id	sid	tid	token	lemma	pos
ap-5981	1	1	acta	acta	PROPN
ap-5981	1	2	polytechnica	polytechnica	PROPN
ap-5981	1	3	doi:10.14311	doi:10.14311	PROPN
ap-5981	1	4	/	/	PROPN
ap-5981	1	5	ap.2020.60.0502	ap.2020.60.0502	PROPN
ap-5981	1	6	acta	acta	PROPN
ap-5981	1	7	polytechnica	polytechnica	PROPN
ap-5981	1	8	60(6):502–511	60(6):502–511	PROPN
ap-5981	1	9	,	,	PUNCT
ap-5981	1	10	2020	2020	NUM
ap-5981	1	11	©	©	PROPN
ap-5981	1	12	czech	czech	PROPN
ap-5981	1	13	technical	technical	PROPN
ap-5981	1	14	university	university	PROPN
ap-5981	1	15	in	in	ADP
ap-5981	1	16	prague	prague	PROPN
ap-5981	1	17	,	,	PUNCT
ap-5981	1	18	2020	2020	NUM
ap-5981	1	19	available	available	ADJ
ap-5981	1	20	online	online	ADV
ap-5981	1	21	at	at	ADP
ap-5981	1	22	https://ojs.cvut.cz/ojs/index.php/ap	https://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-5981	1	23	newmark	newmark	NOUN
ap-5981	1	24	algorithm	algorithm	NOUN
ap-5981	1	25	for	for	ADP
ap-5981	1	26	dynamic	dynamic	ADJ
ap-5981	1	27	analysis	analysis	NOUN
ap-5981	1	28	with	with	ADP
ap-5981	1	29	maxwell	maxwell	PROPN
ap-5981	1	30	chain	chain	NOUN
ap-5981	1	31	model	model	PROPN
ap-5981	1	32	jaroslav	jaroslav	PROPN
ap-5981	1	33	schmidt∗	schmidt∗	PROPN
ap-5981	1	34	,	,	PUNCT
ap-5981	1	35	tomáš	tomáš	PROPN
ap-5981	1	36	janda	janda	PROPN
ap-5981	1	37	,	,	PUNCT
ap-5981	1	38	alena	alena	PROPN
ap-5981	1	39	zemanová	zemanová	PROPN
ap-5981	1	40	,	,	PUNCT
ap-5981	1	41	jan	jan	PROPN
ap-5981	1	42	zeman	zeman	PROPN
ap-5981	1	43	,	,	PUNCT
ap-5981	1	44	michal	michal	PROPN
ap-5981	1	45	šejnoha	šejnoha	PROPN
ap-5981	1	46	czech	czech	PROPN
ap-5981	1	47	technical	technical	PROPN
ap-5981	1	48	university	university	PROPN
ap-5981	1	49	in	in	ADP
ap-5981	1	50	prague	prague	PROPN
ap-5981	1	51	,	,	PUNCT
ap-5981	1	52	faculty	faculty	NOUN
ap-5981	1	53	of	of	ADP
ap-5981	1	54	civil	civil	ADJ
ap-5981	1	55	engineering	engineering	NOUN
ap-5981	1	56	,	,	PUNCT
ap-5981	1	57	department	department	NOUN
ap-5981	1	58	of	of	ADP
ap-5981	1	59	mechanics	mechanic	NOUN
ap-5981	1	60	,	,	PUNCT
ap-5981	1	61	thákurova	thákurova	X
ap-5981	1	62	7	7	NUM
ap-5981	1	63	,	,	PUNCT
ap-5981	1	64	166	166	NUM
ap-5981	1	65	29	29	NUM
ap-5981	1	66	praha	praha	NOUN
ap-5981	1	67	,	,	PUNCT
ap-5981	1	68	czech	czech	PROPN
ap-5981	1	69	republic	republic	NOUN
ap-5981	1	70	∗	∗	NOUN
ap-5981	1	71	corresponding	correspond	VERB
ap-5981	1	72	author	author	NOUN
ap-5981	1	73	:	:	PUNCT
ap-5981	1	74	jaroslav.schmidt@cvut.cz	jaroslav.schmidt@cvut.cz	NOUN
ap-5981	1	75	abstract	abstract	NOUN
ap-5981	1	76	.	.	PUNCT
ap-5981	2	1	this	this	DET
ap-5981	2	2	paper	paper	NOUN
ap-5981	2	3	investigates	investigate	VERB
ap-5981	2	4	a	a	DET
ap-5981	2	5	time	time	NOUN
ap-5981	2	6	-	-	PUNCT
ap-5981	2	7	stepping	step	VERB
ap-5981	2	8	procedure	procedure	NOUN
ap-5981	2	9	of	of	ADP
ap-5981	2	10	the	the	DET
ap-5981	2	11	newmark	newmark	NOUN
ap-5981	2	12	type	type	NOUN
ap-5981	2	13	for	for	ADP
ap-5981	2	14	dynamic	dynamic	ADJ
ap-5981	2	15	analyses	analysis	NOUN
ap-5981	2	16	of	of	ADP
ap-5981	2	17	viscoelastic	viscoelastic	ADJ
ap-5981	2	18	structures	structure	NOUN
ap-5981	2	19	characterized	characterize	VERB
ap-5981	2	20	by	by	ADP
ap-5981	2	21	a	a	DET
ap-5981	2	22	generalized	generalized	ADJ
ap-5981	2	23	maxwell	maxwell	PROPN
ap-5981	2	24	model	model	NOUN
ap-5981	2	25	.	.	PUNCT
ap-5981	3	1	we	we	PRON
ap-5981	3	2	depart	depart	VERB
ap-5981	3	3	from	from	ADP
ap-5981	3	4	a	a	DET
ap-5981	3	5	scheme	scheme	NOUN
ap-5981	3	6	developed	develop	VERB
ap-5981	3	7	for	for	ADP
ap-5981	3	8	a	a	DET
ap-5981	3	9	three	three	NUM
ap-5981	3	10	-	-	PUNCT
ap-5981	3	11	parameter	parameter	NOUN
ap-5981	3	12	model	model	NOUN
ap-5981	3	13	by	by	ADP
ap-5981	3	14	hatada	hatada	PROPN
ap-5981	3	15	et	et	PROPN
ap-5981	3	16	al	al	PROPN
ap-5981	3	17	.	.	PUNCT
ap-5981	4	1	[	[	X
ap-5981	4	2	1	1	NUM
ap-5981	4	3	]	]	PUNCT
ap-5981	4	4	,	,	PUNCT
ap-5981	4	5	which	which	PRON
ap-5981	4	6	we	we	PRON
ap-5981	4	7	extend	extend	VERB
ap-5981	4	8	to	to	ADP
ap-5981	4	9	a	a	DET
ap-5981	4	10	generic	generic	ADJ
ap-5981	4	11	maxwell	maxwell	NOUN
ap-5981	4	12	chain	chain	NOUN
ap-5981	4	13	and	and	CCONJ
ap-5981	4	14	demonstrate	demonstrate	VERB
ap-5981	4	15	that	that	SCONJ
ap-5981	4	16	the	the	DET
ap-5981	4	17	resulting	result	VERB
ap-5981	4	18	algorithm	algorithm	NOUN
ap-5981	4	19	can	can	AUX
ap-5981	4	20	be	be	AUX
ap-5981	4	21	derived	derive	VERB
ap-5981	4	22	from	from	ADP
ap-5981	4	23	a	a	DET
ap-5981	4	24	suitably	suitably	ADV
ap-5981	4	25	discretized	discretized	ADJ
ap-5981	4	26	hamilton	hamilton	PROPN
ap-5981	4	27	variational	variational	PROPN
ap-5981	4	28	principle	principle	NOUN
ap-5981	4	29	.	.	PUNCT
ap-5981	5	1	this	this	DET
ap-5981	5	2	variational	variational	ADJ
ap-5981	5	3	structure	structure	NOUN
ap-5981	5	4	manifests	manifest	VERB
ap-5981	5	5	itself	itself	PRON
ap-5981	5	6	in	in	ADP
ap-5981	5	7	an	an	DET
ap-5981	5	8	excellent	excellent	ADJ
ap-5981	5	9	stability	stability	NOUN
ap-5981	5	10	and	and	CCONJ
ap-5981	5	11	a	a	DET
ap-5981	5	12	low	low	ADJ
ap-5981	5	13	artificial	artificial	ADJ
ap-5981	5	14	damping	damping	NOUN
ap-5981	5	15	of	of	ADP
ap-5981	5	16	the	the	DET
ap-5981	5	17	integrator	integrator	NOUN
ap-5981	5	18	,	,	PUNCT
ap-5981	5	19	as	as	SCONJ
ap-5981	5	20	we	we	PRON
ap-5981	5	21	confirm	confirm	VERB
ap-5981	5	22	with	with	ADP
ap-5981	5	23	a	a	DET
ap-5981	5	24	mass	mass	ADJ
ap-5981	5	25	-	-	PUNCT
ap-5981	5	26	spring	spring	NOUN
ap-5981	5	27	-	-	PUNCT
ap-5981	5	28	dashpot	dashpot	NOUN
ap-5981	5	29	example	example	NOUN
ap-5981	5	30	.	.	PUNCT
ap-5981	6	1	after	after	ADP
ap-5981	6	2	a	a	DET
ap-5981	6	3	straightforward	straightforward	ADJ
ap-5981	6	4	generalization	generalization	NOUN
ap-5981	6	5	to	to	ADP
ap-5981	6	6	distributed	distribute	VERB
ap-5981	6	7	systems	system	NOUN
ap-5981	6	8	,	,	PUNCT
ap-5981	6	9	the	the	DET
ap-5981	6	10	integrator	integrator	NOUN
ap-5981	6	11	may	may	AUX
ap-5981	6	12	find	find	VERB
ap-5981	6	13	use	use	NOUN
ap-5981	6	14	in	in	ADP
ap-5981	6	15	,	,	PUNCT
ap-5981	6	16	e.g.	e.g.	ADV
ap-5981	6	17	,	,	PUNCT
ap-5981	6	18	fracture	fracture	NOUN
ap-5981	6	19	simulations	simulation	NOUN
ap-5981	6	20	of	of	ADP
ap-5981	6	21	laminated	laminated	ADJ
ap-5981	6	22	glass	glass	NOUN
ap-5981	6	23	units	unit	NOUN
ap-5981	6	24	,	,	PUNCT
ap-5981	6	25	once	once	ADV
ap-5981	6	26	combined	combine	VERB
ap-5981	6	27	with	with	ADP
ap-5981	6	28	variationally	variationally	ADV
ap-5981	6	29	-	-	PUNCT
ap-5981	6	30	based	base	VERB
ap-5981	6	31	fracture	fracture	NOUN
ap-5981	6	32	models	model	NOUN
ap-5981	6	33	.	.	PUNCT
ap-5981	7	1	keywords	keyword	NOUN
ap-5981	7	2	:	:	PUNCT
ap-5981	7	3	newmark	newmark	NOUN
ap-5981	7	4	method	method	PROPN
ap-5981	7	5	,	,	PUNCT
ap-5981	7	6	maxwell	maxwell	PROPN
ap-5981	7	7	chain	chain	NOUN
ap-5981	7	8	model	model	NOUN
ap-5981	7	9	,	,	PUNCT
ap-5981	7	10	variational	variational	ADJ
ap-5981	7	11	integrators	integrator	NOUN
ap-5981	7	12	.	.	PUNCT
ap-5981	8	1	1	1	X
ap-5981	8	2	.	.	X
ap-5981	8	3	introduction	introduction	NOUN
ap-5981	8	4	the	the	DET
ap-5981	8	5	motivation	motivation	NOUN
ap-5981	8	6	of	of	ADP
ap-5981	8	7	this	this	DET
ap-5981	8	8	work	work	NOUN
ap-5981	8	9	comes	come	VERB
ap-5981	8	10	from	from	ADP
ap-5981	8	11	the	the	DET
ap-5981	8	12	field	field	NOUN
ap-5981	8	13	of	of	ADP
ap-5981	8	14	dynamics	dynamic	NOUN
ap-5981	8	15	of	of	ADP
ap-5981	8	16	laminated	laminated	ADJ
ap-5981	8	17	glass	glass	NOUN
ap-5981	8	18	structures	structure	NOUN
ap-5981	8	19	.	.	PUNCT
ap-5981	9	1	these	these	DET
ap-5981	9	2	sandwich	sandwich	NOUN
ap-5981	9	3	structures	structure	NOUN
ap-5981	9	4	consist	consist	VERB
ap-5981	9	5	of	of	ADP
ap-5981	9	6	multiple	multiple	ADJ
ap-5981	9	7	glass	glass	NOUN
ap-5981	9	8	layers	layer	NOUN
ap-5981	9	9	connected	connect	VERB
ap-5981	9	10	with	with	ADP
ap-5981	9	11	transparent	transparent	ADJ
ap-5981	9	12	polymer	polymer	NOUN
ap-5981	9	13	interlayers	interlayer	NOUN
ap-5981	9	14	.	.	PUNCT
ap-5981	10	1	combining	combine	VERB
ap-5981	10	2	stiff	stiff	ADJ
ap-5981	10	3	,	,	PUNCT
ap-5981	10	4	brittle	brittle	ADJ
ap-5981	10	5	glass	glass	NOUN
ap-5981	10	6	with	with	ADP
ap-5981	10	7	compliant	compliant	ADJ
ap-5981	10	8	viscoelastic	viscoelastic	ADJ
ap-5981	10	9	polymers	polymer	NOUN
ap-5981	10	10	improves	improve	VERB
ap-5981	10	11	structural	structural	ADJ
ap-5981	10	12	safety	safety	NOUN
ap-5981	10	13	,	,	PUNCT
ap-5981	10	14	but	but	CCONJ
ap-5981	10	15	the	the	DET
ap-5981	10	16	through	through	NOUN
ap-5981	10	17	-	-	PUNCT
ap-5981	10	18	thickness	thickness	NOUN
ap-5981	10	19	heterogeneity	heterogeneity	NOUN
ap-5981	10	20	renders	render	VERB
ap-5981	10	21	mechanics	mechanic	NOUN
ap-5981	10	22	of	of	ADP
ap-5981	10	23	laminated	laminated	ADJ
ap-5981	10	24	glass	glass	NOUN
ap-5981	10	25	structures	structure	NOUN
ap-5981	10	26	intricate	intricate	ADJ
ap-5981	10	27	,	,	PUNCT
ap-5981	10	28	e.g.	e.g.	ADV
ap-5981	10	29	[	[	X
ap-5981	10	30	2	2	NUM
ap-5981	10	31	]	]	PUNCT
ap-5981	10	32	.	.	PUNCT
ap-5981	11	1	in	in	ADP
ap-5981	11	2	particular	particular	ADJ
ap-5981	11	3	,	,	PUNCT
ap-5981	11	4	timeand	timeand	NOUN
ap-5981	11	5	temperature	temperature	NOUN
ap-5981	11	6	-	-	PUNCT
ap-5981	11	7	dependent	dependent	ADJ
ap-5981	11	8	interlayer	interlayer	NOUN
ap-5981	11	9	properties	property	NOUN
ap-5981	11	10	must	must	AUX
ap-5981	11	11	be	be	AUX
ap-5981	11	12	accounted	account	VERB
ap-5981	11	13	for	for	ADP
ap-5981	11	14	even	even	ADV
ap-5981	11	15	in	in	ADP
ap-5981	11	16	quasi	quasi	ADJ
ap-5981	11	17	-	-	ADJ
ap-5981	11	18	static	static	ADJ
ap-5981	11	19	analyses	analysis	NOUN
ap-5981	11	20	,	,	PUNCT
ap-5981	11	21	e.g.	e.g.	ADV
ap-5981	11	22	,	,	PUNCT
ap-5981	11	23	[	[	X
ap-5981	11	24	3–6	3–6	X
ap-5981	11	25	]	]	PUNCT
ap-5981	11	26	and	and	CCONJ
ap-5981	11	27	references	reference	NOUN
ap-5981	11	28	therein	therein	ADV
ap-5981	11	29	.	.	PUNCT
ap-5981	12	1	earlier	early	ADJ
ap-5981	12	2	studies	study	NOUN
ap-5981	12	3	[	[	X
ap-5981	12	4	7–10	7–10	X
ap-5981	12	5	]	]	PUNCT
ap-5981	12	6	have	have	AUX
ap-5981	12	7	shown	show	VERB
ap-5981	12	8	that	that	SCONJ
ap-5981	12	9	the	the	DET
ap-5981	12	10	response	response	NOUN
ap-5981	12	11	of	of	ADP
ap-5981	12	12	commonly	commonly	ADV
ap-5981	12	13	used	use	VERB
ap-5981	12	14	interlayer	interlayer	NOUN
ap-5981	12	15	materials	material	NOUN
ap-5981	12	16	can	can	AUX
ap-5981	12	17	be	be	AUX
ap-5981	12	18	captured	capture	VERB
ap-5981	12	19	well	well	ADV
ap-5981	12	20	with	with	ADP
ap-5981	12	21	the	the	DET
ap-5981	12	22	maxwell	maxwell	PROPN
ap-5981	12	23	chain	chain	NOUN
ap-5981	12	24	model	model	NOUN
ap-5981	12	25	combined	combine	VERB
ap-5981	12	26	with	with	ADP
ap-5981	12	27	the	the	DET
ap-5981	12	28	time	time	NOUN
ap-5981	12	29	-	-	PUNCT
ap-5981	12	30	temperature	temperature	NOUN
ap-5981	12	31	superposition	superposition	NOUN
ap-5981	12	32	principle	principle	NOUN
ap-5981	12	33	.	.	PUNCT
ap-5981	13	1	because	because	SCONJ
ap-5981	13	2	the	the	DET
ap-5981	13	3	viscoelastic	viscoelastic	NOUN
ap-5981	13	4	model	model	NOUN
ap-5981	13	5	concurrently	concurrently	ADV
ap-5981	13	6	predicts	predict	VERB
ap-5981	13	7	material	material	ADJ
ap-5981	13	8	damping	damping	NOUN
ap-5981	13	9	,	,	PUNCT
ap-5981	13	10	vibrations	vibration	NOUN
ap-5981	13	11	of	of	ADP
ap-5981	13	12	laminated	laminated	ADJ
ap-5981	13	13	glass	glass	NOUN
ap-5981	13	14	structures	structure	NOUN
ap-5981	13	15	can	can	AUX
ap-5981	13	16	be	be	AUX
ap-5981	13	17	described	describe	VERB
ap-5981	13	18	more	more	ADV
ap-5981	13	19	accurately	accurately	ADV
ap-5981	13	20	than	than	ADP
ap-5981	13	21	in	in	ADP
ap-5981	13	22	conventional	conventional	ADJ
ap-5981	13	23	structural	structural	ADJ
ap-5981	13	24	analyses	analysis	NOUN
ap-5981	13	25	that	that	PRON
ap-5981	13	26	mostly	mostly	ADV
ap-5981	13	27	employ	employ	VERB
ap-5981	13	28	the	the	DET
ap-5981	13	29	rayleigh	rayleigh	NOUN
ap-5981	13	30	damping	damping	NOUN
ap-5981	13	31	,	,	PUNCT
ap-5981	13	32	e.g.	e.g.	ADV
ap-5981	13	33	[	[	X
ap-5981	13	34	11	11	NUM
ap-5981	13	35	,	,	PUNCT
ap-5981	13	36	section	section	NOUN
ap-5981	13	37	12.5	12.5	NUM
ap-5981	13	38	]	]	PUNCT
ap-5981	13	39	.	.	PUNCT
ap-5981	14	1	this	this	DET
ap-5981	14	2	added	add	VERB
ap-5981	14	3	value	value	NOUN
ap-5981	14	4	has	have	AUX
ap-5981	14	5	been	be	AUX
ap-5981	14	6	addressed	address	VERB
ap-5981	14	7	in	in	ADP
ap-5981	14	8	detail	detail	NOUN
ap-5981	14	9	for	for	ADP
ap-5981	14	10	free	free	ADJ
ap-5981	14	11	vibrations	vibration	NOUN
ap-5981	14	12	of	of	ADP
ap-5981	14	13	laminated	laminated	ADJ
ap-5981	14	14	glass	glass	NOUN
ap-5981	14	15	units	unit	NOUN
ap-5981	14	16	,	,	PUNCT
ap-5981	14	17	e.g.	e.g.	ADV
ap-5981	14	18	[	[	X
ap-5981	14	19	12–14	12–14	NUM
ap-5981	14	20	]	]	X
ap-5981	14	21	;	;	PUNCT
ap-5981	14	22	an	an	DET
ap-5981	14	23	extension	extension	NOUN
ap-5981	14	24	towards	towards	ADP
ap-5981	14	25	the	the	DET
ap-5981	14	26	response	response	NOUN
ap-5981	14	27	under	under	ADP
ap-5981	14	28	general	general	ADJ
ap-5981	14	29	dynamic	dynamic	ADJ
ap-5981	14	30	loads	load	NOUN
ap-5981	14	31	requires	require	VERB
ap-5981	14	32	the	the	DET
ap-5981	14	33	development	development	NOUN
ap-5981	14	34	of	of	ADP
ap-5981	14	35	dedicated	dedicated	ADJ
ap-5981	14	36	time	time	NOUN
ap-5981	14	37	-	-	PUNCT
ap-5981	14	38	stepping	step	VERB
ap-5981	14	39	schemes	scheme	NOUN
ap-5981	14	40	that	that	PRON
ap-5981	14	41	are	be	AUX
ap-5981	14	42	in	in	ADP
ap-5981	14	43	the	the	DET
ap-5981	14	44	focus	focus	NOUN
ap-5981	14	45	of	of	ADP
ap-5981	14	46	the	the	DET
ap-5981	14	47	current	current	ADJ
ap-5981	14	48	work	work	NOUN
ap-5981	14	49	.	.	PUNCT
ap-5981	15	1	related	relate	VERB
ap-5981	15	2	work	work	NOUN
ap-5981	15	3	.	.	PUNCT
ap-5981	16	1	dynamics	dynamic	NOUN
ap-5981	16	2	of	of	ADP
ap-5981	16	3	viscoelastic	viscoelastic	ADJ
ap-5981	16	4	solids	solid	NOUN
ap-5981	16	5	described	describe	VERB
ap-5981	16	6	by	by	ADP
ap-5981	16	7	the	the	DET
ap-5981	16	8	maxwell	maxwell	PROPN
ap-5981	16	9	chain	chain	NOUN
ap-5981	16	10	model	model	NOUN
ap-5981	16	11	leads	lead	VERB
ap-5981	16	12	to	to	ADP
ap-5981	16	13	the	the	DET
ap-5981	16	14	system	system	NOUN
ap-5981	16	15	of	of	ADP
ap-5981	16	16	initial	initial	ADJ
ap-5981	16	17	value	value	NOUN
ap-5981	16	18	problems	problem	NOUN
ap-5981	16	19	coupling	couple	VERB
ap-5981	16	20	the	the	DET
ap-5981	16	21	equation	equation	NOUN
ap-5981	16	22	of	of	ADP
ap-5981	16	23	motion	motion	NOUN
ap-5981	16	24	with	with	ADP
ap-5981	16	25	the	the	DET
ap-5981	16	26	local	local	ADJ
ap-5981	16	27	evolution	evolution	NOUN
ap-5981	16	28	of	of	ADP
ap-5981	16	29	constitutive	constitutive	ADJ
ap-5981	16	30	variables	variable	NOUN
ap-5981	16	31	,	,	PUNCT
ap-5981	16	32	see	see	VERB
ap-5981	16	33	section	section	NOUN
ap-5981	16	34	2.1	2.1	NUM
ap-5981	16	35	for	for	ADP
ap-5981	16	36	illustration	illustration	NOUN
ap-5981	16	37	.	.	PUNCT
ap-5981	17	1	because	because	SCONJ
ap-5981	17	2	numerically	numerically	ADV
ap-5981	17	3	integrating	integrate	VERB
ap-5981	17	4	the	the	DET
ap-5981	17	5	full	full	ADJ
ap-5981	17	6	system	system	NOUN
ap-5981	17	7	would	would	AUX
ap-5981	17	8	be	be	AUX
ap-5981	17	9	costly	costly	ADJ
ap-5981	17	10	,	,	PUNCT
ap-5981	17	11	we	we	PRON
ap-5981	17	12	will	will	AUX
ap-5981	17	13	follow	follow	VERB
ap-5981	17	14	an	an	DET
ap-5981	17	15	alternative	alternative	ADJ
ap-5981	17	16	approach	approach	NOUN
ap-5981	17	17	in	in	ADP
ap-5981	17	18	which	which	PRON
ap-5981	17	19	only	only	ADV
ap-5981	17	20	the	the	DET
ap-5981	17	21	equations	equation	NOUN
ap-5981	17	22	of	of	ADP
ap-5981	17	23	motion	motion	NOUN
ap-5981	17	24	are	be	AUX
ap-5981	17	25	solved	solve	VERB
ap-5981	17	26	approximately	approximately	ADV
ap-5981	17	27	,	,	PUNCT
ap-5981	17	28	whereas	whereas	SCONJ
ap-5981	17	29	the	the	DET
ap-5981	17	30	evolutionary	evolutionary	ADJ
ap-5981	17	31	constitutive	constitutive	ADJ
ap-5981	17	32	equations	equation	NOUN
ap-5981	17	33	are	be	AUX
ap-5981	17	34	resolved	resolve	VERB
ap-5981	17	35	in	in	ADP
ap-5981	17	36	the	the	DET
ap-5981	17	37	closed	closed	ADJ
ap-5981	17	38	form	form	NOUN
ap-5981	17	39	,	,	PUNCT
ap-5981	17	40	leading	lead	VERB
ap-5981	17	41	to	to	ADP
ap-5981	17	42	an	an	DET
ap-5981	17	43	inexpensive	inexpensive	ADJ
ap-5981	17	44	update	update	NOUN
ap-5981	17	45	formulas	formula	NOUN
ap-5981	17	46	for	for	ADP
ap-5981	17	47	internal	internal	ADJ
ap-5981	17	48	variables	variable	NOUN
ap-5981	17	49	entering	enter	VERB
ap-5981	17	50	the	the	DET
ap-5981	17	51	equations	equation	NOUN
ap-5981	17	52	of	of	ADP
ap-5981	17	53	motion	motion	NOUN
ap-5981	17	54	.	.	PUNCT
ap-5981	18	1	this	this	DET
ap-5981	18	2	approach	approach	NOUN
ap-5981	18	3	has	have	AUX
ap-5981	18	4	been	be	AUX
ap-5981	18	5	pioneered	pioneer	VERB
ap-5981	18	6	for	for	ADP
ap-5981	18	7	quasistatic	quasistatic	ADJ
ap-5981	18	8	problems	problem	NOUN
ap-5981	18	9	by	by	ADP
ap-5981	18	10	zienkiewicz	zienkiewicz	PROPN
ap-5981	18	11	et	et	PROPN
ap-5981	18	12	al	al	PROPN
ap-5981	18	13	.	.	PUNCT
ap-5981	19	1	[	[	X
ap-5981	19	2	15	15	NUM
ap-5981	19	3	]	]	PUNCT
ap-5981	19	4	;	;	PUNCT
ap-5981	19	5	see	see	VERB
ap-5981	19	6	also	also	ADV
ap-5981	19	7	[	[	X
ap-5981	19	8	16	16	NUM
ap-5981	19	9	,	,	PUNCT
ap-5981	19	10	section	section	NOUN
ap-5981	19	11	5.2	5.2	NUM
ap-5981	19	12	]	]	PUNCT
ap-5981	19	13	for	for	ADP
ap-5981	19	14	a	a	DET
ap-5981	19	15	comprehensive	comprehensive	ADJ
ap-5981	19	16	review	review	NOUN
ap-5981	19	17	.	.	PUNCT
ap-5981	20	1	to	to	ADP
ap-5981	20	2	the	the	DET
ap-5981	20	3	best	good	ADJ
ap-5981	20	4	of	of	ADP
ap-5981	20	5	our	our	PRON
ap-5981	20	6	knowledge	knowledge	NOUN
ap-5981	20	7	,	,	PUNCT
ap-5981	20	8	hatada	hatada	PROPN
ap-5981	20	9	et	et	PROPN
ap-5981	20	10	al	al	PROPN
ap-5981	20	11	.	.	PUNCT
ap-5981	21	1	[	[	X
ap-5981	21	2	1	1	X
ap-5981	21	3	]	]	PUNCT
ap-5981	21	4	were	be	AUX
ap-5981	21	5	the	the	DET
ap-5981	21	6	only	only	ADJ
ap-5981	21	7	ones	one	NOUN
ap-5981	21	8	who	who	PRON
ap-5981	21	9	used	use	VERB
ap-5981	21	10	this	this	DET
ap-5981	21	11	strategy	strategy	NOUN
ap-5981	21	12	in	in	ADP
ap-5981	21	13	dynamics	dynamic	NOUN
ap-5981	21	14	,	,	PUNCT
ap-5981	21	15	although	although	SCONJ
ap-5981	21	16	no	no	DET
ap-5981	21	17	reference	reference	NOUN
ap-5981	21	18	to	to	ADP
ap-5981	21	19	the	the	DET
ap-5981	21	20	original	original	ADJ
ap-5981	21	21	work	work	NOUN
ap-5981	21	22	[	[	X
ap-5981	21	23	15	15	NUM
ap-5981	21	24	]	]	PUNCT
ap-5981	21	25	was	be	AUX
ap-5981	21	26	made	make	VERB
ap-5981	21	27	.	.	PUNCT
ap-5981	22	1	in	in	ADP
ap-5981	22	2	particular	particular	ADJ
ap-5981	22	3	,	,	PUNCT
ap-5981	22	4	they	they	PRON
ap-5981	22	5	developed	develop	VERB
ap-5981	22	6	a	a	DET
ap-5981	22	7	newmark	newmark	NOUN
ap-5981	22	8	-	-	PUNCT
ap-5981	22	9	type	type	NOUN
ap-5981	22	10	[	[	X
ap-5981	22	11	17	17	NUM
ap-5981	22	12	]	]	PUNCT
ap-5981	22	13	algorithm	algorithm	NOUN
ap-5981	22	14	for	for	ADP
ap-5981	22	15	the	the	DET
ap-5981	22	16	three	three	NUM
ap-5981	22	17	-	-	PUNCT
ap-5981	22	18	parameter	parameter	NOUN
ap-5981	22	19	maxwell	maxwell	PROPN
ap-5981	22	20	model	model	NOUN
ap-5981	22	21	and	and	CCONJ
ap-5981	22	22	used	use	VERB
ap-5981	22	23	it	it	PRON
ap-5981	22	24	to	to	PART
ap-5981	22	25	predict	predict	VERB
ap-5981	22	26	the	the	DET
ap-5981	22	27	response	response	NOUN
ap-5981	22	28	of	of	ADP
ap-5981	22	29	planar	planar	ADJ
ap-5981	22	30	frames	frame	NOUN
ap-5981	22	31	to	to	ADP
ap-5981	22	32	earthquake	earthquake	NOUN
ap-5981	22	33	loading	loading	NOUN
ap-5981	22	34	.	.	PUNCT
ap-5981	23	1	novelty	novelty	NOUN
ap-5981	23	2	.	.	PUNCT
ap-5981	24	1	our	our	PRON
ap-5981	24	2	work	work	NOUN
ap-5981	24	3	further	far	ADV
ap-5981	24	4	develops	develop	VERB
ap-5981	24	5	the	the	DET
ap-5981	24	6	contribution	contribution	NOUN
ap-5981	24	7	[	[	X
ap-5981	24	8	1	1	X
ap-5981	24	9	]	]	PUNCT
ap-5981	24	10	in	in	ADP
ap-5981	24	11	three	three	NUM
ap-5981	24	12	aspects	aspect	NOUN
ap-5981	24	13	.	.	PUNCT
ap-5981	25	1	first	first	ADV
ap-5981	25	2	,	,	PUNCT
ap-5981	25	3	in	in	ADP
ap-5981	25	4	section	section	NOUN
ap-5981	25	5	2.2	2.2	NUM
ap-5981	25	6	,	,	PUNCT
ap-5981	25	7	we	we	PRON
ap-5981	25	8	present	present	VERB
ap-5981	25	9	a	a	DET
ap-5981	25	10	compact	compact	ADJ
ap-5981	25	11	derivation	derivation	NOUN
ap-5981	25	12	of	of	ADP
ap-5981	25	13	the	the	DET
ap-5981	25	14	newmark	newmark	PROPN
ap-5981	25	15	scheme	scheme	NOUN
ap-5981	25	16	for	for	ADP
ap-5981	25	17	a	a	DET
ap-5981	25	18	generic	generic	ADJ
ap-5981	25	19	maxwell	maxwell	PROPN
ap-5981	25	20	chain	chain	NOUN
ap-5981	25	21	,	,	PUNCT
ap-5981	25	22	closely	closely	ADV
ap-5981	25	23	following	follow	VERB
ap-5981	25	24	the	the	DET
ap-5981	25	25	original	original	ADJ
ap-5981	25	26	exposition	exposition	NOUN
ap-5981	25	27	[	[	X
ap-5981	25	28	15	15	NUM
ap-5981	25	29	]	]	PUNCT
ap-5981	25	30	.	.	PUNCT
ap-5981	26	1	second	second	ADJ
ap-5981	26	2	,	,	PUNCT
ap-5981	26	3	in	in	ADP
ap-5981	26	4	section	section	NOUN
ap-5981	26	5	3	3	NUM
ap-5981	26	6	,	,	PUNCT
ap-5981	26	7	we	we	PRON
ap-5981	26	8	show	show	VERB
ap-5981	26	9	that	that	SCONJ
ap-5981	26	10	the	the	DET
ap-5981	26	11	algorithm	algorithm	NOUN
ap-5981	26	12	can	can	AUX
ap-5981	26	13	be	be	AUX
ap-5981	26	14	interpreted	interpret	VERB
ap-5981	26	15	as	as	ADP
ap-5981	26	16	a	a	DET
ap-5981	26	17	variational	variational	ADJ
ap-5981	26	18	integrator	integrator	NOUN
ap-5981	27	1	[	[	X
ap-5981	27	2	18	18	NUM
ap-5981	27	3	]	]	PUNCT
ap-5981	27	4	,	,	PUNCT
ap-5981	27	5	in	in	ADP
ap-5981	27	6	the	the	DET
ap-5981	27	7	sense	sense	NOUN
ap-5981	27	8	that	that	SCONJ
ap-5981	27	9	it	it	PRON
ap-5981	27	10	can	can	AUX
ap-5981	27	11	be	be	AUX
ap-5981	27	12	derived	derive	VERB
ap-5981	27	13	from	from	ADP
ap-5981	27	14	the	the	DET
ap-5981	27	15	hamilton	hamilton	PROPN
ap-5981	27	16	variational	variational	PROPN
ap-5981	27	17	principle	principle	NOUN
ap-5981	27	18	combined	combine	VERB
ap-5981	27	19	with	with	ADP
ap-5981	27	20	a	a	DET
ap-5981	27	21	suitable	suitable	ADJ
ap-5981	27	22	time	time	NOUN
ap-5981	27	23	discretization	discretization	NOUN
ap-5981	27	24	.	.	PUNCT
ap-5981	28	1	the	the	DET
ap-5981	28	2	variational	variational	ADJ
ap-5981	28	3	structure	structure	NOUN
ap-5981	28	4	provides	provide	VERB
ap-5981	28	5	the	the	DET
ap-5981	28	6	integrator	integrator	NOUN
ap-5981	28	7	with	with	ADP
ap-5981	28	8	a	a	DET
ap-5981	28	9	good	good	ADJ
ap-5981	28	10	numerical	numerical	ADJ
ap-5981	28	11	stability	stability	NOUN
ap-5981	28	12	and	and	CCONJ
ap-5981	28	13	low	low	ADJ
ap-5981	28	14	numerical	numerical	ADJ
ap-5981	28	15	dissipation	dissipation	NOUN
ap-5981	28	16	,	,	PUNCT
ap-5981	28	17	as	as	SCONJ
ap-5981	28	18	demonstrated	demonstrate	VERB
ap-5981	28	19	in	in	ADP
ap-5981	28	20	section	section	NOUN
ap-5981	28	21	4.1	4.1	NUM
ap-5981	28	22	with	with	ADP
ap-5981	28	23	selected	select	VERB
ap-5981	28	24	examples	example	NOUN
ap-5981	28	25	.	.	PUNCT
ap-5981	29	1	moreover	moreover	ADV
ap-5981	29	2	,	,	PUNCT
ap-5981	29	3	the	the	DET
ap-5981	29	4	scheme	scheme	NOUN
ap-5981	29	5	can	can	AUX
