	the	the	DET
app01-6375	95	23	neumann	neumann	PROPN
app01-6375	95	24	boundary	boundary	NOUN
app01-6375	95	25	,	,	PUNCT
app01-6375	95	26	respectively	respectively	ADV
app01-6375	95	27	.	.	PUNCT
app01-6375	96	1	the	the	DET
app01-6375	96	2	external	external	ADJ
app01-6375	96	3	virtual	virtual	ADJ
app01-6375	96	4	work	work	NOUN
app01-6375	96	5	depends	depend	VERB
app01-6375	96	6	on	on	ADP
app01-6375	96	7	the	the	DET
app01-6375	96	8	boundary	boundary	ADJ
app01-6375	96	9	forces	force	NOUN
app01-6375	96	10	t	t	PROPN
app01-6375	96	11	,	,	PUNCT
app01-6375	96	12	body	body	NOUN
app01-6375	96	13	forces	force	NOUN
app01-6375	96	14	b	b	NOUN
app01-6375	96	15	and	and	CCONJ
app01-6375	96	16	material	material	NOUN
app01-6375	96	17	density	density	NOUN
app01-6375	96	18	ρ0	ρ0	PROPN
app01-6375	96	19	.	.	PUNCT
app01-6375	97	1	by	by	ADP
app01-6375	97	2	substitution	substitution	NOUN
app01-6375	97	3	of	of	ADP
app01-6375	97	4	expressions	expression	NOUN
app01-6375	97	5	for	for	ADP
app01-6375	97	6	the	the	DET
app01-6375	97	7	virtual	virtual	ADJ
app01-6375	97	8	greenlagrange	greenlagrange	NOUN
app01-6375	97	9	strain	strain	NOUN
app01-6375	97	10	tensor	tensor	NOUN
app01-6375	97	11	obtained	obtain	VERB
app01-6375	97	12	from	from	ADP
app01-6375	97	13	(	(	PUNCT
app01-6375	97	14	15	15	NUM
app01-6375	97	15	)	)	PUNCT
app01-6375	97	16	,	,	PUNCT
app01-6375	97	17	constitutive	constitutive	ADJ
app01-6375	97	18	relations	relation	NOUN
app01-6375	97	19	(	(	PUNCT
app01-6375	97	20	19	19	NUM
app01-6375	97	21	)	)	PUNCT
app01-6375	97	22	and	and	CCONJ
app01-6375	97	23	performing	perform	VERB
app01-6375	97	24	linearization	linearization	NOUN
app01-6375	97	25	the	the	DET
app01-6375	97	26	following	follow	VERB
app01-6375	97	27	incremental	incremental	ADJ
app01-6375	97	28	relation	relation	NOUN
app01-6375	97	29	can	can	AUX
app01-6375	97	30	be	be	AUX
app01-6375	97	31	obtained	obtain	VERB
app01-6375	97	32	∑	∑	PROPN
app01-6375	97	33	s	s	PART
app01-6375	97	34	krs∆us	krs∆us	PROPN
app01-6375	97	35	=	=	SYM
app01-6375	97	36	−rr	−rr	PROPN
app01-6375	97	37	,	,	PUNCT
app01-6375	97	38	(	(	PUNCT
app01-6375	97	39	23	23	NUM
app01-6375	97	40	)	)	PUNCT
app01-6375	97	41	where	where	SCONJ
app01-6375	97	42	∆us	∆u	NOUN
app01-6375	97	43	are	be	AUX
app01-6375	97	44	the	the	DET
app01-6375	97	45	displacement	displacement	ADJ
app01-6375	97	46	increments	increment	NOUN
app01-6375	97	47	and	and	CCONJ
app01-6375	97	48	rr	rr	NOUN
app01-6375	97	49	=	=	SYM
app01-6375	97	50	−(f	−(f	PROPN
app01-6375	97	51	intr	intr	VERB
app01-6375	97	52	+	+	CCONJ
app01-6375	97	53	f	f	PROPN
app01-6375	97	54	extr	extr	PROPN
app01-6375	97	55	)	)	PUNCT
app01-6375	97	56	(	(	PUNCT
app01-6375	97	57	24	24	NUM
app01-6375	97	58	)	)	PUNCT
app01-6375	97	59	=	=	PRON
app01-6375	97	60	∂wint	∂wint	NUM
app01-6375	97	61	∂ur	∂ur	PROPN
app01-6375	97	62	+	+	CCONJ
app01-6375	97	63	∂wext	∂wext	PROPN
app01-6375	97	64	∂ur	∂ur	PROPN
app01-6375	97	65	,	,	PUNCT
app01-6375	97	66	(	(	PUNCT
app01-6375	97	67	25	25	NUM
app01-6375	97	68	)	)	PUNCT
app01-6375	97	69	krs	krs	NOUN
app01-6375	97	70	=	=	PUNCT
app01-6375	98	1	∂rr	∂rr	PROPN
app01-6375	98	2	∂us	∂us	NOUN
app01-6375	98	3	=	=	SYM
app01-6375	98	4	∂2wint	∂2wint	NOUN
app01-6375	98	5	∂ur∂us	∂ur∂us	NOUN
app01-6375	98	6	.	.	PUNCT
app01-6375	99	1	(	(	PUNCT
app01-6375	99	2	26	26	NUM
app01-6375	99	3	)	)	PUNCT
app01-6375	99	4	4	4	NUM
app01-6375	99	5	.	.	PUNCT
app01-6375	99	6	numerical	numerical	PROPN
app01-6375	99	7	example	example	NOUN
app01-6375	100	1	the	the	DET
app01-6375	100	2	described	describe	VERB
app01-6375	100	3	beam	beam	NOUN
app01-6375	100	4	element	element	NOUN
app01-6375	100	5	has	have	AUX
app01-6375	100	6	been	be	AUX
app01-6375	100	7	implemented	implement	VERB
app01-6375	100	8	and	and	CCONJ
app01-6375	100	9	tested	test	VERB
app01-6375	100	10	on	on	ADP
app01-6375	100	11	the	the	DET
app01-6375	100	12	example	example	NOUN
app01-6375	100	13	of	of	ADP
app01-6375	100	14	helicoidal	helicoidal	ADJ
app01-6375	100	15	spring	spring	NOUN
app01-6375	100	16	(	(	PUNCT
app01-6375	100	17	see	see	VERB
app01-6375	100	18	figure	figure	NOUN
app01-6375	100	19	4	4	NUM
app01-6375	100	20	)	)	PUNCT
app01-6375	100	21	.	.	PUNCT
app01-6375	101	1	this	this	DET
app01-6375	101	2	problem	problem	NOUN
app01-6375	101	3	represents	represent	VERB
app01-6375	101	4	fully	fully	ADV
app01-6375	101	5	threedimensional	threedimensional	ADJ
app01-6375	101	6	structure	structure	NOUN
app01-6375	101	7	where	where	SCONJ
app01-6375	101	8	the	the	DET
app01-6375	101	9	all	all	DET
app01-6375	101	10	membrane	membrane	NOUN
app01-6375	101	11	,	,	PUNCT
app01-6375	101	12	bending	bending	NOUN
app01-6375	101	13	and	and	CCONJ
app01-6375	101	14	torsion	torsion	NOUN
app01-6375	101	15	effects	effect	NOUN
app01-6375	101	16	are	be	AUX
app01-6375	101	17	present	present	ADJ
app01-6375	101	18	.	.	PUNCT
app01-6375	102	1	the	the	DET
app01-6375	102	2	geometry	geometry	NOUN
app01-6375	102	3	is	be	AUX
app01-6375	102	4	f	f	NOUN
app01-6375	102	5	=	=	SYM
app01-6375	102	6	1	1	NUM
app01-6375	102	7	t	t	NOUN
app01-6375	102	8	t	t	X
app01-6375	102	9	e	e	X
app01-6375	102	10	=	=	SYM
app01-6375	102	11	108	108	NUM
app01-6375	102	12	ν	ν	X
app01-6375	102	13	=	=	SYM
app01-6375	102	14	0.0	0.0	NUM
app01-6375	102	15	figure	figure	NOUN
app01-6375	102	16	4	4	NUM
app01-6375	102	17	.	.	NOUN
app01-6375	102	18	helicoidal	helicoidal	ADJ
app01-6375	102	19	spring	spring	NOUN
app01-6375	102	20	cantilever	cantilever	NOUN
app01-6375	102	21	subjected	subject	VERB
app01-6375	102	22	to	to	ADP
app01-6375	102	23	the	the	DET
app01-6375	102	24	unit	unit	NOUN
app01-6375	102	25	force	force	NOUN
app01-6375	102	26	tip	tip	NOUN
app01-6375	102	27	load	load	NOUN
app01-6375	102	28	and	and	CCONJ
app01-6375	102	29	its	its	PRON
app01-6375	102	30	cross	cross	NOUN
app01-6375	102	31	-	-	NOUN
app01-6375	102	32	section	section	NOUN
app01-6375	102	33	.	.	PUNCT
app01-6375	103	1	figure	figure	NOUN
app01-6375	103	2	5	5	NUM
app01-6375	103	3	.	.	PUNCT
app01-6375	103	4	helicoidal	helicoidal	ADJ
app01-6375	103	5	spring	spring	NOUN
app01-6375	103	6	geometry	geometry	NOUN
app01-6375	103	7	for	for	ADP
app01-6375	103	8	different	different	ADJ
app01-6375	103	9	thickness	thickness	NOUN
app01-6375	103	10	/	/	SYM
app01-6375	103	11	length	length	NOUN
app01-6375	103	12	ratios	ratio	NOUN
app01-6375	103	13	:	:	PUNCT
app01-6375	103	14	0.1	0.1	NUM
app01-6375	103	15	,	,	PUNCT
app01-6375	103	16	0.05	0.05	NUM
app01-6375	103	17	,	,	PUNCT
app01-6375	103	18	0.025	0.025	NUM
app01-6375	103	19	,	,	PUNCT
app01-6375	103	20	0.0125	0.0125	NUM
app01-6375	103	21	.	.	PUNCT
app01-6375	104	1	given	give	VERB
app01-6375	104	2	by	by	ADP
app01-6375	104	3	xc(θ1	xc(θ1	PUNCT
app01-6375	104	4	)	)	PUNCT
app01-6375	105	1	=	=	PUNCT
app01-6375	105	2			NOUN
app01-6375	105	3	10	10	NUM
app01-6375	105	4	sin	sin	NOUN
app01-6375	105	5	(	(	PUNCT
app01-6375	105	6	θ12π	θ12π	NOUN
app01-6375	105	7	)	)	PUNCT
app01-6375	105	8	10	10	NUM
app01-6375	105	9	cos	cos	PROPN
app01-6375	105	10	(	(	PUNCT
app01-6375	105	11	θ12π	θ12π	PROPN
app01-6375	105	12	)	)	PUNCT
app01-6375	105	13	20	20	NUM
app01-6375	105	14	θ1	θ1	NOUN
app01-6375	105	15			NOUN
app01-6375	105	16	.	.	PUNCT
app01-6375	106	1	(	(	PUNCT
app01-6375	106	2	27	27	NUM
app01-6375	106	3	)	)	PUNCT
app01-6375	106	4	the	the	DET
app01-6375	106	5	structure	structure	NOUN
app01-6375	106	6	is	be	AUX
app01-6375	106	7	subjected	subject	VERB
app01-6375	106	8	to	to	ADP
app01-6375	106	9	the	the	DET
app01-6375	106	10	unit	unit	NOUN
app01-6375	106	11	tip	tip	PROPN
app01-6375	106	12	force	force	NOUN
app01-6375	106	13	load	load	NOUN
app01-6375	106	14	.	.	PUNCT
app01-6375	107	1	different	different	ADJ
app01-6375	107	2	dimensions	dimension	NOUN
app01-6375	107	3	of	of	ADP
app01-6375	107	4	the	the	DET
app01-6375	107	5	square	square	ADJ
app01-6375	107	6	cross	cross	NOUN
app01-6375	107	7	-	-	NOUN
app01-6375	107	8	section	section	NOUN
app01-6375	107	9	have	have	AUX
app01-6375	107	10	been	be	AUX
app01-6375	107	11	used	use	VERB
app01-6375	107	12	in	in	ADP
app01-6375	107	13	the	the	DET
app01-6375	107	14	analysis	analysis	NOUN
app01-6375	107	15	,	,	PUNCT
app01-6375	107	16	in	in	ADP
app01-6375	107	17	order	order	NOUN
app01-6375	107	18	to	to	PART
app01-6375	107	19	evaluate	evaluate	VERB
app01-6375	107	20	the	the	DET
app01-6375	107	21	performance	performance	NOUN
app01-6375	107	22	and	and	CCONJ
app01-6375	107	23	the	the	DET
app01-6375	107	24	applicability	applicability	NOUN
app01-6375	107	25	of	of	ADP
app01-6375	107	26	the	the	DET
app01-6375	107	27	underlying	underlie	VERB
app01-6375	107	28	assumptions	assumption	NOUN
app01-6375	107	29	.	.	PUNCT
app01-6375	108	1	the	the	DET
app01-6375	108	2	studied	study	VERB
app01-6375	108	3	geometries	geometry	NOUN
app01-6375	108	4	can	can	AUX
app01-6375	108	5	be	be	AUX
app01-6375	108	6	observed	observe	VERB
app01-6375	108	7	in	in	ADP
app01-6375	108	8	figure	figure	NOUN
app01-6375	108	9	5	5	NUM
app01-6375	108	10	,	,	PUNCT
app01-6375	108	11	where	where	SCONJ
app01-6375	108	12	helicoidal	helicoidal	ADJ
app01-6375	108	13	springs	spring	NOUN
app01-6375	108	14	with	with	ADP
app01-6375	108	15	different	different	ADJ
app01-6375	108	16	thickness	thickness	NOUN
app01-6375	108	17	/	/	SYM
app01-6375	108	18	length	length	NOUN
app01-6375	108	19	(	(	PUNCT
app01-6375	108	20	t	t	PROPN
app01-6375	108	21	/	/	SYM
app01-6375	108	22	l	l	NOUN
app01-6375	108	23	)	)	PUNCT
app01-6375	108	24	ratios	ratio	NOUN
app01-6375	108	25	(	(	PUNCT
app01-6375	108	26	0.1	0.1	NUM
app01-6375	108	27	,	,	PUNCT
app01-6375	108	28	0.05	0.05	NUM
app01-6375	108	29	,	,	PUNCT
app01-6375	108	30	0.025	0.025	NUM
app01-6375	108	31	and	and	CCONJ
app01-6375	108	32	0.0125	0.0125	NUM
app01-6375	108	33	)	)	PUNCT
app01-6375	108	34	are	be	AUX
app01-6375	108	35	illustrated	illustrate	VERB
app01-6375	108	36	.	.	PUNCT