ap-5981	29	6	easily	easily	ADV
ap-5981	29	7	be	be	AUX
ap-5981	29	8	combined	combine	VERB
ap-5981	29	9	with	with	ADP
ap-5981	29	10	variational	variational	ADJ
ap-5981	29	11	approaches	approach	NOUN
ap-5981	29	12	to	to	ADP
ap-5981	29	13	fracture	fracture	NOUN
ap-5981	29	14	,	,	PUNCT
ap-5981	29	15	e.g.	e.g.	ADV
ap-5981	29	16	,	,	PUNCT
ap-5981	29	17	[	[	X
ap-5981	29	18	19–21	19–21	NUM
ap-5981	29	19	]	]	X
ap-5981	29	20	,	,	PUNCT
ap-5981	29	21	which	which	PRON
ap-5981	29	22	is	be	AUX
ap-5981	29	23	of	of	ADP
ap-5981	29	24	independent	independent	ADJ
ap-5981	29	25	interest	interest	NOUN
ap-5981	29	26	when	when	SCONJ
ap-5981	29	27	simulating	simulate	VERB
ap-5981	29	28	the	the	DET
ap-5981	29	29	behaviour	behaviour	NOUN
ap-5981	29	30	of	of	ADP
ap-5981	29	31	laminated	laminated	ADJ
ap-5981	29	32	glass	glass	NOUN
ap-5981	29	33	under	under	ADP
ap-5981	29	34	impact	impact	NOUN
ap-5981	29	35	loads	load	NOUN
ap-5981	29	36	.	.	PUNCT
ap-5981	30	1	third	third	ADJ
ap-5981	30	2	,	,	PUNCT
ap-5981	30	3	in	in	ADP
ap-5981	30	4	section	section	NOUN
ap-5981	30	5	4.2	4.2	NUM
ap-5981	30	6	,	,	PUNCT
ap-5981	30	7	we	we	PRON
ap-5981	30	8	outline	outline	VERB
ap-5981	30	9	how	how	SCONJ
ap-5981	30	10	to	to	PART
ap-5981	30	11	extend	extend	VERB
ap-5981	30	12	the	the	DET
ap-5981	30	13	algorithm	algorithm	NOUN
ap-5981	30	14	to	to	ADP
ap-5981	30	15	a	a	DET
ap-5981	30	16	continuum	continuum	ADJ
ap-5981	30	17	formulation	formulation	NOUN
ap-5981	30	18	and	and	CCONJ
ap-5981	30	19	complement	complement	VERB
ap-5981	30	20	the	the	DET
ap-5981	30	21	theoretical	theoretical	ADJ
ap-5981	30	22	considerations	consideration	NOUN
ap-5981	30	23	with	with	ADP
ap-5981	30	24	an	an	DET
ap-5981	30	25	illustrative	illustrative	ADJ
ap-5981	30	26	3d	3d	NUM
ap-5981	30	27	finite	finite	PROPN
ap-5981	30	28	element	element	PROPN
ap-5981	30	29	simulation	simulation	PROPN
ap-5981	30	30	.	.	PUNCT
ap-5981	31	1	notation	notation	NOUN
ap-5981	31	2	.	.	PUNCT
ap-5981	32	1	we	we	PRON
ap-5981	32	2	employ	employ	VERB
ap-5981	32	3	the	the	DET
ap-5981	32	4	conventional	conventional	ADJ
ap-5981	32	5	notation	notation	NOUN
ap-5981	32	6	through	through	ADP
ap-5981	32	7	the	the	DET
ap-5981	32	8	text	text	NOUN
ap-5981	32	9	,	,	PUNCT
ap-5981	32	10	in	in	ADP
ap-5981	32	11	which	which	PRON
ap-5981	32	12	scalar	scalar	ADJ
ap-5981	32	13	quantities	quantity	NOUN
ap-5981	32	14	are	be	AUX
ap-5981	32	15	denoted	denote	VERB
ap-5981	32	16	by	by	ADP
ap-5981	32	17	a	a	DET
ap-5981	32	18	plain	plain	ADJ
ap-5981	32	19	font	font	NOUN
ap-5981	32	20	,	,	PUNCT
ap-5981	32	21	whereas	whereas	SCONJ
ap-5981	32	22	bold	bold	ADJ
ap-5981	32	23	-	-	PUNCT
ap-5981	32	24	face	face	NOUN
ap-5981	32	25	letters	letter	NOUN
ap-5981	32	26	in502	in502	PROPN
ap-5981	32	27	https://doi.org/10.14311/ap.2020.60.0502	https://doi.org/10.14311/ap.2020.60.0502	PUNCT
ap-5981	32	28	https://ojs.cvut.cz/ojs/index.php/ap	https://ojs.cvut.cz/ojs/index.php/ap	NUM
ap-5981	32	29	vol	vol	NOUN
ap-5981	32	30	.	.	PUNCT
ap-5981	33	1	60	60	NUM
ap-5981	33	2	no	no	INTJ
ap-5981	33	3	.	.	PUNCT
ap-5981	34	1	6/2020	6/2020	NUM
ap-5981	34	2	newmark	newmark	NOUN
ap-5981	34	3	algorithm	algorithm	NOUN
ap-5981	34	4	for	for	ADP
ap-5981	34	5	dynamic	dynamic	ADJ
ap-5981	34	6	analysis	analysis	NOUN
ap-5981	34	7	of	of	ADP
ap-5981	34	8	viscoelastic	viscoelastic	ADJ
ap-5981	34	9	materials	material	NOUN
ap-5981	34	10	k∞	k∞	PROPN
ap-5981	35	1	ηpη3η2η1	ηpη3η2η1	PROPN
ap-5981	35	2	k1	k1	PROPN
ap-5981	35	3	k2	k2	PROPN
ap-5981	35	4	k3	k3	VERB
ap-5981	35	5	kp	kp	PROPN
ap-5981	35	6	m	m	PROPN
ap-5981	35	7	f	f	PROPN
ap-5981	35	8	(	(	PUNCT
ap-5981	35	9	t	t	PROPN
ap-5981	35	10	)	)	PUNCT
ap-5981	35	11	r(t	r(t	NOUN
ap-5981	35	12	)	)	PUNCT
ap-5981	35	13	re,1(t	re,1(t	PROPN
ap-5981	35	14	)	)	PUNCT
ap-5981	35	15	rv,1(t	rv,1(t	PROPN
ap-5981	35	16	)	)	PUNCT
ap-5981	35	17	figure	figure	NOUN
ap-5981	35	18	1	1	NUM
ap-5981	35	19	.	.	PUNCT
ap-5981	35	20	scheme	scheme	NOUN
ap-5981	35	21	of	of	ADP
ap-5981	35	22	the	the	DET
ap-5981	35	23	single	single	ADJ
ap-5981	35	24	-	-	PUNCT
ap-5981	35	25	degree	degree	NOUN
ap-5981	35	26	-	-	PUNCT
ap-5981	35	27	of	of	ADP
ap-5981	35	28	-	-	PUNCT
ap-5981	35	29	freedom	freedom	NOUN
ap-5981	35	30	viscoelastic	viscoelastic	ADJ
ap-5981	35	31	dynamic	dynamic	ADJ
ap-5981	35	32	problem	problem	NOUN
ap-5981	35	33	.	.	PUNCT
ap-5981	36	1	dicate	dicate	VERB
ap-5981	36	2	vectors	vector	NOUN
ap-5981	36	3	or	or	CCONJ
ap-5981	36	4	higher	high	ADJ
ap-5981	36	5	-	-	PUNCT
ap-5981	36	6	order	order	NOUN
ap-5981	36	7	tensors	tensor	NOUN
ap-5981	36	8	.	.	PUNCT
ap-5981	37	1	additional	additional	ADJ
ap-5981	37	2	nomenclature	nomenclature	NOUN
ap-5981	37	3	is	be	AUX
ap-5981	37	4	introduced	introduce	VERB
ap-5981	37	5	when	when	SCONJ
ap-5981	37	6	needed	need	VERB
ap-5981	37	7	.	.	PUNCT
ap-5981	38	1	2	2	X
ap-5981	38	2	.	.	X
ap-5981	38	3	newmark	newmark	PROPN
ap-5981	38	4	method	method	NOUN
ap-5981	38	5	in	in	ADP
ap-5981	38	6	this	this	DET
ap-5981	38	7	section	section	NOUN
ap-5981	38	8	,	,	PUNCT
ap-5981	38	9	we	we	PRON
ap-5981	38	10	analyse	analyse	VERB
ap-5981	38	11	a	a	DET
ap-5981	38	12	single	single	ADJ
ap-5981	38	13	degree	degree	NOUN
ap-5981	38	14	of	of	ADP
ap-5981	38	15	freedom	freedom	NOUN
ap-5981	38	16	(	(	PUNCT
ap-5981	38	17	sdof	sdof	ADJ
ap-5981	38	18	)	)	PUNCT
ap-5981	38	19	model	model	NOUN
ap-5981	38	20	of	of	ADP
ap-5981	38	21	a	a	DET
ap-5981	38	22	mass	mass	NOUN
ap-5981	38	23	supported	support	VERB
ap-5981	38	24	with	with	ADP
ap-5981	38	25	a	a	DET
ap-5981	38	26	maxwell	maxwell	PROPN
ap-5981	38	27	chain	chain	NOUN
ap-5981	38	28	,	,	PUNCT
ap-5981	38	29	consisting	consist	VERB
ap-5981	38	30	of	of	ADP
ap-5981	38	31	the	the	DET
ap-5981	38	32	parallel	parallel	ADJ
ap-5981	38	33	connection	connection	NOUN
ap-5981	38	34	of	of	ADP
ap-5981	38	35	an	an	DET
ap-5981	38	36	elastic	elastic	ADJ
ap-5981	38	37	spring	spring	NOUN
ap-5981	38	38	and	and	CCONJ
ap-5981	38	39	multiple	multiple	ADJ
ap-5981	38	40	spring	spring	NOUN
ap-5981	38	41	-	-	PUNCT
ap-5981	38	42	dashpot	dashpot	NOUN
ap-5981	38	43	cells	cell	NOUN
ap-5981	38	44	,	,	PUNCT
ap-5981	38	45	see	see	VERB
ap-5981	38	46	figure	figure	NOUN
ap-5981	38	47	1	1	NUM
ap-5981	38	48	for	for	ADP
ap-5981	38	49	illustration	illustration	NOUN
ap-5981	38	50	and	and	CCONJ
ap-5981	38	51	,	,	PUNCT
ap-5981	38	52	e.g.	e.g.	ADV
ap-5981	38	53	,	,	PUNCT
ap-5981	38	54	[	[	X
ap-5981	38	55	16	16	NUM
ap-5981	38	56	,	,	PUNCT
ap-5981	38	57	section	section	NOUN
ap-5981	38	58	a	a	X
ap-5981	38	59	]	]	X
ap-5981	38	60	for	for	ADP
ap-5981	38	61	further	further	ADJ
ap-5981	38	62	details	detail	NOUN
ap-5981	38	63	.	.	PUNCT
ap-5981	39	1	in	in	ADP
ap-5981	39	2	particular	particular	ADJ
ap-5981	39	3	,	,	PUNCT
ap-5981	39	4	in	in	ADP
ap-5981	39	5	section	section	NOUN
ap-5981	39	6	2.1	2.1	NUM
ap-5981	39	7	,	,	PUNCT
ap-5981	39	8	we	we	PRON
ap-5981	39	9	review	review	VERB
ap-5981	39	10	the	the	DET
ap-5981	39	11	equations	equation	NOUN
ap-5981	39	12	of	of	ADP
ap-5981	39	13	motion	motion	NOUN
ap-5981	39	14	,	,	PUNCT
ap-5981	39	15	which	which	PRON
ap-5981	39	16	we	we	PRON
ap-5981	39	17	subsequently	subsequently	ADV
ap-5981	39	18	discretize	discretize	VERB
ap-5981	39	19	with	with	ADP
ap-5981	39	20	the	the	DET
ap-5981	39	21	average	average	ADJ
ap-5981	39	22	acceleration	acceleration	NOUN
ap-5981	39	23	version	version	NOUN
ap-5981	39	24	of	of	ADP
ap-5981	39	25	the	the	DET
ap-5981	39	26	newmark	newmark	NOUN
ap-5981	39	27	method	method	NOUN
ap-5981	40	1	[	[	X
ap-5981	40	2	17	17	NUM
ap-5981	40	3	]	]	PUNCT
ap-5981	40	4	in	in	ADP
ap-5981	40	5	section	section	NOUN
ap-5981	40	6	2.2	2.2	NUM
ap-5981	40	7	.	.	PUNCT
ap-5981	41	1	2.1	2.1	NUM
ap-5981	41	2	.	.	PUNCT
ap-5981	42	1	governing	govern	VERB
ap-5981	42	2	equations	equation	NOUN
ap-5981	42	3	as	as	SCONJ
ap-5981	42	4	follows	follow	VERB
ap-5981	42	5	from	from	ADP
ap-5981	42	6	the	the	DET
ap-5981	42	7	scheme	scheme	NOUN
ap-5981	42	8	in	in	ADP
ap-5981	42	9	figure	figure	NOUN
ap-5981	42	10	1	1	NUM
ap-5981	42	11	,	,	PUNCT
ap-5981	42	12	the	the	DET
ap-5981	42	13	problem	problem	NOUN
ap-5981	42	14	under	under	ADP
ap-5981	42	15	consideration	consideration	NOUN
ap-5981	42	16	is	be	AUX
ap-5981	42	17	specified	specify	VERB
ap-5981	42	18	with	with	ADP
ap-5981	42	19	the	the	DET
ap-5981	42	20	timedependent	timedependent	NOUN
ap-5981	42	21	load	load	NOUN
ap-5981	42	22	f	f	PROPN
ap-5981	42	23	(	(	PUNCT
ap-5981	42	24	t	t	PROPN
ap-5981	42	25	)	)	PUNCT
ap-5981	42	26	,	,	PUNCT
ap-5981	42	27	the	the	DET
ap-5981	42	28	particle	particle	NOUN
ap-5981	42	29	mass	mass	PROPN
ap-5981	42	30	m	m	PROPN
ap-5981	42	31	and	and	CCONJ
ap-5981	42	32	the	the	DET
ap-5981	42	33	maxwell	maxwell	PROPN
ap-5981	42	34	chain	chain	NOUN
ap-5981	42	35	model	model	NOUN
ap-5981	42	36	parameters	parameter	NOUN
ap-5981	42	37	:	:	PUNCT
ap-5981	42	38	stiffness	stiffness	NOUN
ap-5981	42	39	of	of	ADP
ap-5981	42	40	the	the	DET
ap-5981	42	41	elastic	elastic	ADJ
ap-5981	42	42	spring	spring	NOUN
ap-5981	42	43	k∞	k∞	PROPN
ap-5981	42	44	,	,	PUNCT
ap-5981	42	45	spring	spring	NOUN
ap-5981	42	46	stiffness	stiffness	NOUN
ap-5981	42	47	kp	kp	PROPN
ap-5981	42	48	and	and	CCONJ
ap-5981	42	49	damper	damper	NOUN
ap-5981	42	50	viscosity	viscosity	NOUN
ap-5981	42	51	ηp	ηp	ADP
ap-5981	42	52	of	of	ADP
ap-5981	42	53	the	the	DET
ap-5981	42	54	p	p	PROPN
ap-5981	42	55	-	-	PUNCT
ap-5981	42	56	th	th	VERB
ap-5981	42	57	maxwell	maxwell	NOUN
ap-5981	42	58	cell	cell	NOUN
ap-5981	42	59	;	;	PUNCT
ap-5981	42	60	p	p	NOUN
ap-5981	42	61	stands	stand	VERB
ap-5981	42	62	for	for	ADP
ap-5981	42	63	the	the	DET
ap-5981	42	64	number	number	NOUN
ap-5981	42	65	of	of	ADP
ap-5981	42	66	maxwell	maxwell	PROPN
ap-5981	42	67	cells	cell	NOUN
ap-5981	42	68	.	.	PUNCT
ap-5981	43	1	equilibrium	equilibrium	NOUN
ap-5981	43	2	of	of	ADP
ap-5981	43	3	the	the	DET
ap-5981	43	4	forces	force	NOUN
ap-5981	43	5	acting	act	VERB
ap-5981	43	6	on	on	ADP
ap-5981	43	7	the	the	DET
ap-5981	43	8	mass	mass	NOUN
ap-5981	43	9	requires	require	VERB
ap-5981	43	10	mr̈(t	mr̈(t	NOUN
ap-5981	43	11	)	)	PUNCT
ap-5981	44	1	+	+	CCONJ
ap-5981	44	2	k∞r(t	k∞r(t	NOUN
ap-5981	44	3	)	)	PUNCT
ap-5981	45	1	+	+	NUM
ap-5981	45	2	p∑	p∑	NOUN
ap-5981	45	3	p=1	p=1	NOUN
ap-5981	45	4	fp(t	fp(t	NOUN
ap-5981	45	5	)	)	PUNCT
ap-5981	46	1	=	=	SYM
ap-5981	46	2	f	f	PROPN
ap-5981	46	3	(	(	PUNCT
ap-5981	46	4	t	t	PROPN
ap-5981	46	5	)	)	PUNCT
ap-5981	46	6	,	,	PUNCT
ap-5981	46	7	(	(	PUNCT
ap-5981	46	8	1	1	X
ap-5981	46	9	)	)	PUNCT
ap-5981	46	10	where	where	SCONJ
ap-5981	46	11	r	r	NOUN
ap-5981	46	12	denotes	denote	VERB
ap-5981	46	13	the	the	DET
ap-5981	46	14	displacement	displacement	NOUN
ap-5981	46	15	of	of	ADP
ap-5981	46	16	the	the	DET
ap-5981	46	17	mass	mass	NOUN
ap-5981	46	18	,	,	PUNCT
ap-5981	46	19	r̈	r̈	VERB
ap-5981	46	20	its	its	PRON
ap-5981	46	21	acceleration	acceleration	NOUN
ap-5981	46	22	,	,	PUNCT
ap-5981	46	23	and	and	CCONJ
ap-5981	46	24	fp	fp	X
ap-5981	46	25	the	the	DET
ap-5981	46	26	restoring	restore	VERB
ap-5981	46	27	force	force	NOUN
ap-5981	46	28	of	of	ADP
ap-5981	46	29	the	the	DET
ap-5981	46	30	p	p	NOUN
ap-5981	46	31	-	-	PUNCT
ap-5981	46	32	th	th	VERB
ap-5981	46	33	cell	cell	NOUN
ap-5981	46	34	.	.	PUNCT
ap-5981	47	1	for	for	ADP
ap-5981	47	2	the	the	DET
ap-5981	47	3	p	p	PROPN
ap-5981	47	4	-	-	PUNCT
ap-5981	47	5	th	th	VERB
ap-5981	47	6	maxwell	maxwell	NOUN
ap-5981	47	7	cell	cell	NOUN
ap-5981	47	8	,	,	PUNCT
ap-5981	47	9	the	the	DET
ap-5981	47	10	displacement	displacement	NOUN
ap-5981	47	11	r	r	NOUN
ap-5981	47	12	splits	split	VERB
ap-5981	47	13	into	into	ADP
ap-5981	47	14	an	an	DET
ap-5981	47	15	elastic	elastic	ADJ
ap-5981	47	16	part	part	NOUN
ap-5981	47	17	of	of	ADP
ap-5981	47	18	the	the	DET
ap-5981	47	19	spring	spring	NOUN
ap-5981	47	20	re	re	NOUN
ap-5981	47	21	,	,	PUNCT
ap-5981	47	22	p	p	NOUN
ap-5981	47	23	and	and	CCONJ
ap-5981	47	24	a	a	DET
ap-5981	47	25	viscous	viscous	ADJ
ap-5981	47	26	part	part	NOUN
ap-5981	47	27	of	of	ADP
ap-5981	47	28	the	the	DET
ap-5981	47	29	damper	damper	NOUN
ap-5981	47	30	rv	rv	PROPN
ap-5981	47	31	,	,	PUNCT
ap-5981	47	32	p	p	X
ap-5981	47	33	:	:	PUNCT
ap-5981	47	34	r(t	r(t	NOUN
ap-5981	47	35	)	)	PUNCT
ap-5981	47	36	=	=	SYM
ap-5981	47	37	re	re	NOUN
ap-5981	47	38	,	,	PUNCT
ap-5981	47	39	p(t	p(t	NOUN
ap-5981	47	40	)	)	PUNCT
ap-5981	48	1	+	+	CCONJ
ap-5981	48	2	rv	rv	PROPN
ap-5981	48	3	,	,	PUNCT
ap-5981	48	4	p(t	p(t	NOUN
ap-5981	48	5	)	)	PUNCT
ap-5981	48	6	;	;	PUNCT
ap-5981	48	7	(	(	PUNCT
ap-5981	48	8	2	2	X
ap-5981	48	9	)	)	PUNCT
ap-5981	48	10	recall	recall	NOUN
ap-5981	48	11	figure	figure	NOUN
ap-5981	48	12	1	1	NUM
ap-5981	48	13	.	.	PUNCT
ap-5981	49	1	the	the	DET
ap-5981	49	2	restoring	restore	VERB
ap-5981	49	3	force	force	NOUN
ap-5981	49	4	of	of	ADP
ap-5981	49	5	the	the	DET
ap-5981	49	6	p	p	PROPN
ap-5981	49	7	-	-	PUNCT
ap-5981	49	8	th	th	VERB
ap-5981	49	9	maxwell	maxwell	NOUN
ap-5981	49	10	cell	cell	NOUN
ap-5981	49	11	satisfies	satisfie	NOUN
ap-5981	49	12	fp(t	fp(t	NOUN
ap-5981	49	13	)	)	PUNCT
ap-5981	49	14	=	=	SYM
ap-5981	49	15	kpre	kpre	NOUN
ap-5981	49	16	,	,	PUNCT
ap-5981	49	17	p(t	p(t	NOUN
ap-5981	49	18	)	)	PUNCT
ap-5981	49	19	=	=	SYM
ap-5981	49	20	ηpṙv	ηpṙv	NOUN
ap-5981	49	21	,	,	PUNCT
ap-5981	49	22	p(t	p(t	NOUN
ap-5981	49	23	)	)	PUNCT
ap-5981	49	24	,	,	PUNCT
ap-5981	49	25	(	(	PUNCT
ap-5981	49	26	3	3	X
ap-5981	49	27	)	)	PUNCT
ap-5981	49	28	because	because	SCONJ
ap-5981	49	29	of	of	ADP
ap-5981	49	30	the	the	DET
ap-5981	49	31	serial	serial	ADJ
ap-5981	49	32	arrangement	arrangement	NOUN
ap-5981	49	33	of	of	ADP
ap-5981	49	34	the	the	DET
ap-5981	49	35	spring	spring	NOUN
ap-5981	49	36	and	and	CCONJ
ap-5981	49	37	the	the	DET
ap-5981	49	38	damper	damper	NOUN
ap-5981	49	39	in	in	ADP
ap-5981	49	40	the	the	DET
ap-5981	49	41	cell	cell	NOUN
ap-5981	49	42	.	.	PUNCT
ap-5981	50	1	differentiating	differentiate	VERB
ap-5981	50	2	(	(	PUNCT
ap-5981	50	3	2	2	NUM
ap-5981	50	4	)	)	PUNCT
ap-5981	50	5	with	with	ADP
ap-5981	50	6	respect	respect	NOUN
ap-5981	50	7	to	to	ADP
ap-5981	50	8	time	time	NOUN
ap-5981	50	9	and	and	CCONJ
ap-5981	50	10	using	use	VERB
ap-5981	50	11	(	(	PUNCT
ap-5981	50	12	3	3	NUM
ap-5981	50	13	)	)	PUNCT
ap-5981	50	14	,	,	PUNCT
ap-5981	50	15	we	we	PRON
ap-5981	50	16	obtain	obtain	VERB
ap-5981	50	17	ḟp(t	ḟp(t	NUM
ap-5981	50	18	)	)	PUNCT
ap-5981	50	19	kp	kp	PROPN
ap-5981	51	1	+	+	CCONJ
ap-5981	52	1	fp(t	fp(t	NOUN
ap-5981	52	2	)	)	PUNCT
ap-5981	53	1	ηp	ηp	ADP
ap-5981	53	2	=	=	SYM
ap-5981	53	3	ṙ(t	ṙ(t	PROPN
ap-5981	53	4	)	)	PUNCT
ap-5981	53	5	.	.	PUNCT
ap-5981	54	1	(	(	PUNCT
ap-5981	54	2	4	4	X
ap-5981	54	3	)	)	PUNCT
ap-5981	54	4	in	in	ADP
ap-5981	54	5	summary	summary	NOUN
ap-5981	54	6	,	,	PUNCT
ap-5981	54	7	the	the	DET
ap-5981	54	8	motion	motion	NOUN
ap-5981	54	9	of	of	ADP
ap-5981	54	10	the	the	DET
ap-5981	54	11	sdof	sdof	ADJ
ap-5981	54	12	model	model	NOUN
ap-5981	54	13	is	be	AUX
ap-5981	54	14	described	describe	VERB
ap-5981	54	15	with	with	ADP
ap-5981	54	16	the	the	DET
ap-5981	54	17	coupled	couple	VERB
ap-5981	54	18	system	system	NOUN
ap-5981	54	19	of	of	ADP
ap-5981	54	20	(	(	PUNCT
ap-5981	54	21	p	p	X
ap-5981	54	22	+	+	NOUN
ap-5981	54	23	1	1	NUM
ap-5981	54	24	)	)	PUNCT
ap-5981	54	25	ordinary	ordinary	ADJ
ap-5981	54	26	differential	differential	ADJ
ap-5981	54	27	equations	equation	NOUN
ap-5981	54	28	(	(	PUNCT
ap-5981	54	29	odes	ode	NOUN
ap-5981	54	30	)	)	PUNCT
ap-5981	54	31	(	(	PUNCT
ap-5981	54	32	1	1	X
ap-5981	54	33	)	)	PUNCT
ap-5981	54	34	and	and	CCONJ
ap-5981	54	35	(	(	PUNCT
ap-5981	54	36	4	4	NUM
ap-5981	54	37	)	)	PUNCT
ap-5981	54	38	,	,	PUNCT
ap-5981	54	39	complemented	complement	VERB
ap-5981	54	40	with	with	ADP
ap-5981	54	41	the	the	DET
ap-5981	54	42	initial	initial	ADJ
ap-5981	54	43	conditions	condition	NOUN
ap-5981	54	44	r(0	r(0	PROPN
ap-5981	54	45	)	)	PUNCT
ap-5981	54	46	=	=	SYM
ap-5981	54	47	r0	r0	NOUN
ap-5981	54	48	,	,	PUNCT
ap-5981	54	49	ṙ(0	ṙ(0	PROPN
ap-5981	54	50	)	)	PUNCT
ap-5981	54	51	=	=	SYM
ap-5981	54	52	v0	v0	PROPN
ap-5981	54	53	,	,	PUNCT
ap-5981	54	54	fp(0	fp(0	NOUN
ap-5981	54	55	)	)	PUNCT
ap-5981	55	1	=	=	SYM
ap-5981	55	2	fp,0	fp,0	PROPN
ap-5981	55	3	,	,	PUNCT
ap-5981	55	4	(	(	PUNCT
ap-5981	55	5	5	5	NUM
ap-5981	55	6	)	)	PUNCT
ap-5981	55	7	where	where	SCONJ
ap-5981	55	8	r0	r0	NOUN
ap-5981	55	9	and	and	CCONJ
ap-5981	55	10	v0	v0	NOUN
ap-5981	55	11	stand	stand	NOUN
ap-5981	55	12	for	for	ADP
ap-5981	55	13	the	the	DET
ap-5981	55	14	initial	initial	ADJ
ap-5981	55	15	mass	mass	ADJ
ap-5981	55	16	displacement	displacement	NOUN
ap-5981	55	17	and	and	CCONJ
ap-5981	55	18	velocity	velocity	NOUN
ap-5981	55	19	,	,	PUNCT
ap-5981	55	20	respectively	respectively	ADV
ap-5981	55	21	,	,	PUNCT
ap-5981	55	22	fp,0	fp,0	PROPN
ap-5981	55	23	is	be	AUX
ap-5981	55	24	the	the	DET
ap-5981	55	25	initial	initial	ADJ
ap-5981	55	26	force	force	NOUN
ap-5981	55	27	in	in	ADP
ap-5981	55	28	the	the	DET
ap-5981	55	29	p	p	PROPN
ap-5981	55	30	-	-	PUNCT
ap-5981	55	31	th	th	VERB
ap-5981	55	32	maxwell	maxwell	NOUN
ap-5981	55	33	cell	cell	NOUN
ap-5981	55	34	,	,	PUNCT
ap-5981	55	35	and	and	CCONJ
ap-5981	55	36	p	p	X
ap-5981	55	37	=	=	NOUN
ap-5981	55	38	1	1	NUM
ap-5981	55	39	,	,	PUNCT
ap-5981	55	40	.	.	PUNCT
ap-5981	55	41	.	.	PUNCT
ap-5981	56	1	.	.	PUNCT
ap-5981	57	1	,	,	PUNCT
ap-5981	58	1	p	p	X
ap-5981	58	2	.	.	PUNCT
ap-5981	59	1	2.2	2.2	NUM
ap-5981	59	2	.	.	PUNCT
ap-5981	59	3	discretization	discretization	VERB
ap-5981	59	4	the	the	DET
ap-5981	59	5	time	time	NOUN
ap-5981	59	6	interval	interval	NOUN
ap-5981	59	7	of	of	ADP
ap-5981	59	8	interest	interest	NOUN
ap-5981	59	9	〈	〈	PROPN
ap-5981	59	10	0	0	NUM
ap-5981	59	11	,	,	PUNCT
ap-5981	59	12	t	t	PROPN
ap-5981	59	13	〉	〉	PROPN
ap-5981	59	14	is	be	AUX
ap-5981	59	15	divided	divide	VERB
ap-5981	59	16	into	into	ADP
ap-5981	59	17	(	(	PUNCT
ap-5981	59	18	n	n	X
ap-5981	59	19	+	+	CCONJ
ap-5981	59	20	1	1	NUM
ap-5981	59	21	)	)	PUNCT
ap-5981	59	22	time	time	NOUN
ap-5981	59	23	instants	instant	VERB
ap-5981	59	24	0	0	NUM
ap-5981	60	1	=	=	SYM
ap-5981	60	2	t0	t0	PROPN
ap-5981	60	3	<	<	X
ap-5981	60	4	t1	t1	NOUN
ap-5981	60	5	<	<	X
ap-5981	60	6	t2	t2	PROPN
ap-5981	60	7	<	<	X
ap-5981	60	8	·	·	PUNCT
ap-5981	60	9	·	·	PUNCT
ap-5981	60	10	·	·	PUNCT
ap-5981	61	1	<	<	X
ap-5981	61	2	tn−1	tn−1	PROPN
ap-5981	61	3	<	<	X
ap-5981	61	4	tn	tn	NOUN
ap-5981	61	5	=	=	SYM
ap-5981	61	6	tmax	tmax	X
ap-5981	61	7	;	;	PUNCT
ap-5981	61	8	for	for	ADP
ap-5981	61	9	notational	notational	ADJ
ap-5981	61	10	simplicity	simplicity	NOUN
ap-5981	61	11	,	,	PUNCT
ap-5981	61	12	we	we	PRON
ap-5981	61	13	assume	assume	VERB
ap-5981	61	14	equidistant	equidistant	ADJ
ap-5981	61	15	partitioning	partitioning	NOUN
ap-5981	61	16	of	of	ADP
ap-5981	61	17	the	the	DET
ap-5981	61	18	constant	constant	ADJ
ap-5981	61	19	time	time	NOUN
ap-5981	61	20	step	step	NOUN
ap-5981	61	21	∆t	∆t	PROPN
ap-5981	61	22	=	=	SYM
ap-5981	62	1	ti+1	ti+1	ADV
ap-5981	62	2	−	−	NOUN
ap-5981	62	3	ti	ti	NOUN
ap-5981	62	4	.	.	PUNCT
ap-5981	62	5	considering	consider	VERB
ap-5981	62	6	the	the	DET
ap-5981	62	7	newmark	newmark	PROPN
ap-5981	62	8	integration	integration	NOUN
ap-5981	62	9	scheme	scheme	NOUN
ap-5981	62	10	[	[	X
ap-5981	62	11	17	17	NUM
ap-5981	62	12	]	]	PUNCT
ap-5981	62	13	with	with	ADP
ap-5981	62	14	an	an	DET
ap-5981	62	15	average	average	ADJ
ap-5981	62	16	acceleration	acceleration	NOUN
ap-5981	62	17	(	(	PUNCT
ap-5981	62	18	r̈i	r̈i	NOUN
ap-5981	62	19	+	+	CCONJ
ap-5981	62	20	r̈i+1)/2	r̈i+1)/2	NOUN
ap-5981	62	21	on	on	ADP
ap-5981	62	22	the	the	DET
ap-5981	62	23	time	time	NOUN
ap-5981	62	24	interval	interval	NOUN
ap-5981	62	25	〈	〈	PROPN
ap-5981	62	26	ti	ti	NOUN
ap-5981	62	27	,	,	PUNCT
ap-5981	62	28	ti+1	ti+1	PROPN
ap-5981	62	29	〉	〉	NUM
ap-5981	62	30	,	,	PUNCT
ap-5981	62	31	the	the	DET
ap-5981	62	32	velocity	velocity	NOUN
ap-5981	62	33	and	and	CCONJ
ap-5981	62	34	displacement	displacement	NOUN
ap-5981	62	35	within	within	ADP
ap-5981	62	36	the	the	DET
ap-5981	62	37	interval	interval	NOUN
ap-5981	62	38	vary	vary	VERB
ap-5981	62	39	as	as	ADP
ap-5981	62	40	ṙ(ti	ṙ(ti	NOUN
ap-5981	62	41	+	+	CCONJ
ap-5981	62	42	τ	τ	X
ap-5981	62	43	)	)	PUNCT
ap-5981	62	44	=	=	PUNCT
ap-5981	62	45	ṙi	ṙi	NOUN
ap-5981	62	46	+	+	CCONJ
ap-5981	62	47	1	1	NUM
ap-5981	62	48	2	2	NUM
ap-5981	62	49	(	(	PUNCT
ap-5981	62	50	r̈i	r̈i	NOUN
ap-5981	62	51	+	+	CCONJ
ap-5981	62	52	r̈i+1	r̈i+1	NOUN
ap-5981	62	53	)	)	PUNCT
ap-5981	62	54	τ	τ	PROPN
ap-5981	62	55	,	,	PUNCT
ap-5981	62	56	(	(	PUNCT
ap-5981	62	57	6a	6a	NOUN
ap-5981	62	58	)	)	PUNCT
ap-5981	62	59	r(ti	r(ti	NOUN
ap-5981	62	60	+	+	CCONJ
ap-5981	62	61	τ	τ	PROPN
ap-5981	62	62	)	)	PUNCT
ap-5981	62	63	=	=	SYM
ap-5981	62	64	ri	ri	PROPN
ap-5981	63	1	+	+	NOUN
ap-5981	63	2	ṙiτ	ṙiτ	NOUN
ap-5981	63	3	+	+	CCONJ
ap-5981	63	4	1	1	NUM
ap-5981	63	5	4	4	NUM
ap-5981	63	6	(	(	PUNCT
ap-5981	63	7	r̈	r̈	PROPN
ap-5981	63	8	+	+	CCONJ
ap-5981	63	9	r̈i+1	r̈i+1	NOUN
ap-5981	63	10	)	)	PUNCT
ap-5981	63	11	τ2	τ2	PROPN
ap-5981	63	12	,	,	PUNCT
ap-5981	63	13	(	(	PUNCT
ap-5981	63	14	6b	6b	NOUN
ap-5981	63	15	)	)	PUNCT
ap-5981	63	16	where	where	SCONJ
ap-5981	63	17	τ	τ	PROPN
ap-5981	63	18	∈	∈	PROPN
ap-5981	63	19	〈	〈	PROPN
ap-5981	63	20	0,∆t	0,∆t	NOUN
ap-5981	63	21	〉	〉	PROPN
ap-5981	63	22	is	be	AUX
ap-5981	63	23	the	the	DET
ap-5981	63	24	local	local	ADJ
ap-5981	63	25	time	time	NOUN
ap-5981	63	26	variable	variable	ADJ
ap-5981	63	27	within	within	ADP
ap-5981	63	28	the	the	DET
ap-5981	63	29	interval	interval	NOUN
ap-5981	63	30	and	and	CCONJ
ap-5981	63	31	•i	•i	NOUN
ap-5981	63	32	abbreviates	abbreviate	NOUN
ap-5981	63	33	•(ti	•(ti	NOUN
ap-5981	63	34	)	)	PUNCT
ap-5981	63	35	to	to	PART
ap-5981	63	36	render	render	VERB
ap-5981	63	37	the	the	DET
ap-5981	63	38	notation	notation	NOUN
ap-5981	63	39	compact	compact	ADJ
ap-5981	63	40	.	.	PUNCT
ap-5981	64	1	substituting	substitute	VERB
ap-5981	64	2	(	(	PUNCT
ap-5981	64	3	6a	6a	NOUN
ap-5981	64	4	)	)	PUNCT
ap-5981	64	5	into	into	ADP
ap-5981	64	6	(	(	PUNCT
ap-5981	64	7	4	4	NUM
ap-5981	64	8	)	)	PUNCT
ap-5981	64	9	reveals	reveal	VERB
ap-5981	64	10	that	that	SCONJ
ap-5981	64	11	the	the	DET
ap-5981	64	12	evolution	evolution	NOUN
ap-5981	64	13	of	of	ADP
ap-5981	64	14	the	the	DET
ap-5981	64	15	restoring	restore	VERB
ap-5981	64	16	force	force	NOUN
ap-5981	64	17	fp	fp	ADP
ap-5981	64	18	satisfies	satisfie	NOUN
ap-5981	64	19	ḟp(ti	ḟp(ti	NOUN
ap-5981	64	20	+	+	CCONJ
ap-5981	64	21	τ	τ	PROPN
ap-5981	64	22	)	)	PUNCT
ap-5981	64	23	kp	kp	PROPN
ap-5981	65	1	+	+	CCONJ
ap-5981	65	2	fp(ti	fp(ti	NOUN
ap-5981	65	3	+	+	CCONJ
ap-5981	65	4	τ	τ	PROPN
ap-5981	65	5	)	)	PUNCT
ap-5981	65	6	ηp	ηp	PROPN
ap-5981	66	1	=	=	PUNCT
ap-5981	66	2	ṙi	ṙi	NOUN
ap-5981	66	3	+	+	CCONJ
ap-5981	66	4	1	1	NUM
ap-5981	66	5	2	2	NUM
ap-5981	66	6	(	(	PUNCT
ap-5981	66	7	r̈i	r̈i	NOUN
ap-5981	66	8	+	+	CCONJ
ap-5981	66	9	r̈i+1)τ	r̈i+1)τ	PROPN
ap-5981	66	10	.	.	PUNCT
ap-5981	67	1	(	(	PUNCT
ap-5981	67	2	7	7	X
ap-5981	67	3	)	)	PUNCT
ap-5981	67	4	this	this	DET
ap-5981	67	5	cauchy	cauchy	ADJ
ap-5981	67	6	problem	problem	NOUN
ap-5981	67	7	with	with	ADP
ap-5981	67	8	the	the	DET
ap-5981	67	9	initial	initial	ADJ
ap-5981	67	10	condition	condition	NOUN
ap-5981	67	11	fp(ti	fp(ti	NOUN
ap-5981	67	12	)	)	PUNCT
ap-5981	68	1	=	=	SYM
ap-5981	68	2	fp	fp	X
ap-5981	68	3	,	,	PUNCT
ap-5981	68	4	i	i	PRON
ap-5981	68	5	has	have	VERB
ap-5981	68	6	the	the	DET
ap-5981	68	7	solution	solution	NOUN
ap-5981	68	8	fp(ti	fp(ti	NOUN
ap-5981	68	9	+	+	CCONJ
ap-5981	68	10	τ	τ	PROPN
ap-5981	68	11	)	)	PUNCT
ap-5981	68	12	=(	=(	NOUN
ap-5981	69	1	fp	fp	INTJ
ap-5981	69	2	,	,	PUNCT
ap-5981	69	3	i	i	PRON
ap-5981	69	4	−	−	PROPN
ap-5981	69	5	ηpṙi	ηpṙi	NOUN
ap-5981	69	6	+	+	NUM
ap-5981	69	7	η2	η2	PROPN
ap-5981	69	8	p	p	NOUN
ap-5981	69	9	2kp	2kp	ADJ
ap-5981	69	10	(	(	PUNCT
ap-5981	69	11	r̈i	r̈i	NOUN
ap-5981	69	12	+	+	CCONJ
ap-5981	69	13	r̈i+1	r̈i+1	NOUN
ap-5981	69	14	)	)	PUNCT
ap-5981	69	15	)	)	PUNCT
ap-5981	69	16	exp	exp	NOUN
ap-5981	69	17	(	(	PUNCT
ap-5981	69	18	−kp	−kp	NOUN
ap-5981	69	19	ηp	ηp	PROPN
ap-5981	69	20	τ	τ	PROPN
ap-5981	69	21	)	)	PUNCT
ap-5981	70	1	+	+	PUNCT
ap-5981	70	2	ηpṙi	ηpṙi	NOUN
ap-5981	70	3	+	+	CCONJ
ap-5981	70	4	ηpτkp	ηpτkp	NOUN
ap-5981	70	5	−	−	PROPN
ap-5981	70	6	η2	η2	PROPN
ap-5981	70	7	p	p	NOUN
ap-5981	70	8	2kp	2kp	ADJ
ap-5981	70	9	(	(	PUNCT
ap-5981	70	10	r̈i	r̈i	NOUN
ap-5981	70	11	+	+	CCONJ
ap-5981	70	12	r̈i+1	r̈i+1	NOUN
ap-5981	70	13	)	)	PUNCT
ap-5981	70	14	.	.	PUNCT
ap-5981	71	1	(	(	PUNCT
ap-5981	71	2	8)	8)	NUM
ap-5981	71	3	thus	thus	ADV
ap-5981	71	4	,	,	PUNCT
ap-5981	71	5	at	at	ADP
ap-5981	71	6	the	the	DET
ap-5981	71	7	end	end	NOUN
ap-5981	71	8	of	of	ADP
ap-5981	71	9	the	the	DET
ap-5981	71	10	time	time	NOUN
ap-5981	71	11	interval	interval	NOUN
ap-5981	71	12	with	with	ADP
ap-5981	71	13	τ	τ	PROPN
ap-5981	71	14	=	=	SYM
ap-5981	71	15	∆t	∆t	PROPN
ap-5981	71	16	,	,	PUNCT
ap-5981	71	17	we	we	PRON
ap-5981	71	18	have	have	VERB
ap-5981	71	19	fp	fp	NOUN
ap-5981	71	20	,	,	PUNCT
ap-5981	71	21	i+1	i+1	NOUN
ap-5981	71	22	=	=	NOUN
ap-5981	71	23	apfp	apfp	NOUN
ap-5981	71	24	,	,	PUNCT
ap-5981	71	25	i	i	PROPN
ap-5981	71	26	+	+	NOUN
ap-5981	71	27	kpθ̂pṙi	kpθ̂pṙi	NOUN
ap-5981	72	1	+	+	NOUN
ap-5981	72	2	bp	bp	PROPN
ap-5981	72	3	(	(	PUNCT
ap-5981	72	4	r̈i	r̈i	PROPN
ap-5981	72	5	+	+	CCONJ
ap-5981	72	6	r̈i+1	r̈i+1	NOUN
ap-5981	72	7	)	)	PUNCT
ap-5981	72	8	,	,	PUNCT
ap-5981	72	9	(	(	PUNCT
ap-5981	72	10	9	9	X
ap-5981	72	11	)	)	PUNCT
ap-5981	72	12	where	where	SCONJ
ap-5981	72	13	θ̂p	θ̂p	ADV
ap-5981	72	14	=	=	SYM
ap-5981	72	15	ηp	ηp	PROPN
ap-5981	72	16	kp	kp	PROPN
ap-5981	72	17	(	(	PUNCT
ap-5981	72	18	1−	1−	NUM
ap-5981	72	19	exp	exp	NOUN
ap-5981	72	20	(	(	PUNCT
ap-5981	72	21	−kp	−kp	NOUN
ap-5981	72	22	ηp	ηp	ADP
ap-5981	72	23	∆t	∆t	PROPN
ap-5981	72	24	)	)	PUNCT
ap-5981	72	25	)	)	PUNCT
ap-5981	72	26	(	(	PUNCT
ap-5981	72	27	10	10	X
ap-5981	72	28	)	)	PUNCT
ap-5981	72	29	denotes	denote	VERB
ap-5981	72	30	the	the	DET
ap-5981	72	31	effective	effective	ADJ
ap-5981	72	32	relaxation	relaxation	NOUN
ap-5981	72	33	time	time	NOUN
ap-5981	72	34	of	of	ADP
ap-5981	72	35	the	the	DET
ap-5981	72	36	p	p	NOUN
ap-5981	72	37	-	-	PUNCT
ap-5981	72	38	th	th	X
ap-5981	72	39	cell	cell	NOUN
ap-5981	72	40	and	and	CCONJ
ap-5981	72	41	the	the	DET
ap-5981	72	42	auxiliary	auxiliary	ADJ
ap-5981	72	43	factors	factor	NOUN
ap-5981	72	44	are	be	AUX
ap-5981	72	45	given	give	VERB
ap-5981	72	46	by	by	ADP
ap-5981	72	47	ap	ap	PROPN
ap-5981	72	48	=	=	PUNCT
ap-5981	73	1	(	(	PUNCT
ap-5981	73	2	1−	1−	NUM
ap-5981	73	3	kp	kp	PROPN
ap-5981	73	4	ηp	ηp	PROPN
ap-5981	73	5	θ̂p	θ̂p	PROPN
ap-5981	73	6	)	)	PUNCT
ap-5981	73	7	,	,	PUNCT
ap-5981	73	8	bp	bp	PROPN
ap-5981	73	9	=	=	SYM
ap-5981	73	10	1	1	NUM
ap-5981	73	11	2ηp	2ηp	ADV
ap-5981	73	12	(	(	PUNCT
ap-5981	73	13	∆t−	∆t−	PROPN
ap-5981	73	14	θ̂p	θ̂p	ADJ
ap-5981	73	15	)	)	PUNCT
ap-5981	73	16	.	.	PUNCT
ap-5981	74	1	(	(	PUNCT
ap-5981	74	2	11	11	NUM
ap-5981	74	3	)	)	PUNCT
ap-5981	74	4	503	503	NUM
ap-5981	74	5	j.	j.	PROPN
ap-5981	74	6	schmidt	schmidt	PROPN
ap-5981	74	7	,	,	PUNCT
ap-5981	74	8	t.	t.	PROPN
ap-5981	74	9	janda	janda	PROPN
ap-5981	74	10	,	,	PUNCT
ap-5981	74	11	a.	a.	PROPN
ap-5981	74	12	zemanová	zemanová	PROPN
ap-5981	74	13	et	et	PROPN
ap-5981	74	14	al	al	PROPN
ap-5981	74	15	.	.	PROPN
ap-5981	74	16	acta	acta	PROPN
ap-5981	74	17	polytechnica	polytechnica	PROPN
ap-5981	74	18	finally	finally	ADV
ap-5981	74	19	,	,	PUNCT
ap-5981	74	20	substituting	substitute	VERB
ap-5981	74	21	equations	equation	NOUN
ap-5981	74	22	(	(	PUNCT
ap-5981	74	23	6b	6b	NOUN
ap-5981	74	24	)	)	PUNCT
ap-5981	74	25	and	and	CCONJ
ap-5981	74	26	(	(	PUNCT
ap-5981	74	27	9	9	NUM
ap-5981	74	28	)	)	PUNCT
ap-5981	74	29	into	into	ADP
ap-5981	74	30	(	(	PUNCT
ap-5981	74	31	1	1	X
ap-5981	74	32	)	)	PUNCT
ap-5981	74	33	expressed	express	VERB
ap-5981	74	34	at	at	ADP
ap-5981	74	35	ti+1	ti+1	NOUN
ap-5981	74	36	=	=	SYM
ap-5981	74	37	ti	ti	PROPN
ap-5981	74	38	+	+	CCONJ
ap-5981	74	39	∆t	∆t	PROPN
ap-5981	74	40	and	and	CCONJ
ap-5981	74	41	rearranging	rearrange	VERB
ap-5981	74	42	the	the	DET
ap-5981	74	43	terms	term	NOUN
ap-5981	74	44	yields	yield	NOUN
ap-5981	74	45	(	(	PUNCT
ap-5981	74	46	m+	m+	NUM
ap-5981	74	47	1	1	NUM
ap-5981	74	48	4k∞∆t2	4k∞∆t2	NUM
ap-5981	74	49	+	+	NUM
ap-5981	74	50	p∑	p∑	ADJ
ap-5981	74	51	p=1	p=1	NOUN
ap-5981	74	52	bp	bp	PROPN
ap-5981	74	53	)	)	PUNCT
ap-5981	74	54	r̈i+1	r̈i+1	VERB
ap-5981	74	55	=	=	SYM
ap-5981	74	56	fi+1	fi+1	NOUN
ap-5981	75	1	−	−	PROPN
ap-5981	75	2	p∑	p∑	PROPN
ap-5981	75	3	p=1	p=1	NOUN
ap-5981	75	4	apfp	apfp	NOUN
ap-5981	75	5	,	,	PUNCT
ap-5981	75	6	i	i	PRON
ap-5981	75	7	−k∞ri	−k∞ri	VERB
ap-5981	75	8	−	−	PROPN
ap-5981	76	1	(	(	PUNCT
ap-5981	76	2	k∞∆t+	k∞∆t+	PROPN
ap-5981	76	3	p∑	p∑	X
ap-5981	76	4	p=1	p=1	X
ap-5981	76	5	kpθ̂p	kpθ̂p	PROPN
ap-5981	76	6	)	)	PUNCT
ap-5981	76	7	ṙi	ṙi	NOUN
ap-5981	76	8	−	−	PROPN
ap-5981	77	1	(	(	PUNCT
ap-5981	77	2	1	1	NUM
ap-5981	77	3	4k∞∆t2	4k∞∆t2	NUM
ap-5981	77	4	+	+	NUM
ap-5981	77	5	p∑	p∑	ADJ
ap-5981	77	6	p=1	p=1	NOUN
ap-5981	77	7	bp	bp	PROPN
ap-5981	77	8	)	)	PUNCT
ap-5981	77	9	r̈i	r̈i	VERB
ap-5981	77	10	.	.	PUNCT
ap-5981	78	1	(	(	PUNCT
ap-5981	78	2	12	12	NUM
ap-5981	78	3	)	)	PUNCT
ap-5981	78	4	after	after	ADP
ap-5981	78	5	solving	solve	VERB
ap-5981	78	6	eq	eq	ADP
ap-5981	78	7	.	.	PUNCT
ap-5981	79	1	(	(	PUNCT
ap-5981	79	2	12	12	NUM
ap-5981	79	3	)	)	PUNCT
ap-5981	79	4	for	for	ADP
ap-5981	79	5	the	the	DET
ap-5981	79	6	acceleration	acceleration	NOUN
ap-5981	79	7	r̈i+1	r̈i+1	NOUN
ap-5981	79	8	,	,	PUNCT
ap-5981	79	9	we	we	PRON
ap-5981	79	10	update	update	VERB
ap-5981	79	11	velocity	velocity	NOUN
ap-5981	79	12	ṙi+1	ṙi+1	NOUN
ap-5981	79	13	,	,	PUNCT
ap-5981	79	14	displacement	displacement	ADJ
ap-5981	79	15	ri+1	ri+1	NOUN
ap-5981	79	16	,	,	PUNCT
ap-5981	79	17	and	and	CCONJ
ap-5981	79	18	restoring	restore	VERB
ap-5981	79	19	forces	force	NOUN
ap-5981	79	20	fp	fp	NOUN
ap-5981	79	21	,	,	PUNCT
ap-5981	79	22	i	i	PRON
ap-5981	79	23	according	accord	VERB
ap-5981	79	24	to	to	ADP
ap-5981	79	25	equations	equation	NOUN
ap-5981	79	26	(	(	PUNCT
ap-5981	79	27	6a	6a	NOUN
ap-5981	79	28	)	)	PUNCT
ap-5981	79	29	,	,	PUNCT
ap-5981	79	30	(	(	PUNCT
ap-5981	79	31	6b	6b	NOUN
ap-5981	79	32	)	)	PUNCT
ap-5981	79	33	,	,	PUNCT
ap-5981	79	34	and	and	CCONJ
ap-5981	79	35	(	(	PUNCT
ap-5981	79	36	9	9	NUM
ap-5981	79	37	)	)	PUNCT
ap-5981	79	38	,	,	PUNCT
ap-5981	79	39	respectively	respectively	ADV
ap-5981	79	40	,	,	PUNCT
ap-5981	79	41	and	and	CCONJ
ap-5981	79	42	proceed	proceed	VERB
ap-5981	79	43	to	to	ADP
ap-5981	79	44	the	the	DET
ap-5981	79	45	next	next	ADJ
ap-5981	79	46	time	time	NOUN
ap-5981	79	47	interval	interval	NOUN
ap-5981	79	48	.	.	PUNCT
ap-5981	80	1	note	note	VERB
ap-5981	80	2	that	that	SCONJ
ap-5981	80	3	the	the	DET
ap-5981	80	4	initial	initial	ADJ
ap-5981	80	5	acceleration	acceleration	NOUN
ap-5981	80	6	r̈0	r̈0	NOUN
ap-5981	80	7	,	,	PUNCT
ap-5981	80	8	needed	need	VERB
ap-5981	80	9	in	in	ADP
ap-5981	80	10	the	the	DET
ap-5981	80	11	first	first	ADJ
ap-5981	80	12	step	step	NOUN
ap-5981	80	13	of	of	ADP
ap-5981	80	14	the	the	DET
ap-5981	80	15	algorithm	algorithm	NOUN
ap-5981	80	16	,	,	PUNCT
ap-5981	80	17	is	be	AUX
ap-5981	80	18	set	set	VERB
ap-5981	80	19	to	to	PART
ap-5981	80	20	r̈0	r̈0	VERB
ap-5981	80	21	=	=	PUNCT
ap-5981	80	22	1	1	NUM
ap-5981	80	23	m	m	NOUN
ap-5981	80	24	(	(	PUNCT
ap-5981	80	25	f	f	X
ap-5981	80	26	(	(	PUNCT
ap-5981	80	27	0)−	0)−	NOUN
ap-5981	80	28	k∞r0	k∞r0	VERB
ap-5981	80	29	−	−	PROPN
ap-5981	81	1	p∑	p∑	NOUN
ap-5981	82	1	p=1	p=1	NOUN
ap-5981	83	1	fp,0	fp,0	PROPN
ap-5981	83	2	)	)	PUNCT
ap-5981	83	3	,	,	PUNCT
ap-5981	83	4	(	(	PUNCT
ap-5981	83	5	13	13	NUM
ap-5981	83	6	)	)	PUNCT
ap-5981	83	7	according	accord	VERB
ap-5981	83	8	to	to	ADP
ap-5981	83	9	the	the	DET
ap-5981	83	10	equilibrium	equilibrium	NOUN
ap-5981	83	11	(	(	PUNCT
ap-5981	83	12	1	1	NUM
ap-5981	83	13	)	)	PUNCT
ap-5981	83	14	and	and	CCONJ
ap-5981	83	15	initial	initial	ADJ
ap-5981	83	16	(	(	PUNCT
ap-5981	83	17	5	5	NUM
ap-5981	83	18	)	)	PUNCT
ap-5981	83	19	conditions	condition	NOUN
ap-5981	83	20	.	.	PUNCT
ap-5981	84	1	3	3	X
ap-5981	84	2	.	.	X
ap-5981	84	3	variational	variational	ADJ
ap-5981	84	4	integrators	integrator	NOUN
ap-5981	84	5	having	having	AUX
ap-5981	84	6	derived	derive	VERB
ap-5981	84	7	the	the	DET
ap-5981	84	8	newmark	newmark	PROPN
ap-5981	84	9	viscoelastic	viscoelastic	PROPN
ap-5981	84	10	algorithm	algorithm	NOUN
ap-5981	84	11	by	by	ADP
ap-5981	84	12	conventional	conventional	ADJ
ap-5981	84	13	means	mean	NOUN
ap-5981	84	14	,	,	PUNCT
ap-5981	84	15	we	we	PRON
ap-5981	84	16	now	now	ADV
ap-5981	84	17	demonstrate	demonstrate	VERB
ap-5981	84	18	its	its	PRON
ap-5981	84	19	variational	variational	ADJ
ap-5981	84	20	structure	structure	NOUN
ap-5981	84	21	,	,	PUNCT
ap-5981	84	22	by	by	ADP
ap-5981	84	23	adapting	adapt	VERB
ap-5981	84	24	the	the	DET
ap-5981	84	25	general	general	ADJ
ap-5981	84	26	arguments	argument	NOUN
ap-5981	84	27	on	on	ADP
ap-5981	84	28	variational	variational	ADJ
ap-5981	84	29	integrators	integrator	NOUN
ap-5981	84	30	by	by	ADP
ap-5981	84	31	kane	kane	PROPN
ap-5981	84	32	et	et	PROPN
ap-5981	84	33	al	al	PROPN
ap-5981	84	34	.	.	PUNCT
ap-5981	85	1	[	[	X
ap-5981	85	2	18	18	NUM
ap-5981	85	3	]	]	PUNCT
ap-5981	85	4	to	to	ADP
ap-5981	85	5	the	the	DET
ap-5981	85	6	current	current	ADJ
ap-5981	85	7	setting	setting	NOUN
ap-5981	85	8	.	.	PUNCT
ap-5981	86	1	we	we	PRON
ap-5981	86	2	will	will	AUX
ap-5981	86	3	proceed	proceed	VERB
ap-5981	86	4	in	in	ADP
ap-5981	86	5	four	four	NUM
ap-5981	86	6	steps	step	NOUN
ap-5981	86	7	.	.	PUNCT
ap-5981	87	1	in	in	ADP
ap-5981	87	2	section	section	NOUN
ap-5981	87	3	3.1	3.1	NUM
ap-5981	87	4	,	,	PUNCT
ap-5981	87	5	we	we	PRON
ap-5981	87	6	show	show	VERB
ap-5981	87	7	that	that	SCONJ
ap-5981	87	8	the	the	DET
ap-5981	87	9	governing	govern	VERB
ap-5981	87	10	equations	equation	NOUN
ap-5981	87	11	from	from	ADP
ap-5981	87	12	section	section	NOUN
ap-5981	87	13	2.1	2.1	NUM
ap-5981	87	14	follow	follow	NOUN
ap-5981	87	15	from	from	ADP
ap-5981	87	16	the	the	DET
ap-5981	87	17	euler	euler	NOUN
ap-5981	87	18	-	-	PUNCT
ap-5981	87	19	lagrange	lagrange	NOUN
ap-5981	87	20	(	(	PUNCT
ap-5981	87	21	e	e	NOUN
ap-5981	87	22	-	-	NOUN
ap-5981	87	23	l	l	NOUN
ap-5981	87	24	)	)	PUNCT
ap-5981	87	25	equations	equation	NOUN
ap-5981	87	26	of	of	ADP
ap-5981	87	27	a	a	DET
ap-5981	87	28	suitably	suitably	ADV
ap-5981	87	29	defined	define	VERB
ap-5981	87	30	energy	energy	NOUN
ap-5981	87	31	functional	functional	ADJ
ap-5981	87	32	.	.	PUNCT
ap-5981	88	1	its	its	PRON
ap-5981	88	2	discretization	discretization	NOUN
ap-5981	88	3	then	then	ADV
ap-5981	88	4	provides	provide	VERB
ap-5981	88	5	the	the	DET
ap-5981	88	6	governing	govern	VERB
ap-5981	88	7	equations	equation	NOUN
ap-5981	88	8	of	of	ADP
ap-5981	88	9	the	the	DET
ap-5981	88	10	corresponding	corresponding	ADJ
ap-5981	88	11	variational	variational	ADJ
ap-5981	88	12	integrator	integrator	NOUN
ap-5981	88	13	introduced	introduce	VERB
ap-5981	88	14	in	in	ADP
ap-5981	88	15	section	section	NOUN
ap-5981	88	16	3.2	3.2	NUM
ap-5981	88	17	.	.	PUNCT
ap-5981	89	1	in	in	ADP
ap-5981	89	2	section	section	NOUN
ap-5981	89	3	3.3	3.3	NUM
ap-5981	89	4	,	,	PUNCT
ap-5981	89	5	we	we	PRON
ap-5981	89	6	demonstrate	demonstrate	VERB
ap-5981	89	7	the	the	DET
ap-5981	89	8	equivalence	equivalence	NOUN
ap-5981	89	9	of	of	ADP
ap-5981	89	10	the	the	DET
ap-5981	89	11	integrator	integrator	NOUN
ap-5981	89	12	to	to	ADP
ap-5981	89	13	the	the	DET
ap-5981	89	14	newmark	newmark	PROPN
ap-5981	89	15	algorithm	algorithm	NOUN
ap-5981	89	16	from	from	ADP
ap-5981	89	17	section	section	NOUN
ap-5981	89	18	2.2	2.2	NUM
ap-5981	89	19	.	.	PUNCT
ap-5981	90	1	in	in	ADP
ap-5981	90	2	the	the	DET
ap-5981	90	3	last	last	ADJ
ap-5981	90	4	step	step	NOUN
ap-5981	90	5	,	,	PUNCT
ap-5981	90	6	section	section	NOUN
ap-5981	90	7	3.4	3.4	NUM
ap-5981	90	8	,	,	PUNCT
ap-5981	90	9	we	we	PRON
ap-5981	90	10	comment	comment	VERB
ap-5981	90	11	on	on	ADP
ap-5981	90	12	the	the	DET
ap-5981	90	13	energy	energy	NOUN
ap-5981	90	14	conservation	conservation	NOUN
ap-5981	90	15	properties	property	NOUN
ap-5981	90	16	of	of	ADP
ap-5981	90	17	the	the	DET
ap-5981	90	18	time	time	NOUN
ap-5981	90	19	integration	integration	NOUN
ap-5981	90	20	scheme	scheme	NOUN
ap-5981	90	21	.	.	PUNCT
ap-5981	91	1	3.1	3.1	NUM
ap-5981	91	2	.	.	PUNCT
ap-5981	91	3	variational	variational	ADJ
ap-5981	91	4	framework	framework	NOUN
ap-5981	91	5	we	we	PRON
ap-5981	91	6	postulate	postulate	VERB
ap-5981	91	7	that	that	SCONJ
ap-5981	91	8	the	the	DET
ap-5981	91	9	trajectory	trajectory	NOUN
ap-5981	91	10	q	q	X
ap-5981	91	11	:	:	PUNCT
ap-5981	91	12	(	(	PUNCT
ap-5981	91	13	0	0	NUM
ap-5981	91	14	,	,	PUNCT
ap-5981	91	15	t	t	NOUN
ap-5981	91	16	)	)	PUNCT
ap-5981	91	17	→	→	SYM
ap-5981	91	18	q	q	NOUN
ap-5981	91	19	of	of	ADP
ap-5981	91	20	a	a	DET
ap-5981	91	21	constrained	constrain	VERB
ap-5981	91	22	dissipative	dissipative	ADJ
ap-5981	91	23	mechanical	mechanical	ADJ
ap-5981	91	24	system	system	NOUN
ap-5981	91	25	in	in	ADP
ap-5981	91	26	the	the	DET
ap-5981	91	27	state	state	NOUN
ap-5981	91	28	space	space	NOUN
ap-5981	91	29	q	q	NOUN
ap-5981	91	30	is	be	AUX
ap-5981	91	31	given	give	VERB
ap-5981	91	32	by	by	ADP
ap-5981	91	33	the	the	DET
ap-5981	91	34	generalised	generalise	VERB
ap-5981	91	35	euler	euler	PROPN
ap-5981	91	36	-	-	PUNCT
ap-5981	91	37	lagrange	lagrange	PROPN
ap-5981	91	38	equations1	equations1	NOUN
ap-5981	91	39	,	,	PUNCT
ap-5981	91	40	e.g.	e.g.	ADV
ap-5981	91	41	,	,	PUNCT
ap-5981	91	42	[	[	X
ap-5981	91	43	22	22	NUM
ap-5981	91	44	,	,	PUNCT
ap-5981	91	45	section	section	NOUN
ap-5981	91	46	1.3	1.3	NUM
ap-5981	91	47	]	]	PUNCT
ap-5981	91	48	∂r(q̇(t	∂r(q̇(t	NOUN
ap-5981	91	49	)	)	PUNCT
ap-5981	91	50	)	)	PUNCT
ap-5981	92	1	∂q̇	∂q̇	NOUN
ap-5981	93	1	=	=	SYM
ap-5981	93	2	∂l(t	∂l(t	PROPN
ap-5981	93	3	,	,	PUNCT
ap-5981	93	4	q(t	q(t	PROPN
ap-5981	93	5	)	)	PUNCT
ap-5981	93	6	,	,	PUNCT
ap-5981	93	7	q̇(t),λ(t	q̇(t),λ(t	NOUN
ap-5981	93	8	)	)	PUNCT
ap-5981	93	9	)	)	PUNCT
ap-5981	94	1	∂q	∂q	NOUN
ap-5981	94	2	−	−	PROPN
ap-5981	94	3	∂	∂	NOUN
ap-5981	95	1	∂t	∂t	PROPN
ap-5981	95	2	∂l(t	∂l(t	PROPN
ap-5981	95	3	,	,	PUNCT
ap-5981	95	4	q(t	q(t	PROPN
ap-5981	95	5	)	)	PUNCT
ap-5981	95	6	,	,	PUNCT
ap-5981	95	7	q̇(t),λ(t	q̇(t),λ(t	NOUN
ap-5981	95	8	)	)	PUNCT
ap-5981	95	9	)	)	PUNCT
ap-5981	95	10	∂q̇	∂q̇	NOUN
ap-5981	95	11	,	,	PUNCT
ap-5981	95	12	(	(	PUNCT
ap-5981	95	13	14a	14a	NOUN
ap-5981	95	14	)	)	PUNCT
ap-5981	95	15	0	0	NUM
ap-5981	96	1	=	=	NUM
ap-5981	96	2	α(q(t	α(q(t	NUM
ap-5981	96	3	)	)	PUNCT
ap-5981	96	4	)	)	PUNCT
ap-5981	96	5	.	.	PUNCT
ap-5981	97	1	(	(	PUNCT
ap-5981	97	2	14b	14b	NUM
ap-5981	97	3	)	)	PUNCT
ap-5981	97	4	1the	1the	ADJ
ap-5981	97	5	term	term	NOUN
ap-5981	97	6	generalised	generalise	VERB
ap-5981	97	7	corresponds	correspond	NOUN
ap-5981	97	8	to	to	ADP
ap-5981	97	9	the	the	DET
ap-5981	97	10	appearance	appearance	NOUN
ap-5981	97	11	of	of	ADP
ap-5981	97	12	the	the	DET
ap-5981	97	13	non	non	ADJ
ap-5981	97	14	-	-	ADJ
ap-5981	97	15	conservative	conservative	ADJ
ap-5981	97	16	forces	force	NOUN
ap-5981	97	17	in	in	ADP
ap-5981	97	18	eq	eq	ADP
ap-5981	97	19	.	.	PUNCT
ap-5981	97	20	(	(	PUNCT
ap-5981	97	21	14a	14a	NOUN
ap-5981	97	22	)	)	PUNCT
ap-5981	97	23	.	.	PUNCT
ap-5981	98	1	here	here	ADV
ap-5981	98	2	,	,	PUNCT
ap-5981	98	3	r	r	NOUN
ap-5981	98	4	stands	stand	VERB
ap-5981	98	5	for	for	ADP
ap-5981	98	6	the	the	DET
ap-5981	98	7	dissipation	dissipation	NOUN
ap-5981	98	8	potential	potential	NOUN
ap-5981	98	9	,	,	PUNCT
ap-5981	98	10	l	l	NOUN
ap-5981	98	11	for	for	ADP
ap-5981	98	12	the	the	DET
ap-5981	98	13	lagrangian	lagrangian	NOUN
ap-5981	98	14	of	of	ADP
ap-5981	98	15	the	the	DET
ap-5981	98	16	problem	problem	NOUN
ap-5981	98	17	,	,	PUNCT
ap-5981	98	18	and	and	CCONJ
ap-5981	98	19	λ	λ	X
ap-5981	98	20	:	:	PUNCT
ap-5981	98	21	(	(	PUNCT
ap-5981	98	22	0	0	NUM
ap-5981	98	23	,	,	PUNCT
ap-5981	98	24	t	t	NOUN
ap-5981	98	25	)	)	PUNCT
ap-5981	98	26	→	→	PUNCT
ap-5981	98	27	λ	λ	PROPN
ap-5981	98	28	denotes	denote	VERB
ap-5981	98	29	the	the	DET
ap-5981	98	30	lagrange	lagrange	PROPN
ap-5981	98	31	multipliers	multiplier	NOUN
ap-5981	98	32	associated	associate	VERB
ap-5981	98	33	with	with	ADP
ap-5981	98	34	the	the	DET
ap-5981	98	35	kinematic	kinematic	ADJ
ap-5981	98	36	constraint	constraint	NOUN
ap-5981	98	37	function	function	NOUN
ap-5981	98	38	α	α	NOUN
ap-5981	98	39	.	.	PUNCT
ap-5981	99	1	besides	besides	ADV
ap-5981	99	2	,	,	PUNCT
ap-5981	99	3	these	these	DET
ap-5981	99	4	equations	equation	NOUN
ap-5981	99	5	correspond	correspond	VERB
ap-5981	99	6	to	to	ADP
ap-5981	99	7	the	the	DET
ap-5981	99	8	stationarity	stationarity	NOUN
ap-5981	99	9	conditions	condition	NOUN
ap-5981	99	10	of	of	ADP
ap-5981	99	11	the	the	DET
ap-5981	99	12	action	action	NOUN
ap-5981	99	13	functional	functional	ADJ
ap-5981	99	14	s(q̂	s(q̂	PROPN
ap-5981	99	15	,	,	PUNCT
ap-5981	99	16	λ̂	λ̂	X
ap-5981	99	17	)	)	PUNCT
ap-5981	100	1	=	=	SYM
ap-5981	101	1	∫	∫	PROPN
ap-5981	102	1	t	t	NOUN
ap-5981	102	2	0	0	NUM
ap-5981	102	3	l	l	NOUN
ap-5981	102	4	(	(	PUNCT
ap-5981	102	5	t	t	PROPN
ap-5981	102	6	,	,	PUNCT
ap-5981	102	7	q̂(t	q̂(t	ADJ
ap-5981	102	8	)	)	PUNCT
ap-5981	102	9	,	,	PUNCT
ap-5981	102	10	̂̇q(t	̂̇q(t	PROPN
ap-5981	102	11	)	)	PUNCT
ap-5981	102	12	,	,	PUNCT
ap-5981	102	13	λ̂(t	λ̂(t	NOUN
ap-5981	102	14	)	)	PUNCT
ap-5981	102	15	)	)	PUNCT
ap-5981	102	16	dt	dt	X
ap-5981	103	1	(	(	PUNCT
ap-5981	103	2	15	15	NUM
ap-5981	103	3	)	)	PUNCT
ap-5981	103	4	perturbed	perturb	VERB
ap-5981	103	5	by	by	ADP
ap-5981	103	6	the	the	DET
ap-5981	103	7	dissipative	dissipative	ADJ
ap-5981	103	8	forces	force	NOUN
ap-5981	103	9	∂q̇r	∂q̇r	VERB
ap-5981	103	10	.	.	PUNCT
ap-5981	104	1	note	note	VERB
ap-5981	104	2	that	that	SCONJ
ap-5981	104	3	the	the	DET
ap-5981	104	4	hat	hat	NOUN
ap-5981	104	5	symbol	symbol	NOUN
ap-5981	104	6	in	in	ADP
ap-5981	104	7	(	(	PUNCT
ap-5981	104	8	15	15	NUM
ap-5981	104	9	)	)	PUNCT
ap-5981	104	10	now	now	ADV
ap-5981	104	11	distinguishes	distinguish	VERB
ap-5981	104	12	the	the	DET
ap-5981	104	13	test	test	NOUN
ap-5981	104	14	quantities	quantity	NOUN
ap-5981	104	15	from	from	ADP
ap-5981	104	16	the	the	DET
ap-5981	104	17	true	true	ADJ
ap-5981	104	18	trajectories	trajectory	NOUN
ap-5981	104	19	defined	define	VERB
ap-5981	104	20	with	with	ADP
ap-5981	104	21	(	(	PUNCT
ap-5981	104	22	14	14	NUM
ap-5981	104	23	)	)	PUNCT
ap-5981	104	24	.	.	PUNCT
ap-5981	105	1	for	for	ADP
ap-5981	105	2	the	the	DET
ap-5981	105	3	problem	problem	NOUN
ap-5981	105	4	from	from	ADP
ap-5981	105	5	figure	figure	NOUN
ap-5981	105	6	1	1	NUM
ap-5981	105	7	,	,	PUNCT
ap-5981	105	8	the	the	DET
ap-5981	105	9	state	state	NOUN
ap-5981	105	10	variable	variable	NOUN
ap-5981	105	11	q̂(t	q̂(t	NOUN
ap-5981	105	12	)	)	PUNCT
ap-5981	105	13	=	=	PUNCT
ap-5981	106	1	[	[	PUNCT
ap-5981	106	2	r̂(t	r̂(t	NOUN
ap-5981	106	3	)	)	PUNCT
ap-5981	106	4	,	,	PUNCT
ap-5981	106	5	{	{	PUNCT
ap-5981	106	6	r̂(t)e	r̂(t)e	PROPN
ap-5981	106	7	,	,	PUNCT
ap-5981	106	8	p}pp=1	p}pp=1	NUM
ap-5981	106	9	,	,	PUNCT
ap-5981	106	10	{	{	PUNCT
ap-5981	106	11	r̂(t)v	r̂(t)v	PROPN
ap-5981	106	12	,	,	PUNCT
ap-5981	106	13	p}pp=1	p}pp=1	NUM
ap-5981	106	14	]	]	PUNCT
ap-5981	106	15	t	t	PROPN
ap-5981	106	16	(	(	PUNCT
ap-5981	106	17	16	16	NUM
ap-5981	106	18	)	)	PUNCT
ap-5981	106	19	collects	collect	VERB
ap-5981	106	20	the	the	DET
ap-5981	106	21	total	total	ADJ
ap-5981	106	22	displacement	displacement	NOUN
ap-5981	106	23	and	and	CCONJ
ap-5981	106	24	the	the	DET
ap-5981	106	25	displacements	displacement	NOUN
ap-5981	106	26	of	of	ADP
ap-5981	106	27	both	both	DET
ap-5981	106	28	components	component	NOUN
ap-5981	106	29	of	of	ADP
ap-5981	106	30	each	each	DET
ap-5981	106	31	maxwell	maxwell	PROPN
ap-5981	106	32	cell	cell	NOUN
ap-5981	106	33	;	;	PUNCT
ap-5981	106	34	the	the	DET
ap-5981	106	35	state	state	NOUN
ap-5981	106	36	space	space	NOUN
ap-5981	106	37	q	q	PROPN
ap-5981	107	1	=	=	PUNCT
ap-5981	107	2	r2p+1	r2p+1	NOUN
ap-5981	107	3	.	.	PUNCT
ap-5981	108	1	the	the	DET
ap-5981	108	2	lagrangian	lagrangian	NOUN
ap-5981	108	3	has	have	VERB
ap-5981	108	4	the	the	DET
ap-5981	108	5	standard	standard	ADJ
ap-5981	108	6	form	form	NOUN
ap-5981	108	7	l(t	l(t	NOUN
ap-5981	108	8	,	,	PUNCT
ap-5981	108	9	q̂	q̂	NUM
ap-5981	108	10	,	,	PUNCT
ap-5981	108	11	̂̇q	̂̇q	X
ap-5981	108	12	,	,	PUNCT
ap-5981	108	13	λ̂	λ̂	X
ap-5981	108	14	)	)	PUNCT
ap-5981	109	1	=	=	SYM
ap-5981	109	2	k(̂̇q)−	k(̂̇q)−	PROPN
ap-5981	109	3	e(q̂	e(q̂	PROPN
ap-5981	109	4	)	)	PUNCT
ap-5981	110	1	+	+	CCONJ
ap-5981	110	2	fext(t)tq̂	fext(t)tq̂	NOUN
ap-5981	110	3	+	+	CCONJ
ap-5981	110	4	λ̂tα(q̂	λ̂tα(q̂	PROPN
ap-5981	110	5	)	)	PUNCT
ap-5981	110	6	(	(	PUNCT
ap-5981	110	7	17	17	NUM
ap-5981	110	8	)	)	PUNCT
ap-5981	110	9	involving	involve	VERB
ap-5981	110	10	the	the	DET
ap-5981	110	11	kinetic	kinetic	ADJ
ap-5981	110	12	energy	energy	NOUN
ap-5981	110	13	k	k	NOUN
ap-5981	110	14	,	,	PUNCT
ap-5981	110	15	potential	potential	ADJ
ap-5981	110	16	energy	energy	NOUN
ap-5981	110	17	of	of	ADP
ap-5981	110	18	deformation	deformation	NOUN
ap-5981	110	19	e	e	NOUN
ap-5981	110	20	,	,	PUNCT
ap-5981	110	21	and	and	CCONJ
ap-5981	110	22	external	external	ADJ
ap-5981	110	23	forces	force	NOUN
ap-5981	110	24	fext	fext	NOUN
ap-5981	110	25	given	give	VERB
ap-5981	110	26	by	by	ADP
ap-5981	110	27	k(̂̇q	k(̂̇q	NOUN
ap-5981	110	28	)	)	PUNCT
ap-5981	110	29	=	=	SYM
ap-5981	110	30	1	1	NUM
ap-5981	110	31	2m(̂̇r)2	2m(̂̇r)2	NUM
ap-5981	110	32	,	,	PUNCT
ap-5981	110	33	(	(	PUNCT
ap-5981	110	34	18a	18a	NOUN
ap-5981	110	35	)	)	PUNCT
ap-5981	110	36	e(q̂	e(q̂	PROPN
ap-5981	110	37	)	)	PUNCT
ap-5981	110	38	=	=	SYM
ap-5981	110	39	1	1	NUM
ap-5981	110	40	2k∞r̂	2k∞r̂	NUM
ap-5981	110	41	2	2	NUM
ap-5981	110	42	+	+	CCONJ
ap-5981	110	43	1	1	NUM
ap-5981	110	44	2	2	NUM
ap-5981	110	45	p∑	p∑	NOUN
ap-5981	110	46	p=1	p=1	PROPN
ap-5981	110	47	kp(r̂e	kp(r̂e	PROPN
ap-5981	110	48	,	,	PUNCT
ap-5981	110	49	p)2	p)2	NOUN
ap-5981	110	50	,	,	PUNCT
ap-5981	110	51	(	(	PUNCT
ap-5981	110	52	18b	18b	X
ap-5981	110	53	)	)	PUNCT
ap-5981	110	54	fext(t	fext(t	NOUN
ap-5981	110	55	)	)	PUNCT
ap-5981	110	56	=	=	PUNCT
ap-5981	111	1	[	[	PUNCT
ap-5981	111	2	f	f	X
ap-5981	111	3	(	(	PUNCT
ap-5981	111	4	t	t	PROPN
ap-5981	111	5	)	)	PUNCT
ap-5981	111	6	,	,	PUNCT
ap-5981	111	7	01×2p	01×2p	NUM
ap-5981	111	8	]	]	PUNCT
ap-5981	111	9	t.	t.	PROPN
ap-5981	111	10	(	(	PUNCT