app01-6375	109	1	the	the	DET
app01-6375	109	2	results	result	NOUN
app01-6375	109	3	have	have	AUX
app01-6375	109	4	been	be	AUX
app01-6375	109	5	compared	compare	VERB
app01-6375	109	6	with	with	ADP
app01-6375	109	7	results	result	NOUN
app01-6375	109	8	obtained	obtain	VERB
app01-6375	109	9	using	use	VERB
app01-6375	109	10	standard	standard	ADJ
app01-6375	109	11	fem	fem	NOUN
app01-6375	109	12	straight	straight	ADJ
app01-6375	109	13	beam	beam	NOUN
app01-6375	109	14	element	element	NOUN
app01-6375	109	15	with	with	ADP
app01-6375	109	16	cubic	cubic	ADJ
app01-6375	109	17	approximation	approximation	NOUN
app01-6375	109	18	[	[	X
app01-6375	109	19	6	6	NUM
app01-6375	109	20	]	]	PUNCT
app01-6375	109	21	.	.	PUNCT
app01-6375	110	1	this	this	DET
app01-6375	110	2	element	element	NOUN
app01-6375	110	3	allows	allow	VERB
app01-6375	110	4	for	for	ADP
app01-6375	110	5	the	the	DET
app01-6375	110	6	analysis	analysis	NOUN
app01-6375	110	7	of	of	ADP
app01-6375	110	8	both	both	CCONJ
app01-6375	110	9	thick	thick	ADJ
app01-6375	110	10	and	and	CCONJ
app01-6375	110	11	thin	thin	ADJ
app01-6375	110	12	beams	beam	NOUN
app01-6375	110	13	and	and	CCONJ
app01-6375	110	14	is	be	AUX
app01-6375	110	15	naturally	naturally	ADV
app01-6375	110	16	locking	locking	NOUN
app01-6375	110	17	-	-	PUNCT
app01-6375	110	18	free	free	ADJ
app01-6375	110	19	.	.	PUNCT
app01-6375	111	1	the	the	DET
app01-6375	111	2	beam	beam	NOUN
app01-6375	111	3	has	have	AUX
app01-6375	111	4	been	be	AUX
app01-6375	111	5	used	use	VERB
app01-6375	111	6	in	in	ADP
app01-6375	111	7	two	two	NUM
app01-6375	111	8	different	different	ADJ
app01-6375	111	9	configurations	configuration	NOUN
app01-6375	111	10	:	:	PUNCT
app01-6375	112	1	i	i	X
app01-6375	112	2	)	)	PUNCT
app01-6375	112	3	the	the	DET
app01-6375	112	4	element	element	NOUN
app01-6375	112	5	satisfying	satisfy	VERB
app01-6375	112	6	bernoulli	bernoulli	PROPN
app01-6375	112	7	assumptions	assumption	NOUN
app01-6375	112	8	;	;	PUNCT
app01-6375	112	9	ii	ii	X
app01-6375	112	10	)	)	PUNCT
app01-6375	112	11	the	the	DET
app01-6375	112	12	element	element	NOUN
app01-6375	112	13	accounting	accounting	NOUN
app01-6375	112	14	also	also	ADV
app01-6375	112	15	for	for	ADP
app01-6375	112	16	the	the	DET
app01-6375	112	17	shear	shear	NOUN
app01-6375	112	18	effects	effect	NOUN
app01-6375	112	19	.	.	PUNCT
app01-6375	113	1	the	the	DET
app01-6375	113	2	results	result	NOUN
app01-6375	113	3	can	can	AUX
app01-6375	113	4	be	be	AUX
app01-6375	113	5	observed	observe	VERB
app01-6375	113	6	in	in	ADP
app01-6375	113	7	the	the	DET
app01-6375	113	8	figure	figure	NOUN
app01-6375	113	9	6	6	NUM
app01-6375	113	10	.	.	PUNCT
app01-6375	113	11	as	as	SCONJ
app01-6375	113	12	expected	expect	VERB
app01-6375	113	13	,	,	PUNCT
app01-6375	113	14	for	for	ADP
app01-6375	113	15	the	the	DET
app01-6375	113	16	thick	thick	ADJ
app01-6375	113	17	beam	beam	NOUN
app01-6375	113	18	configuration	configuration	NOUN
app01-6375	113	19	the	the	DET
app01-6375	113	20	results	result	NOUN
app01-6375	113	21	obtained	obtain	VERB
app01-6375	113	22	using	use	VERB
app01-6375	113	23	classical	classical	ADJ
app01-6375	113	24	fem	fem	NOUN
app01-6375	113	25	or	or	CCONJ
app01-6375	113	26	iga	iga	PROPN
app01-6375	113	27	elements	element	NOUN
app01-6375	113	28	with	with	ADP
app01-6375	113	29	bernoulli	bernoulli	PROPN
app01-6375	113	30	assumptions	assumption	NOUN
app01-6375	113	31	differ	differ	VERB
app01-6375	113	32	from	from	ADP
app01-6375	113	33	the	the	DET
app01-6375	113	34	standard	standard	ADJ
app01-6375	113	35	fem	fem	NOUN
app01-6375	113	36	beam	beam	PROPN
app01-6375	113	37	element	element	NOUN
app01-6375	113	38	with	with	ADP
app01-6375	113	39	account	account	NOUN
app01-6375	113	40	for	for	ADP
app01-6375	113	41	the	the	DET
app01-6375	113	42	shear	shear	NOUN
app01-6375	113	43	deforma27	deforma27	PROPN
app01-6375	113	44	edita	edita	PROPN
app01-6375	113	45	dvořáková	dvořáková	PROPN
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app01-6375	113	47	bořek	bořek	PROPN
app01-6375	113	48	patzák	patzák	VERB
app01-6375	113	49	acta	acta	PROPN
app01-6375	113	50	polytechnica	polytechnica	PROPN
app01-6375	113	51	ctu	ctu	NOUN
app01-6375	113	52	proceedings	proceeding	NOUN
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app01-6375	113	54	-1.00e-06	-1.00e-06	PROPN
app01-6375	113	55	-9.90e-07	-9.90e-07	ADJ
app01-6375	113	56	-9.80e-07	-9.80e-07	NOUN
app01-6375	113	57	-9.70e-07	-9.70e-07	NOUN
app01-6375	113	58	-9.60e-07	-9.60e-07	NOUN
app01-6375	113	59	-9.50e-07	-9.50e-07	NOUN
app01-6375	113	60	-9.40e-07	-9.40e-07	ADJ
app01-6375	113	61	-9.30e-07	-9.30e-07	ADJ
app01-6375	113	62	-9.20e-07	-9.20e-07	NOUN
app01-6375	113	63	-9.10e-07	-9.10e-07	ADJ
app01-6375	113	64	10	10	NUM
app01-6375	113	65	15	15	NUM
app01-6375	113	66	20	20	NUM
app01-6375	113	67	25	25	NUM
app01-6375	113	68	30	30	NUM
app01-6375	113	69	35	35	NUM
app01-6375	113	70	40	40	NUM