ap-5981	111	11	18c	18c	NUM
ap-5981	111	12	)	)	PUNCT
ap-5981	111	13	the	the	DET
ap-5981	111	14	kinematical	kinematical	ADJ
ap-5981	111	15	constraints	constraint	NOUN
ap-5981	111	16	take	take	VERB
ap-5981	111	17	the	the	DET
ap-5981	111	18	form	form	NOUN
ap-5981	111	19	αp(q̂	αp(q̂	NUM
ap-5981	111	20	)	)	PUNCT
ap-5981	111	21	=	=	SYM
ap-5981	111	22	r̂e	r̂e	PROPN
ap-5981	111	23	,	,	PUNCT
ap-5981	111	24	p	p	NOUN
ap-5981	111	25	+	+	X
ap-5981	111	26	r̂v	r̂v	ADJ
ap-5981	111	27	,	,	PUNCT
ap-5981	111	28	p	p	NOUN
ap-5981	111	29	−	−	PROPN
ap-5981	111	30	r̂	r̂	NOUN
ap-5981	111	31	,	,	PUNCT
ap-5981	111	32	p	p	NOUN
ap-5981	111	33	=	=	NOUN
ap-5981	111	34	1	1	NUM
ap-5981	111	35	,	,	PUNCT
ap-5981	111	36	.	.	PUNCT
ap-5981	111	37	.	.	PUNCT
ap-5981	112	1	.	.	PUNCT
ap-5981	113	1	,	,	PUNCT
ap-5981	113	2	p	p	X
ap-5981	113	3	;	;	PUNCT
ap-5981	113	4	(	(	PUNCT
ap-5981	113	5	19	19	NUM
ap-5981	113	6	)	)	PUNCT
ap-5981	113	7	the	the	DET
ap-5981	113	8	space	space	NOUN
ap-5981	113	9	of	of	ADP
ap-5981	113	10	the	the	DET
ap-5981	113	11	lagrange	lagrange	NOUN
ap-5981	113	12	multipliers	multiplier	NOUN
ap-5981	113	13	λ	λ	PROPN
ap-5981	113	14	then	then	ADV
ap-5981	113	15	becomes	become	VERB
ap-5981	113	16	rp	rp	NOUN
ap-5981	113	17	.	.	PUNCT
ap-5981	114	1	the	the	DET
ap-5981	114	2	last	last	ADJ
ap-5981	114	3	component	component	NOUN
ap-5981	114	4	of	of	ADP
ap-5981	114	5	the	the	DET
ap-5981	114	6	general	general	ADJ
ap-5981	114	7	framework	framework	NOUN
ap-5981	114	8	(	(	PUNCT
ap-5981	114	9	14	14	NUM
ap-5981	114	10	)	)	PUNCT
ap-5981	114	11	is	be	AUX
ap-5981	114	12	provided	provide	VERB
ap-5981	114	13	by	by	ADP
ap-5981	114	14	the	the	DET
ap-5981	114	15	dissipation	dissipation	NOUN
ap-5981	114	16	potential	potential	ADJ
ap-5981	114	17	r(̂̇q	r(̂̇q	NOUN
ap-5981	114	18	)	)	PUNCT
ap-5981	114	19	=	=	SYM
ap-5981	114	20	1	1	NUM
ap-5981	114	21	2	2	NUM
ap-5981	114	22	p∑	p∑	NOUN
ap-5981	114	23	p=1	p=1	PROPN
ap-5981	114	24	ηp(̂̇rv	ηp(̂̇rv	PROPN
ap-5981	114	25	,	,	PUNCT
ap-5981	114	26	p)2	p)2	NOUN
ap-5981	114	27	(	(	PUNCT
ap-5981	114	28	20	20	NUM
ap-5981	114	29	)	)	PUNCT
ap-5981	114	30	involving	involve	VERB
ap-5981	114	31	solely	solely	ADV
ap-5981	114	32	the	the	DET
ap-5981	114	33	viscous	viscous	ADJ
ap-5981	114	34	displacements	displacement	NOUN
ap-5981	114	35	of	of	ADP
ap-5981	114	36	all	all	DET
ap-5981	114	37	cells	cell	NOUN
ap-5981	114	38	.	.	PUNCT
ap-5981	115	1	in	in	ADP
ap-5981	115	2	this	this	DET
ap-5981	115	3	setting	setting	NOUN
ap-5981	115	4	,	,	PUNCT
ap-5981	115	5	the	the	DET
ap-5981	115	6	e	e	NOUN
ap-5981	115	7	-	-	NOUN
ap-5981	115	8	l	l	ADJ
ap-5981	115	9	equation	equation	NOUN
ap-5981	115	10	(	(	PUNCT
ap-5981	115	11	14a	14a	NOUN
ap-5981	115	12	)	)	PUNCT
ap-5981	115	13	represents	represent	VERB
ap-5981	115	14	the	the	DET
ap-5981	115	15	system	system	NOUN
ap-5981	115	16	of	of	ADP
ap-5981	115	17	(	(	PUNCT
ap-5981	115	18	1	1	NUM
ap-5981	115	19	+	+	CCONJ
ap-5981	115	20	2p	2p	NUM
ap-5981	115	21	)	)	PUNCT
ap-5981	115	22	optimality	optimality	NOUN
ap-5981	115	23	conditions	condition	NOUN
ap-5981	115	24	.	.	PUNCT
ap-5981	116	1	the	the	DET
ap-5981	116	2	first	first	ADJ
ap-5981	116	3	one	one	NUM
ap-5981	116	4	,	,	PUNCT
ap-5981	116	5	corresponding	correspond	VERB
ap-5981	116	6	to	to	ADP
ap-5981	116	7	the	the	DET
ap-5981	116	8	total	total	ADJ
ap-5981	116	9	displacement	displacement	ADJ
ap-5981	116	10	r	r	NOUN
ap-5981	116	11	,	,	PUNCT
ap-5981	116	12	takes	take	VERB
ap-5981	116	13	the	the	DET
ap-5981	116	14	form	form	NOUN
ap-5981	116	15	mr̈(t	mr̈(t	NOUN
ap-5981	116	16	)	)	PUNCT
ap-5981	116	17	+	+	CCONJ
ap-5981	116	18	k∞r(t	k∞r(t	NOUN
ap-5981	116	19	)	)	PUNCT
ap-5981	117	1	+	+	NUM
ap-5981	117	2	p∑	p∑	X
ap-5981	117	3	p=1	p=1	X
ap-5981	117	4	λp(t	λp(t	NOUN
ap-5981	117	5	)	)	PUNCT
ap-5981	117	6	=	=	SYM
ap-5981	117	7	f	f	PROPN
ap-5981	117	8	(	(	PUNCT
ap-5981	117	9	t	t	PROPN
ap-5981	117	10	)	)	PUNCT
ap-5981	117	11	,	,	PUNCT
ap-5981	117	12	(	(	PUNCT
ap-5981	117	13	21	21	NUM
ap-5981	117	14	)	)	PUNCT
ap-5981	117	15	while	while	SCONJ
ap-5981	117	16	the	the	DET
ap-5981	117	17	remaining	remain	VERB
ap-5981	117	18	2p	2p	NUM
ap-5981	117	19	conditions	condition	NOUN
ap-5981	117	20	read	read	VERB
ap-5981	117	21	as	as	ADP
ap-5981	117	22	λp(t	λp(t	NOUN
ap-5981	117	23	)	)	PUNCT
ap-5981	117	24	=	=	SYM
ap-5981	117	25	kpre	kpre	NOUN
ap-5981	117	26	,	,	PUNCT
ap-5981	117	27	p(t	p(t	NOUN
ap-5981	117	28	)	)	PUNCT
ap-5981	117	29	,	,	PUNCT
ap-5981	117	30	λp(t	λp(t	PUNCT
ap-5981	117	31	)	)	PUNCT
ap-5981	117	32	=	=	SYM
ap-5981	117	33	ηpṙv	ηpṙv	NOUN
ap-5981	117	34	,	,	PUNCT
ap-5981	117	35	p(t	p(t	NOUN
ap-5981	117	36	)	)	PUNCT
ap-5981	117	37	,	,	PUNCT
ap-5981	117	38	(	(	PUNCT
ap-5981	117	39	22	22	NUM
ap-5981	117	40	)	)	PUNCT
ap-5981	117	41	with	with	ADP
ap-5981	117	42	p	p	NOUN
ap-5981	117	43	=	=	NOUN
ap-5981	117	44	1	1	NUM
ap-5981	117	45	,	,	PUNCT
ap-5981	117	46	.	.	PUNCT
ap-5981	117	47	.	.	PUNCT
ap-5981	117	48	.	.	PUNCT
ap-5981	118	1	,	,	PUNCT
ap-5981	118	2	p	p	X
ap-5981	118	3	.	.	PUNCT
ap-5981	119	1	it	it	PRON
ap-5981	119	2	is	be	AUX
ap-5981	119	3	thus	thus	ADV
ap-5981	119	4	evident	evident	ADJ
ap-5981	119	5	that	that	SCONJ
ap-5981	119	6	the	the	DET
ap-5981	119	7	multipliers	multiplier	NOUN
ap-5981	119	8	λp	λp	PART
ap-5981	119	9	play	play	VERB
ap-5981	119	10	a	a	DET
ap-5981	119	11	role	role	NOUN
ap-5981	119	12	of	of	ADP
ap-5981	119	13	the	the	DET
ap-5981	119	14	viscous	viscous	ADJ
ap-5981	119	15	force	force	NOUN
ap-5981	119	16	fp	fp	NOUN
ap-5981	119	17	and	and	CCONJ
ap-5981	119	18	,	,	PUNCT
ap-5981	119	19	because	because	SCONJ
ap-5981	119	20	the	the	DET
ap-5981	119	21	optimality	optimality	NOUN
ap-5981	119	22	(	(	PUNCT
ap-5981	119	23	14b	14b	NUM
ap-5981	119	24	)	)	PUNCT
ap-5981	119	25	and	and	CCONJ
ap-5981	119	26	compatibility	compatibility	NOUN
ap-5981	119	27	(	(	PUNCT
ap-5981	119	28	4	4	NUM
ap-5981	119	29	)	)	PUNCT
ap-5981	119	30	conditions	condition	NOUN
ap-5981	119	31	coincide	coincide	NOUN
ap-5981	119	32	,	,	PUNCT
ap-5981	119	33	the	the	DET
ap-5981	119	34	current	current	ADJ
ap-5981	119	35	setting	setting	NOUN
ap-5981	119	36	is	be	AUX
ap-5981	119	37	equivalent	equivalent	ADJ
ap-5981	119	38	to	to	ADP
ap-5981	119	39	the	the	DET
ap-5981	119	40	one	one	NUM
ap-5981	119	41	of	of	ADP
ap-5981	119	42	section	section	NOUN
ap-5981	119	43	2.1	2.1	NUM
ap-5981	119	44	.	.	PUNCT
ap-5981	119	45	504	504	NUM
ap-5981	119	46	vol	vol	NOUN
ap-5981	119	47	.	.	PUNCT
ap-5981	120	1	60	60	NUM
ap-5981	120	2	no	no	INTJ
ap-5981	120	3	.	.	PUNCT
ap-5981	121	1	6/2020	6/2020	NUM
ap-5981	121	2	newmark	newmark	NOUN
ap-5981	121	3	algorithm	algorithm	NOUN
ap-5981	121	4	for	for	ADP
ap-5981	121	5	dynamic	dynamic	ADJ
ap-5981	121	6	analysis	analysis	NOUN
ap-5981	121	7	of	of	ADP
ap-5981	121	8	viscoelastic	viscoelastic	ADJ
ap-5981	121	9	materials	material	NOUN
ap-5981	121	10	3.2	3.2	NUM
ap-5981	121	11	.	.	PUNCT
ap-5981	122	1	discretization	discretization	NOUN
ap-5981	122	2	recall	recall	VERB
ap-5981	122	3	that	that	SCONJ
ap-5981	122	4	the	the	DET
ap-5981	122	5	incremental	incremental	ADJ
ap-5981	122	6	algorithm	algorithm	NOUN
ap-5981	122	7	of	of	ADP
ap-5981	122	8	section	section	NOUN
ap-5981	122	9	2.2	2.2	NUM
ap-5981	122	10	relies	relie	NOUN
ap-5981	122	11	on	on	ADP
ap-5981	122	12	the	the	DET
ap-5981	122	13	discretization	discretization	NOUN
ap-5981	122	14	of	of	ADP
ap-5981	122	15	the	the	DET
ap-5981	122	16	total	total	ADJ
ap-5981	122	17	displacements	displacement	NOUN
ap-5981	122	18	,	,	PUNCT
ap-5981	122	19	from	from	ADP
ap-5981	122	20	which	which	PRON
ap-5981	122	21	the	the	DET
ap-5981	122	22	evolution	evolution	NOUN
ap-5981	122	23	of	of	ADP
ap-5981	122	24	cell	cell	NOUN
ap-5981	122	25	-	-	PUNCT
ap-5981	122	26	related	relate	VERB
ap-5981	122	27	variables	variable	NOUN
ap-5981	122	28	re	re	ADP
ap-5981	122	29	,	,	PUNCT
ap-5981	122	30	p	p	PRON
ap-5981	122	31	,	,	PUNCT
ap-5981	122	32	rv	rv	PROPN
ap-5981	122	33	,	,	PUNCT
ap-5981	122	34	p	p	X
ap-5981	122	35	,	,	PUNCT
ap-5981	122	36	and	and	CCONJ
ap-5981	122	37	fp	fp	PROPN
ap-5981	122	38	follows	follow	VERB
ap-5981	122	39	in	in	ADP
ap-5981	122	40	the	the	DET
ap-5981	122	41	closed	closed	ADJ
ap-5981	122	42	form	form	NOUN
ap-5981	122	43	.	.	PUNCT
ap-5981	123	1	to	to	PART
ap-5981	123	2	mimic	mimic	VERB
ap-5981	123	3	this	this	DET
ap-5981	123	4	structure	structure	NOUN
ap-5981	123	5	,	,	PUNCT
ap-5981	123	6	only	only	ADV
ap-5981	123	7	the	the	DET
ap-5981	123	8	total	total	ADJ
ap-5981	123	9	displacements	displacement	NOUN
ap-5981	123	10	r	r	NOUN
ap-5981	123	11	will	will	AUX
ap-5981	123	12	be	be	AUX
ap-5981	123	13	determined	determine	VERB
ap-5981	123	14	from	from	ADP
ap-5981	123	15	the	the	DET
ap-5981	123	16	discrete	discrete	ADJ
ap-5981	123	17	(	(	PUNCT
ap-5981	123	18	non	non	ADJ
ap-5981	123	19	-	-	ADJ
ap-5981	123	20	dissipative	dissipative	ADJ
ap-5981	123	21	)	)	PUNCT
ap-5981	123	22	el	el	PROPN
ap-5981	123	23	equations	equation	NOUN
ap-5981	123	24	,	,	PUNCT
ap-5981	123	25	whereas	whereas	SCONJ
ap-5981	123	26	the	the	DET
ap-5981	123	27	remaining	remain	VERB
ap-5981	123	28	quantities	quantity	NOUN
ap-5981	123	29	are	be	AUX
ap-5981	123	30	determined	determine	VERB
ap-5981	123	31	from	from	ADP
ap-5981	123	32	the	the	DET
ap-5981	123	33	non	non	ADJ
ap-5981	123	34	-	-	ADJ
ap-5981	123	35	discretized	discretized	ADJ
ap-5981	123	36	optimality	optimality	NOUN
ap-5981	123	37	conditions	condition	NOUN
ap-5981	123	38	(	(	PUNCT
ap-5981	123	39	22	22	NUM
ap-5981	123	40	)	)	PUNCT
ap-5981	123	41	and	and	CCONJ
ap-5981	123	42	(	(	PUNCT
ap-5981	123	43	14b	14b	NUM
ap-5981	123	44	)	)	PUNCT
ap-5981	123	45	.	.	PUNCT
ap-5981	124	1	to	to	ADP
ap-5981	124	2	this	this	DET
ap-5981	124	3	goal	goal	NOUN
ap-5981	124	4	,	,	PUNCT
ap-5981	124	5	we	we	PRON
ap-5981	124	6	consider	consider	VERB
ap-5981	124	7	the	the	DET
ap-5981	124	8	same	same	ADJ
ap-5981	124	9	discretization	discretization	NOUN
ap-5981	124	10	of	of	ADP
ap-5981	124	11	the	the	DET
ap-5981	124	12	time	time	NOUN
ap-5981	124	13	interval	interval	NOUN
ap-5981	124	14	〈	〈	PROPN
ap-5981	124	15	0	0	NUM
ap-5981	124	16	,	,	PUNCT
ap-5981	124	17	t	t	PROPN
ap-5981	124	18	〉	〉	NUM
ap-5981	124	19	as	as	ADP
ap-5981	124	20	in	in	ADP
ap-5981	124	21	section	section	NOUN
ap-5981	124	22	2.2	2.2	NUM
ap-5981	124	23	and	and	CCONJ
ap-5981	124	24	introduce	introduce	VERB
ap-5981	124	25	the	the	DET
ap-5981	124	26	discretized	discretized	ADJ
ap-5981	124	27	action	action	NOUN
ap-5981	124	28	functional	functional	ADJ
ap-5981	124	29	s(r̂	s(r̂	PROPN
ap-5981	124	30	,	,	PUNCT
ap-5981	124	31	λ̂	λ̂	X
ap-5981	124	32	)	)	PUNCT
ap-5981	125	1	≈	≈	ADV
ap-5981	125	2	sd	sd	ADP
ap-5981	125	3	(	(	PUNCT
ap-5981	125	4	{	{	PUNCT
ap-5981	125	5	r̂i}ni=0	r̂i}ni=0	NOUN
ap-5981	125	6	,	,	PUNCT
ap-5981	125	7	{	{	PUNCT
ap-5981	125	8	λ̂i}ni=0	λ̂i}ni=0	ADJ
ap-5981	125	9	)	)	PUNCT
ap-5981	125	10	=	=	SYM
ap-5981	125	11	∆t	∆t	PROPN
ap-5981	125	12	n−1∑	n−1∑	PROPN
ap-5981	125	13	i=0	i=0	PROPN
ap-5981	125	14	ld	ld	PROPN
ap-5981	125	15	(	(	PUNCT
ap-5981	125	16	r̂i	r̂i	PROPN
ap-5981	125	17	,	,	PUNCT
ap-5981	125	18	r̂i+1	r̂i+1	NOUN
ap-5981	125	19	,	,	PUNCT
ap-5981	125	20	λ̂i	λ̂i	X
ap-5981	125	21	,	,	PUNCT
ap-5981	125	22	λ̂i+1	λ̂i+1	PROPN
ap-5981	125	23	)	)	PUNCT
ap-5981	125	24	,	,	PUNCT
ap-5981	125	25	(	(	PUNCT
ap-5981	125	26	23	23	NUM
ap-5981	125	27	)	)	PUNCT
ap-5981	125	28	with	with	ADP
ap-5981	125	29	the	the	DET
ap-5981	125	30	discrete	discrete	ADJ
ap-5981	125	31	lagrangian	lagrangian	NOUN
ap-5981	125	32	given	give	VERB
ap-5981	125	33	by	by	ADP
ap-5981	125	34	[	[	X
ap-5981	125	35	18	18	NUM
ap-5981	125	36	,	,	PUNCT
ap-5981	125	37	eq	eq	NOUN
ap-5981	125	38	.	.	PUNCT
ap-5981	125	39	(	(	PUNCT
ap-5981	125	40	2	2	NUM
ap-5981	125	41	)	)	PUNCT
ap-5981	125	42	]	]	PUNCT
ap-5981	125	43	ld	ld	PROPN
ap-5981	125	44	(	(	PUNCT
ap-5981	125	45	r̂i	r̂i	PROPN
ap-5981	125	46	,	,	PUNCT
ap-5981	125	47	r̂i+1	r̂i+1	NOUN
ap-5981	125	48	,	,	PUNCT
ap-5981	125	49	λ̂i	λ̂i	X
ap-5981	125	50	,	,	PUNCT
ap-5981	125	51	λ̂i+1	λ̂i+1	NOUN
ap-5981	125	52	)	)	PUNCT
ap-5981	126	1	=	=	SYM
ap-5981	126	2	1	1	NUM
ap-5981	126	3	2	2	NUM
ap-5981	126	4	m	m	VERB
ap-5981	126	5	(	(	PUNCT
ap-5981	126	6	r̂i+1	r̂i+1	NOUN
ap-5981	126	7	−	−	NOUN
ap-5981	126	8	r̂i	r̂i	NOUN
ap-5981	126	9	∆t	∆t	PROPN
ap-5981	126	10	)	)	PUNCT
ap-5981	126	11	2	2	NUM
ap-5981	126	12	(	(	PUNCT
ap-5981	126	13	24	24	NUM
ap-5981	126	14	)	)	PUNCT
ap-5981	126	15	−	−	PROPN
ap-5981	126	16	1	1	NUM
ap-5981	126	17	2k∞	2k∞	NUM
ap-5981	126	18	(	(	PUNCT
ap-5981	126	19	r̂i+1	r̂i+1	NOUN
ap-5981	126	20	+	+	CCONJ
ap-5981	126	21	r̂i	r̂i	NOUN
ap-5981	126	22	2	2	NUM
ap-5981	126	23	)	)	SYM
ap-5981	126	24	2	2	NUM
ap-5981	126	25	+	+	CCONJ
ap-5981	126	26	1	1	NUM
ap-5981	126	27	4	4	NUM
ap-5981	126	28	(	(	PUNCT
ap-5981	126	29	r̂i	r̂i	NOUN
ap-5981	126	30	+	+	CCONJ
ap-5981	126	31	r̂i+1)(fi	r̂i+1)(fi	ADJ
ap-5981	126	32	+	+	CCONJ
ap-5981	126	33	fi+1	fi+1	NOUN
ap-5981	126	34	)	)	PUNCT
ap-5981	126	35	−	−	NOUN
ap-5981	126	36	1	1	NUM
ap-5981	126	37	4	4	NUM
ap-5981	126	38	p∑	p∑	NOUN
ap-5981	126	39	p=1	p=1	X
ap-5981	127	1	(	(	PUNCT
ap-5981	127	2	r̂i	r̂i	NOUN
ap-5981	127	3	+	+	NOUN
ap-5981	127	4	r̂i+1)(λ̂p	r̂i+1)(λ̂p	ADJ
ap-5981	127	5	,	,	PUNCT
ap-5981	127	6	i	i	PRON
ap-5981	127	7	+	+	X
ap-5981	127	8	λ̂p	λ̂p	PRON
ap-5981	127	9	,	,	PUNCT
ap-5981	127	10	i+1	i+1	NOUN
ap-5981	127	11	)	)	PUNCT
ap-5981	127	12	.	.	PUNCT
ap-5981	128	1	the	the	DET
ap-5981	128	2	stationarity	stationarity	NOUN
ap-5981	128	3	conditions	condition	NOUN
ap-5981	128	4	at	at	ADP
ap-5981	128	5	time	time	NOUN
ap-5981	128	6	ti	ti	NOUN
ap-5981	128	7	,	,	PUNCT
ap-5981	128	8	∂sd/∂ri	∂sd/∂ri	NUM
ap-5981	128	9	=	=	SYM
ap-5981	128	10	0	0	NUM
ap-5981	128	11	,	,	PUNCT
ap-5981	128	12	with	with	ADP
ap-5981	128	13	i	i	PROPN
ap-5981	128	14	=	=	NOUN
ap-5981	128	15	1	1	NUM
ap-5981	128	16	,	,	PUNCT
ap-5981	128	17	.	.	PUNCT
ap-5981	128	18	.	.	PUNCT
ap-5981	128	19	.	.	PUNCT
ap-5981	129	1	,	,	PUNCT
ap-5981	129	2	n	n	CCONJ
ap-5981	129	3	−	−	PROPN
ap-5981	129	4	1,2	1,2	NUM
ap-5981	129	5	read	read	NOUN
ap-5981	129	6	as	as	ADP
ap-5981	129	7	0	0	NUM
ap-5981	129	8	=	=	SYM
ap-5981	129	9	∂ld(ri−1	∂ld(ri−1	PROPN
ap-5981	129	10	,	,	PUNCT
ap-5981	129	11	ri	ri	PROPN
ap-5981	129	12	,	,	PUNCT
ap-5981	129	13	λi−1,λi	λi−1,λi	PROPN
ap-5981	129	14	)	)	PUNCT
ap-5981	130	1	∂ri	∂ri	PROPN
ap-5981	130	2	+	+	CCONJ
ap-5981	130	3	∂ld(ri	∂ld(ri	NOUN
ap-5981	130	4	,	,	PUNCT
ap-5981	130	5	ri+1,λi	ri+1,λi	PROPN
ap-5981	130	6	,	,	PUNCT
ap-5981	130	7	λi+1	λi+1	NOUN
ap-5981	130	8	)	)	PUNCT
ap-5981	130	9	∂ri	∂ri	PROPN
ap-5981	130	10	(	(	PUNCT
ap-5981	130	11	25	25	NUM
ap-5981	130	12	)	)	PUNCT
ap-5981	130	13	which	which	PRON
ap-5981	130	14	delivers	deliver	VERB
ap-5981	130	15	the	the	DET
ap-5981	130	16	governing	govern	VERB
ap-5981	130	17	equations	equation	NOUN
ap-5981	130	18	of	of	ADP
ap-5981	130	19	the	the	DET
ap-5981	130	20	variational	variational	ADJ
ap-5981	130	21	integrator	integrator	NOUN
ap-5981	130	22	in	in	ADP
ap-5981	130	23	the	the	DET
ap-5981	130	24	form3	form3	NOUN
ap-5981	130	25	m	m	VERB
ap-5981	130	26	ri+1	ri+1	NOUN
ap-5981	130	27	−	−	NOUN
ap-5981	130	28	2ri	2ri	NOUN
ap-5981	131	1	+	+	CCONJ
ap-5981	132	1	ri−1	ri−1	NOUN
ap-5981	132	2	∆t2	∆t2	NOUN
ap-5981	132	3	+	+	CCONJ
ap-5981	132	4	1	1	NUM
ap-5981	132	5	4k∞(ri+1	4k∞(ri+1	NOUN
ap-5981	132	6	+	+	CCONJ
ap-5981	132	7	2ri	2ri	ADJ
ap-5981	132	8	+	+	CCONJ
ap-5981	132	9	ri−1	ri−1	PROPN
ap-5981	132	10	)	)	PUNCT
ap-5981	132	11	+	+	NUM
ap-5981	132	12	p∑	p∑	NOUN
ap-5981	132	13	p=1	p=1	NOUN
ap-5981	133	1	1	1	NUM
ap-5981	133	2	4	4	NUM
ap-5981	133	3	(	(	PUNCT
ap-5981	133	4	λp	λp	PROPN
ap-5981	133	5	,	,	PUNCT
ap-5981	133	6	i+1	i+1	NOUN
ap-5981	133	7	+	+	X
ap-5981	133	8	2λp	2λp	ADJ
ap-5981	133	9	,	,	PUNCT
ap-5981	133	10	i	i	PRON
ap-5981	133	11	+	+	X
ap-5981	134	1	λp	λp	PROPN
ap-5981	134	2	,	,	PUNCT
ap-5981	134	3	i−1	i−1	PROPN
ap-5981	134	4	)	)	PUNCT
ap-5981	134	5	=	=	SYM
ap-5981	134	6	1	1	NUM
ap-5981	134	7	4	4	NUM
ap-5981	134	8	(	(	PUNCT
ap-5981	134	9	fi−1	fi−1	PROPN
ap-5981	134	10	+	+	CCONJ
ap-5981	134	11	2fi	2fi	ADJ
ap-5981	134	12	+	+	CCONJ
ap-5981	134	13	fi+1	fi+1	NOUN
ap-5981	134	14	)	)	PUNCT
ap-5981	134	15	.	.	PUNCT
ap-5981	135	1	(	(	PUNCT
ap-5981	135	2	26	26	NUM
ap-5981	135	3	)	)	PUNCT
ap-5981	135	4	3.3	3.3	NUM
ap-5981	135	5	.	.	PUNCT
ap-5981	136	1	equivalence	equivalence	NOUN
ap-5981	136	2	to	to	ADP
ap-5981	136	3	newmark	newmark	PROPN
ap-5981	136	4	we	we	PRON
ap-5981	136	5	will	will	AUX
ap-5981	136	6	proceed	proceed	VERB
ap-5981	136	7	with	with	ADP
ap-5981	136	8	two	two	NUM
ap-5981	136	9	additional	additional	ADJ
ap-5981	136	10	steps	step	NOUN
ap-5981	136	11	to	to	PART
ap-5981	136	12	show	show	VERB
ap-5981	136	13	that	that	SCONJ
ap-5981	136	14	the	the	DET
ap-5981	136	15	optimality	optimality	NOUN
ap-5981	136	16	conditions	condition	NOUN
ap-5981	136	17	(	(	PUNCT
ap-5981	136	18	26	26	NUM
ap-5981	136	19	)	)	PUNCT
ap-5981	136	20	correspond	correspond	VERB
ap-5981	136	21	to	to	ADP
ap-5981	136	22	the	the	DET
ap-5981	136	23	newmark	newmark	NOUN
ap-5981	136	24	integration	integration	NOUN
ap-5981	136	25	scheme	scheme	NOUN
ap-5981	136	26	from	from	ADP
ap-5981	136	27	section	section	NOUN
ap-5981	136	28	2	2	NUM
ap-5981	136	29	.	.	PUNCT
ap-5981	137	1	first	first	ADV
ap-5981	137	2	,	,	PUNCT
ap-5981	137	3	2notice	2notice	NUM
ap-5981	137	4	that	that	SCONJ
ap-5981	137	5	the	the	DET
ap-5981	137	6	optimality	optimality	NOUN
ap-5981	137	7	conditions	condition	NOUN
ap-5981	137	8	exclude	exclude	VERB
ap-5981	137	9	the	the	DET
ap-5981	137	10	initial	initial	ADJ
ap-5981	137	11	and	and	CCONJ
ap-5981	137	12	final	final	ADJ
ap-5981	137	13	times	time	NOUN
ap-5981	137	14	t0	t0	PROPN
ap-5981	137	15	and	and	CCONJ
ap-5981	137	16	tn	tn	PROPN
ap-5981	137	17	.	.	PUNCT
ap-5981	138	1	this	this	PRON
ap-5981	138	2	mirrors	mirror	VERB
ap-5981	138	3	the	the	DET
ap-5981	138	4	standard	standard	ADJ
ap-5981	138	5	treatment	treatment	NOUN
ap-5981	138	6	of	of	ADP
ap-5981	138	7	the	the	DET
ap-5981	138	8	time	time	NOUN
ap-5981	138	9	-	-	PUNCT
ap-5981	138	10	continuous	continuous	ADJ
ap-5981	138	11	case	case	NOUN
ap-5981	138	12	,	,	PUNCT
ap-5981	138	13	in	in	ADP
ap-5981	138	14	which	which	PRON
ap-5981	138	15	the	the	DET
ap-5981	138	16	stationarity	stationarity	NOUN
ap-5981	138	17	conditions	condition	NOUN
ap-5981	138	18	of	of	ADP
ap-5981	138	19	the	the	DET
ap-5981	138	20	action	action	NOUN
ap-5981	138	21	functional	functional	ADJ
ap-5981	138	22	are	be	AUX
ap-5981	138	23	derived	derive	VERB
ap-5981	138	24	under	under	ADP
ap-5981	138	25	the	the	DET
ap-5981	138	26	assumption	assumption	NOUN
ap-5981	138	27	that	that	SCONJ
ap-5981	138	28	the	the	DET
ap-5981	138	29	state	state	NOUN
ap-5981	138	30	variables	variable	NOUN
ap-5981	138	31	remain	remain	VERB
ap-5981	138	32	fixed	fix	VERB
ap-5981	138	33	at	at	ADP
ap-5981	138	34	both	both	DET
ap-5981	138	35	times	time	NOUN
ap-5981	138	36	,	,	PUNCT
ap-5981	138	37	e.g.	e.g.	ADV
ap-5981	138	38	[	[	X
ap-5981	138	39	22	22	NUM
ap-5981	138	40	]	]	PUNCT
ap-5981	138	41	.	.	PUNCT
ap-5981	139	1	3notice	3notice	NUM
ap-5981	139	2	that	that	PRON
ap-5981	139	3	we	we	PRON
ap-5981	139	4	assume	assume	VERB
ap-5981	139	5	the	the	DET
ap-5981	139	6	lagrange	lagrange	PROPN
ap-5981	139	7	multipliers	multiplier	NOUN
ap-5981	140	1	λp	λp	PROPN
ap-5981	140	2	,	,	PUNCT
ap-5981	140	3	i	i	PRON
ap-5981	140	4	to	to	PART
ap-5981	140	5	be	be	AUX
ap-5981	140	6	given	give	VERB
ap-5981	140	7	arbitrary	arbitrary	ADJ
ap-5981	140	8	quantities	quantity	NOUN
ap-5981	140	9	,	,	PUNCT
ap-5981	140	10	similarly	similarly	ADV
ap-5981	140	11	to	to	ADP
ap-5981	140	12	the	the	DET
ap-5981	140	13	forcing	force	VERB
ap-5981	140	14	terms	term	NOUN
ap-5981	140	15	fi	fi	NOUN
ap-5981	140	16	.	.	PUNCT
ap-5981	141	1	once	once	SCONJ
ap-5981	141	2	we	we	PRON
ap-5981	141	3	establish	establish	VERB
ap-5981	141	4	the	the	DET
ap-5981	141	5	equivalence	equivalence	NOUN
ap-5981	141	6	to	to	ADP
ap-5981	141	7	the	the	DET
ap-5981	141	8	newmark	newmark	PROPN
ap-5981	141	9	algorithm	algorithm	NOUN
ap-5981	141	10	,	,	PUNCT
ap-5981	141	11	their	their	PRON
ap-5981	141	12	values	value	NOUN
ap-5981	141	13	follow	follow	VERB
ap-5981	141	14	from	from	ADP
ap-5981	141	15	the	the	DET
ap-5981	141	16	update	update	NOUN
ap-5981	141	17	formula	formula	NOUN
ap-5981	141	18	(	(	PUNCT
ap-5981	141	19	9	9	NUM
ap-5981	141	20	)	)	PUNCT
ap-5981	141	21	from	from	ADP
ap-5981	141	22	section	section	NOUN
ap-5981	141	23	2	2	NUM
ap-5981	141	24	.	.	PUNCT
ap-5981	142	1	we	we	PRON
ap-5981	142	2	demonstrate	demonstrate	VERB
ap-5981	142	3	that	that	SCONJ
ap-5981	142	4	the	the	DET
ap-5981	142	5	displacements	displacement	NOUN
ap-5981	142	6	{	{	PUNCT
ap-5981	142	7	ri}ni=0	ri}ni=0	NOUN
ap-5981	142	8	provide	provide	VERB
ap-5981	142	9	definitions	definition	NOUN
ap-5981	142	10	of	of	ADP
ap-5981	142	11	velocities	velocity	NOUN
ap-5981	142	12	{	{	PUNCT
ap-5981	142	13	ṙi}ni=0	ṙi}ni=0	NOUN
ap-5981	142	14	and	and	CCONJ
ap-5981	142	15	accelerations	acceleration	NOUN
ap-5981	142	16	{	{	PUNCT
ap-5981	142	17	r̈i}ni=0	r̈i}ni=0	ADJ
ap-5981	142	18	consistent	consistent	ADJ
ap-5981	142	19	with	with	ADP
ap-5981	142	20	the	the	DET
ap-5981	142	21	kinematic	kinematic	ADJ
ap-5981	142	22	assumptions	assumption	NOUN
ap-5981	142	23	in	in	ADP
ap-5981	142	24	eq	eq	ADP
ap-5981	142	25	.	.	PUNCT
ap-5981	143	1	(	(	PUNCT
ap-5981	143	2	6	6	NUM
ap-5981	143	3	)	)	PUNCT
ap-5981	143	4	.	.	PUNCT
ap-5981	144	1	second	second	ADJ
ap-5981	144	2	,	,	PUNCT
ap-5981	144	3	we	we	PRON
ap-5981	144	4	show	show	VERB
ap-5981	144	5	that	that	SCONJ
ap-5981	144	6	the	the	DET
ap-5981	144	7	discrete	discrete	NOUN
ap-5981	144	8	-	-	PUNCT
ap-5981	144	9	in	in	ADP
ap-5981	144	10	-	-	PUNCT
ap-5981	144	11	time	time	NOUN
ap-5981	144	12	quantities	quantity	NOUN
ap-5981	144	13	satisfy	satisfy	VERB
ap-5981	144	14	the	the	DET
ap-5981	144	15	equations	equation	NOUN
ap-5981	144	16	of	of	ADP
ap-5981	144	17	motion	motion	NOUN
ap-5981	144	18	(	(	PUNCT
ap-5981	144	19	1	1	NUM
ap-5981	144	20	)	)	PUNCT
ap-5981	144	21	.	.	PUNCT
ap-5981	145	1	kinematics	kinematic	NOUN
ap-5981	145	2	.	.	PUNCT
ap-5981	146	1	following	follow	VERB
ap-5981	146	2	[	[	X
ap-5981	146	3	18	18	NUM
ap-5981	146	4	,	,	PUNCT
ap-5981	146	5	section	section	NOUN
ap-5981	146	6	2.2	2.2	NUM
ap-5981	146	7	]	]	PUNCT
ap-5981	146	8	,	,	PUNCT
ap-5981	146	9	we	we	PRON
ap-5981	146	10	start	start	VERB
ap-5981	146	11	by	by	ADP
ap-5981	146	12	introducing	introduce	VERB
ap-5981	146	13	auxiliary	auxiliary	ADJ
ap-5981	146	14	accelerations	acceleration	NOUN
ap-5981	146	15	mr̈i+1/2	mr̈i+1/2	NOUN
ap-5981	147	1	=	=	VERB
ap-5981	147	2	−k∞2	−k∞2	PROPN
ap-5981	147	3	(	(	PUNCT
ap-5981	147	4	ri	ri	PROPN
ap-5981	147	5	+	+	CCONJ
ap-5981	147	6	ri+1	ri+1	NOUN
ap-5981	147	7	)	)	PUNCT
ap-5981	147	8	+	+	CCONJ
ap-5981	147	9	1	1	NUM
ap-5981	147	10	2	2	NUM
ap-5981	147	11	(	(	PUNCT
ap-5981	147	12	fi	fi	NOUN
ap-5981	147	13	+	+	CCONJ
ap-5981	147	14	fi+1	fi+1	NOUN
ap-5981	147	15	)	)	PUNCT
ap-5981	147	16	−	−	NOUN
ap-5981	147	17	p∑	p∑	INTJ
ap-5981	147	18	p=1	p=1	NOUN
ap-5981	148	1	1	1	NUM
ap-5981	148	2	2	2	NUM