app01-6375	113	71	45	45	NUM
app01-6375	113	72	t	t	PROPN
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app01-6375	113	74	l	l	NOUN
app01-6375	113	75	=	=	SYM
app01-6375	114	1	0.1	0.1	NUM
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app01-6375	114	10	10	10	NUM
app01-6375	114	11	15	15	NUM
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app01-6375	114	13	25	25	NUM
app01-6375	114	14	30	30	NUM
app01-6375	114	15	35	35	NUM
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app01-6375	114	18	t	t	PROPN
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app01-6375	114	20	l	l	NOUN
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app01-6375	114	23	-2.55e-04	-2.55e-04	CCONJ
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app01-6375	115	2	15	15	NUM
app01-6375	115	3	20	20	NUM
app01-6375	115	4	25	25	NUM
app01-6375	115	5	30	30	NUM
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app01-6375	115	11	l	l	NOUN
app01-6375	115	12	=	=	PUNCT
app01-6375	115	13	0.025	0.025	NUM
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app01-6375	115	17	-3.90e-03	-3.90e-03	PROPN
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app01-6375	116	1	10	10	NUM
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app01-6375	116	4	25	25	NUM
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app01-6375	116	6	35	35	NUM
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app01-6375	116	12	=	=	SYM
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app01-6375	116	18	iga	iga	PROPN
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app01-6375	116	20	fem	fem	PROPN
app01-6375	116	21	thin	thin	PROPN
app01-6375	116	22	fem	fem	PROPN
app01-6375	116	23	shear	shear	NOUN
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app01-6375	116	26	-9.90e-07	-9.90e-07	ADJ
app01-6375	116	27	-9.80e-07	-9.80e-07	NOUN
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app01-6375	116	32	-9.30e-07	-9.30e-07	ADJ
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app01-6375	116	35	10	10	NUM
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app01-6375	116	38	25	25	NUM
app01-6375	116	39	30	30	NUM
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app01-6375	116	41	40	40	NUM
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app01-6375	116	46	=	=	SYM
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app01-6375	117	2	10	10	NUM
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app01-6375	118	2	15	15	NUM
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app01-6375	118	4	25	25	NUM
app01-6375	118	5	30	30	NUM
app01-6375	118	6	35	35	NUM
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app01-6375	118	12	=	=	PUNCT
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app01-6375	118	16	-3.95e-03	-3.95e-03	PROPN
app01-6375	118	17	-3.90e-03	-3.90e-03	PROPN
app01-6375	118	18	-3.85e-03	-3.85e-03	PROPN
app01-6375	118	19	-3.80e-03	-3.80e-03	PROPN
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app01-6375	119	1	10	10	NUM
app01-6375	119	2	15	15	NUM
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app01-6375	119	4	25	25	NUM
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app01-6375	119	12	=	=	SYM
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app01-6375	120	2	10	10	NUM
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app01-6375	122	45	=	=	NOUN
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app01-6375	122	49	hexic	hexic	ADV
app01-6375	122	50	(	(	PUNCT
app01-6375	122	51	iga	iga	PROPN
app01-6375	122	52	p	p	NOUN
app01-6375	122	53	=	=	NOUN
app01-6375	122	54	6	6	NUM
app01-6375	122	55	)	)	PUNCT
app01-6375	122	56	approximation	approximation	NOUN
app01-6375	122	57	with	with	ADP
app01-6375	122	58	standard	standard	ADJ
app01-6375	122	59	fem	fem	NOUN
app01-6375	122	60	straight	straight	ADJ
app01-6375	122	61	beam	beam	NOUN
app01-6375	122	62	element	element	NOUN
app01-6375	122	63	with	with	ADP
app01-6375	122	64	bernoulli	bernoulli	PROPN
app01-6375	122	65	assumptions	assumption	NOUN
app01-6375	122	66	(	(	PUNCT
app01-6375	122	67	fem	fem	NOUN
app01-6375	122	68	thin	thin	ADJ
app01-6375	122	69	)	)	PUNCT
app01-6375	122	70	and	and	CCONJ
app01-6375	122	71	with	with	ADP
app01-6375	122	72	account	account	NOUN
app01-6375	122	73	for	for	ADP
app01-6375	122	74	shear	shear	NOUN
app01-6375	122	75	effects	effect	NOUN
app01-6375	122	76	(	(	PUNCT
app01-6375	122	77	fem	fem	NOUN
app01-6375	122	78	shear	shear	NOUN
app01-6375	122	79	)	)	PUNCT
app01-6375	122	80	.	.	PUNCT
app01-6375	123	1	the	the	DET
app01-6375	123	2	vertical	vertical	ADJ
app01-6375	123	3	axis	axis	NOUN
app01-6375	123	4	corresponds	correspond	VERB
app01-6375	123	5	to	to	ADP
app01-6375	123	6	the	the	DET
app01-6375	123	7	vertical	vertical	ADJ
app01-6375	123	8	tip	tip	PROPN
app01-6375	123	9	displacement	displacement	PROPN
app01-6375	123	10	w	w	PROPN
app01-6375	123	11	,	,	PUNCT