ap-5981	148	3	(	(	PUNCT
ap-5981	148	4	λp	λp	PROPN
ap-5981	148	5	,	,	PUNCT
ap-5981	148	6	i	i	PROPN
ap-5981	148	7	+	+	X
ap-5981	148	8	λp	λp	PROPN
ap-5981	148	9	,	,	PUNCT
ap-5981	148	10	i+1	i+1	NUM
ap-5981	148	11	)	)	PUNCT
ap-5981	148	12	,	,	PUNCT
ap-5981	148	13	(	(	PUNCT
ap-5981	148	14	27	27	NUM
ap-5981	148	15	)	)	PUNCT
ap-5981	148	16	for	for	ADP
ap-5981	148	17	i	i	PROPN
ap-5981	148	18	=	=	SYM
ap-5981	148	19	0	0	NUM
ap-5981	148	20	,	,	PUNCT
ap-5981	148	21	1	1	NUM
ap-5981	148	22	,	,	PUNCT
ap-5981	148	23	.	.	PUNCT
ap-5981	148	24	.	.	PUNCT
ap-5981	148	25	.	.	PUNCT
ap-5981	149	1	,	,	PUNCT
ap-5981	150	1	n	n	CCONJ
ap-5981	150	2	−	−	PROPN
ap-5981	150	3	1	1	NUM
ap-5981	150	4	.	.	PUNCT
ap-5981	150	5	summing	sum	VERB
ap-5981	150	6	mr̈i−1/2	mr̈i−1/2	NOUN
ap-5981	150	7	with	with	ADP
ap-5981	150	8	mr̈i+1/2	mr̈i+1/2	NOUN
ap-5981	150	9	and	and	CCONJ
ap-5981	150	10	comparing	compare	VERB
ap-5981	150	11	the	the	DET
ap-5981	150	12	result	result	NOUN
ap-5981	150	13	with	with	ADP
ap-5981	150	14	(	(	PUNCT
ap-5981	150	15	26	26	NUM
ap-5981	150	16	)	)	PUNCT
ap-5981	150	17	provides	provide	VERB
ap-5981	150	18	ri+1	ri+1	PRON
ap-5981	150	19	−	−	NOUN
ap-5981	150	20	2ri	2ri	NOUN
ap-5981	151	1	+	+	CCONJ
ap-5981	151	2	ri−1	ri−1	NOUN
ap-5981	151	3	∆t2	∆t2	NOUN
ap-5981	151	4	=	=	SYM
ap-5981	151	5	1	1	NUM
ap-5981	151	6	2	2	NUM
ap-5981	151	7	(	(	PUNCT
ap-5981	151	8	r̈i+1/2	r̈i+1/2	VERB
ap-5981	151	9	+	+	CCONJ
ap-5981	151	10	r̈i−1/2	r̈i−1/2	ADJ
ap-5981	151	11	)	)	PUNCT
ap-5981	151	12	,	,	PUNCT
ap-5981	151	13	(	(	PUNCT
ap-5981	151	14	28	28	NUM
ap-5981	151	15	)	)	PUNCT
ap-5981	151	16	with	with	ADP
ap-5981	151	17	i	i	PROPN
ap-5981	151	18	=	=	NOUN
ap-5981	151	19	1	1	NUM
ap-5981	151	20	,	,	PUNCT
ap-5981	151	21	.	.	PUNCT
ap-5981	151	22	.	.	PUNCT
ap-5981	151	23	.	.	PUNCT
ap-5981	152	1	,	,	PUNCT
ap-5981	153	1	n	n	CCONJ
ap-5981	153	2	−	−	PROPN
ap-5981	153	3	1	1	NUM
ap-5981	153	4	.	.	PUNCT
ap-5981	154	1	the	the	DET
ap-5981	154	2	discrete	discrete	ADJ
ap-5981	154	3	linear	linear	PROPN
ap-5981	154	4	momenta	momenta	NOUN
ap-5981	154	5	follow	follow	NOUN
ap-5981	154	6	standardly	standardly	ADV
ap-5981	154	7	from	from	ADP
ap-5981	154	8	pi	pi	NOUN
ap-5981	154	9	=	=	SYM
ap-5981	154	10	∂ld(ri−1	∂ld(ri−1	PROPN
ap-5981	154	11	,	,	PUNCT
ap-5981	154	12	ri	ri	PROPN
ap-5981	154	13	,	,	PUNCT
ap-5981	154	14	λi−1,λi	λi−1,λi	PROPN
ap-5981	154	15	)	)	PUNCT
ap-5981	155	1	∂ri	∂ri	PROPN
ap-5981	155	2	∆t	∆t	PROPN
ap-5981	155	3	,	,	PUNCT
ap-5981	155	4	(	(	PUNCT
ap-5981	155	5	29	29	NUM
ap-5981	155	6	)	)	PUNCT
ap-5981	155	7	and	and	CCONJ
ap-5981	155	8	,	,	PUNCT
ap-5981	155	9	using	use	VERB
ap-5981	155	10	r̈i−1/2	r̈i−1/2	PROPN
ap-5981	155	11	from	from	ADP
ap-5981	155	12	eq	eq	NOUN
ap-5981	155	13	.	.	PUNCT
ap-5981	156	1	(	(	PUNCT
ap-5981	156	2	27	27	NUM
ap-5981	156	3	)	)	PUNCT
ap-5981	156	4	,	,	PUNCT
ap-5981	156	5	they	they	PRON
ap-5981	156	6	can	can	AUX
ap-5981	156	7	be	be	AUX
ap-5981	156	8	evaluated	evaluate	VERB
ap-5981	156	9	as	as	ADP
ap-5981	156	10	pi	pi	NOUN
ap-5981	156	11	=	=	SYM
ap-5981	156	12	mṙi	mṙi	NOUN
ap-5981	156	13	=	=	SYM
ap-5981	156	14	m	m	PROPN
ap-5981	156	15	ri	ri	PROPN
ap-5981	157	1	−	−	NOUN
ap-5981	157	2	ri−1	ri−1	PROPN
ap-5981	157	3	∆t	∆t	PROPN
ap-5981	158	1	+	+	PROPN
ap-5981	158	2	m	m	VERB
ap-5981	158	3	r̈i−1/2	r̈i−1/2	ADJ
ap-5981	158	4	2	2	NUM
ap-5981	158	5	∆t	∆t	NOUN
ap-5981	158	6	.	.	PUNCT
ap-5981	159	1	(	(	PUNCT
ap-5981	159	2	30	30	NUM
ap-5981	159	3	)	)	PUNCT
ap-5981	159	4	expressing	express	VERB
ap-5981	159	5	pi+1	pi+1	NUM
ap-5981	159	6	according	accord	VERB
ap-5981	159	7	to	to	ADP
ap-5981	159	8	the	the	DET
ap-5981	159	9	previous	previous	ADJ
ap-5981	159	10	relation	relation	NOUN
ap-5981	159	11	and	and	CCONJ
ap-5981	159	12	employing	employ	VERB
ap-5981	159	13	(	(	PUNCT
ap-5981	159	14	28	28	NUM
ap-5981	159	15	)	)	PUNCT
ap-5981	159	16	provides	provide	VERB
ap-5981	159	17	pi+1	pi+1	NUM
ap-5981	159	18	=	=	PUNCT
ap-5981	159	19	pi	pi	NOUN
ap-5981	159	20	+	+	NOUN
ap-5981	159	21	mr̈i+1/2∆t	mr̈i+1/2∆t	PROPN
ap-5981	159	22	,	,	PUNCT
ap-5981	159	23	(	(	PUNCT
ap-5981	159	24	31	31	NUM
ap-5981	159	25	)	)	PUNCT
ap-5981	159	26	from	from	ADP
ap-5981	159	27	which	which	PRON
ap-5981	159	28	we	we	PRON
ap-5981	159	29	obtain	obtain	VERB
ap-5981	159	30	ṙi+1	ṙi+1	NOUN
ap-5981	159	31	=	=	PUNCT
ap-5981	159	32	ṙi	ṙi	NOUN
ap-5981	159	33	+	+	CCONJ
ap-5981	159	34	∆tr̈i+1/2	∆tr̈i+1/2	NOUN
ap-5981	159	35	.	.	PUNCT
ap-5981	160	1	(	(	PUNCT
ap-5981	160	2	32	32	NUM
ap-5981	160	3	)	)	PUNCT
ap-5981	160	4	likewise	likewise	ADV
ap-5981	160	5	,	,	PUNCT
ap-5981	160	6	expressing	express	VERB
ap-5981	160	7	ri	ri	NOUN
ap-5981	160	8	from	from	ADP
ap-5981	160	9	(	(	PUNCT
ap-5981	160	10	28	28	NUM
ap-5981	160	11	)	)	PUNCT
ap-5981	160	12	and	and	CCONJ
ap-5981	160	13	employing	employ	VERB
ap-5981	160	14	the	the	DET
ap-5981	160	15	velocity	velocity	NOUN
ap-5981	160	16	ṙi	ṙi	NOUN
ap-5981	160	17	from	from	ADP
ap-5981	160	18	(	(	PUNCT
ap-5981	160	19	30	30	NUM
ap-5981	160	20	)	)	PUNCT
ap-5981	160	21	provides	provide	VERB
ap-5981	160	22	ri+1	ri+1	NOUN
ap-5981	160	23	=	=	SYM
ap-5981	160	24	ri	ri	PROPN
ap-5981	161	1	+	+	CCONJ
ap-5981	161	2	ṙi∆t+	ṙi∆t+	ADJ
ap-5981	161	3	1	1	NUM
ap-5981	161	4	2	2	NUM
ap-5981	161	5	r̈i+1/2∆t2	r̈i+1/2∆t2	PROPN
ap-5981	161	6	.	.	PUNCT
ap-5981	162	1	(	(	PUNCT
ap-5981	162	2	33	33	NUM
ap-5981	162	3	)	)	PUNCT
ap-5981	162	4	hence	hence	ADV
ap-5981	162	5	,	,	PUNCT
ap-5981	162	6	expressions	expression	NOUN
ap-5981	162	7	(	(	PUNCT
ap-5981	162	8	33	33	NUM
ap-5981	162	9	)	)	PUNCT
ap-5981	162	10	and	and	CCONJ
ap-5981	162	11	(	(	PUNCT
ap-5981	162	12	32	32	NUM
ap-5981	162	13	)	)	PUNCT
ap-5981	162	14	become	become	VERB
ap-5981	162	15	identical	identical	ADJ
ap-5981	162	16	to	to	ADP
ap-5981	162	17	the	the	DET
ap-5981	162	18	ones	one	NOUN
ap-5981	162	19	of	of	ADP
ap-5981	162	20	the	the	DET
ap-5981	162	21	newmark	newmark	NOUN
ap-5981	162	22	method	method	NOUN
ap-5981	162	23	(	(	PUNCT
ap-5981	162	24	6	6	NUM
ap-5981	162	25	)	)	PUNCT
ap-5981	162	26	once	once	ADV
ap-5981	162	27	setting	set	VERB
ap-5981	162	28	r̈i+1/2	r̈i+1/2	ADJ
ap-5981	162	29	=	=	SYM
ap-5981	162	30	1	1	NUM
ap-5981	162	31	2	2	NUM
ap-5981	162	32	(	(	PUNCT
ap-5981	162	33	r̈i	r̈i	NOUN
ap-5981	162	34	+	+	CCONJ
ap-5981	162	35	r̈i+1	r̈i+1	NOUN
ap-5981	162	36	)	)	PUNCT
ap-5981	162	37	.	.	PUNCT
ap-5981	163	1	(	(	PUNCT
ap-5981	163	2	34	34	NUM
ap-5981	163	3	)	)	PUNCT
ap-5981	163	4	equilibrium	equilibrium	NOUN
ap-5981	163	5	.	.	PUNCT
ap-5981	164	1	employing	employ	VERB
ap-5981	164	2	the	the	DET
ap-5981	164	3	nodal	nodal	NOUN
ap-5981	164	4	accelerations	acceleration	NOUN
ap-5981	164	5	r̈i−1/2	r̈i−1/2	ADJ
ap-5981	164	6	and	and	CCONJ
ap-5981	164	7	r̈i+1/2	r̈i+1/2	VERB
ap-5981	164	8	from	from	ADP
ap-5981	164	9	(	(	PUNCT
ap-5981	164	10	34	34	NUM
ap-5981	164	11	)	)	PUNCT
ap-5981	164	12	in	in	ADP
ap-5981	164	13	the	the	DET
ap-5981	164	14	identity	identity	NOUN
ap-5981	164	15	(	(	PUNCT
ap-5981	164	16	28	28	NUM
ap-5981	164	17	)	)	PUNCT
ap-5981	164	18	reveals	reveal	VERB
ap-5981	164	19	that	that	SCONJ
ap-5981	164	20	ri+1	ri+1	VERB
ap-5981	164	21	−	−	NOUN
ap-5981	164	22	2ri	2ri	NOUN
ap-5981	165	1	+	+	CCONJ
ap-5981	165	2	ri−1	ri−1	NOUN
ap-5981	165	3	∆t2	∆t2	NOUN
ap-5981	165	4	=	=	SYM
ap-5981	165	5	1	1	NUM
ap-5981	165	6	4	4	NUM
ap-5981	165	7	(	(	PUNCT
ap-5981	165	8	r̈i−1	r̈i−1	PROPN
ap-5981	165	9	+	+	CCONJ
ap-5981	165	10	2r̈i	2r̈i	ADJ
ap-5981	165	11	+	+	CCONJ
ap-5981	165	12	r̈i+1	r̈i+1	NOUN
ap-5981	165	13	)	)	PUNCT
ap-5981	165	14	.	.	PUNCT
ap-5981	166	1	(	(	PUNCT
ap-5981	166	2	35	35	NUM
ap-5981	166	3	)	)	PUNCT
ap-5981	166	4	furthermore	furthermore	ADV
ap-5981	166	5	,	,	PUNCT
ap-5981	166	6	by	by	ADP
ap-5981	166	7	expressing	express	VERB
ap-5981	166	8	the	the	DET
ap-5981	166	9	difference	difference	NOUN
ap-5981	166	10	m(r̈i+1/2	m(r̈i+1/2	ADV
ap-5981	166	11	−	−	PROPN
ap-5981	166	12	r̈i−1/2	r̈i−1/2	PROPN
ap-5981	166	13	)	)	PUNCT
ap-5981	166	14	using	use	VERB
ap-5981	166	15	(	(	PUNCT
ap-5981	166	16	27	27	NUM
ap-5981	166	17	)	)	PUNCT
ap-5981	166	18	,	,	PUNCT
ap-5981	166	19	we	we	PRON
ap-5981	166	20	find	find	VERB
ap-5981	166	21	that	that	SCONJ
ap-5981	166	22	1	1	NUM
ap-5981	166	23	2m(r̈i+1	2m(r̈i+1	NUM
ap-5981	166	24	−	−	NOUN
ap-5981	166	25	r̈i−1	r̈i−1	PROPN
ap-5981	166	26	)	)	PUNCT
ap-5981	167	1	+	+	CCONJ
ap-5981	168	1	1	1	NUM
ap-5981	168	2	2k∞(ri+1	2k∞(ri+1	X
ap-5981	168	3	−	−	PROPN
ap-5981	168	4	ri−1	ri−1	PROPN
ap-5981	168	5	)	)	PUNCT
ap-5981	169	1	+	+	NUM
ap-5981	169	2	p∑	p∑	NOUN
ap-5981	169	3	p=1	p=1	NOUN
ap-5981	170	1	1	1	NUM
ap-5981	170	2	2	2	NUM
ap-5981	170	3	(	(	PUNCT
ap-5981	170	4	λp	λp	PROPN
ap-5981	170	5	,	,	PUNCT
ap-5981	170	6	i+1	i+1	NOUN
ap-5981	170	7	−	−	PROPN
ap-5981	170	8	λp	λp	PROPN
ap-5981	170	9	,	,	PUNCT
ap-5981	170	10	i−1	i−1	PROPN
ap-5981	170	11	)	)	PUNCT
ap-5981	170	12	=	=	SYM
ap-5981	170	13	1	1	NUM
ap-5981	170	14	2	2	NUM
ap-5981	170	15	(	(	PUNCT
ap-5981	170	16	fi+1	fi+1	NOUN
ap-5981	170	17	−	−	PROPN
ap-5981	170	18	fi−1	fi−1	PROPN
ap-5981	170	19	)	)	PUNCT
ap-5981	170	20	.	.	PUNCT
ap-5981	171	1	(	(	PUNCT
ap-5981	171	2	36	36	NUM
ap-5981	171	3	)	)	PUNCT
ap-5981	171	4	505	505	NUM
ap-5981	171	5	j.	j.	PROPN
ap-5981	171	6	schmidt	schmidt	PROPN
ap-5981	171	7	,	,	PUNCT
ap-5981	171	8	t.	t.	PROPN
ap-5981	171	9	janda	janda	PROPN
ap-5981	171	10	,	,	PUNCT
ap-5981	171	11	a.	a.	PROPN
ap-5981	171	12	zemanová	zemanová	PROPN
ap-5981	171	13	et	et	PROPN
ap-5981	171	14	al	al	PROPN
ap-5981	171	15	.	.	PROPN
ap-5981	171	16	acta	acta	PROPN
ap-5981	171	17	polytechnica	polytechnica	PROPN
ap-5981	171	18	now	now	ADV
ap-5981	171	19	,	,	PUNCT
ap-5981	171	20	after	after	ADP
ap-5981	171	21	inserting	insert	VERB
ap-5981	171	22	the	the	DET
ap-5981	171	23	identity	identity	NOUN
ap-5981	171	24	(	(	PUNCT
ap-5981	171	25	35	35	NUM
ap-5981	171	26	)	)	PUNCT
ap-5981	171	27	into	into	ADP
ap-5981	171	28	the	the	DET
ap-5981	171	29	discrete	discrete	ADJ
ap-5981	171	30	euler	euler	NOUN
ap-5981	171	31	-	-	PUNCT
ap-5981	171	32	lagrange	lagrange	NOUN
ap-5981	171	33	equations	equation	NOUN
ap-5981	171	34	(	(	PUNCT
ap-5981	171	35	26	26	NUM
ap-5981	171	36	)	)	PUNCT
ap-5981	171	37	and	and	CCONJ
ap-5981	171	38	subtracting	subtract	VERB
ap-5981	171	39	(	(	PUNCT
ap-5981	171	40	36	36	NUM
ap-5981	171	41	)	)	PUNCT
ap-5981	171	42	from	from	ADP
ap-5981	171	43	the	the	DET
ap-5981	171	44	result	result	NOUN
ap-5981	171	45	,	,	PUNCT
ap-5981	171	46	we	we	PRON
ap-5981	171	47	infer	infer	VERB
ap-5981	171	48	that	that	SCONJ
ap-5981	171	49	m(r̈i−1	m(r̈i−1	NOUN
ap-5981	171	50	+	+	CCONJ
ap-5981	171	51	r̈i	r̈i	NOUN
ap-5981	171	52	)	)	PUNCT
ap-5981	171	53	+	+	CCONJ
ap-5981	171	54	k∞(ri−1	k∞(ri−1	PROPN
ap-5981	171	55	+	+	CCONJ
ap-5981	171	56	ri	ri	PROPN
ap-5981	171	57	)	)	PUNCT
ap-5981	171	58	+	+	NUM
ap-5981	171	59	p∑	p∑	X
ap-5981	171	60	p=1	p=1	X
ap-5981	171	61	(	(	PUNCT
ap-5981	171	62	λp	λp	PROPN
ap-5981	171	63	,	,	PUNCT
ap-5981	171	64	i−1	i−1	PROPN
ap-5981	171	65	+	+	PROPN
ap-5981	171	66	λp	λp	PROPN
ap-5981	171	67	,	,	PUNCT
ap-5981	171	68	i	i	NOUN
ap-5981	171	69	)	)	PUNCT
ap-5981	172	1	=	=	PUNCT
ap-5981	172	2	fi−1	fi−1	PROPN
ap-5981	172	3	+	+	CCONJ
ap-5981	172	4	fi	fi	NOUN
ap-5981	172	5	,	,	PUNCT
ap-5981	172	6	(	(	PUNCT
ap-5981	172	7	37	37	NUM
ap-5981	172	8	)	)	PUNCT
ap-5981	172	9	which	which	PRON
ap-5981	172	10	can	can	AUX
ap-5981	172	11	be	be	AUX
ap-5981	172	12	reduced	reduce	VERB
ap-5981	172	13	to	to	ADP
ap-5981	172	14	the	the	DET
ap-5981	172	15	final	final	ADJ
ap-5981	172	16	form	form	NOUN
ap-5981	172	17	mr̈i	mr̈i	VERB
ap-5981	172	18	+	+	NUM
ap-5981	172	19	k∞ri	k∞ri	NOUN
ap-5981	172	20	+	+	CCONJ
ap-5981	172	21	p∑	p∑	NOUN
ap-5981	172	22	p=1	p=1	X
ap-5981	173	1	λp	λp	PROPN
ap-5981	173	2	,	,	PUNCT
ap-5981	173	3	i	i	NOUN
ap-5981	173	4	=	=	PUNCT
ap-5981	173	5	fi	fi	NOUN
ap-5981	173	6	.	.	PUNCT
ap-5981	174	1	(	(	PUNCT
ap-5981	174	2	38	38	NUM
ap-5981	174	3	)	)	PUNCT
ap-5981	174	4	indeed	indeed	ADV
ap-5981	174	5	,	,	PUNCT
ap-5981	174	6	the	the	DET
ap-5981	174	7	equivalence	equivalence	NOUN
ap-5981	174	8	between	between	ADP
ap-5981	174	9	(	(	PUNCT
ap-5981	174	10	38	38	NUM
ap-5981	174	11	)	)	PUNCT
ap-5981	174	12	and	and	CCONJ
ap-5981	174	13	(	(	PUNCT
ap-5981	174	14	37	37	NUM
ap-5981	174	15	)	)	PUNCT
ap-5981	174	16	for	for	ADP
ap-5981	174	17	i	i	PRON
ap-5981	174	18	=	=	SYM
ap-5981	174	19	1	1	NUM
ap-5981	174	20	holds	hold	VERB
ap-5981	174	21	because	because	SCONJ
ap-5981	174	22	of	of	ADP
ap-5981	174	23	the	the	DET
ap-5981	174	24	choice	choice	NOUN
ap-5981	174	25	of	of	ADP
ap-5981	174	26	the	the	DET
ap-5981	174	27	initial	initial	ADJ
ap-5981	174	28	acceleration	acceleration	NOUN
ap-5981	174	29	(	(	PUNCT
ap-5981	174	30	13	13	NUM
ap-5981	174	31	)	)	PUNCT
ap-5981	174	32	,	,	PUNCT
ap-5981	174	33	and	and	CCONJ
ap-5981	174	34	for	for	ADP
ap-5981	174	35	i	i	PRON
ap-5981	174	36	=	=	NOUN
ap-5981	174	37	2	2	NUM
ap-5981	174	38	,	,	PUNCT
ap-5981	174	39	.	.	PUNCT
ap-5981	174	40	.	.	PUNCT
ap-5981	175	1	.	.	PUNCT
ap-5981	176	1	,	,	PUNCT
ap-5981	176	2	n	n	CCONJ
ap-5981	176	3	−	−	PROPN
ap-5981	176	4	1	1	NUM
ap-5981	176	5	it	it	PRON
ap-5981	176	6	follows	follow	VERB
ap-5981	176	7	by	by	ADP
ap-5981	176	8	induction	induction	NOUN
ap-5981	176	9	.	.	PUNCT
ap-5981	177	1	3.4	3.4	NUM
ap-5981	177	2	.	.	PUNCT
ap-5981	177	3	energy	energy	NOUN
ap-5981	177	4	balance	balance	NOUN
ap-5981	177	5	the	the	DET
ap-5981	177	6	variational	variational	ADJ
ap-5981	177	7	framework	framework	NOUN
ap-5981	177	8	(	(	PUNCT
ap-5981	177	9	14	14	NUM
ap-5981	177	10	)	)	PUNCT
ap-5981	177	11	additionally	additionally	ADV
ap-5981	177	12	reveals	reveal	VERB
ap-5981	177	13	that	that	SCONJ
ap-5981	177	14	the	the	DET
ap-5981	177	15	trajectory	trajectory	NOUN
ap-5981	177	16	q	q	X
ap-5981	177	17	satisfies	satisfy	VERB
ap-5981	177	18	the	the	DET
ap-5981	177	19	energy	energy	NOUN
ap-5981	177	20	balance	balance	NOUN
ap-5981	177	21	condition	condition	NOUN
ap-5981	177	22	,	,	PUNCT
ap-5981	177	23	e.g.	e.g.	ADV
ap-5981	177	24	,	,	PUNCT
ap-5981	177	25	[	[	X
ap-5981	177	26	23	23	NUM
ap-5981	177	27	,	,	PUNCT
ap-5981	177	28	section	section	NOUN
ap-5981	177	29	5.1	5.1	NUM
ap-5981	177	30	]	]	SYM
ap-5981	177	31	eint(t	eint(t	PROPN
ap-5981	177	32	)	)	PUNCT
ap-5981	177	33	+	+	NOUN
ap-5981	177	34	d(t	d(t	X
ap-5981	177	35	)	)	PUNCT
ap-5981	177	36	=	=	SYM
ap-5981	177	37	eint(0	eint(0	PROPN
ap-5981	177	38	)	)	PUNCT
ap-5981	178	1	+	+	VERB
ap-5981	178	2	w(t	w(t	X
ap-5981	178	3	)	)	PUNCT
ap-5981	178	4	for	for	ADP
ap-5981	178	5	0	0	NUM
ap-5981	178	6	≤	≤	NUM
ap-5981	178	7	t	t	PROPN
ap-5981	178	8	≤	≤	PROPN
ap-5981	178	9	t	t	PROPN
ap-5981	178	10	,	,	PUNCT
ap-5981	178	11	(	(	PUNCT
ap-5981	178	12	39	39	NUM
ap-5981	178	13	)	)	PUNCT
ap-5981	178	14	with	with	ADP
ap-5981	178	15	the	the	DET
ap-5981	178	16	internal	internal	ADJ
ap-5981	178	17	energy	energy	NOUN
ap-5981	178	18	eint	eint	NOUN
ap-5981	178	19	,	,	PUNCT
ap-5981	178	20	dissipated	dissipate	VERB
ap-5981	178	21	energy	energy	NOUN
ap-5981	178	22	d	d	NOUN
ap-5981	178	23	,	,	PUNCT
ap-5981	178	24	and	and	CCONJ
ap-5981	178	25	the	the	DET
ap-5981	178	26	work	work	NOUN
ap-5981	178	27	done	do	VERB
ap-5981	178	28	by	by	ADP
ap-5981	178	29	external	external	ADJ
ap-5981	178	30	forces	force	NOUN
ap-5981	178	31	w	w	NOUN
ap-5981	178	32	given	give	VERB
ap-5981	178	33	by	by	ADP
ap-5981	178	34	eint(t	eint(t	PROPN
ap-5981	178	35	)	)	PUNCT
ap-5981	178	36	=	=	SYM
ap-5981	178	37	1	1	NUM
ap-5981	178	38	2mṙ	2mṙ	NUM
ap-5981	178	39	2(t	2(t	NUM
ap-5981	178	40	)	)	PUNCT
ap-5981	179	1	+	+	CCONJ
ap-5981	179	2	1	1	NUM
ap-5981	179	3	2k∞r	2k∞r	NUM
ap-5981	179	4	2(t	2(t	NUM
ap-5981	179	5	)	)	PUNCT
ap-5981	180	1	+	+	CCONJ
ap-5981	180	2	p∑	p∑	ADJ
ap-5981	180	3	p=1	p=1	NOUN
ap-5981	181	1	1	1	NUM
ap-5981	181	2	2kpr	2kpr	NUM
ap-5981	181	3	2	2	NUM
ap-5981	181	4	e	e	NOUN
ap-5981	181	5	,	,	PUNCT
ap-5981	181	6	p(t	p(t	NOUN
ap-5981	181	7	)	)	PUNCT
ap-5981	181	8	,	,	PUNCT
ap-5981	181	9	(	(	PUNCT
ap-5981	181	10	40a	40a	X
ap-5981	181	11	)	)	PUNCT
ap-5981	181	12	d(t	d(t	PROPN
ap-5981	181	13	)	)	PUNCT
ap-5981	181	14	=	=	SYM
ap-5981	182	1	p∑	p∑	X
ap-5981	183	1	p=1	p=1	X
ap-5981	184	1	∫	∫	PROPN
ap-5981	184	2	t	t	NOUN
ap-5981	184	3	0	0	NUM
ap-5981	185	1	ηpṙ	ηpṙ	PROPN
ap-5981	185	2	2	2	NUM
ap-5981	185	3	v	v	NOUN
ap-5981	185	4	,	,	PUNCT
ap-5981	185	5	p(τ)dτ	p(τ)dτ	PROPN
ap-5981	185	6	,	,	PUNCT
ap-5981	185	7	(	(	PUNCT
ap-5981	185	8	40b	40b	X
ap-5981	185	9	)	)	PUNCT
ap-5981	185	10	w(t	w(t	PROPN
ap-5981	185	11	)	)	PUNCT
ap-5981	186	1	=	=	SYM
ap-5981	187	1	∫	∫	PROPN
ap-5981	187	2	t	t	NOUN
ap-5981	187	3	0	0	NUM
ap-5981	188	1	f	f	PROPN
ap-5981	188	2	(	(	PUNCT
ap-5981	188	3	τ)ṙ(τ)dτ	τ)ṙ(τ)dτ	PROPN
ap-5981	188	4	.	.	PUNCT
ap-5981	188	5	(	(	PUNCT
ap-5981	188	6	40c	40c	NOUN
ap-5981	188	7	)	)	PUNCT
ap-5981	188	8	to	to	PART
ap-5981	188	9	later	later	ADV
ap-5981	188	10	quantify	quantify	VERB
ap-5981	188	11	the	the	DET
ap-5981	188	12	artificial	artificial	ADJ
ap-5981	188	13	dissipation	dissipation	NOUN
ap-5981	188	14	induced	induce	VERB
ap-5981	188	15	by	by	ADP
ap-5981	188	16	time	time	NOUN
ap-5981	188	17	discretization	discretization	NOUN
ap-5981	188	18	,	,	PUNCT
ap-5981	188	19	we	we	PRON
ap-5981	188	20	also	also	ADV
ap-5981	188	21	consider	consider	VERB
ap-5981	188	22	the	the	DET
ap-5981	188	23	time	time	NOUN
ap-5981	188	24	-	-	PUNCT
ap-5981	188	25	discrete	discrete	ADJ
ap-5981	188	26	quantities	quantity	NOUN
ap-5981	188	27	eint(ti	eint(ti	NOUN
ap-5981	188	28	)	)	PUNCT
ap-5981	188	29	=	=	SYM
ap-5981	189	1	1	1	NUM
ap-5981	189	2	2mṙ	2mṙ	NUM
ap-5981	189	3	2	2	NUM
ap-5981	190	1	i	i	PRON
ap-5981	190	2	+	+	NOUN
ap-5981	190	3	1	1	NUM
ap-5981	190	4	2k∞r	2k∞r	NUM
ap-5981	190	5	2	2	NUM
ap-5981	190	6	i	i	PRON
ap-5981	190	7	+	+	NUM
ap-5981	190	8	p∑	p∑	ADJ
ap-5981	190	9	p=1	p=1	X
ap-5981	190	10	λ2	λ2	NOUN
ap-5981	190	11	p	p	NOUN
ap-5981	190	12	,	,	PUNCT
ap-5981	190	13	i	i	PROPN
ap-5981	190	14	2kp	2kp	NOUN
ap-5981	190	15	,	,	PUNCT
ap-5981	190	16	(	(	PUNCT
ap-5981	190	17	41a	41a	NOUN
ap-5981	190	18	)	)	PUNCT
ap-5981	190	19	dd(ti	dd(ti	NOUN
ap-5981	190	20	)	)	PUNCT
ap-5981	191	1	=	=	PUNCT
ap-5981	191	2	i−1∑	i−1∑	NUM
ap-5981	191	3	k=0	k=0	PROPN
ap-5981	191	4	p∑	p∑	X
ap-5981	191	5	p=1	p=1	NOUN
ap-5981	192	1	1	1	NUM
ap-5981	192	2	2ηp	2ηp	ADV
ap-5981	192	3	(	(	PUNCT
ap-5981	192	4	λ2	λ2	NOUN
ap-5981	192	5	p	p	NOUN
ap-5981	192	6	,	,	PUNCT
ap-5981	192	7	k	k	PROPN
ap-5981	192	8	+	+	NUM
ap-5981	192	9	λ2	λ2	PROPN
ap-5981	192	10	p	p	NOUN
ap-5981	192	11	,	,	PUNCT
ap-5981	192	12	k+1	k+1	X
ap-5981	192	13	)	)	PUNCT
ap-5981	192	14	∆t	∆t	PROPN
ap-5981	192	15	,	,	PUNCT
ap-5981	192	16	(	(	PUNCT
ap-5981	192	17	41b	41b	NOUN
ap-5981	192	18	)	)	PUNCT
ap-5981	192	19	wd(ti	wd(ti	NOUN
ap-5981	192	20	)	)	PUNCT
ap-5981	192	21	=	=	PUNCT
ap-5981	192	22	i−1∑	i−1∑	NUM
ap-5981	192	23	k=0	k=0	PROPN
ap-5981	192	24	1	1	NUM
ap-5981	192	25	2	2	NUM
ap-5981	192	26	(	(	PUNCT
ap-5981	192	27	fkṙk	fkṙk	PROPN
ap-5981	192	28	+	+	CCONJ
ap-5981	192	29	fk+1ṙk+1	fk+1ṙk+1	PROPN
ap-5981	192	30	)	)	PUNCT
ap-5981	192	31	∆t	∆t	PROPN
ap-5981	192	32	;	;	PUNCT
ap-5981	192	33	(	(	PUNCT
ap-5981	192	34	41c	41c	NOUN
ap-5981	192	35	)	)	PUNCT
ap-5981	192	36	the	the	DET
ap-5981	192	37	last	last	ADJ
ap-5981	192	38	two	two	NUM
ap-5981	192	39	expressions	expression	NOUN
ap-5981	192	40	correspond	correspond	VERB
ap-5981	192	41	to	to	ADP
ap-5981	192	42	the	the	DET
ap-5981	192	43	approximations	approximation	NOUN
ap-5981	192	44	of	of	ADP
ap-5981	192	45	integrals	integral	NOUN
ap-5981	192	46	in	in	ADP
ap-5981	192	47	(	(	PUNCT
ap-5981	192	48	40	40	NUM
ap-5981	192	49	)	)	PUNCT
ap-5981	192	50	with	with	ADP
ap-5981	192	51	the	the	DET
ap-5981	192	52	trapezoidal	trapezoidal	ADJ
ap-5981	192	53	rule	rule	NOUN
ap-5981	192	54	and	and	CCONJ
ap-5981	192	55	employing	employ	VERB
ap-5981	192	56	the	the	DET
ap-5981	192	57	identities	identity	NOUN
ap-5981	192	58	(	(	PUNCT
ap-5981	192	59	22	22	NUM
ap-5981	192	60	)	)	PUNCT
ap-5981	192	61	.	.	PUNCT
ap-5981	193	1	4	4	X
ap-5981	193	2	.	.	X
ap-5981	193	3	examples	example	NOUN
ap-5981	193	4	in	in	ADP
ap-5981	193	5	this	this	DET
ap-5981	193	6	section	section	NOUN
ap-5981	193	7	,	,	PUNCT
ap-5981	193	8	we	we	PRON
ap-5981	193	9	demonstrate	demonstrate	VERB
ap-5981	193	10	the	the	DET
ap-5981	193	11	performance	performance	NOUN
ap-5981	193	12	of	of	ADP
ap-5981	193	13	the	the	DET
ap-5981	193	14	developed	develop	VERB
ap-5981	193	15	newmark	newmark	NOUN
ap-5981	193	16	algorithm	algorithm	NOUN
ap-5981	193	17	on	on	ADP
ap-5981	193	18	two	two	NUM
ap-5981	193	19	examples	example	NOUN
ap-5981	193	20	.	.	PUNCT
ap-5981	194	1	kp	kp	PROPN
ap-5981	195	1	[	[	X
ap-5981	195	2	knm−1	knm−1	X
ap-5981	195	3	]	]	X
ap-5981	195	4	θp	θp	ADP
ap-5981	195	5	[	[	X
ap-5981	195	6	s	s	X
ap-5981	195	7	]	]	X
ap-5981	195	8	kp	kp	PROPN
ap-5981	196	1	[	[	X
ap-5981	196	2	knm−1	knm−1	X
ap-5981	196	3	]	]	X
ap-5981	196	4	θp	θp	ADP
ap-5981	196	5	[	[	X
ap-5981	196	6	s	s	X
ap-5981	196	7	]	]	X
ap-5981	196	8	6933.9	6933.9	NUM
ap-5981	196	9	10−9	10−9	NUM
ap-5981	196	10	445.1	445.1	NUM
ap-5981	196	11	102	102	NUM
ap-5981	196	12	3898.6	3898.6	NUM
ap-5981	196	13	10−8	10−8	NUM
ap-5981	196	14	300.1	300.1	NUM
ap-5981	196	15	103	103	NUM
ap-5981	196	16	2289.2	2289.2	NUM
ap-5981	196	17	10−7	10−7	NUM
ap-5981	196	18	401.60	401.60	NUM
ap-5981	196	19	104	104	NUM
ap-5981	196	20	1672.7	1672.7	NUM
ap-5981	196	21	10−6	10−6	NUM
ap-5981	196	22	348.1	348.1	NUM
ap-5981	196	23	105	105	NUM
ap-5981	196	24	761.60	761.60	NUM
ap-5981	196	25	10−5	10−5	NUM
ap-5981	196	26	111.6	111.6	NUM
ap-5981	196	27	106	106	NUM
ap-5981	196	28	2401.0	2401.0	NUM
ap-5981	196	29	10−4	10−4	NUM
ap-5981	196	30	127.2	127.2	NUM
ap-5981	196	31	107	107	NUM
ap-5981	196	32	65.200	65.200	NUM
ap-5981	196	33	10−3	10−3	NUM
ap-5981	196	34	137.8	137.8	NUM
ap-5981	196	35	108	108	NUM
ap-5981	196	36	248.00	248.00	NUM
ap-5981	196	37	10−2	10−2	NUM
ap-5981	196	38	50.5	50.5	NUM
ap-5981	196	39	109	109	NUM
ap-5981	196	40	575.60	575.60	NUM
ap-5981	196	41	10−1	10−1	NUM
ap-5981	196	42	322.9	322.9	NUM
ap-5981	196	43	1010	1010	NUM
ap-5981	196	44	56.30	56.30	NUM
ap-5981	196	45	100	100	NUM
ap-5981	196	46	100.0	100.0	NUM
ap-5981	196	47	1011	1011	NUM
ap-5981	196	48	188.6	188.6	NUM
ap-5981	196	49	101	101	NUM
ap-5981	196	50	199.9	199.9	NUM
ap-5981	196	51	1012	1012	NUM
ap-5981	196	52	table	table	NOUN
ap-5981	196	53	1	1	NUM
ap-5981	196	54	.	.	PUNCT
ap-5981	197	1	parameters	parameter	NOUN
ap-5981	197	2	of	of	ADP
ap-5981	197	3	maxwell	maxwell	PROPN
ap-5981	197	4	chain	chain	NOUN
ap-5981	197	5	model	model	NOUN
ap-5981	197	6	[	[	X
ap-5981	197	7	10	10	NUM
ap-5981	197	8	]	]	PUNCT
ap-5981	197	9	,	,	PUNCT
ap-5981	197	10	with	with	ADP
ap-5981	197	11	θp	θp	ADP
ap-5981	197	12	=	=	PUNCT
ap-5981	197	13	ηp	ηp	PROPN
ap-5981	197	14	/	/	SYM
ap-5981	197	15	kp	kp	PROPN
ap-5981	197	16	and	and	CCONJ
ap-5981	197	17	k∞	k∞	PROPN
ap-5981	197	18	=	=	PUNCT
ap-5981	198	1	682.18	682.18	NUM
ap-5981	198	2	knm−1	knm−1	PROPN
ap-5981	198	3	.	.	PUNCT
ap-5981	199	1	note	note	VERB
ap-5981	199	2	that	that	SCONJ
ap-5981	199	3	in	in	ADP
ap-5981	199	4	section	section	NOUN
ap-5981	199	5	4.2	4.2	NUM
ap-5981	199	6	,	,	PUNCT
ap-5981	199	7	the	the	DET
ap-5981	199	8	stiffnesses	stiffness	NOUN
ap-5981	199	9	k•	k•	VERB
ap-5981	199	10	correspond	correspond	NOUN
ap-5981	199	11	to	to	ADP
ap-5981	199	12	shear	shear	NOUN
ap-5981	199	13	moduli	modulus	NOUN
ap-5981	199	14	g•	g•	PROPN
ap-5981	200	1	[	[	X
ap-5981	200	2	mpa	mpa	NOUN
ap-5981	200	3	]	]	X
ap-5981	200	4	.	.	PUNCT
ap-5981	201	1	the	the	DET
ap-5981	201	2	first	first	ADJ
ap-5981	201	3	one	one	NUM
ap-5981	201	4	in	in	ADP
ap-5981	201	5	section	section	NOUN
ap-5981	201	6	4.1	4.1	NUM
ap-5981	201	7	addresses	address	NOUN
ap-5981	201	8	the	the	DET
ap-5981	201	9	accuracy	accuracy	NOUN
ap-5981	201	10	and	and	CCONJ
ap-5981	201	11	numerical	numerical	ADJ
ap-5981	201	12	energy	energy	NOUN
ap-5981	201	13	dissipation	dissipation	NOUN
ap-5981	201	14	of	of	ADP
ap-5981	201	15	the	the	DET
ap-5981	201	16	integrator	integrator	NOUN
ap-5981	201	17	for	for	ADP
ap-5981	201	18	the	the	DET
ap-5981	201	19	single	single	ADJ
ap-5981	201	20	-	-	PUNCT
ap-5981	201	21	degree	degree	NOUN
ap-5981	201	22	-	-	PUNCT
ap-5981	201	23	of	of	ADP
ap-5981	201	24	-	-	PUNCT
ap-5981	201	25	freedom	freedom	NOUN
ap-5981	201	26	system	system	NOUN
ap-5981	201	27	from	from	ADP
ap-5981	201	28	figure	figure	NOUN
ap-5981	201	29	1	1	NUM
ap-5981	201	30	.	.	PUNCT
ap-5981	202	1	the	the	DET
ap-5981	202	2	follow	follow	NOUN
ap-5981	202	3	-	-	PUNCT
ap-5981	202	4	up	up	NOUN
ap-5981	202	5	example	example	NOUN
ap-5981	202	6	in	in	ADP
ap-5981	202	7	section	section	NOUN
ap-5981	202	8	4.2	4.2	NUM
ap-5981	202	9	outlines	outline	VERB
ap-5981	202	10	an	an	DET
ap-5981	202	11	extension	extension	NOUN
ap-5981	202	12	of	of	ADP
ap-5981	202	13	the	the	DET
ap-5981	202	14	scheme	scheme	NOUN
ap-5981	202	15	towards	towards	ADP
ap-5981	202	16	continuum	continuum	ADJ
ap-5981	202	17	models	model	NOUN
ap-5981	202	18	.	.	PUNCT
ap-5981	203	1	data	datum	NOUN
ap-5981	203	2	of	of	ADP
ap-5981	203	3	the	the	DET
ap-5981	203	4	generalized	generalized	ADJ
ap-5981	203	5	maxwell	maxwell	PROPN
ap-5981	203	6	chain	chain	NOUN
ap-5981	203	7	used	use	VERB
ap-5981	203	8	in	in	ADP
ap-5981	203	9	both	both	DET
ap-5981	203	10	examples	example	NOUN
ap-5981	203	11	appear	appear	VERB
ap-5981	203	12	in	in	ADP
ap-5981	203	13	table	table	NOUN
ap-5981	203	14	1	1	NUM
ap-5981	203	15	;	;	PUNCT
ap-5981	203	16	they	they	PRON
ap-5981	203	17	represent	represent	VERB
ap-5981	203	18	real	real	ADJ
ap-5981	203	19	polyvinyl	polyvinyl	NOUN
ap-5981	203	20	butyral	butyral	ADJ
ap-5981	203	21	(	(	PUNCT
ap-5981	203	22	pvb	pvb	NOUN
ap-5981	203	23	)	)	PUNCT
ap-5981	203	24	material	material	NOUN
ap-5981	203	25	with	with	ADP
ap-5981	203	26	sufficiently	sufficiently	ADV
ap-5981	203	27	short	short	ADJ
ap-5981	203	28	and	and	CCONJ
ap-5981	203	29	long	long	ADJ
ap-5981	203	30	relaxation	relaxation	NOUN
ap-5981	203	31	times	time	NOUN
ap-5981	203	32	for	for	ADP
ap-5981	203	33	testing	test	VERB
ap-5981	203	34	the	the	DET
ap-5981	203	35	algorithm	algorithm	NOUN
ap-5981	203	36	robustness	robustness	NOUN
ap-5981	203	37	.	.	PUNCT
ap-5981	204	1	for	for	ADP
ap-5981	204	2	more	more	ADJ
ap-5981	204	3	information	information	NOUN
ap-5981	204	4	on	on	ADP
ap-5981	204	5	experimental	experimental	ADJ
ap-5981	204	6	procedures	procedure	NOUN
ap-5981	204	7	to	to	PART
ap-5981	204	8	determine	determine	VERB
ap-5981	204	9	these	these	DET
ap-5981	204	10	parameters	parameter	NOUN
ap-5981	204	11	,	,	PUNCT
ap-5981	204	12	see	see	VERB
ap-5981	204	13	[	[	X
ap-5981	204	14	10	10	NUM
ap-5981	204	15	]	]	PUNCT
ap-5981	204	16	.	.	PUNCT
ap-5981	205	1	all	all	DET
ap-5981	205	2	results	result	NOUN
ap-5981	205	3	presented	present	VERB
ap-5981	205	4	in	in	ADP
ap-5981	205	5	this	this	DET
ap-5981	205	6	section	section	NOUN
ap-5981	205	7	are	be	AUX
ap-5981	205	8	reproducible	reproducible	ADJ
ap-5981	205	9	with	with	ADP
ap-5981	205	10	python	python	NOUN
ap-5981	205	11	-	-	PUNCT
ap-5981	205	12	based	base	VERB
ap-5981	205	13	scripts	script	NOUN
ap-5981	205	14	available	available	ADJ
ap-5981	205	15	at	at	ADP
ap-5981	205	16	[	[	X
ap-5981	205	17	24	24	NUM
ap-5981	205	18	]	]	PUNCT
ap-5981	205	19	.	.	PUNCT
ap-5981	206	1	4.1	4.1	NUM
ap-5981	206	2	.	.	PUNCT
ap-5981	206	3	discrete	discrete	ADJ
ap-5981	206	4	problem	problem	NOUN
ap-5981	206	5	we	we	PRON
ap-5981	206	6	consider	consider	VERB
ap-5981	206	7	the	the	DET
ap-5981	206	8	following	follow	VERB
ap-5981	206	9	two	two	NUM
ap-5981	206	10	types	type	NOUN
ap-5981	206	11	of	of	ADP
ap-5981	206	12	loading	loading	NOUN
ap-5981	206	13	:	:	PUNCT
ap-5981	206	14	f	f	PROPN
ap-5981	206	15	(	(	PUNCT
ap-5981	206	16	t	t	PROPN
ap-5981	206	17	)	)	PUNCT
ap-5981	207	1	=	=	SYM
ap-5981	207	2	f	f	PROPN
ap-5981	207	3	for	for	ADP
ap-5981	207	4	t	t	PROPN
ap-5981	207	5	≥	≥	PROPN
ap-5981	207	6	0	0	NUM
ap-5981	207	7	,	,	PUNCT
ap-5981	207	8	(	(	PUNCT
ap-5981	207	9	42a	42a	NOUN
ap-5981	207	10	)	)	PUNCT
ap-5981	207	11	f	f	PROPN
ap-5981	207	12	(	(	PUNCT
ap-5981	207	13	t	t	PROPN
ap-5981	207	14	)	)	PUNCT
ap-5981	207	15	=	=	SYM
ap-5981	208	1	f	f	PROPN
ap-5981	208	2	sin	sin	PROPN
ap-5981	208	3	t	t	PROPN
ap-5981	208	4	for	for	ADP
ap-5981	208	5	t	t	PROPN
ap-5981	208	6	≥	≥	PROPN
ap-5981	208	7	0	0	NUM
ap-5981	208	8	,	,	PUNCT
ap-5981	208	9	(	(	PUNCT
ap-5981	208	10	42b	42b	NOUN
ap-5981	208	11	)	)	PUNCT
ap-5981	208	12	corresponding	correspond	VERB
ap-5981	208	13	to	to	PART
ap-5981	208	14	step	step	VERB
ap-5981	208	15	and	and	CCONJ
ap-5981	208	16	harmonic	harmonic	ADJ
ap-5981	208	17	loads	load	NOUN
ap-5981	208	18	,	,	PUNCT
ap-5981	208	19	respectively	respectively	ADV
ap-5981	208	20	.	.	PUNCT
ap-5981	209	1	in	in	ADP
ap-5981	209	2	both	both	DET
ap-5981	209	3	cases	case	NOUN
ap-5981	209	4	,	,	PUNCT
ap-5981	209	5	we	we	PRON
ap-5981	209	6	set	set	VERB
ap-5981	209	7	the	the	DET
ap-5981	209	8	amplitude	amplitude	NOUN
ap-5981	209	9	f	f	NOUN
ap-5981	209	10	=	=	SYM
ap-5981	209	11	1	1	NUM
ap-5981	209	12	mn	mn	PROPN
ap-5981	209	13	and	and	CCONJ
ap-5981	209	14	the	the	DET
ap-5981	209	15	mass	mass	NOUN
ap-5981	209	16	m	m	NOUN
ap-5981	209	17	=	=	SYM
ap-5981	209	18	106	106	NUM
ap-5981	209	19	kg	kg	NOUN
ap-5981	209	20	to	to	PART
ap-5981	209	21	scale	scale	VERB
ap-5981	209	22	the	the	DET
ap-5981	209	23	displacement	displacement	ADJ
ap-5981	209	24	amplitude	amplitude	NOUN
ap-5981	209	25	to	to	ADP
ap-5981	209	26	≈	≈	PROPN
ap-5981	209	27	1	1	NUM
ap-5981	209	28	m.	m.	NOUN
ap-5981	209	29	initial	initial	ADJ
ap-5981	209	30	displacement	displacement	NOUN
ap-5981	209	31	,	,	PUNCT
ap-5981	209	32	velocity	velocity	NOUN
ap-5981	209	33	,	,	PUNCT
ap-5981	209	34	and	and	CCONJ
ap-5981	209	35	forces	force	NOUN
ap-5981	209	36	in	in	ADP
ap-5981	209	37	maxwell	maxwell	PROPN
ap-5981	209	38	cells	cell	NOUN
ap-5981	209	39	were	be	AUX
ap-5981	209	40	set	set	VERB
ap-5981	209	41	to	to	ADP
ap-5981	209	42	zero	zero	NUM
ap-5981	209	43	;	;	PUNCT
ap-5981	209	44	recall	recall	NOUN
ap-5981	209	45	(	(	PUNCT
ap-5981	209	46	5	5	NUM
ap-5981	209	47	)	)	PUNCT
ap-5981	209	48	.	.	PUNCT
ap-5981	210	1	as	as	ADP
ap-5981	210	2	for	for	ADP
ap-5981	210	3	the	the	DET
ap-5981	210	4	newmark	newmark	PROPN
ap-5981	210	5	algorithm	algorithm	NOUN
ap-5981	210	6	,	,	PUNCT
ap-5981	210	7	we	we	PRON
ap-5981	210	8	set	set	VERB
ap-5981	210	9	the	the	DET
ap-5981	210	10	time	time	NOUN
ap-5981	210	11	steps	step	NOUN
ap-5981	210	12	∆t	∆t	PROPN
ap-5981	210	13	to	to	ADP
ap-5981	210	14	1.0	1.0	NUM
ap-5981	210	15	,	,	PUNCT
ap-5981	210	16	0.5	0.5	NUM
ap-5981	210	17	,	,	PUNCT
ap-5981	210	18	and	and	CCONJ
ap-5981	210	19	0.2	0.2	NUM
ap-5981	210	20	s.	s.	PROPN
ap-5981	210	21	accuracy	accuracy	NOUN
ap-5981	210	22	of	of	ADP
ap-5981	210	23	the	the	DET
ap-5981	210	24	newmark	newmark	PROPN
ap-5981	210	25	algorithm	algorithm	PROPN
ap-5981	210	26	is	be	AUX
ap-5981	210	27	checked	check	VERB
ap-5981	210	28	by	by	ADP
ap-5981	210	29	comparing	compare	VERB
ap-5981	210	30	its	its	PRON
ap-5981	210	31	trajectories	trajectory	NOUN
ap-5981	210	32	with	with	ADP
ap-5981	210	33	the	the	DET
ap-5981	210	34	reference	reference	NOUN
ap-5981	210	35	ones	one	NOUN
ap-5981	210	36	,	,	PUNCT
ap-5981	210	37	obtained	obtain	VERB
ap-5981	210	38	with	with	ADP
ap-5981	210	39	the	the	DET
ap-5981	210	40	adaptive	adaptive	ADJ
ap-5981	210	41	solver	solver	NOUN
ap-5981	210	42	lsoda	lsoda	NOUN
ap-5981	211	1	[	[	X
ap-5981	211	2	25	25	NUM
ap-5981	211	3	]	]	PUNCT
ap-5981	211	4	—	—	PUNCT
ap-5981	211	5	available	available	ADJ
ap-5981	211	6	through	through	ADP
ap-5981	211	7	odeint	odeint	NOUN
ap-5981	211	8	function	function	NOUN
ap-5981	211	9	of	of	ADP
ap-5981	211	10	scipy	scipy	NOUN
ap-5981	211	11	library	library	NOUN
ap-5981	212	1	[	[	X
ap-5981	212	2	26	26	NUM
ap-5981	212	3	]	]	PUNCT
ap-5981	212	4	—	—	PUNCT
ap-5981	212	5	applied	apply	VERB
ap-5981	212	6	to	to	ADP
ap-5981	212	7	the	the	DET
ap-5981	212	8	full	full	ADJ
ap-5981	212	9	initial	initial	ADJ
ap-5981	212	10	value	value	NOUN
ap-5981	212	11	problem	problem	NOUN
ap-5981	212	12	(	(	PUNCT
ap-5981	212	13	1	1	NUM
ap-5981	212	14	)	)	PUNCT
ap-5981	212	15	,	,	PUNCT
ap-5981	212	16	(	(	PUNCT
ap-5981	212	17	4	4	NUM
ap-5981	212	18	)	)	PUNCT
ap-5981	212	19	,	,	PUNCT
ap-5981	212	20	and	and	CCONJ
ap-5981	212	21	(	(	PUNCT
ap-5981	212	22	5	5	NUM
ap-5981	212	23	)	)	PUNCT
ap-5981	212	24	.	.	PUNCT
ap-5981	213	1	the	the	DET
ap-5981	213	2	results	result	NOUN
ap-5981	213	3	appear	appear	VERB
ap-5981	213	4	in	in	ADP
ap-5981	213	5	figure	figure	NOUN
ap-5981	213	6	3	3	NUM
ap-5981	213	7	and	and	CCONJ
ap-5981	213	8	demonstrate	demonstrate	VERB
ap-5981	213	9	that	that	SCONJ
ap-5981	213	10	the	the	DET
ap-5981	213	11	newmark	newmark	PROPN
ap-5981	213	12	algorithm	algorithm	PROPN
ap-5981	213	13	is	be	AUX
ap-5981	213	14	stable	stable	ADJ
ap-5981	213	15	even	even	ADV
ap-5981	213	16	for	for	ADP
ap-5981	213	17	coarse	coarse	ADJ
ap-5981	213	18	time	time	NOUN
ap-5981	213	19	steps	step	NOUN
ap-5981	213	20	.	.	PUNCT
ap-5981	214	1	the	the	DET
ap-5981	214	2	errors	error	NOUN
ap-5981	214	3	behave	behave	VERB
ap-5981	214	4	consistently	consistently	ADV
ap-5981	214	5	with	with	ADP
ap-5981	214	6	findings	finding	NOUN
ap-5981	214	7	for	for	ADP
ap-5981	214	8	newmark	newmark	NOUN
ap-5981	214	9	-	-	PUNCT
ap-5981	214	10	family	family	NOUN
ap-5981	214	11	methods	method	NOUN
ap-5981	214	12	applied	apply	VERB
ap-5981	214	13	to	to	ADP
ap-5981	214	14	linearly	linearly	ADV
ap-5981	214	15	damped	damp	VERB
ap-5981	214	16	systems	system	NOUN
ap-5981	214	17	,	,	PUNCT
ap-5981	215	1	e.g.	e.g.	ADV
ap-5981	215	2	[	[	X
ap-5981	215	3	27	27	NUM
ap-5981	215	4	,	,	PUNCT
ap-5981	215	5	section	section	NOUN
ap-5981	215	6	b.ii.5	b.ii.5	NOUN
ap-5981	215	7	]	]	PUNCT
ap-5981	215	8	.	.	PUNCT
ap-5981	216	1	in	in	ADP
ap-5981	216	2	particular	particular	ADJ
ap-5981	216	3	,	,	PUNCT
ap-5981	216	4	the	the	DET
ap-5981	216	5	numerical	numerical	ADJ
ap-5981	216	6	dispersion	dispersion	NOUN
ap-5981	216	7	(	(	PUNCT
ap-5981	216	8	understood	understand	VERB
ap-5981	216	9	as	as	ADP
ap-5981	216	10	the	the	DET
ap-5981	216	11	error	error	NOUN
ap-5981	216	12	in	in	ADP
ap-5981	216	13	periods	period	NOUN
ap-5981	216	14	)	)	PUNCT
ap-5981	216	15	and	and	CCONJ
ap-5981	216	16	dissipation	dissipation	NOUN
ap-5981	216	17	(	(	PUNCT
ap-5981	216	18	error	error	NOUN
ap-5981	216	19	in	in	ADP
ap-5981	216	20	amplitudes	amplitude	NOUN
ap-5981	216	21	)	)	PUNCT
ap-5981	216	22	decays	decay	NOUN
ap-5981	216	23	as	as	ADP
ap-5981	216	24	506	506	NUM
ap-5981	216	25	vol	vol	NOUN
ap-5981	216	26	.	.	PUNCT
ap-5981	217	1	60	60	NUM
ap-5981	217	2	no	no	INTJ
ap-5981	217	3	.	.	PUNCT
ap-5981	218	1	6/2020	6/2020	NUM
ap-5981	218	2	newmark	newmark	NOUN
ap-5981	218	3	algorithm	algorithm	NOUN
ap-5981	218	4	for	for	ADP
ap-5981	218	5	dynamic	dynamic	ADJ
ap-5981	218	6	analysis	analysis	NOUN
ap-5981	218	7	of	of	ADP
ap-5981	218	8	viscoelastic	viscoelastic	ADJ
ap-5981	218	9	materials	material	NOUN
ap-5981	218	10	10	10	NUM
ap-5981	218	11	-	-	SYM
ap-5981	218	12	2	2	NUM
ap-5981	218	13	10	10	NUM
ap-5981	218	14	-	-	SYM
ap-5981	218	15	1	1	NUM
ap-5981	218	16	100	100	NUM
ap-5981	218	17	time	time	NOUN
ap-5981	218	18	step	step	NOUN
ap-5981	218	19	∆t	∆t	PROPN
ap-5981	219	1	[	[	X
ap-5981	219	2	s	s	X
ap-5981	219	3	]	]	X
ap-5981	219	4	10	10	NUM
ap-5981	219	5	-	-	SYM
ap-5981	219	6	6	6	NUM
ap-5981	219	7	10	10	NUM
ap-5981	219	8	-	-	SYM
ap-5981	219	9	5	5	NUM
ap-5981	219	10	10	10	NUM
ap-5981	219	11	-	-	SYM
ap-5981	219	12	4	4	NUM
ap-5981	219	13	10	10	NUM
ap-5981	219	14	-	-	SYM
ap-5981	219	15	3	3	NUM
ap-5981	219	16	10	10	NUM
ap-5981	219	17	-	-	SYM
ap-5981	219	18	2	2	NUM
ap-5981	219	19	10	10	NUM
ap-5981	219	20	-	-	SYM
ap-5981	219	21	1	1	NUM
ap-5981	219	22	100	100	NUM
ap-5981	219	23	re	re	X
ap-5981	219	24	la	la	PROPN
ap-5981	219	25	tiv	tiv	PROPN
ap-5981	219	26	e	e	PROPN
ap-5981	219	27	er	er	INTJ
ap-5981	219	28	ro	ro	CCONJ
ap-5981	219	29	r	r	NOUN
ap-5981	219	30	[	[	PUNCT
ap-5981	219	31	-	-	PUNCT
ap-5981	219	32	]	]	X
ap-5981	219	33	numerical	numerical	ADJ
ap-5981	219	34	errors	error	NOUN
ap-5981	219	35	quadratic	quadratic	ADJ
ap-5981	219	36	order	order	NOUN
ap-5981	219	37	figure	figure	NOUN
ap-5981	219	38	2	2	NUM
ap-5981	219	39	.	.	PUNCT
ap-5981	219	40	convergence	convergence	NOUN
ap-5981	219	41	diagram	diagram	NOUN
ap-5981	219	42	for	for	ADP
ap-5981	219	43	the	the	DET
ap-5981	219	44	step	step	NOUN
ap-5981	219	45	loading	loading	NOUN
ap-5981	219	46	.	.	PUNCT
ap-5981	220	1	crosses	crosse	NOUN
ap-5981	220	2	represent	represent	VERB
ap-5981	220	3	the	the	DET
ap-5981	220	4	relative	relative	ADJ
ap-5981	220	5	numerical	numerical	ADJ
ap-5981	220	6	errors	error	NOUN
ap-5981	220	7	for	for	ADP
ap-5981	220	8	different	different	ADJ
ap-5981	220	9	time	time	NOUN
ap-5981	220	10	steps	step	NOUN
ap-5981	220	11	,	,	PUNCT
ap-5981	220	12	the	the	DET
ap-5981	220	13	solid	solid	ADJ
ap-5981	220	14	line	line	NOUN
ap-5981	220	15	a	a	DET
ap-5981	220	16	quadratic	quadratic	ADJ
ap-5981	220	17	function	function	NOUN
ap-5981	220	18	.	.	PUNCT
ap-5981	221	1	o((ω∆t)2	o((ω∆t)2	NOUN
ap-5981	221	2	)	)	PUNCT
ap-5981	221	3	,	,	PUNCT
ap-5981	221	4	where	where	SCONJ
ap-5981	221	5	ω	ω	PROPN
ap-5981	221	6	stands	stand	VERB
ap-5981	221	7	for	for	ADP
ap-5981	221	8	the	the	DET
ap-5981	221	9	eigenfrequency	eigenfrequency	NOUN
ap-5981	221	10	of	of	ADP
ap-5981	221	11	the	the	DET
ap-5981	221	12	undamped	undamped	ADJ
ap-5981	221	13	system	system	NOUN
ap-5981	221	14	.	.	PUNCT
ap-5981	222	1	for	for	ADP
ap-5981	222	2	∆t	∆t	PROPN
ap-5981	222	3	=	=	SYM
ap-5981	222	4	0.2	0.2	NUM
ap-5981	222	5	s	s	PROPN
ap-5981	222	6	,	,	PUNCT
ap-5981	222	7	the	the	DET
ap-5981	222	8	trajectories	trajectory	NOUN
ap-5981	222	9	predicted	predict	VERB
ap-5981	222	10	by	by	ADP
ap-5981	222	11	the	the	DET
ap-5981	222	12	newmark	newmark	PROPN
ap-5981	222	13	scheme	scheme	NOUN
ap-5981	222	14	closely	closely	ADV
ap-5981	222	15	match	match	VERB
ap-5981	222	16	the	the	DET
ap-5981	222	17	reference	reference	NOUN
ap-5981	222	18	ones	one	NOUN
ap-5981	222	19	.	.	PUNCT
ap-5981	223	1	to	to	PART
ap-5981	223	2	demonstrate	demonstrate	VERB
ap-5981	223	3	the	the	DET
ap-5981	223	4	second	second	ADJ
ap-5981	223	5	-	-	PUNCT
ap-5981	223	6	order	order	NOUN
ap-5981	223	7	accuracy	accuracy	NOUN
ap-5981	223	8	qualitatively	qualitatively	ADV
ap-5981	223	9	,	,	PUNCT
ap-5981	223	10	in	in	ADP
ap-5981	223	11	figure	figure	NOUN
ap-5981	223	12	2	2	NUM
ap-5981	223	13	,	,	PUNCT
ap-5981	223	14	we	we	PRON
ap-5981	223	15	plot	plot	VERB
ap-5981	223	16	the	the	DET
ap-5981	223	17	decay	decay	NOUN
ap-5981	223	18	of	of	ADP
ap-5981	223	19	a	a	DET
ap-5981	223	20	relative	relative	ADJ
ap-5981	223	21	error	error	NOUN
ap-5981	223	22	with	with	ADP
ap-5981	223	23	a	a	DET
ap-5981	223	24	decreasing	decrease	VERB
ap-5981	223	25	time	time	NOUN
ap-5981	223	26	step	step	NOUN
ap-5981	223	27	∆t	∆t	PROPN
ap-5981	223	28	.	.	PUNCT
ap-5981	224	1	the	the	DET
ap-5981	224	2	relative	relative	ADJ
ap-5981	224	3	errors	error	NOUN
ap-5981	224	4	were	be	AUX
ap-5981	224	5	calculated	calculate	VERB
ap-5981	224	6	according	accord	VERB
ap-5981	224	7	to	to	ADP
ap-5981	224	8	||r∆t	||r∆t	NUM
ap-5981	224	9	−	−	PROPN
ap-5981	224	10	rref	rref	NOUN
ap-5981	224	11	∆t||2/||rref	∆t||2/||rref	X
ap-5981	225	1	∆t||2	∆t||2	NOUN
ap-5981	225	2	,	,	PUNCT
ap-5981	225	3	where	where	SCONJ
ap-5981	225	4	r∆t	r∆t	ADJ
ap-5981	225	5	stores	store	NOUN
ap-5981	225	6	displacements	displacement	NOUN
ap-5981	225	7	of	of	ADP
ap-5981	225	8	all	all	DET
ap-5981	225	9	time	time	NOUN
ap-5981	225	10	instants	instant	NOUN
ap-5981	225	11	for	for	ADP
ap-5981	225	12	time	time	NOUN
ap-5981	225	13	step	step	NOUN
ap-5981	225	14	∆t	∆t	PROPN
ap-5981	225	15	,	,	PUNCT
ap-5981	225	16	rref	rref	NOUN
ap-5981	225	17	∆t	∆t	PROPN
ap-5981	225	18	the	the	DET
ap-5981	225	19	reference	reference	NOUN
ap-5981	225	20	solution	solution	NOUN
ap-5981	225	21	of	of	ADP
ap-5981	225	22	odeint	odeint	NOUN
ap-5981	225	23	at	at	ADP
ap-5981	225	24	the	the	DET
ap-5981	225	25	same	same	ADJ
ap-5981	225	26	times	time	NOUN
ap-5981	225	27	,	,	PUNCT
ap-5981	225	28	and	and	CCONJ
ap-5981	225	29	‖	‖	PROPN
ap-5981	225	30	•	•	PROPN
ap-5981	225	31	‖	‖	PROPN
ap-5981	225	32	denotes	denote	NOUN
ap-5981	225	33	the	the	DET
ap-5981	225	34	euclidean	euclidean	PROPN
ap-5981	225	35	norm	norm	NOUN
ap-5981	225	36	.	.	PUNCT
ap-5981	226	1	a	a	DET
ap-5981	226	2	comparison	comparison	NOUN
ap-5981	226	3	with	with	ADP
ap-5981	226	4	the	the	DET
ap-5981	226	5	quadratic	quadratic	ADJ
ap-5981	226	6	function	function	NOUN
ap-5981	226	7	(	(	PUNCT
ap-5981	226	8	solid	solid	ADJ
ap-5981	226	9	line	line	NOUN
ap-5981	226	10	)	)	PUNCT
ap-5981	226	11	confirms	confirm	VERB
ap-5981	226	12	the	the	DET
ap-5981	226	13	second	second	ADJ
ap-5981	226	14	-	-	PUNCT
ap-5981	226	15	order	order	NOUN
ap-5981	226	16	accuracy	accuracy	NOUN
ap-5981	226	17	.	.	PUNCT
ap-5981	227	1	note	note	VERB
ap-5981	227	2	that	that	SCONJ
ap-5981	227	3	the	the	DET
ap-5981	227	4	deviation	deviation	NOUN
ap-5981	227	5	visible	visible	ADJ
ap-5981	227	6	for	for	ADP
ap-5981	227	7	short	short	ADJ
ap-5981	227	8	time	time	NOUN
ap-5981	227	9	steps	step	NOUN
ap-5981	227	10	results	result	NOUN
ap-5981	227	11	from	from	ADP
ap-5981	227	12	a	a	DET
ap-5981	227	13	prescribed	prescribed	ADJ
ap-5981	227	14	tolerance	tolerance	NOUN
ap-5981	227	15	of	of	ADP
ap-5981	227	16	the	the	DET
ap-5981	227	17	odeint	odeint	NOUN
ap-5981	227	18	solver	solver	ADV
ap-5981	227	19	.	.	PUNCT
ap-5981	228	1	numerical	numerical	ADJ
ap-5981	228	2	dissipation	dissipation	PROPN
ap-5981	228	3	.	.	PUNCT
ap-5981	229	1	as	as	SCONJ
ap-5981	229	2	follows	follow	VERB
ap-5981	229	3	from	from	ADP
ap-5981	229	4	the	the	DET
ap-5981	229	5	energy	energy	NOUN
ap-5981	229	6	equality	equality	NOUN
ap-5981	229	7	(	(	PUNCT
ap-5981	229	8	39	39	NUM
ap-5981	229	9	)	)	PUNCT
ap-5981	229	10	,	,	PUNCT
ap-5981	229	11	the	the	DET
ap-5981	229	12	additional	additional	ADJ
ap-5981	229	13	dissipation	dissipation	NOUN
ap-5981	229	14	induced	induce	VERB
ap-5981	229	15	by	by	ADP
ap-5981	229	16	the	the	DET
ap-5981	229	17	integrator	integrator	NOUN
ap-5981	229	18	can	can	AUX
ap-5981	229	19	be	be	AUX
ap-5981	229	20	estimated	estimate	VERB
ap-5981	229	21	as	as	ADP
ap-5981	229	22	∆d(ti	∆d(ti	NOUN
ap-5981	229	23	)	)	PUNCT
ap-5981	229	24	=	=	PUNCT
ap-5981	229	25	|eint(0	|eint(0	X
ap-5981	229	26	)	)	PUNCT
ap-5981	230	1	+	+	NOUN
ap-5981	230	2	wd(ti)−	wd(ti)−	PROPN
ap-5981	230	3	eint(ti)−dd(ti)|	eint(ti)−dd(ti)|	INTJ
ap-5981	230	4	,	,	PUNCT
ap-5981	230	5	(	(	PUNCT
ap-5981	230	6	43	43	NUM
ap-5981	230	7	)	)	PUNCT
ap-5981	230	8	with	with	ADP
ap-5981	230	9	the	the	DET
ap-5981	230	10	individual	individual	ADJ
ap-5981	230	11	terms	term	NOUN
ap-5981	230	12	provided	provide	VERB
ap-5981	230	13	by	by	ADP
ap-5981	230	14	eq	eq	PROPN
ap-5981	230	15	.	.	PUNCT
ap-5981	231	1	(	(	PUNCT
ap-5981	231	2	41	41	NUM
ap-5981	231	3	)	)	PUNCT
ap-5981	231	4	.	.	PUNCT
ap-5981	232	1	the	the	DET
ap-5981	232	2	evolution	evolution	NOUN
ap-5981	232	3	of	of	ADP
ap-5981	232	4	these	these	DET
ap-5981	232	5	quantities	quantity	NOUN
ap-5981	232	6	for	for	ADP
ap-5981	232	7	the	the	DET
ap-5981	232	8	step	step	NOUN
ap-5981	232	9	and	and	CCONJ
ap-5981	232	10	harmonic	harmonic	ADJ
ap-5981	232	11	loading	loading	NOUN
ap-5981	232	12	appears	appear	VERB
ap-5981	232	13	in	in	ADP
ap-5981	232	14	figure	figure	NOUN
ap-5981	232	15	4	4	NUM
ap-5981	232	16	,	,	PUNCT
ap-5981	232	17	considering	consider	VERB
ap-5981	232	18	the	the	DET
ap-5981	232	19	time	time	NOUN
ap-5981	232	20	interval	interval	NOUN
ap-5981	232	21	〈	〈	PROPN
ap-5981	232	22	0	0	NUM
ap-5981	232	23	,	,	PUNCT
ap-5981	232	24	300	300	NUM
ap-5981	232	25	〉	〉	PROPN
ap-5981	232	26	s.	s.	PROPN
ap-5981	232	27	for	for	ADP
ap-5981	232	28	both	both	DET
ap-5981	232	29	loads	load	NOUN
ap-5981	232	30	,	,	PUNCT
ap-5981	232	31	we	we	PRON
ap-5981	232	32	observe	observe	VERB
ap-5981	232	33	that	that	SCONJ
ap-5981	232	34	the	the	DET
ap-5981	232	35	work	work	NOUN
ap-5981	232	36	done	do	VERB
ap-5981	232	37	by	by	ADP
ap-5981	232	38	external	external	ADJ
ap-5981	232	39	forces	force	NOUN
ap-5981	232	40	eventually	eventually	ADV
ap-5981	232	41	distributes	distribute	VERB
ap-5981	232	42	between	between	ADP
ap-5981	232	43	the	the	DET
ap-5981	232	44	internal	internal	ADJ
ap-5981	232	45	and	and	CCONJ
ap-5981	232	46	dissipated	dissipate	VERB
ap-5981	232	47	energies	energy	NOUN
ap-5981	232	48	;	;	PUNCT
ap-5981	232	49	the	the	DET
ap-5981	232	50	ratio	ratio	NOUN
ap-5981	232	51	dd	dd	PROPN
ap-5981	232	52	/	/	SYM
ap-5981	232	53	wd	wd	PROPN
ap-5981	232	54	stabilizes	stabilize	VERB
ap-5981	232	55	at	at	ADP
ap-5981	232	56	0.4	0.4	NUM
ap-5981	232	57	for	for	ADP
ap-5981	232	58	the	the	DET
ap-5981	232	59	step	step	NOUN
ap-5981	232	60	load	load	NOUN
ap-5981	232	61	and	and	CCONJ
ap-5981	232	62	for	for	ADP
ap-5981	232	63	the	the	DET
ap-5981	232	64	harmonic	harmonic	ADJ
ap-5981	232	65	loading	loading	NOUN
ap-5981	232	66	,	,	PUNCT
ap-5981	232	67	the	the	DET
ap-5981	232	68	ratio	ratio	NOUN
ap-5981	232	69	reaches	reach	VERB
ap-5981	232	70	about	about	ADP
ap-5981	232	71	0.9	0.9	NUM
ap-5981	232	72	.	.	PUNCT
ap-5981	233	1	the	the	DET
ap-5981	233	2	artificial	artificial	ADJ
ap-5981	233	3	dissipation	dissipation	NOUN
ap-5981	233	4	is	be	AUX
ap-5981	233	5	only	only	ADV
ap-5981	233	6	significant	significant	ADJ
ap-5981	233	7	for	for	ADP
ap-5981	233	8	the	the	DET
ap-5981	233	9	coarsest	coarse	ADJ
ap-5981	233	10	step	step	NOUN
ap-5981	233	11	of	of	ADP
ap-5981	233	12	∆t	∆t	NOUN
ap-5981	233	13	=	=	SYM
ap-5981	233	14	1.0	1.0	NUM
ap-5981	233	15	s	s	NOUN
ap-5981	233	16	;	;	PUNCT
ap-5981	233	17	for	for	ADP
ap-5981	233	18	∆t	∆t	NOUN
ap-5981	233	19	=	=	SYM
ap-5981	233	20	0.1	0.1	NUM
ap-5981	233	21	s	s	NOUN
ap-5981	233	22	it	it	PRON
ap-5981	233	23	reaches	reach	VERB
ap-5981	233	24	the	the	DET
ap-5981	233	25	value	value	NOUN
ap-5981	233	26	of	of	ADP
ap-5981	233	27	about	about	ADV
ap-5981	233	28	1	1	NUM
ap-5981	233	29	‰	‰	NOUN
ap-5981	233	30	and	and	CCONJ
ap-5981	233	31	further	far	ADV
ap-5981	233	32	deteriorates	deteriorate	VERB
ap-5981	233	33	with	with	ADP
ap-5981	233	34	a	a	DET
ap-5981	233	35	decreasing	decrease	VERB