app01-6375	123	12	the	the	DET
app01-6375	123	13	horizontal	horizontal	ADJ
app01-6375	123	14	axis	axis	NOUN
app01-6375	123	15	corresponds	correspond	VERB
app01-6375	123	16	to	to	ADP
app01-6375	123	17	the	the	DET
app01-6375	123	18	number	number	NOUN
app01-6375	123	19	of	of	ADP
app01-6375	123	20	nodes	node	NOUN
app01-6375	123	21	(	(	PUNCT
app01-6375	123	22	control	control	NOUN
app01-6375	123	23	points	point	NOUN
app01-6375	123	24	)	)	PUNCT
app01-6375	123	25	.	.	PUNCT
app01-6375	124	1	tion	tion	NOUN
app01-6375	124	2	.	.	PUNCT
app01-6375	125	1	this	this	DET
app01-6375	125	2	difference	difference	NOUN
app01-6375	125	3	is	be	AUX
app01-6375	125	4	diminishing	diminish	VERB
app01-6375	125	5	with	with	ADP
app01-6375	125	6	the	the	DET
app01-6375	125	7	smaller	small	ADJ
app01-6375	125	8	thickness	thickness	NOUN
app01-6375	125	9	/	/	SYM
app01-6375	125	10	length	length	NOUN
app01-6375	125	11	ratio	ratio	NOUN
app01-6375	125	12	.	.	PUNCT
app01-6375	126	1	in	in	ADP
app01-6375	126	2	addition	addition	NOUN
app01-6375	126	3	to	to	ADP
app01-6375	126	4	the	the	DET
app01-6375	126	5	beam	beam	NOUN
app01-6375	126	6	elements	element	NOUN
app01-6375	126	7	,	,	PUNCT
app01-6375	126	8	the	the	DET
app01-6375	126	9	fully	fully	ADV
app01-6375	126	10	threedimensional	threedimensional	ADJ
app01-6375	126	11	analysis	analysis	NOUN
app01-6375	126	12	has	have	AUX
app01-6375	126	13	been	be	AUX
app01-6375	126	14	assessed	assess	VERB
app01-6375	126	15	.	.	PUNCT
app01-6375	127	1	the	the	DET
app01-6375	127	2	enormous	enormous	ADJ
app01-6375	127	3	number	number	NOUN
app01-6375	127	4	of	of	ADP
app01-6375	127	5	nodes	node	NOUN
app01-6375	127	6	,	,	PUNCT
app01-6375	127	7	in	in	ADP
app01-6375	127	8	comparison	comparison	NOUN
app01-6375	127	9	with	with	ADP
app01-6375	127	10	beam	beam	NOUN
app01-6375	127	11	elements	element	NOUN
app01-6375	127	12	,	,	PUNCT
app01-6375	127	13	have	have	VERB
app01-6375	127	14	to	to	PART
app01-6375	127	15	be	be	AUX
app01-6375	127	16	used	use	VERB
app01-6375	127	17	in	in	ADP
app01-6375	127	18	order	order	NOUN
app01-6375	127	19	to	to	PART
app01-6375	127	20	obtain	obtain	VERB
app01-6375	127	21	sufficiently	sufficiently	ADV
app01-6375	127	22	accurate	accurate	ADJ
app01-6375	127	23	results	result	NOUN
app01-6375	127	24	.	.	PUNCT
app01-6375	128	1	finally	finally	ADV
app01-6375	128	2	,	,	PUNCT
app01-6375	128	3	the	the	DET
app01-6375	128	4	mesh	mesh	NOUN
app01-6375	128	5	consisting	consist	VERB
app01-6375	128	6	of	of	ADP
app01-6375	128	7	102800	102800	NUM
app01-6375	128	8	nodes	node	NOUN
app01-6375	128	9	(	(	PUNCT
app01-6375	128	10	20×	20×	NUM
app01-6375	128	11	20×	20×	NUM
app01-6375	128	12	257	257	NUM
app01-6375	128	13	)	)	PUNCT
app01-6375	128	14	has	have	AUX
app01-6375	128	15	been	be	AUX
app01-6375	128	16	used	use	VERB
app01-6375	128	17	.	.	PUNCT
app01-6375	129	1	for	for	ADP
app01-6375	129	2	the	the	DET
app01-6375	129	3	thin	thin	ADJ
app01-6375	129	4	beam	beam	NOUN
app01-6375	129	5	with	with	ADP
app01-6375	129	6	t	t	PROPN
app01-6375	129	7	/	/	SYM
app01-6375	129	8	l	l	NOUN
app01-6375	129	9	=	=	SYM
app01-6375	129	10	0.0125	0.0125	NUM
app01-6375	129	11	,	,	PUNCT
app01-6375	129	12	the	the	DET
app01-6375	129	13	obtained	obtain	VERB
app01-6375	129	14	deflection	deflection	NOUN
app01-6375	129	15	is	be	AUX
app01-6375	129	16	w	w	NOUN
app01-6375	129	17	=	=	NOUN
app01-6375	129	18	−3.877e−3	−3.877e−3	NOUN
app01-6375	129	19	.	.	PUNCT
app01-6375	130	1	this	this	DET
app01-6375	130	2	result	result	NOUN
app01-6375	130	3	is	be	AUX
app01-6375	130	4	slightly	slightly	ADV
app01-6375	130	5	higher	high	ADJ
app01-6375	130	6	than	than	ADP
app01-6375	130	7	the	the	DET
app01-6375	130	8	results	result	NOUN
app01-6375	130	9	obtained	obtain	VERB
app01-6375	130	10	using	use	VERB
app01-6375	130	11	beam	beam	NOUN
app01-6375	130	12	assumptions	assumption	NOUN
app01-6375	130	13	.	.	PUNCT
app01-6375	131	1	the	the	DET
app01-6375	131	2	difference	difference	NOUN
app01-6375	131	3	between	between	ADP
app01-6375	131	4	the	the	DET
app01-6375	131	5	full	full	ADJ
app01-6375	131	6	3d	3d	NOUN
app01-6375	131	7	and	and	CCONJ
app01-6375	131	8	beam	beam	NOUN
app01-6375	131	9	models	model	NOUN
app01-6375	131	10	is	be	AUX
app01-6375	131	11	getting	get	VERB
app01-6375	131	12	bigger	big	ADJ
app01-6375	131	13	as	as	ADP
app01-6375	131	14	the	the	DET
app01-6375	131	15	height	height	NOUN
app01-6375	131	16	to	to	PART
app01-6375	131	17	length	length	VERB
app01-6375	131	18	ratio	ratio	NOUN
app01-6375	131	19	increases	increase	NOUN
app01-6375	131	20	.	.	PUNCT
app01-6375	132	1	this	this	DET
app01-6375	132	2	difference	difference	NOUN
app01-6375	132	3	is	be	AUX
app01-6375	132	4	indicating	indicate	VERB
app01-6375	132	5	,	,	PUNCT
app01-6375	132	6	that	that	SCONJ
app01-6375	132	7	the	the	DET
app01-6375	132	8	beam	beam	NOUN
app01-6375	132	9	theory	theory	NOUN
app01-6375	132	10	assumptions	assumption	NOUN