ap-5981	233	36	time	time	NOUN
ap-5981	233	37	step	step	NOUN
ap-5981	233	38	.	.	PUNCT
ap-5981	234	1	this	this	PRON
ap-5981	234	2	confirms	confirm	VERB
ap-5981	234	3	excellent	excellent	ADJ
ap-5981	234	4	energy	energy	NOUN
ap-5981	234	5	conservation	conservation	NOUN
ap-5981	234	6	properties	property	NOUN
ap-5981	234	7	of	of	ADP
ap-5981	234	8	the	the	DET
ap-5981	234	9	scheme	scheme	NOUN
ap-5981	234	10	,	,	PUNCT
ap-5981	234	11	especially	especially	ADV
ap-5981	234	12	when	when	SCONJ
ap-5981	234	13	taking	take	VERB
ap-5981	234	14	into	into	ADP
ap-5981	234	15	account	account	NOUN
ap-5981	234	16	that	that	SCONJ
ap-5981	234	17	the	the	DET
ap-5981	234	18	error	error	NOUN
ap-5981	234	19	introduced	introduce	VERB
ap-5981	234	20	by	by	ADP
ap-5981	234	21	the	the	DET
ap-5981	234	22	trapezoidal	trapezoidal	ADJ
ap-5981	234	23	rule	rule	NOUN
ap-5981	234	24	in	in	ADP
ap-5981	234	25	(	(	PUNCT
ap-5981	234	26	41	41	NUM
ap-5981	234	27	)	)	PUNCT
ap-5981	234	28	is	be	AUX
ap-5981	234	29	of	of	ADP
ap-5981	234	30	order	order	NOUN
ap-5981	234	31	o(∆t2	o(∆t2	ADV
ap-5981	234	32	)	)	PUNCT
ap-5981	234	33	.	.	PUNCT
ap-5981	235	1	4.2	4.2	NUM
ap-5981	235	2	.	.	PUNCT
ap-5981	235	3	generalization	generalization	NOUN
ap-5981	235	4	additional	additional	ADJ
ap-5981	235	5	constitutive	constitutive	ADJ
ap-5981	235	6	assumptions	assumption	NOUN
ap-5981	235	7	must	must	AUX
ap-5981	235	8	be	be	AUX
ap-5981	235	9	adopted	adopt	VERB
ap-5981	235	10	to	to	PART
ap-5981	235	11	extend	extend	VERB
ap-5981	235	12	the	the	DET
ap-5981	235	13	sdof	sdof	ADJ
ap-5981	235	14	models	model	NOUN
ap-5981	235	15	into	into	ADP
ap-5981	235	16	a	a	DET
ap-5981	235	17	continuum	continuum	ADJ
ap-5981	235	18	formulation	formulation	NOUN
ap-5981	235	19	.	.	PUNCT
ap-5981	236	1	here	here	ADV
ap-5981	236	2	,	,	PUNCT
ap-5981	236	3	we	we	PRON
ap-5981	236	4	assume	assume	VERB
ap-5981	236	5	that	that	SCONJ
ap-5981	236	6	the	the	DET
ap-5981	236	7	maxwell	maxwell	PROPN
ap-5981	236	8	model	model	NOUN
ap-5981	236	9	applies	apply	VERB
ap-5981	236	10	when	when	SCONJ
ap-5981	236	11	modelling	model	VERB
ap-5981	236	12	the	the	DET
ap-5981	236	13	response	response	NOUN
ap-5981	236	14	under	under	ADP
ap-5981	236	15	shear	shear	NOUN
ap-5981	236	16	.	.	PUNCT
ap-5981	237	1	the	the	DET
ap-5981	237	2	spring	spring	NOUN
ap-5981	237	3	stiffnesses	stiffness	NOUN
ap-5981	237	4	k•	k•	AUX
ap-5981	237	5	thus	thus	ADV
ap-5981	237	6	become	become	VERB
ap-5981	237	7	shear	shear	ADJ
ap-5981	237	8	moduli	modulus	NOUN
ap-5981	237	9	g•	g•	ADJ
ap-5981	237	10	,	,	PUNCT
ap-5981	237	11	and	and	CCONJ
ap-5981	237	12	the	the	DET
ap-5981	237	13	poisson	poisson	NOUN
ap-5981	237	14	ratio	ratio	NOUN
ap-5981	237	15	ν	ν	PROPN
ap-5981	237	16	is	be	AUX
ap-5981	237	17	a	a	DET
ap-5981	237	18	time	time	NOUN
ap-5981	237	19	-	-	PUNCT
ap-5981	237	20	independent	independent	ADJ
ap-5981	237	21	material	material	NOUN
ap-5981	237	22	constant	constant	ADJ
ap-5981	237	23	.	.	PUNCT
ap-5981	238	1	this	this	DET
ap-5981	238	2	assumption	assumption	NOUN
ap-5981	238	3	considerably	considerably	ADV
ap-5981	238	4	simplifies	simplify	VERB
ap-5981	238	5	the	the	DET
ap-5981	238	6	multi	multi	ADJ
ap-5981	238	7	-	-	ADJ
ap-5981	238	8	dimensional	dimensional	ADJ
ap-5981	238	9	constitutive	constitutive	ADJ
ap-5981	238	10	law	law	NOUN
ap-5981	238	11	,	,	PUNCT
ap-5981	238	12	e.g.	e.g.	ADV
ap-5981	238	13	,	,	PUNCT
ap-5981	238	14	[	[	X
ap-5981	238	15	16	16	NUM
ap-5981	238	16	,	,	PUNCT
ap-5981	238	17	section	section	NOUN
ap-5981	238	18	2.4	2.4	NUM
ap-5981	238	19	]	]	PUNCT
ap-5981	238	20	,	,	PUNCT
ap-5981	238	21	and	and	CCONJ
ap-5981	238	22	provides	provide	VERB
ap-5981	238	23	the	the	DET
ap-5981	238	24	same	same	ADJ
ap-5981	238	25	results	result	NOUN
ap-5981	238	26	as	as	ADP
ap-5981	238	27	the	the	DET
ap-5981	238	28	conventional	conventional	ADJ
ap-5981	238	29	volumetric	volumetric	NOUN
ap-5981	238	30	-	-	PUNCT
ap-5981	238	31	deviatoric	deviatoric	NOUN
ap-5981	238	32	split	split	NOUN
ap-5981	238	33	for	for	ADP
ap-5981	238	34	our	our	PRON
ap-5981	238	35	target	target	NOUN
ap-5981	238	36	applications	application	NOUN
ap-5981	238	37	[	[	X
ap-5981	238	38	5	5	NUM
ap-5981	238	39	]	]	PUNCT
ap-5981	238	40	.	.	PUNCT
ap-5981	239	1	under	under	ADP
ap-5981	239	2	these	these	DET
ap-5981	239	3	assumptions	assumption	NOUN
ap-5981	239	4	,	,	PUNCT
ap-5981	239	5	the	the	DET
ap-5981	239	6	weak	weak	ADJ
ap-5981	239	7	form	form	NOUN
ap-5981	239	8	of	of	ADP
ap-5981	239	9	the	the	DET
ap-5981	239	10	equations	equation	NOUN
ap-5981	239	11	of	of	ADP
ap-5981	239	12	motion	motion	NOUN
ap-5981	239	13	take	take	VERB
ap-5981	239	14	the	the	DET
ap-5981	239	15	form	form	NOUN
ap-5981	239	16	,	,	PUNCT
ap-5981	239	17	e.g.	e.g.	ADV
ap-5981	239	18	[	[	X
ap-5981	239	19	11	11	NUM
ap-5981	239	20	,	,	PUNCT
ap-5981	239	21	part	part	NOUN
ap-5981	239	22	iii	iii	NOUN
ap-5981	239	23	]	]	X
ap-5981	239	24	:	:	PUNCT
ap-5981	239	25	δfext(t	δfext(t	NOUN
ap-5981	239	26	,	,	PUNCT
ap-5981	239	27	δu	δu	NOUN
ap-5981	239	28	)	)	PUNCT
ap-5981	239	29	=	=	SYM
ap-5981	239	30	∫	∫	PROPN
ap-5981	239	31	ω	ω	PROPN
ap-5981	239	32	δu	δu	X
ap-5981	239	33	·	·	PUNCT
ap-5981	239	34	ρü(t	ρü(t	NUM
ap-5981	239	35	)	)	PUNCT
ap-5981	239	36	dω	dω	VERB
ap-5981	240	1	+	+	CCONJ
ap-5981	240	2	∫	∫	PROPN
ap-5981	240	3	ω	ω	NUM
ap-5981	240	4	δε	δε	PROPN
ap-5981	240	5	:	:	PUNCT
ap-5981	240	6	(	(	PUNCT
ap-5981	240	7	g∞dν	g∞dν	X
ap-5981	240	8	:	:	PUNCT
ap-5981	240	9	ε(t	ε(t	NOUN
ap-5981	240	10	)	)	PUNCT
ap-5981	241	1	+	+	CCONJ
ap-5981	241	2	p∑	p∑	X
ap-5981	241	3	p=1	p=1	NOUN
ap-5981	241	4	σp(t	σp(t	PROPN
ap-5981	241	5	)	)	PUNCT
ap-5981	241	6	)	)	PUNCT
ap-5981	242	1	dω	dω	ADP
ap-5981	242	2	,	,	PUNCT
ap-5981	242	3	(	(	PUNCT
ap-5981	242	4	44	44	NUM
ap-5981	242	5	)	)	PUNCT
ap-5981	242	6	where	where	SCONJ
ap-5981	242	7	δfext	δfext	NOUN
ap-5981	242	8	stands	stand	VERB
ap-5981	242	9	for	for	ADP
ap-5981	242	10	the	the	DET
ap-5981	242	11	virtual	virtual	ADJ
ap-5981	242	12	work	work	NOUN
ap-5981	242	13	done	do	VERB
ap-5981	242	14	by	by	ADP
ap-5981	242	15	external	external	ADJ
ap-5981	242	16	loads	load	NOUN
ap-5981	242	17	on	on	ADP
ap-5981	242	18	a	a	DET
ap-5981	242	19	virtual	virtual	ADJ
ap-5981	242	20	displacement	displacement	NOUN
ap-5981	242	21	δu	δu	ADP
ap-5981	242	22	,	,	PUNCT
ap-5981	242	23	ü	ü	PART
ap-5981	242	24	denotes	denote	VERB
ap-5981	242	25	the	the	DET
ap-5981	242	26	acceleration	acceleration	NOUN
ap-5981	242	27	,	,	PUNCT
ap-5981	242	28	and	and	CCONJ
ap-5981	242	29	the	the	DET
ap-5981	242	30	small	small	ADJ
ap-5981	242	31	strain	strain	NOUN
ap-5981	242	32	tensor	tensor	NOUN
ap-5981	242	33	ε	ε	PROPN
ap-5981	242	34	is	be	AUX
ap-5981	242	35	obtained	obtain	VERB
ap-5981	242	36	as	as	ADP
ap-5981	242	37	the	the	DET
ap-5981	242	38	symmetric	symmetric	ADJ
ap-5981	242	39	part	part	NOUN
ap-5981	242	40	of	of	ADP
ap-5981	242	41	the	the	DET
ap-5981	242	42	displacement	displacement	ADJ
ap-5981	242	43	gradient	gradient	NOUN
ap-5981	242	44	,	,	PUNCT
ap-5981	242	45	ε	ε	PROPN
ap-5981	242	46	=	=	SYM
ap-5981	242	47	∇su	∇su	PROPN
ap-5981	242	48	;	;	PUNCT
ap-5981	242	49	virtual	virtual	ADJ
ap-5981	242	50	strain	strain	NOUN
ap-5981	242	51	δε	δε	NOUN
ap-5981	242	52	is	be	AUX
ap-5981	242	53	defined	define	VERB
ap-5981	242	54	in	in	ADP
ap-5981	242	55	the	the	DET
ap-5981	242	56	same	same	ADJ
ap-5981	242	57	way	way	NOUN
ap-5981	242	58	.	.	PUNCT
ap-5981	243	1	the	the	DET
ap-5981	243	2	material	material	NOUN
ap-5981	243	3	is	be	AUX
ap-5981	243	4	characterized	characterize	VERB
ap-5981	243	5	by	by	ADP
ap-5981	243	6	its	its	PRON
ap-5981	243	7	density	density	NOUN
ap-5981	243	8	ρ	ρ	NOUN
ap-5981	243	9	,	,	PUNCT
ap-5981	243	10	long	long	ADJ
ap-5981	243	11	-	-	PUNCT
ap-5981	243	12	term	term	NOUN
ap-5981	243	13	shear	shear	NOUN
ap-5981	243	14	modulus	modulus	NOUN
ap-5981	243	15	of	of	ADP
ap-5981	243	16	the	the	DET
ap-5981	243	17	maxwell	maxwell	PROPN
ap-5981	243	18	chain	chain	NOUN
ap-5981	243	19	g∞	g∞	PROPN
ap-5981	243	20	,	,	PUNCT
ap-5981	243	21	and	and	CCONJ
ap-5981	243	22	the	the	DET
ap-5981	243	23	dimensionless	dimensionless	NOUN
ap-5981	243	24	tensor	tensor	NOUN
ap-5981	243	25	dν	dν	AUX
ap-5981	243	26	corresponding	correspond	VERB
ap-5981	243	27	to	to	ADP
ap-5981	243	28	the	the	DET
ap-5981	243	29	stiffness	stiffness	ADJ
ap-5981	243	30	tensor	tensor	NOUN
ap-5981	243	31	of	of	ADP
ap-5981	243	32	an	an	DET
ap-5981	243	33	isotropic	isotropic	ADJ
ap-5981	243	34	material	material	NOUN
ap-5981	243	35	of	of	ADP
ap-5981	243	36	the	the	DET
ap-5981	243	37	unit	unit	NOUN
ap-5981	243	38	shear	shear	NOUN
ap-5981	243	39	modulus	modulus	NOUN
ap-5981	243	40	and	and	CCONJ
ap-5981	243	41	the	the	DET
ap-5981	243	42	poisson	poisson	NOUN
ap-5981	243	43	ratio	ratio	NOUN
ap-5981	243	44	of	of	ADP
ap-5981	243	45	ν	ν	PROPN
ap-5981	243	46	.	.	PUNCT
ap-5981	244	1	the	the	DET
ap-5981	244	2	stresses	stress	NOUN
ap-5981	244	3	σp	σp	PART
ap-5981	244	4	carried	carry	VERB
ap-5981	244	5	by	by	ADP
ap-5981	244	6	individual	individual	ADJ
ap-5981	244	7	cells	cell	NOUN
ap-5981	244	8	follow	follow	VERB
ap-5981	244	9	as	as	ADP
ap-5981	244	10	the	the	DET
ap-5981	244	11	solution	solution	NOUN
ap-5981	244	12	of	of	ADP
ap-5981	244	13	initial	initial	ADJ
ap-5981	244	14	value	value	NOUN
ap-5981	244	15	problems	problem	NOUN
ap-5981	244	16	σ̇p(t	σ̇p(t	NOUN
ap-5981	244	17	)	)	PUNCT
ap-5981	244	18	gp	gp	NOUN
ap-5981	245	1	+	+	CCONJ
ap-5981	245	2	σp(t	σp(t	X
ap-5981	245	3	)	)	PUNCT
ap-5981	245	4	ηp	ηp	NOUN
ap-5981	245	5	=	=	SYM
ap-5981	245	6	dν	dν	PROPN
ap-5981	245	7	ε̇(t	ε̇(t	ADJ
ap-5981	245	8	)	)	PUNCT
ap-5981	245	9	,	,	PUNCT
ap-5981	245	10	p	p	NOUN
ap-5981	245	11	=	=	NOUN
ap-5981	245	12	1	1	NUM
ap-5981	245	13	,	,	PUNCT
ap-5981	245	14	2	2	NUM
ap-5981	245	15	,	,	PUNCT
ap-5981	245	16	.	.	PUNCT
ap-5981	245	17	.	.	PUNCT
ap-5981	246	1	.	.	PUNCT
ap-5981	247	1	,	,	PUNCT
ap-5981	247	2	p.	p.	NOUN
ap-5981	247	3	(	(	PUNCT
ap-5981	247	4	45	45	NUM
ap-5981	247	5	)	)	PUNCT
ap-5981	247	6	the	the	DET
ap-5981	247	7	evolution	evolution	NOUN
ap-5981	247	8	of	of	ADP
ap-5981	247	9	the	the	DET
ap-5981	247	10	state	state	NOUN
ap-5981	247	11	variables	variable	VERB
ap-5981	247	12	u	u	NOUN
ap-5981	247	13	and	and	CCONJ
ap-5981	247	14	σp	σp	PROPN
ap-5981	247	15	is	be	AUX
ap-5981	247	16	specified	specify	VERB
ap-5981	247	17	with	with	ADP
ap-5981	247	18	the	the	DET
ap-5981	247	19	initial	initial	ADJ
ap-5981	247	20	conditions	condition	NOUN
ap-5981	247	21	on	on	ADP
ap-5981	247	22	the	the	DET
ap-5981	247	23	displacements	displacement	NOUN
ap-5981	247	24	,	,	PUNCT
ap-5981	247	25	velocities	velocity	NOUN
ap-5981	247	26	,	,	PUNCT
ap-5981	247	27	and	and	CCONJ
ap-5981	247	28	cell	cell	NOUN
ap-5981	247	29	stresses	stress	NOUN
ap-5981	247	30	:	:	PUNCT
ap-5981	247	31	u(0	u(0	NOUN
ap-5981	247	32	)	)	PUNCT
ap-5981	247	33	=	=	SYM
ap-5981	247	34	u0	u0	PROPN
ap-5981	247	35	,	,	PUNCT
ap-5981	247	36	u̇(0	u̇(0	PROPN
ap-5981	247	37	)	)	PUNCT
ap-5981	247	38	=	=	SYM
ap-5981	247	39	v0	v0	PROPN
ap-5981	247	40	,	,	PUNCT
ap-5981	247	41	σp(0	σp(0	NOUN
ap-5981	247	42	)	)	PUNCT
ap-5981	247	43	=	=	SYM
ap-5981	247	44	σp,0	σp,0	PROPN
ap-5981	247	45	.	.	PUNCT
ap-5981	248	1	(	(	PUNCT
ap-5981	248	2	46	46	NUM
ap-5981	248	3	)	)	PUNCT
ap-5981	248	4	the	the	DET
ap-5981	248	5	comparison	comparison	NOUN
ap-5981	248	6	of	of	ADP
ap-5981	248	7	the	the	DET
ap-5981	248	8	initial	initial	ADJ
ap-5981	248	9	value	value	NOUN
ap-5981	248	10	problems	problem	NOUN
ap-5981	248	11	specified	specify	VERB
ap-5981	248	12	with	with	ADP
ap-5981	248	13	eqs	eqs	PROPN
ap-5981	248	14	.	.	PUNCT
ap-5981	249	1	(	(	PUNCT
ap-5981	249	2	1	1	NUM
ap-5981	249	3	)	)	PUNCT
ap-5981	249	4	,	,	PUNCT
ap-5981	249	5	(	(	PUNCT
ap-5981	249	6	4	4	NUM
ap-5981	249	7	)	)	PUNCT
ap-5981	249	8	,	,	PUNCT
ap-5981	249	9	and	and	CCONJ
ap-5981	249	10	(	(	PUNCT
ap-5981	249	11	5	5	NUM
ap-5981	249	12	)	)	PUNCT
ap-5981	249	13	and	and	CCONJ
ap-5981	249	14	eqs	eqs	PROPN
ap-5981	249	15	.	.	PUNCT
ap-5981	250	1	(	(	PUNCT
ap-5981	250	2	44	44	NUM
ap-5981	250	3	)	)	PUNCT
ap-5981	250	4	,	,	PUNCT
ap-5981	250	5	(	(	PUNCT
ap-5981	250	6	45	45	NUM
ap-5981	250	7	)	)	PUNCT
ap-5981	250	8	,	,	PUNCT
ap-5981	250	9	and	and	CCONJ
ap-5981	250	10	(	(	PUNCT
ap-5981	250	11	46	46	NUM
ap-5981	250	12	)	)	PUNCT
ap-5981	250	13	reveals	reveal	VERB
ap-5981	250	14	that	that	SCONJ
ap-5981	250	15	the	the	DET
ap-5981	250	16	derivation	derivation	NOUN
ap-5981	250	17	of	of	ADP
ap-5981	250	18	the	the	DET
ap-5981	250	19	newmarktype	newmarktype	NOUN
ap-5981	250	20	scheme	scheme	NOUN
ap-5981	250	21	follows	follow	VERB
ap-5981	250	22	exactly	exactly	ADV
ap-5981	250	23	the	the	DET
ap-5981	250	24	steps	step	NOUN
ap-5981	250	25	as	as	ADP
ap-5981	250	26	in	in	ADP
ap-5981	250	27	section	section	NOUN
ap-5981	250	28	2.2	2.2	NUM
ap-5981	250	29	.	.	PUNCT
ap-5981	251	1	as	as	ADP
ap-5981	251	2	a	a	DET
ap-5981	251	3	result	result	NOUN
ap-5981	251	4	,	,	PUNCT
ap-5981	251	5	the	the	DET
ap-5981	251	6	following	follow	VERB
ap-5981	251	7	variational	variational	ADJ
ap-5981	251	8	problem	problem	NOUN
ap-5981	251	9	needs	need	VERB
ap-5981	251	10	to	to	PART
ap-5981	251	11	be	be	AUX
ap-5981	251	12	solved	solve	VERB
ap-5981	251	13	at	at	ADP
ap-5981	251	14	a	a	DET
ap-5981	251	15	time	time	NOUN
ap-5981	251	16	ti+1:∫	ti+1:∫	NOUN
ap-5981	251	17	ω	ω	X
ap-5981	251	18	δu	δu	X
ap-5981	251	19	·	·	PUNCT
ap-5981	251	20	ρüi+1	ρüi+1	ADV
ap-5981	252	1	dω	dω	ADP
ap-5981	252	2	+	+	CCONJ
ap-5981	252	3	∫	∫	PROPN
ap-5981	252	4	ω	ω	NUM
ap-5981	252	5	δε	δε	PROPN
ap-5981	252	6	:	:	PUNCT
ap-5981	252	7	(	(	PUNCT
ap-5981	252	8	1	1	NUM
ap-5981	252	9	4g∞∆t2	4g∞∆t2	NUM
ap-5981	252	10	+	+	NUM
ap-5981	252	11	p∑	p∑	ADJ
ap-5981	252	12	p=1	p=1	NOUN
ap-5981	252	13	bp	bp	PROPN
ap-5981	252	14	)	)	PUNCT
ap-5981	252	15	dν	dν	VERB
ap-5981	252	16	:	:	PUNCT
ap-5981	252	17	ε̈i+1	ε̈i+1	NOUN
ap-5981	252	18	dω	dω	NOUN
ap-5981	252	19	=	=	SYM
ap-5981	252	20	δfext(ti+1	δfext(ti+1	PROPN
ap-5981	252	21	,	,	PUNCT
ap-5981	252	22	δu)−	δu)−	NOUN
ap-5981	252	23	∫	∫	PROPN
ap-5981	252	24	ω	ω	NUM
ap-5981	252	25	δε	δε	PROPN
ap-5981	252	26	:	:	PUNCT
ap-5981	252	27	(	(	PUNCT
ap-5981	252	28	p∑	p∑	NOUN
ap-5981	252	29	p=1	p=1	X
ap-5981	252	30	apσp	apσp	ADJ
ap-5981	252	31	,	,	PUNCT
ap-5981	252	32	i	i	PROPN
ap-5981	252	33	)	)	PUNCT
ap-5981	253	1	dω	dω	ADP
ap-5981	253	2	−	−	PROPN
ap-5981	253	3	∫	∫	PROPN
ap-5981	253	4	ω	ω	NUM
ap-5981	253	5	δε	δε	PROPN
ap-5981	253	6	:	:	PUNCT
ap-5981	253	7	g∞dν	g∞dν	NOUN
ap-5981	253	8	:	:	PUNCT
ap-5981	253	9	εi	εi	VERB
ap-5981	253	10	dω	dω	PROPN
ap-5981	253	11	507	507	NUM
ap-5981	253	12	j.	j.	PROPN
ap-5981	253	13	schmidt	schmidt	PROPN
ap-5981	253	14	,	,	PUNCT
ap-5981	253	15	t.	t.	PROPN
ap-5981	253	16	janda	janda	PROPN
ap-5981	253	17	,	,	PUNCT
ap-5981	253	18	a.	a.	PROPN
ap-5981	253	19	zemanová	zemanová	PROPN
ap-5981	253	20	et	et	PROPN
ap-5981	253	21	al	al	PROPN
ap-5981	253	22	.	.	PROPN
ap-5981	254	1	acta	acta	PROPN
ap-5981	254	2	polytechnica	polytechnica	PROPN
ap-5981	254	3	0	0	NUM
ap-5981	254	4	5	5	NUM
ap-5981	255	1	10	10	NUM
ap-5981	255	2	15	15	NUM
ap-5981	255	3	20	20	NUM
ap-5981	255	4	25	25	NUM
ap-5981	255	5	30	30	NUM
ap-5981	255	6	time	time	NOUN
ap-5981	255	7	t	t	NOUN
ap-5981	255	8	[	[	X
ap-5981	255	9	s	s	X
ap-5981	255	10	]	]	X
ap-5981	255	11	0.0	0.0	NUM
ap-5981	255	12	0.1	0.1	NUM
ap-5981	255	13	0.2	0.2	NUM
ap-5981	255	14	0.3	0.3	NUM
ap-5981	255	15	0.4	0.4	NUM
ap-5981	255	16	0.5	0.5	NUM
ap-5981	255	17	0.6	0.6	NUM
ap-5981	255	18	di	di	NOUN
ap-5981	255	19	sp	sp	ADP
ap-5981	255	20	la	la	PROPN
ap-5981	255	21	ce	ce	PROPN
ap-5981	255	22	m	m	PROPN
ap-5981	255	23	en	en	PROPN
ap-5981	255	24	t	t	PROPN
ap-5981	255	25	r	r	NOUN
ap-5981	255	26	(	(	PUNCT
ap-5981	255	27	t	t	PROPN
ap-5981	255	28	)	)	PUNCT
ap-5981	256	1	[	[	PUNCT
ap-5981	256	2	m	m	X
ap-5981	256	3	]	]	X
ap-5981	256	4	reference	reference	NOUN
ap-5981	256	5	newmark	newmark	NOUN
ap-5981	256	6	0	0	NUM
ap-5981	256	7	5	5	NUM
ap-5981	256	8	10	10	NUM
ap-5981	256	9	15	15	NUM
ap-5981	256	10	20	20	NUM
ap-5981	256	11	25	25	NUM
ap-5981	256	12	30	30	NUM
ap-5981	256	13	time	time	NOUN
ap-5981	256	14	t	t	NOUN
ap-5981	257	1	[	[	X
ap-5981	257	2	s	s	X
ap-5981	257	3	]	]	X
ap-5981	257	4	0.8	0.8	NUM
ap-5981	257	5	0.6	0.6	NUM
ap-5981	257	6	0.4	0.4	NUM
ap-5981	257	7	0.2	0.2	NUM
ap-5981	257	8	0.0	0.0	NUM
ap-5981	257	9	0.2	0.2	NUM
ap-5981	257	10	0.4	0.4	NUM
ap-5981	257	11	0.6	0.6	NUM
ap-5981	257	12	di	di	NOUN
ap-5981	257	13	sp	sp	ADP
ap-5981	257	14	la	la	PROPN
ap-5981	257	15	ce	ce	PROPN
ap-5981	257	16	m	m	PROPN
ap-5981	257	17	en	en	PROPN
ap-5981	257	18	t	t	PROPN
ap-5981	257	19	r	r	NOUN
ap-5981	257	20	(	(	PUNCT
ap-5981	257	21	t	t	PROPN
ap-5981	257	22	)	)	PUNCT
ap-5981	257	23	[	[	PUNCT
ap-5981	257	24	m	m	X
ap-5981	257	25	]	]	X
ap-5981	257	26	reference	reference	NOUN
ap-5981	257	27	newmark	newmark	NOUN
ap-5981	257	28	0	0	NUM
ap-5981	257	29	5	5	NUM
ap-5981	257	30	10	10	NUM
ap-5981	257	31	15	15	NUM
ap-5981	257	32	20	20	NUM
ap-5981	257	33	25	25	NUM
ap-5981	257	34	30	30	NUM
ap-5981	257	35	time	time	NOUN
ap-5981	257	36	t	t	NOUN
ap-5981	257	37	[	[	X
ap-5981	257	38	s	s	X
ap-5981	257	39	]	]	X
ap-5981	257	40	0.0	0.0	NUM
ap-5981	257	41	0.1	0.1	NUM
ap-5981	257	42	0.2	0.2	NUM
ap-5981	257	43	0.3	0.3	NUM
ap-5981	257	44	0.4	0.4	NUM
ap-5981	257	45	0.5	0.5	NUM
ap-5981	257	46	0.6	0.6	NUM
ap-5981	257	47	di	di	NOUN
ap-5981	257	48	sp	sp	ADP
ap-5981	257	49	la	la	PROPN
ap-5981	257	50	ce	ce	PROPN
ap-5981	257	51	m	m	PROPN
ap-5981	257	52	en	en	PROPN
ap-5981	257	53	t	t	PROPN
ap-5981	257	54	r	r	NOUN
ap-5981	257	55	(	(	PUNCT
ap-5981	257	56	t	t	PROPN
ap-5981	257	57	)	)	PUNCT
ap-5981	258	1	[	[	PUNCT
ap-5981	258	2	m	m	X
ap-5981	258	3	]	]	X
ap-5981	258	4	reference	reference	NOUN
ap-5981	258	5	newmark	newmark	NOUN
ap-5981	258	6	0	0	NUM
ap-5981	258	7	5	5	NUM
ap-5981	258	8	10	10	NUM
ap-5981	258	9	15	15	NUM
ap-5981	258	10	20	20	NUM
ap-5981	258	11	25	25	NUM
ap-5981	258	12	30	30	NUM
ap-5981	258	13	time	time	NOUN
ap-5981	258	14	t	t	NOUN
ap-5981	259	1	[	[	X
ap-5981	259	2	s	s	X
ap-5981	259	3	]	]	X
ap-5981	259	4	0.8	0.8	NUM
ap-5981	259	5	0.6	0.6	NUM
ap-5981	259	6	0.4	0.4	NUM
ap-5981	259	7	0.2	0.2	NUM
ap-5981	259	8	0.0	0.0	NUM
ap-5981	259	9	0.2	0.2	NUM
ap-5981	259	10	0.4	0.4	NUM
ap-5981	259	11	0.6	0.6	NUM
ap-5981	259	12	di	di	NOUN
ap-5981	259	13	sp	sp	ADP
ap-5981	259	14	la	la	PROPN
ap-5981	259	15	ce	ce	PROPN
ap-5981	259	16	m	m	PROPN
ap-5981	259	17	en	en	PROPN
ap-5981	259	18	t	t	PROPN
ap-5981	259	19	r	r	NOUN
ap-5981	259	20	(	(	PUNCT
ap-5981	259	21	t	t	PROPN
ap-5981	259	22	)	)	PUNCT
ap-5981	259	23	[	[	PUNCT
ap-5981	259	24	m	m	X
ap-5981	259	25	]	]	X
ap-5981	259	26	reference	reference	NOUN
ap-5981	259	27	newmark	newmark	NOUN
ap-5981	259	28	0	0	NUM
ap-5981	259	29	5	5	NUM
ap-5981	259	30	10	10	NUM
ap-5981	259	31	15	15	NUM
ap-5981	259	32	20	20	NUM
ap-5981	259	33	25	25	NUM
ap-5981	259	34	30	30	NUM
ap-5981	259	35	time	time	NOUN
ap-5981	259	36	t	t	NOUN
ap-5981	259	37	[	[	X
ap-5981	259	38	s	s	X
ap-5981	259	39	]	]	X
ap-5981	259	40	0.0	0.0	NUM
ap-5981	259	41	0.1	0.1	NUM
ap-5981	259	42	0.2	0.2	NUM
ap-5981	259	43	0.3	0.3	NUM
ap-5981	259	44	0.4	0.4	NUM
ap-5981	259	45	0.5	0.5	NUM
ap-5981	259	46	0.6	0.6	NUM
ap-5981	259	47	di	di	NOUN
ap-5981	259	48	sp	sp	ADP
ap-5981	259	49	la	la	PROPN
ap-5981	259	50	ce	ce	PROPN
ap-5981	259	51	m	m	PROPN
ap-5981	259	52	en	en	PROPN
ap-5981	259	53	t	t	PROPN
ap-5981	259	54	r	r	NOUN
ap-5981	259	55	(	(	PUNCT
ap-5981	259	56	t	t	PROPN
ap-5981	259	57	)	)	PUNCT
ap-5981	260	1	[	[	PUNCT
ap-5981	260	2	m	m	X
ap-5981	260	3	]	]	X
ap-5981	260	4	reference	reference	NOUN
ap-5981	260	5	newmark	newmark	NOUN
ap-5981	260	6	0	0	NUM
ap-5981	260	7	5	5	NUM
ap-5981	260	8	10	10	NUM
ap-5981	260	9	15	15	NUM
ap-5981	260	10	20	20	NUM
ap-5981	260	11	25	25	NUM
ap-5981	260	12	30	30	NUM
ap-5981	260	13	time	time	NOUN
ap-5981	260	14	t	t	NOUN
ap-5981	261	1	[	[	X
ap-5981	261	2	s	s	X
ap-5981	261	3	]	]	X
ap-5981	261	4	0.6	0.6	NUM
ap-5981	261	5	0.4	0.4	NUM
ap-5981	261	6	0.2	0.2	NUM
ap-5981	261	7	0.0	0.0	NUM
ap-5981	261	8	0.2	0.2	NUM
ap-5981	261	9	0.4	0.4	NUM
ap-5981	261	10	0.6	0.6	NUM
ap-5981	261	11	di	di	NOUN
ap-5981	261	12	sp	sp	ADP
ap-5981	261	13	la	la	PROPN
ap-5981	261	14	ce	ce	PROPN
ap-5981	261	15	m	m	PROPN
ap-5981	261	16	en	en	PROPN
ap-5981	261	17	t	t	PROPN
ap-5981	261	18	r	r	NOUN
ap-5981	261	19	(	(	PUNCT
ap-5981	261	20	t	t	PROPN
ap-5981	261	21	)	)	PUNCT
ap-5981	261	22	[	[	PUNCT
ap-5981	261	23	m	m	X
ap-5981	261	24	]	]	X
ap-5981	261	25	reference	reference	NOUN
ap-5981	261	26	newmark	newmark	PROPN
ap-5981	261	27	figure	figure	NOUN
ap-5981	261	28	3	3	NUM
ap-5981	261	29	.	.	PUNCT
ap-5981	261	30	accuracy	accuracy	NOUN
ap-5981	261	31	of	of	ADP
ap-5981	261	32	the	the	DET
ap-5981	261	33	viscous	viscous	ADJ
ap-5981	261	34	newmark	newmark	NOUN
ap-5981	261	35	method	method	NOUN
ap-5981	261	36	for	for	ADP
ap-5981	261	37	step	step	NOUN
ap-5981	261	38	(	(	PUNCT
ap-5981	261	39	left	left	ADV
ap-5981	261	40	)	)	PUNCT
ap-5981	261	41	and	and	CCONJ
ap-5981	261	42	harmonic	harmonic	ADJ
ap-5981	261	43	(	(	PUNCT
ap-5981	261	44	right	right	ADJ
ap-5981	261	45	)	)	PUNCT
ap-5981	261	46	loadings	loading	NOUN
ap-5981	261	47	defined	define	VERB
ap-5981	261	48	by	by	ADP
ap-5981	261	49	eq	eq	PROPN
ap-5981	261	50	.	.	PUNCT
ap-5981	262	1	(	(	PUNCT
ap-5981	262	2	42	42	NUM
ap-5981	262	3	)	)	PUNCT
ap-5981	262	4	.	.	PUNCT
ap-5981	263	1	top	top	ADJ
ap-5981	263	2	,	,	PUNCT
ap-5981	263	3	center	center	NOUN
ap-5981	263	4	,	,	PUNCT
ap-5981	263	5	and	and	CCONJ
ap-5981	263	6	bottom	bottom	ADJ
ap-5981	263	7	graphs	graph	NOUN
ap-5981	263	8	show	show	VERB
ap-5981	263	9	trajectories	trajectory	NOUN
ap-5981	263	10	for	for	ADP
ap-5981	263	11	time	time	NOUN
ap-5981	263	12	steps	step	NOUN
ap-5981	263	13	∆t	∆t	PROPN
ap-5981	263	14	=	=	SYM
ap-5981	263	15	1.0	1.0	NUM
ap-5981	263	16	s	s	NOUN
ap-5981	263	17	,	,	PUNCT
ap-5981	263	18	∆t	∆t	PROPN
ap-5981	263	19	=	=	SYM
ap-5981	263	20	0.5	0.5	NUM
ap-5981	263	21	s	s	NOUN
ap-5981	263	22	,	,	PUNCT
ap-5981	263	23	and	and	CCONJ
ap-5981	263	24	∆t	∆t	PROPN
ap-5981	263	25	=	=	SYM
ap-5981	263	26	0.2	0.2	NUM
ap-5981	263	27	s	s	NOUN
ap-5981	263	28	respectively	respectively	ADV
ap-5981	263	29	.	.	PUNCT
ap-5981	264	1	−	−	PROPN
ap-5981	265	1	∫	∫	PROPN
ap-5981	265	2	ω	ω	NUM
ap-5981	265	3	δε	δε	PROPN
ap-5981	265	4	:	:	PUNCT
ap-5981	265	5	(	(	PUNCT
ap-5981	265	6	g∞∆t+	g∞∆t+	X
ap-5981	265	7	p∑	p∑	PROPN
ap-5981	265	8	p=1	p=1	NOUN
ap-5981	265	9	gpθ̂p	gpθ̂p	PROPN
ap-5981	265	10	)	)	PUNCT
ap-5981	265	11	dν	dν	VERB
ap-5981	265	12	:	:	PUNCT
ap-5981	265	13	ε̇i	ε̇i	PROPN
ap-5981	265	14	dω	dω	ADP
ap-5981	265	15	−	−	PROPN
ap-5981	265	16	∫	∫	PROPN
ap-5981	265	17	ω	ω	NUM
ap-5981	265	18	δε	δε	PROPN
ap-5981	265	19	:	:	PUNCT
ap-5981	265	20	(	(	PUNCT
ap-5981	265	21	1	1	NUM
ap-5981	265	22	4g∞∆t2	4g∞∆t2	NUM
ap-5981	265	23	+	+	NUM
ap-5981	265	24	p∑	p∑	ADJ
ap-5981	265	25	p=1	p=1	NOUN
ap-5981	265	26	bp	bp	PROPN
ap-5981	265	27	)	)	PUNCT
ap-5981	265	28	dν	dν	VERB
ap-5981	265	29	:	:	PUNCT
ap-5981	265	30	ε̈i	ε̈i	PROPN
ap-5981	265	31	dω	dω	ADP
ap-5981	265	32	,	,	PUNCT
ap-5981	265	33	(	(	PUNCT
ap-5981	265	34	47	47	NUM