app01-6375	132	11	are	be	AUX
app01-6375	132	12	no	no	ADV
app01-6375	132	13	longer	long	ADV
app01-6375	132	14	adequate	adequate	ADJ
app01-6375	132	15	.	.	PUNCT
app01-6375	133	1	overall	overall	ADV
app01-6375	133	2	,	,	PUNCT
app01-6375	133	3	the	the	DET
app01-6375	133	4	results	result	NOUN
app01-6375	133	5	demonstrate	demonstrate	VERB
app01-6375	133	6	the	the	DET
app01-6375	133	7	superior	superior	ADJ
app01-6375	133	8	convergence	convergence	NOUN
app01-6375	133	9	properties	property	NOUN
app01-6375	133	10	of	of	ADP
app01-6375	133	11	the	the	DET
app01-6375	133	12	iga	iga	PROPN
app01-6375	133	13	element	element	NOUN
app01-6375	133	14	.	.	PUNCT
app01-6375	134	1	this	this	PRON
app01-6375	134	2	is	be	AUX
app01-6375	134	3	due	due	ADJ
app01-6375	134	4	to	to	ADP
app01-6375	134	5	its	its	PRON
app01-6375	134	6	ability	ability	NOUN
app01-6375	134	7	to	to	PART
app01-6375	134	8	capture	capture	VERB
app01-6375	134	9	curved	curved	ADJ
app01-6375	134	10	geometry	geometry	NOUN
app01-6375	134	11	and	and	CCONJ
app01-6375	134	12	natural	natural	ADJ
app01-6375	134	13	high	high	ADJ
app01-6375	134	14	-	-	PUNCT
app01-6375	134	15	order	order	NOUN
app01-6375	134	16	interpolation	interpolation	NOUN
app01-6375	134	17	.	.	PUNCT
app01-6375	135	1	5	5	X
app01-6375	135	2	.	.	X
app01-6375	135	3	conclusions	conclusion	NOUN
app01-6375	135	4	the	the	DET
app01-6375	135	5	spatial	spatial	ADJ
app01-6375	135	6	isogeometric	isogeometric	ADJ
app01-6375	135	7	element	element	NOUN
app01-6375	135	8	based	base	VERB
app01-6375	135	9	on	on	ADP
app01-6375	135	10	the	the	DET
app01-6375	135	11	work	work	NOUN
app01-6375	135	12	of	of	ADP
app01-6375	135	13	a.	a.	PROPN
app01-6375	135	14	m.	m.	PROPN
app01-6375	135	15	bauer	bauer	PROPN
app01-6375	135	16	et	et	PROPN
app01-6375	135	17	al	al	PROPN
app01-6375	135	18	.	.	PUNCT
app01-6375	136	1	[	[	X
app01-6375	136	2	1	1	X
app01-6375	136	3	]	]	PUNCT
app01-6375	136	4	has	have	AUX
app01-6375	136	5	been	be	AUX
app01-6375	136	6	implemented	implement	VERB
app01-6375	136	7	and	and	CCONJ
app01-6375	136	8	its	its	PRON
app01-6375	136	9	convergence	convergence	NOUN
app01-6375	136	10	properties	property	NOUN
app01-6375	136	11	have	have	AUX
app01-6375	136	12	been	be	AUX
app01-6375	136	13	evaluated	evaluate	VERB
app01-6375	136	14	in	in	ADP
app01-6375	136	15	this	this	DET
app01-6375	136	16	contribution	contribution	NOUN
app01-6375	136	17	.	.	PUNCT
app01-6375	137	1	the	the	DET
app01-6375	137	2	element	element	NOUN
app01-6375	137	3	formulation	formulation	NOUN
app01-6375	137	4	is	be	AUX
app01-6375	137	5	geometrically	geometrically	ADV
app01-6375	137	6	nonlinear	nonlinear	ADJ
app01-6375	137	7	,	,	PUNCT
app01-6375	137	8	however	however	ADV
app01-6375	137	9	only	only	ADV
app01-6375	137	10	the	the	DET
app01-6375	137	11	geometrically	geometrically	ADV
app01-6375	137	12	linear	linear	ADJ
app01-6375	137	13	analysis	analysis	NOUN
app01-6375	137	14	has	have	AUX
app01-6375	137	15	been	be	AUX
app01-6375	137	16	considered	consider	VERB
app01-6375	137	17	in	in	ADP
app01-6375	137	18	this	this	DET
app01-6375	137	19	paper	paper	NOUN
app01-6375	137	20	.	.	PUNCT
app01-6375	138	1	the	the	DET
app01-6375	138	2	performance	performance	NOUN
app01-6375	138	3	of	of	ADP
app01-6375	138	4	the	the	DET
app01-6375	138	5	presented	present	VERB
app01-6375	138	6	element	element	NOUN
app01-6375	138	7	has	have	AUX
app01-6375	138	8	been	be	AUX
app01-6375	138	9	compared	compare	VERB
app01-6375	138	10	with	with	ADP
app01-6375	138	11	standard	standard	ADJ
app01-6375	138	12	fem	fem	NOUN
app01-6375	138	13	beam	beam	NOUN
app01-6375	138	14	element	element	NOUN
app01-6375	138	15	using	use	VERB
app01-6375	138	16	benchmark	benchmark	NOUN
app01-6375	138	17	problem	problem	NOUN
app01-6375	138	18	of	of	ADP
app01-6375	138	19	helicoidal	helicoidal	ADJ
app01-6375	138	20	spring	spring	NOUN
app01-6375	138	21	.	.	PUNCT
app01-6375	139	1	for	for	ADP
app01-6375	139	2	the	the	DET
app01-6375	139	3	higher	high	ADJ
app01-6375	139	4	thickness	thickness	NOUN
app01-6375	139	5	/	/	SYM
app01-6375	139	6	length	length	NOUN
app01-6375	139	7	ratios	ratio	NOUN
app01-6375	139	8	t	t	PROPN
app01-6375	139	9	/	/	SYM
app01-6375	139	10	l	l	NOUN
app01-6375	139	11	=	=	SYM
app01-6375	139	12	0.1	0.1	NUM
app01-6375	139	13	,	,	PUNCT
app01-6375	139	14	0.5	0.5	NUM
app01-6375	139	15	the	the	DET
app01-6375	139	16	element	element	NOUN
app01-6375	139	17	does	do	AUX
app01-6375	139	18	not	not	PART
app01-6375	139	19	provide	provide	VERB
app01-6375	139	20	good	good	ADJ
app01-6375	139	21	results	result	NOUN
app01-6375	139	22	due	due	ADP
app01-6375	139	23	to	to	ADP
app01-6375	139	24	the	the	DET
app01-6375	139	25	limitations	limitation	NOUN
app01-6375	139	26	of	of	ADP
app01-6375	139	27	bernoulli	bernoulli	PROPN
app01-6375	139	28	assumptions	assumption	NOUN
app01-6375	139	29	.	.	PUNCT
app01-6375	140	1	for	for	ADP
app01-6375	140	2	the	the	DET
app01-6375	140	3	thin	thin	ADJ
app01-6375	140	4	beams	beam	NOUN
app01-6375	140	5	analysed	analyse	VERB
app01-6375	140	6	,	,	PUNCT
app01-6375	140	7	the	the	DET
app01-6375	140	8	excellent	excellent	ADJ
app01-6375	140	9	results	result	NOUN
app01-6375	140	10	are	be	AUX
app01-6375	140	11	obtained	obtain	VERB
app01-6375	140	12	.	.	PUNCT
app01-6375	141	1	acknowledgements	acknowledgement	NOUN
app01-6375	141	2	the	the	DET
app01-6375	141	3	financial	financial	ADJ
app01-6375	141	4	support	support	NOUN
app01-6375	141	5	of	of	ADP
app01-6375	141	6	this	this	DET
app01-6375	141	7	research	research	NOUN
app01-6375	141	8	by	by	ADP
app01-6375	141	9	the	the	DET
app01-6375	141	10	grant	grant	PROPN
app01-6375	141	11	agency	agency	NOUN
app01-6375	141	12	of	of	ADP
app01-6375	141	13	the	the	DET
app01-6375	141	14	czech	czech	PROPN
app01-6375	141	15	technical	technical	PROPN
app01-6375	141	16	university	university	PROPN
app01-6375	141	17	in	in	ADP
app01-6375	141	18	prague	prague	PROPN
app01-6375	141	19	(	(	PUNCT
app01-6375	141	20	sgs	sgs	PROPN
app01-6375	141	21	project	project	NOUN
app01-6375	141	22	no	no	INTJ
app01-6375	141	23	.	.	PUNCT
app01-6375	142	1	sgs19/032	sgs19/032	ADP
app01-6375	142	2	/	/	SYM
app01-6375	142	3	ohk1/1t/11	ohk1/1t/11	PROPN
app01-6375	142	4	)	)	PUNCT
app01-6375	142	5	is	be	AUX
app01-6375	142	6	gratefully	gratefully	ADV
app01-6375	142	7	acknowledged	acknowledge	VERB
app01-6375	142	8	.	.	PUNCT
app01-6375	143	1	28	28	NUM
app01-6375	143	2	vol	vol	NOUN
app01-6375	143	3	.	.	PUNCT
app01-6375	144	1	26/2020	26/2020	NUM
app01-6375	144	2	on	on	ADP
app01-6375	144	3	evaluation	evaluation	NOUN
app01-6375	144	4	of	of	ADP
app01-6375	144	5	the	the	DET
app01-6375	144	6	three	three	NUM
app01-6375	144	7	-	-	PUNCT
app01-6375	144	8	dimensional	dimensional	ADJ
app01-6375	144	9	isogeometric	isogeometric	ADJ
app01-6375	144	10	beam	beam	NOUN
app01-6375	144	11	element	element	NOUN
app01-6375	144	12	references	reference	NOUN
app01-6375	144	13	[	[	X
app01-6375	144	14	1	1	NUM
app01-6375	144	15	]	]	PUNCT
app01-6375	144	16	a.	a.	NOUN
app01-6375	144	17	m.	m.	PROPN
app01-6375	144	18	bauer	bauer	PROPN
app01-6375	144	19	,	,	PUNCT
app01-6375	144	20	m.	m.	NOUN
app01-6375	144	21	breitenberger	breitenberger	PROPN
app01-6375	144	22	,	,	PUNCT
app01-6375	144	23	b.	b.	PROPN
app01-6375	144	24	philipp	philipp	PROPN
app01-6375	144	25	,	,	PUNCT
app01-6375	144	26	et	et	PROPN
app01-6375	144	27	al	al	PROPN
app01-6375	144	28	.	.	PROPN
app01-6375	145	1	nonlinear	nonlinear	PROPN
app01-6375	145	2	isogeometric	isogeometric	PROPN
app01-6375	145	3	spatial	spatial	PROPN
app01-6375	145	4	bernoulli	bernoulli	PROPN
app01-6375	145	5	beam	beam	NOUN
app01-6375	145	6	.	.	PUNCT
app01-6375	146	1	computer	computer	NOUN
app01-6375	146	2	methods	method	NOUN
app01-6375	146	3	in	in	ADP
app01-6375	146	4	applied	applied	ADJ
app01-6375	146	5	mechanics	mechanic	NOUN
app01-6375	146	6	and	and	CCONJ
app01-6375	146	7	engineering	engineering	NOUN
app01-6375	146	8	303:101–127	303:101–127	NUM
app01-6375	146	9	,	,	PUNCT
app01-6375	146	10	2016	2016	NUM
app01-6375	146	11	.	.	PUNCT
app01-6375	147	1	[	[	X
app01-6375	147	2	2	2	X
app01-6375	147	3	]	]	PUNCT
app01-6375	147	4	t.	t.	PROPN
app01-6375	147	5	j.	j.	PROPN
app01-6375	147	6	r.	r.	PROPN
app01-6375	147	7	hughes	hughes	PROPN
app01-6375	147	8	,	,	PUNCT
app01-6375	147	9	j.	j.	PROPN
app01-6375	147	10	a.	a.	PROPN
app01-6375	147	11	cottrell	cottrell	PROPN
app01-6375	147	12	,	,	PUNCT
app01-6375	147	13	y.	y.	PROPN
app01-6375	147	14	bazilevs	bazilevs	PROPN
app01-6375	147	15	.	.	PUNCT
app01-6375	148	1	isogeometric	isogeometric	ADJ
app01-6375	148	2	analysis	analysis	NOUN
app01-6375	148	3	:	:	PUNCT
app01-6375	148	4	cad	cad	NOUN
app01-6375	148	5	,	,	PUNCT
app01-6375	148	6	finite	finite	ADJ
app01-6375	148	7	elements	element	NOUN
app01-6375	148	8	,	,	PUNCT
app01-6375	148	9	nurbs	nurb	NOUN
app01-6375	148	10	,	,	PUNCT
app01-6375	148	11	exact	exact	ADJ
app01-6375	148	12	geometry	geometry	NOUN
app01-6375	148	13	and	and	CCONJ
app01-6375	148	14	mesh	mesh	NOUN
app01-6375	148	15	refinement	refinement	NOUN
app01-6375	148	16	.	.	PUNCT
app01-6375	149	1	comput	comput	NOUN
app01-6375	149	2	methods	method	NOUN
app01-6375	149	3	appl	appl	PROPN
app01-6375	149	4	mech	mech	NOUN
app01-6375	149	5	engrg	engrg	PROPN
app01-6375	149	6	194:4135–4195	194:4135–4195	NUM
app01-6375	149	7	,	,	PUNCT
app01-6375	149	8	2005	2005	NUM
app01-6375	149	9	.	.	PUNCT
app01-6375	150	1	[	[	X
app01-6375	150	2	3	3	X
app01-6375	150	3	]	]	X
app01-6375	150	4	l.	l.	PROPN
app01-6375	150	5	greco	greco	PROPN
app01-6375	150	6	,	,	PUNCT
app01-6375	150	7	m.	m.	PROPN
app01-6375	150	8	cuomo	cuomo	PROPN
app01-6375	150	9	.	.	PUNCT
app01-6375	151	1	b	b	X
app01-6375	151	2	-	-	PUNCT
app01-6375	151	3	spline	spline	NOUN
app01-6375	151	4	interpolation	interpolation	NOUN
app01-6375	151	5	of	of	ADP
app01-6375	151	6	kirchhoff	kirchhoff	NOUN
app01-6375	151	7	-	-	PUNCT
app01-6375	151	8	love	love	NOUN
app01-6375	151	9	space	space	NOUN
app01-6375	151	10	rods	rod	NOUN
app01-6375	151	11	.	.	PUNCT
app01-6375	152	1	computer	computer	NOUN
app01-6375	152	2	methods	method	NOUN
app01-6375	152	3	in	in	ADP
app01-6375	152	4	applied	applied	ADJ
app01-6375	152	5	mechanics	mechanic	NOUN
app01-6375	152	6	and	and	CCONJ
app01-6375	152	7	engineering	engineering	NOUN
app01-6375	152	8	256:251	256:251	PROPN
app01-6375	152	9	–	–	PUNCT
app01-6375	152	10	269	269	NUM
app01-6375	152	11	,	,	PUNCT
app01-6375	152	12	2013	2013	NUM
app01-6375	152	13	.	.	PUNCT
app01-6375	153	1	doi:10.1016	doi:10.1016	PROPN
app01-6375	153	2	/	/	SYM
app01-6375	153	3	j.cma.2012.11.017	j.cma.2012.11.017	PROPN
app01-6375	153	4	.	.	PUNCT
app01-6375	154	1	[	[	X
app01-6375	154	2	4	4	X
app01-6375	154	3	]	]	PUNCT
app01-6375	154	4	l.	l.	PROPN
app01-6375	154	5	piegl	piegl	PROPN
app01-6375	154	6	,	,	PUNCT
app01-6375	154	7	w.	w.	PROPN
app01-6375	154	8	tiller	tiller	NOUN
app01-6375	154	9	.	.	PUNCT
app01-6375	155	1	the	the	DET
app01-6375	155	2	nurbs	nurbs	PROPN
app01-6375	155	3	book	book	PROPN
app01-6375	155	4	.	.	PUNCT
app01-6375	155	5	springer	springer	NOUN
app01-6375	155	6	-	-	PUNCT
app01-6375	155	7	verlag	verlag	PROPN
app01-6375	155	8	berlin	berlin	PROPN
app01-6375	155	9	heidelberg	heidelberg	PROPN
app01-6375	155	10	,	,	PUNCT
app01-6375	155	11	new	new	PROPN
app01-6375	155	12	york	york	PROPN
app01-6375	155	13	,	,	PUNCT
app01-6375	155	14	1997	1997	NUM
app01-6375	155	15	.	.	PUNCT
app01-6375	156	1	[	[	X
app01-6375	156	2	5	5	X
app01-6375	156	3	]	]	PUNCT
app01-6375	156	4	j.	j.	PROPN
app01-6375	156	5	s.	s.	PROPN
app01-6375	156	6	dai	dai	PROPN
app01-6375	156	7	.	.	PROPN
app01-6375	156	8	euler	euler	PROPN
app01-6375	156	9	–	–	PUNCT
app01-6375	156	10	rodrigues	rodrigues	PROPN
app01-6375	156	11	formula	formula	NOUN
app01-6375	156	12	variations	variation	NOUN
app01-6375	156	13	,	,	PUNCT
app01-6375	156	14	quaternion	quaternion	NOUN
app01-6375	156	15	conjugation	conjugation	NOUN
app01-6375	156	16	and	and	CCONJ
app01-6375	156	17	intrinsic	intrinsic	ADJ
app01-6375	156	18	connections	connection	NOUN
app01-6375	156	19	.	.	PUNCT
app01-6375	157	1	mechanism	mechanism	NOUN
app01-6375	157	2	and	and	CCONJ
app01-6375	157	3	machine	machine	NOUN
app01-6375	157	4	theory	theory	NOUN
app01-6375	157	5	92:144–152	92:144–152	PROPN
app01-6375	157	6	,	,	PUNCT
app01-6375	157	7	2015	2015	NUM
app01-6375	157	8	.	.	PUNCT
app01-6375	158	1	[	[	X
app01-6375	158	2	6	6	NUM
app01-6375	158	3	]	]	PUNCT
app01-6375	158	4	z.	z.	PROPN
app01-6375	158	5	bittnar	bittnar	PROPN
app01-6375	158	6	,	,	PUNCT
app01-6375	158	7	j.	j.	PROPN
app01-6375	158	8	šejnoha	šejnoha	PROPN
app01-6375	158	9	.	.	PUNCT
app01-6375	159	1	numerické	numerické	NOUN
app01-6375	159	2	metody	metody	ADJ
app01-6375	159	3	mechaniky	mechaniky	NOUN
app01-6375	159	4	1	1	NUM
app01-6375	159	5	.	.	PUNCT
app01-6375	160	1	české	české	PROPN
app01-6375	160	2	vysoké	vysoké	PROPN
app01-6375	160	3	učení	učení	PROPN
app01-6375	160	4	technické	technické	PROPN
app01-6375	160	5	,	,	PUNCT
app01-6375	160	6	praha	praha	PROPN
app01-6375	160	7	,	,	PUNCT
app01-6375	160	8	1992	1992	NUM
app01-6375	160	9	.	.	PUNCT
app01-6375	161	1	29	29	NUM
app01-6375	161	2	https://doi.org/10.1016/j.cma.2012.11.017	https://doi.org/10.1016/j.cma.2012.11.017	PROPN
app01-6375	161	3	acta	acta	PROPN
app01-6375	161	4	polytechnica	polytechnica	PROPN
app01-6375	161	5	ctu	ctu	NOUN
app01-6375	161	6	proceedings	proceeding	NOUN
app01-6375	161	7	26:24–29	26:24–29	NUM
app01-6375	161	8	,	,	PUNCT
app01-6375	161	9	2020	2020	NUM
app01-6375	161	10	1	1	NUM
app01-6375	161	11	introduction	introduction	NOUN
app01-6375	161	12	2	2	NUM
app01-6375	161	13	nurbs	nurb	NOUN
app01-6375	161	14	-	-	PUNCT
app01-6375	161	15	based	base	VERB
app01-6375	161	16	analysis	analysis	NOUN
app01-6375	161	17	3	3	NUM
app01-6375	161	18	beam	beam	NOUN
app01-6375	161	19	element	element	NOUN
app01-6375	161	20	formulation	formulation	NOUN
app01-6375	161	21	3.1	3.1	NUM
app01-6375	161	22	geometric	geometric	ADJ
app01-6375	161	23	description	description	NOUN
app01-6375	161	24	3.2	3.2	NUM
app01-6375	161	25	green	green	ADJ
app01-6375	161	26	-	-	PUNCT
app01-6375	161	27	lagrange	lagrange	NOUN
app01-6375	161	28	strain	strain	NOUN
app01-6375	161	29	tensor	tensor	NOUN
app01-6375	161	30	3.3	3.3	NUM
app01-6375	161	31	constitutive	constitutive	ADJ
app01-6375	161	32	equations	equation	NOUN
app01-6375	161	33	3.4	3.4	NUM
app01-6375	161	34	principle	principle	NOUN
app01-6375	161	35	of	of	ADP
app01-6375	161	36	virtual	virtual	ADJ
app01-6375	161	37	work	work	NOUN
app01-6375	161	38	4	4	NUM
app01-6375	161	39	numerical	numerical	ADJ
app01-6375	161	40	example	example	NOUN
app01-6375	161	41	5	5	NUM
app01-6375	161	42	conclusions	conclusion	NOUN
app01-6375	161	43	acknowledgements	acknowledgement	NOUN
app01-6375	161	44	references	reference	NOUN