ap-5981	265	35	)	)	PUNCT
ap-5981	265	36	with	with	ADP
ap-5981	265	37	the	the	DET
ap-5981	265	38	parameters	parameter	NOUN
ap-5981	265	39	θ̂p	θ̂p	NOUN
ap-5981	265	40	,	,	PUNCT
ap-5981	265	41	ap	ap	PROPN
ap-5981	265	42	,	,	PUNCT
ap-5981	265	43	and	and	CCONJ
ap-5981	265	44	bp	bp	PROPN
ap-5981	265	45	provided	provide	VERB
ap-5981	265	46	by	by	ADP
ap-5981	265	47	eqs	eqs	PROPN
ap-5981	265	48	.	.	PUNCT
ap-5981	266	1	(	(	PUNCT
ap-5981	266	2	10	10	NUM
ap-5981	266	3	)	)	PUNCT
ap-5981	266	4	and	and	CCONJ
ap-5981	266	5	(	(	PUNCT
ap-5981	266	6	11	11	NUM
ap-5981	266	7	)	)	PUNCT
ap-5981	266	8	;	;	PUNCT
ap-5981	266	9	recall	recall	VERB
ap-5981	266	10	that	that	SCONJ
ap-5981	266	11	δfext	δfext	NOUN
ap-5981	266	12	denotes	denote	VERB
ap-5981	266	13	the	the	DET
ap-5981	266	14	virtual	virtual	ADJ
ap-5981	266	15	work	work	NOUN
ap-5981	266	16	done	do	VERB
ap-5981	266	17	by	by	ADP
ap-5981	266	18	external	external	ADJ
ap-5981	266	19	forces	force	NOUN
ap-5981	266	20	.	.	PUNCT
ap-5981	267	1	once	once	ADV
ap-5981	267	2	the	the	DET
ap-5981	267	3	the	the	DET
ap-5981	267	4	accelerations	acceleration	NOUN
ap-5981	267	5	üi+1	üi+1	NOUN
ap-5981	267	6	are	be	AUX
ap-5981	267	7	obtained	obtain	VERB
ap-5981	267	8	from	from	ADP
ap-5981	267	9	the	the	DET
ap-5981	267	10	weak	weak	ADJ
ap-5981	267	11	form	form	NOUN
ap-5981	267	12	(	(	PUNCT
ap-5981	267	13	47	47	NUM
ap-5981	267	14	)	)	PUNCT
ap-5981	267	15	,	,	PUNCT
ap-5981	267	16	the	the	DET
ap-5981	267	17	displacements	displacement	NOUN
ap-5981	267	18	ui+1	ui+1	NUM
ap-5981	267	19	,	,	PUNCT
ap-5981	267	20	velocities	velocity	NOUN
ap-5981	267	21	u̇i+1	u̇i+1	VERB
ap-5981	267	22	,	,	PUNCT
ap-5981	267	23	and	and	CCONJ
ap-5981	267	24	the	the	DET
ap-5981	267	25	cell	cell	NOUN
ap-5981	267	26	stresses	stress	VERB
ap-5981	267	27	σp	σp	NOUN
ap-5981	267	28	,	,	PUNCT
ap-5981	267	29	i+1	i+1	NOUN
ap-5981	267	30	are	be	AUX
ap-5981	267	31	updated	update	VERB
ap-5981	267	32	according	accord	VERB
ap-5981	267	33	to	to	ADP
ap-5981	267	34	eqs	eqs	PROPN
ap-5981	267	35	.	.	PUNCT
ap-5981	268	1	(	(	PUNCT
ap-5981	268	2	6	6	NUM
ap-5981	268	3	)	)	PUNCT
ap-5981	268	4	and	and	CCONJ
ap-5981	268	5	(	(	PUNCT
ap-5981	268	6	9	9	NUM
ap-5981	268	7	)	)	PUNCT
ap-5981	268	8	,	,	PUNCT
ap-5981	268	9	respectively	respectively	ADV
ap-5981	268	10	.	.	PUNCT
ap-5981	269	1	the	the	DET
ap-5981	269	2	outlined	outline	VERB
ap-5981	269	3	formulation	formulation	NOUN
ap-5981	269	4	(	(	PUNCT
ap-5981	269	5	47	47	NUM
ap-5981	269	6	)	)	PUNCT
ap-5981	269	7	was	be	AUX
ap-5981	269	8	further	far	ADV
ap-5981	269	9	discretized	discretize	VERB
ap-5981	269	10	with	with	ADP
ap-5981	269	11	the	the	DET
ap-5981	269	12	finite	finite	ADJ
ap-5981	269	13	element	element	NOUN
ap-5981	269	14	method	method	NOUN
ap-5981	269	15	and	and	CCONJ
ap-5981	269	16	implemented	implement	VERB
ap-5981	269	17	in	in	ADP
ap-5981	269	18	fenics	fenics	PROPN
ap-5981	269	19	project	project	NOUN
ap-5981	269	20	[	[	X
ap-5981	269	21	28	28	NUM
ap-5981	269	22	,	,	PUNCT
ap-5981	269	23	29	29	NUM
ap-5981	269	24	]	]	PUNCT
ap-5981	269	25	version	version	NOUN
ap-5981	269	26	2018.1	2018.1	NUM
ap-5981	269	27	.	.	PUNCT
ap-5981	270	1	as	as	ADP
ap-5981	270	2	an	an	DET
ap-5981	270	3	indicative	indicative	ADJ
ap-5981	270	4	example	example	NOUN
ap-5981	270	5	,	,	PUNCT
ap-5981	270	6	we	we	PRON
ap-5981	270	7	consider	consider	VERB
ap-5981	270	8	a	a	DET
ap-5981	270	9	unit	unit	NOUN
ap-5981	270	10	cube	cube	NOUN
ap-5981	270	11	,	,	PUNCT
ap-5981	270	12	see	see	VERB
ap-5981	270	13	figure	figure	NOUN
ap-5981	270	14	5	5	NUM
ap-5981	270	15	,	,	PUNCT
ap-5981	270	16	fixed	fix	VERB
ap-5981	270	17	on	on	ADP
ap-5981	270	18	the	the	DET
ap-5981	270	19	bottom	bottom	ADJ
ap-5981	270	20	surface	surface	NOUN
ap-5981	270	21	and	and	CCONJ
ap-5981	270	22	subjected	subject	VERB
ap-5981	270	23	to	to	ADP
ap-5981	270	24	a	a	DET
ap-5981	270	25	step	step	NOUN
ap-5981	270	26	load	load	NOUN
ap-5981	270	27	(	(	PUNCT
ap-5981	270	28	42a	42a	NOUN
ap-5981	270	29	)	)	PUNCT
ap-5981	270	30	with	with	ADP
ap-5981	270	31	the	the	DET
ap-5981	270	32	tensile	tensile	NOUN
ap-5981	270	33	traction	traction	NOUN
ap-5981	270	34	of	of	ADP
ap-5981	270	35	intensity	intensity	NOUN
ap-5981	270	36	1.0	1.0	NUM
ap-5981	270	37	nm−2	nm−2	PROPN
ap-5981	270	38	perpendicular	perpendicular	NOUN
ap-5981	270	39	to	to	ADP
ap-5981	270	40	the	the	DET
ap-5981	270	41	top	top	ADJ
ap-5981	270	42	surface	surface	NOUN
ap-5981	270	43	.	.	PUNCT
ap-5981	271	1	the	the	DET
ap-5981	271	2	material	material	ADJ
ap-5981	271	3	response	response	NOUN
ap-5981	271	4	is	be	AUX
ap-5981	271	5	characterized	characterize	VERB
ap-5981	271	6	by	by	ADP
ap-5981	271	7	the	the	DET
ap-5981	271	8	maxwell	maxwell	PROPN
ap-5981	271	9	chain	chain	NOUN
ap-5981	271	10	parameters	parameter	NOUN
ap-5981	271	11	from	from	ADP
ap-5981	271	12	table	table	NOUN
ap-5981	271	13	1	1	NUM
ap-5981	271	14	and	and	CCONJ
ap-5981	271	15	the	the	DET
ap-5981	271	16	value	value	NOUN
ap-5981	271	17	of	of	ADP
ap-5981	271	18	the	the	DET
ap-5981	271	19	poisson	poisson	NOUN
ap-5981	271	20	ratio	ratio	NOUN
ap-5981	271	21	ν	ν	NOUN
ap-5981	271	22	=	=	NOUN
ap-5981	271	23	0.49	0.49	NUM
ap-5981	271	24	.	.	PUNCT
ap-5981	272	1	in	in	ADP
ap-5981	272	2	the	the	DET
ap-5981	272	3	numerical	numerical	ADJ
ap-5981	272	4	resolution	resolution	NOUN
ap-5981	272	5	,	,	PUNCT
ap-5981	272	6	we	we	PRON
ap-5981	272	7	508	508	NUM
ap-5981	272	8	vol	vol	NOUN
ap-5981	272	9	.	.	PUNCT
ap-5981	272	10	60	60	NUM
ap-5981	272	11	no	no	INTJ
ap-5981	272	12	.	.	PUNCT
ap-5981	273	1	6/2020	6/2020	NUM
ap-5981	273	2	newmark	newmark	NOUN
ap-5981	273	3	algorithm	algorithm	NOUN
ap-5981	273	4	for	for	ADP
ap-5981	273	5	dynamic	dynamic	ADJ
ap-5981	273	6	analysis	analysis	NOUN
ap-5981	273	7	of	of	ADP
ap-5981	273	8	viscoelastic	viscoelastic	ADJ
ap-5981	273	9	materials	material	NOUN
ap-5981	273	10	0	0	NUM
ap-5981	273	11	50	50	NUM
ap-5981	273	12	100	100	NUM
ap-5981	273	13	150	150	NUM
ap-5981	273	14	200	200	NUM
ap-5981	273	15	250	250	NUM
ap-5981	273	16	300	300	NUM
ap-5981	273	17	time	time	NOUN
ap-5981	273	18	t	t	NOUN
ap-5981	274	1	[	[	X
ap-5981	274	2	s	s	X
ap-5981	274	3	]	]	X
ap-5981	274	4	0.0	0.0	NUM
ap-5981	274	5	0.2	0.2	NUM
ap-5981	274	6	0.4	0.4	NUM
ap-5981	274	7	0.6	0.6	NUM
ap-5981	274	8	0.8	0.8	NUM
ap-5981	274	9	1.0	1.0	NUM
ap-5981	274	10	re	re	X
ap-5981	274	11	la	la	PROPN
ap-5981	274	12	tiv	tiv	PROPN
ap-5981	274	13	e	e	PROPN
ap-5981	274	14	en	en	PROPN
ap-5981	274	15	er	er	INTJ
ap-5981	274	16	gy	gy	PROPN
ap-5981	275	1	[	[	X
ap-5981	275	2	]	]	X
ap-5981	275	3	eint	eint	NOUN
ap-5981	275	4	/	/	SYM
ap-5981	275	5	wd	wd	PROPN
ap-5981	275	6	dd	dd	PROPN
ap-5981	275	7	/	/	SYM
ap-5981	275	8	wd	wd	PROPN
ap-5981	275	9	0	0	NUM
ap-5981	275	10	50	50	NUM
ap-5981	275	11	100	100	NUM
ap-5981	275	12	150	150	NUM
ap-5981	275	13	200	200	NUM
ap-5981	275	14	250	250	NUM
ap-5981	275	15	300	300	NUM
ap-5981	275	16	time	time	NOUN
ap-5981	275	17	t	t	NOUN
ap-5981	276	1	[	[	X
ap-5981	276	2	s	s	X
ap-5981	276	3	]	]	X
ap-5981	276	4	10	10	NUM
ap-5981	276	5	-	-	SYM
ap-5981	276	6	9	9	NUM
ap-5981	276	7	10	10	NUM
ap-5981	276	8	-	-	SYM
ap-5981	276	9	8	8	NUM
ap-5981	276	10	10	10	NUM
ap-5981	276	11	-	-	SYM
ap-5981	276	12	7	7	NUM
ap-5981	276	13	10	10	NUM
ap-5981	276	14	-	-	SYM
ap-5981	276	15	6	6	NUM
ap-5981	276	16	10	10	NUM
ap-5981	276	17	-	-	SYM
ap-5981	276	18	5	5	NUM
ap-5981	276	19	10	10	NUM
ap-5981	276	20	-	-	SYM
ap-5981	276	21	4	4	NUM
ap-5981	276	22	10	10	NUM
ap-5981	276	23	-	-	SYM
ap-5981	276	24	3	3	NUM
ap-5981	276	25	10	10	NUM
ap-5981	276	26	-	-	SYM
ap-5981	276	27	2	2	NUM
ap-5981	276	28	10	10	NUM
ap-5981	276	29	-	-	SYM
ap-5981	276	30	1	1	NUM
ap-5981	276	31	100	100	NUM
ap-5981	276	32	re	re	X
ap-5981	276	33	la	la	PROPN
ap-5981	276	34	tiv	tiv	PROPN
ap-5981	276	35	e	e	PROPN
ap-5981	276	36	di	di	NOUN
ap-5981	276	37	ss	ss	PROPN
ap-5981	276	38	ip	ip	NOUN
ap-5981	276	39	at	at	ADP
ap-5981	276	40	io	io	PROPN
ap-5981	276	41	n	n	NOUN
ap-5981	276	42	∆	∆	PROPN
ap-5981	276	43	d	d	PROPN
ap-5981	276	44	/	/	SYM
ap-5981	276	45	w	w	PROPN
ap-5981	276	46	d	d	PROPN
ap-5981	277	1	[	[	X
ap-5981	277	2	]	]	X
ap-5981	277	3	∆t=	∆t=	NOUN
ap-5981	277	4	1.00	1.00	NUM
ap-5981	277	5	∆t=	∆t=	NOUN
ap-5981	277	6	0.10	0.10	NUM
ap-5981	277	7	∆t=	∆t=	NOUN
ap-5981	277	8	0.01	0.01	NUM
ap-5981	277	9	0	0	NUM
ap-5981	277	10	50	50	NUM
ap-5981	277	11	100	100	NUM
ap-5981	277	12	150	150	NUM
ap-5981	277	13	200	200	NUM
ap-5981	277	14	250	250	NUM
ap-5981	277	15	300	300	NUM
ap-5981	277	16	time	time	NOUN
ap-5981	277	17	t	t	NOUN
ap-5981	278	1	[	[	X
ap-5981	278	2	s	s	X
ap-5981	278	3	]	]	X
ap-5981	278	4	0.0	0.0	NUM
ap-5981	278	5	0.2	0.2	NUM
ap-5981	278	6	0.4	0.4	NUM
ap-5981	278	7	0.6	0.6	NUM
ap-5981	278	8	0.8	0.8	NUM
ap-5981	278	9	1.0	1.0	NUM
ap-5981	278	10	re	re	X
ap-5981	278	11	la	la	PROPN
ap-5981	278	12	tiv	tiv	PROPN
ap-5981	278	13	e	e	PROPN
ap-5981	278	14	en	en	PROPN
ap-5981	278	15	er	er	INTJ
ap-5981	278	16	gy	gy	PROPN
ap-5981	279	1	[	[	X
ap-5981	279	2	]	]	X
ap-5981	279	3	eint	eint	NOUN
ap-5981	279	4	/	/	SYM
ap-5981	279	5	wd	wd	PROPN
ap-5981	279	6	dd	dd	PROPN
ap-5981	279	7	/	/	SYM
ap-5981	279	8	wd	wd	PROPN
ap-5981	279	9	0	0	NUM
ap-5981	279	10	50	50	NUM
ap-5981	279	11	100	100	NUM
ap-5981	279	12	150	150	NUM
ap-5981	279	13	200	200	NUM
ap-5981	279	14	250	250	NUM
ap-5981	279	15	300	300	NUM
ap-5981	279	16	time	time	NOUN
ap-5981	279	17	t	t	NOUN
ap-5981	280	1	[	[	X
ap-5981	280	2	s	s	X
ap-5981	280	3	]	]	X
ap-5981	280	4	10	10	NUM
ap-5981	280	5	-	-	SYM
ap-5981	280	6	5	5	NUM
ap-5981	280	7	10	10	NUM
ap-5981	280	8	-	-	SYM
ap-5981	280	9	4	4	NUM
ap-5981	280	10	10	10	NUM
ap-5981	280	11	-	-	SYM
ap-5981	280	12	3	3	NUM
ap-5981	280	13	10	10	NUM
ap-5981	280	14	-	-	SYM
ap-5981	280	15	2	2	NUM
ap-5981	280	16	10	10	NUM
ap-5981	280	17	-	-	SYM
ap-5981	280	18	1	1	NUM
ap-5981	280	19	100	100	NUM
ap-5981	280	20	re	re	X
ap-5981	280	21	la	la	PROPN
ap-5981	280	22	tiv	tiv	PROPN
ap-5981	280	23	e	e	PROPN
ap-5981	280	24	di	di	NOUN
ap-5981	280	25	ss	ss	PROPN
ap-5981	280	26	ip	ip	NOUN
ap-5981	280	27	at	at	ADP
ap-5981	280	28	io	io	PROPN
ap-5981	280	29	n	n	NOUN
ap-5981	280	30	∆	∆	PROPN
ap-5981	280	31	d	d	PROPN
ap-5981	280	32	/	/	SYM
ap-5981	280	33	w	w	PROPN
ap-5981	280	34	d	d	PROPN
ap-5981	281	1	[	[	X
ap-5981	281	2	]	]	X
ap-5981	281	3	∆t=	∆t=	NOUN
ap-5981	281	4	1.00	1.00	NUM
ap-5981	281	5	∆t=	∆t=	NOUN
ap-5981	281	6	0.10	0.10	NUM
ap-5981	281	7	∆t=	∆t=	NOUN
ap-5981	281	8	0.01	0.01	NUM
ap-5981	281	9	figure	figure	NOUN
ap-5981	281	10	4	4	NUM
ap-5981	281	11	.	.	PUNCT
ap-5981	281	12	normalized	normalize	VERB
ap-5981	281	13	energies	energy	NOUN
ap-5981	281	14	corresponding	correspond	VERB
ap-5981	281	15	to	to	ADP
ap-5981	281	16	sdof	sdof	ADJ
ap-5981	281	17	response	response	NOUN
ap-5981	281	18	to	to	PART
ap-5981	281	19	step	step	VERB
ap-5981	281	20	(	(	PUNCT
ap-5981	281	21	top	top	NOUN
ap-5981	281	22	)	)	PUNCT
ap-5981	281	23	and	and	CCONJ
ap-5981	281	24	harmonic	harmonic	ADJ
ap-5981	281	25	loads	load	NOUN
ap-5981	281	26	(	(	PUNCT
ap-5981	281	27	bottom	bottom	NOUN
ap-5981	281	28	)	)	PUNCT
ap-5981	281	29	.	.	PUNCT
ap-5981	282	1	left	leave	VERB
ap-5981	282	2	:	:	PUNCT
ap-5981	282	3	the	the	DET
ap-5981	282	4	evolution	evolution	NOUN
ap-5981	282	5	of	of	ADP
ap-5981	282	6	internal	internal	ADJ
ap-5981	282	7	energy	energy	NOUN
ap-5981	282	8	eint	eint	NOUN
ap-5981	282	9	and	and	CCONJ
ap-5981	282	10	dissipation	dissipation	NOUN
ap-5981	282	11	dd	dd	NOUN
ap-5981	282	12	,	,	PUNCT
ap-5981	282	13	normalized	normalize	VERB
ap-5981	282	14	by	by	ADP
ap-5981	282	15	the	the	DET
ap-5981	282	16	work	work	NOUN
ap-5981	282	17	done	do	VERB
ap-5981	282	18	by	by	ADP
ap-5981	282	19	external	external	ADJ
ap-5981	282	20	forces	force	NOUN
ap-5981	282	21	wd	wd	VERB
ap-5981	282	22	for	for	ADP
ap-5981	282	23	time	time	NOUN
ap-5981	282	24	step	step	NOUN
ap-5981	282	25	∆t	∆t	PROPN
ap-5981	282	26	=	=	SYM
ap-5981	282	27	0.5	0.5	NUM
ap-5981	282	28	s.	s.	PROPN
ap-5981	282	29	right	right	NOUN
ap-5981	282	30	:	:	PUNCT
ap-5981	282	31	the	the	DET
ap-5981	282	32	evolution	evolution	NOUN
ap-5981	282	33	of	of	ADP
ap-5981	282	34	numerical	numerical	ADJ
ap-5981	282	35	dissipation	dissipation	NOUN
ap-5981	282	36	∆d	∆d	PROPN
ap-5981	282	37	,	,	PUNCT
ap-5981	282	38	normalized	normalize	VERB
ap-5981	282	39	by	by	ADP
ap-5981	282	40	the	the	DET
ap-5981	282	41	work	work	NOUN
ap-5981	282	42	done	do	VERB
ap-5981	282	43	by	by	ADP
ap-5981	282	44	external	external	ADJ
ap-5981	282	45	forces	force	NOUN
ap-5981	282	46	wd	wd	PROPN
ap-5981	282	47	.	.	PUNCT
ap-5981	283	1	discretize	discretize	VERB
ap-5981	283	2	the	the	DET
ap-5981	283	3	sample	sample	NOUN
ap-5981	283	4	into	into	ADP
ap-5981	283	5	identical	identical	ADJ
ap-5981	283	6	1,000	1,000	NUM
ap-5981	283	7	hexahedron	hexahedron	NOUN
ap-5981	283	8	elements	element	NOUN
ap-5981	283	9	and	and	CCONJ
ap-5981	283	10	consider	consider	VERB
ap-5981	283	11	the	the	DET
ap-5981	283	12	time	time	NOUN
ap-5981	283	13	step	step	NOUN
ap-5981	283	14	of	of	ADP
ap-5981	283	15	0.01	0.01	NUM
ap-5981	283	16	s.	s.	NOUN
ap-5981	283	17	the	the	DET
ap-5981	283	18	snapshots	snapshot	NOUN
ap-5981	283	19	of	of	ADP
ap-5981	283	20	the	the	DET
ap-5981	283	21	vibrations	vibration	NOUN
ap-5981	283	22	reveal	reveal	VERB
ap-5981	283	23	a	a	DET
ap-5981	283	24	similar	similar	ADJ
ap-5981	283	25	behaviour	behaviour	NOUN
ap-5981	283	26	to	to	ADP
ap-5981	283	27	the	the	DET
ap-5981	283	28	sdof	sdof	ADJ
ap-5981	283	29	example	example	NOUN
ap-5981	283	30	,	,	PUNCT
ap-5981	283	31	recall	recall	NOUN
ap-5981	283	32	figure	figure	NOUN
ap-5981	283	33	3	3	NUM
ap-5981	283	34	,	,	PUNCT
ap-5981	283	35	namely	namely	ADV
ap-5981	283	36	the	the	DET
ap-5981	283	37	attenuation	attenuation	NOUN
ap-5981	283	38	of	of	ADP
ap-5981	283	39	the	the	DET
ap-5981	283	40	propagating	propagate	VERB
ap-5981	283	41	waves	wave	NOUN
ap-5981	283	42	by	by	ADP
ap-5981	283	43	viscous	viscous	ADJ
ap-5981	283	44	damping	damping	NOUN
ap-5981	283	45	.	.	PUNCT
ap-5981	284	1	an	an	DET
ap-5981	284	2	interested	interested	ADJ
ap-5981	284	3	reader	reader	NOUN
ap-5981	284	4	is	be	AUX
ap-5981	284	5	invited	invite	VERB
ap-5981	284	6	to	to	ADP
ap-5981	284	7	the	the	DET
ap-5981	284	8	dataset	dataset	NOUN
ap-5981	284	9	[	[	X
ap-5981	284	10	24	24	NUM
ap-5981	284	11	]	]	PUNCT
ap-5981	284	12	for	for	ADP
ap-5981	284	13	full	full	ADJ
ap-5981	284	14	details	detail	NOUN
ap-5981	284	15	on	on	ADP
ap-5981	284	16	the	the	DET
ap-5981	284	17	simulation	simulation	NOUN
ap-5981	284	18	.	.	PUNCT
ap-5981	285	1	5	5	NUM
ap-5981	285	2	.	.	PUNCT
ap-5981	285	3	conclusions	conclusion	NOUN
ap-5981	285	4	in	in	ADP
ap-5981	285	5	this	this	DET
ap-5981	285	6	contribution	contribution	NOUN
ap-5981	285	7	,	,	PUNCT
ap-5981	285	8	we	we	PRON
ap-5981	285	9	have	have	AUX
ap-5981	285	10	developed	develop	VERB
ap-5981	285	11	a	a	DET
ap-5981	285	12	newmark	newmark	NOUN
ap-5981	285	13	integration	integration	NOUN
ap-5981	285	14	scheme	scheme	NOUN
ap-5981	285	15	for	for	ADP
ap-5981	285	16	viscoelastic	viscoelastic	ADJ
ap-5981	285	17	solids	solid	NOUN
ap-5981	285	18	characterized	characterize	VERB
ap-5981	285	19	by	by	ADP
ap-5981	285	20	the	the	DET
ap-5981	285	21	generalized	generalized	ADJ
ap-5981	285	22	maxwell	maxwell	PROPN
ap-5981	285	23	model	model	NOUN
ap-5981	285	24	.	.	PUNCT
ap-5981	286	1	besides	besides	SCONJ
ap-5981	286	2	the	the	DET
ap-5981	286	3	direct	direct	ADJ
ap-5981	286	4	derivation	derivation	NOUN
ap-5981	286	5	,	,	PUNCT
ap-5981	286	6	we	we	PRON
ap-5981	286	7	have	have	AUX
ap-5981	286	8	shown	show	VERB
ap-5981	286	9	the	the	DET
ap-5981	286	10	scheme	scheme	NOUN
ap-5981	286	11	can	can	AUX
ap-5981	286	12	be	be	AUX
ap-5981	286	13	derived	derive	VERB
ap-5981	286	14	from	from	ADP
ap-5981	286	15	the	the	DET
ap-5981	286	16	hamilton	hamilton	PROPN
ap-5981	286	17	variational	variational	PROPN
ap-5981	286	18	principle	principle	NOUN
ap-5981	286	19	combined	combine	VERB
ap-5981	286	20	with	with	ADP
ap-5981	286	21	a	a	DET
ap-5981	286	22	suitable	suitable	ADJ
ap-5981	286	23	structure	structure	NOUN
ap-5981	286	24	-	-	PUNCT
ap-5981	286	25	preserving	preserve	VERB
ap-5981	286	26	time	time	NOUN
ap-5981	286	27	discretization	discretization	NOUN
ap-5981	286	28	.	.	PUNCT
ap-5981	287	1	this	this	DET
ap-5981	287	2	variational	variational	ADJ
ap-5981	287	3	structure	structure	NOUN
ap-5981	287	4	is	be	AUX
ap-5981	287	5	then	then	ADV
ap-5981	287	6	reflected	reflect	VERB
ap-5981	287	7	in	in	ADP
ap-5981	287	8	low	low	ADJ
ap-5981	287	9	numerical	numerical	ADJ
ap-5981	287	10	energy	energy	NOUN
ap-5981	287	11	dissipation	dissipation	NOUN
ap-5981	287	12	of	of	ADP
ap-5981	287	13	the	the	DET
ap-5981	287	14	resulting	result	VERB
ap-5981	287	15	scheme	scheme	NOUN
ap-5981	287	16	,	,	PUNCT
ap-5981	287	17	which	which	PRON
ap-5981	287	18	has	have	AUX
ap-5981	287	19	been	be	AUX
ap-5981	287	20	confirmed	confirm	VERB
ap-5981	287	21	with	with	ADP
ap-5981	287	22	selected	select	VERB
ap-5981	287	23	numerical	numerical	ADJ
ap-5981	287	24	examples	example	NOUN
ap-5981	287	25	.	.	PUNCT
ap-5981	288	1	as	as	ADP
ap-5981	288	2	the	the	DET
ap-5981	288	3	next	next	ADJ
ap-5981	288	4	step	step	NOUN
ap-5981	288	5	,	,	PUNCT
ap-5981	288	6	we	we	PRON
ap-5981	288	7	will	will	AUX
ap-5981	288	8	combine	combine	VERB
ap-5981	288	9	the	the	DET
ap-5981	288	10	continuum	continuum	ADJ
ap-5981	288	11	framework	framework	NOUN
ap-5981	288	12	outlined	outline	VERB
ap-5981	288	13	in	in	ADP
ap-5981	288	14	section	section	NOUN
ap-5981	288	15	4.2	4.2	NUM
ap-5981	288	16	with	with	ADP
ap-5981	288	17	newmarktype	newmarktype	NOUN
ap-5981	288	18	solvers	solver	NOUN
ap-5981	288	19	for	for	ADP
ap-5981	288	20	variational	variational	ADJ
ap-5981	288	21	fracture	fracture	NOUN
ap-5981	288	22	models	model	NOUN
ap-5981	288	23	,	,	PUNCT
ap-5981	288	24	e.g.	e.g.	ADV
ap-5981	288	25	[	[	X
ap-5981	288	26	30	30	NUM
ap-5981	288	27	,	,	PUNCT
ap-5981	288	28	31	31	NUM
ap-5981	288	29	]	]	PUNCT
ap-5981	288	30	,	,	PUNCT
ap-5981	288	31	to	to	PART
ap-5981	288	32	extend	extend	VERB
ap-5981	288	33	the	the	DET
ap-5981	288	34	currently	currently	ADV
ap-5981	288	35	available	available	ADJ
ap-5981	288	36	approaches	approach	NOUN
ap-5981	288	37	to	to	ADP
ap-5981	288	38	simulating	simulate	VERB
ap-5981	288	39	the	the	DET
ap-5981	288	40	response	response	NOUN
ap-5981	288	41	of	of	ADP
ap-5981	288	42	laminated	laminated	ADJ
ap-5981	288	43	glass	glass	NOUN
ap-5981	288	44	structures	structure	NOUN
ap-5981	288	45	under	under	ADP
ap-5981	288	46	impact	impact	NOUN
ap-5981	288	47	.	.	PUNCT
ap-5981	289	1	acknowledgements	acknowledgement	NOUN
ap-5981	289	2	this	this	DET
ap-5981	289	3	publication	publication	NOUN
ap-5981	289	4	was	be	AUX
ap-5981	289	5	supported	support	VERB
ap-5981	289	6	by	by	ADP
ap-5981	289	7	the	the	DET
ap-5981	289	8	czech	czech	PROPN
ap-5981	289	9	science	science	PROPN
ap-5981	289	10	foundation	foundation	PROPN
ap-5981	289	11	,	,	PUNCT
ap-5981	289	12	the	the	DET
ap-5981	289	13	grant	grant	NOUN
ap-5981	289	14	no	no	NOUN
ap-5981	289	15	.	.	NOUN
ap-5981	289	16	19	19	NUM
ap-5981	289	17	-	-	PUNCT
ap-5981	289	18	15326s	15326s	NUM
ap-5981	289	19	.	.	PUNCT
ap-5981	290	1	we	we	PRON
ap-5981	290	2	wish	wish	VERB
ap-5981	290	3	to	to	PART
ap-5981	290	4	thank	thank	VERB
ap-5981	290	5	an	an	DET
ap-5981	290	6	anonymous	anonymous	ADJ
ap-5981	290	7	reviewer	reviewer	NOUN
ap-5981	290	8	for	for	ADP
ap-5981	290	9	her	she	PRON
ap-5981	290	10	/	/	SYM
ap-5981	290	11	his	his	PRON
ap-5981	290	12	constructive	constructive	ADJ
ap-5981	290	13	criticism	criticism	NOUN
ap-5981	290	14	that	that	PRON
ap-5981	290	15	helped	help	VERB
ap-5981	290	16	us	we	PRON
ap-5981	290	17	clarify	clarify	VERB
ap-5981	290	18	the	the	DET
ap-5981	290	19	original	original	ADJ
ap-5981	290	20	manuscript	manuscript	NOUN
ap-5981	290	21	at	at	ADP
ap-5981	290	22	several	several	ADJ
ap-5981	290	23	places	place	NOUN
ap-5981	290	24	.	.	PUNCT
ap-5981	291	1	references	reference	NOUN
ap-5981	291	2	[	[	X
ap-5981	291	3	1	1	X
ap-5981	291	4	]	]	PUNCT
ap-5981	291	5	t.	t.	PROPN
ap-5981	291	6	hatada	hatada	PROPN
ap-5981	291	7	,	,	PUNCT
ap-5981	291	8	t.	t.	PROPN
ap-5981	291	9	kobori	kobori	PROPN
ap-5981	291	10	,	,	PUNCT
ap-5981	291	11	m.	m.	NOUN
ap-5981	291	12	ishida	ishida	PROPN
ap-5981	291	13	,	,	PUNCT
ap-5981	291	14	n.	n.	PROPN
ap-5981	291	15	niwa	niwa	PROPN
ap-5981	291	16	.	.	PUNCT
ap-5981	292	1	dynamic	dynamic	ADJ
ap-5981	292	2	analysis	analysis	NOUN
ap-5981	292	3	of	of	ADP
ap-5981	292	4	structures	structure	NOUN
ap-5981	292	5	with	with	ADP
ap-5981	292	6	maxwell	maxwell	PROPN
ap-5981	292	7	model	model	PROPN
ap-5981	292	8	.	.	PUNCT
ap-5981	293	1	earthquake	earthquake	NOUN
ap-5981	293	2	engineering	engineering	PROPN
ap-5981	293	3	&	&	CCONJ
ap-5981	293	4	structural	structural	ADJ
ap-5981	293	5	dynamics	dynamic	NOUN
ap-5981	293	6	29(2):159–176	29(2):159–176	PROPN
ap-5981	293	7	,	,	PUNCT
ap-5981	293	8	2000	2000	NUM
ap-5981	293	9	.	.	PUNCT
ap-5981	294	1	doi:10.1002/(sici)10969845(200002)29:2<159::aid	doi:10.1002/(sici)10969845(200002)29:2<159::aid	VERB
ap-5981	294	2	-	-	PUNCT
ap-5981	294	3	eqe895>3.0.co;2	eqe895>3.0.co;2	NOUN
ap-5981	294	4	-	-	PUNCT
ap-5981	294	5	1	1	NUM
ap-5981	294	6	.	.	PUNCT
ap-5981	295	1	[	[	X
ap-5981	295	2	2	2	NUM
ap-5981	295	3	]	]	PUNCT
ap-5981	295	4	m.	m.	NOUN
ap-5981	295	5	haldimann	haldimann	PROPN
ap-5981	295	6	,	,	PUNCT
ap-5981	295	7	a.	a.	NOUN
ap-5981	295	8	luible	luible	ADJ
ap-5981	295	9	,	,	PUNCT
ap-5981	295	10	m.	m.	NOUN
ap-5981	295	11	overend	overend	PROPN
ap-5981	295	12	.	.	PUNCT
ap-5981	296	1	structural	structural	ADJ
ap-5981	296	2	use	use	NOUN
ap-5981	296	3	of	of	ADP
ap-5981	296	4	glass	glass	NOUN
ap-5981	296	5	,	,	PUNCT
ap-5981	296	6	vol	vol	NOUN
ap-5981	296	7	.	.	PROPN
ap-5981	296	8	10	10	NUM
ap-5981	296	9	of	of	ADP
ap-5981	296	10	structural	structural	ADJ
ap-5981	296	11	engineering	engineering	NOUN
ap-5981	296	12	documents	document	NOUN
ap-5981	296	13	.	.	PUNCT
ap-5981	297	1	iabse	iabse	PROPN
ap-5981	297	2	,	,	PUNCT
ap-5981	297	3	zürich	zürich	PROPN
ap-5981	297	4	,	,	PUNCT
ap-5981	297	5	switzerland	switzerland	PROPN
ap-5981	297	6	,	,	PUNCT
ap-5981	297	7	2008	2008	NUM
ap-5981	297	8	.	.	PUNCT
ap-5981	298	1	[	[	X
ap-5981	298	2	3	3	NUM
ap-5981	298	3	]	]	PUNCT
ap-5981	298	4	a.	a.	NOUN
ap-5981	298	5	van	van	PROPN
ap-5981	298	6	duser	duser	NOUN
ap-5981	298	7	,	,	PUNCT
ap-5981	298	8	a.	a.	NOUN
ap-5981	298	9	jagota	jagota	NOUN
ap-5981	298	10	,	,	PUNCT
ap-5981	298	11	s.	s.	PROPN
ap-5981	298	12	j.	j.	PROPN
ap-5981	298	13	bennison	bennison	PROPN
ap-5981	298	14	.	.	PUNCT
ap-5981	299	1	analysis	analysis	NOUN
ap-5981	299	2	of	of	ADP
ap-5981	299	3	glass	glass	NOUN
ap-5981	299	4	/	/	SYM
ap-5981	299	5	polyvinyl	polyvinyl	NOUN
ap-5981	299	6	butyral	butyral	ADJ
ap-5981	299	7	laminates	laminate	NOUN
ap-5981	299	8	subjected	subject	VERB
ap-5981	299	9	to	to	ADP
ap-5981	299	10	uniform	uniform	ADJ
ap-5981	299	11	pressure	pressure	NOUN
ap-5981	299	12	.	.	PUNCT
ap-5981	300	1	journal	journal	NOUN
ap-5981	300	2	of	of	ADP
ap-5981	300	3	engineering	engineering	NOUN
ap-5981	300	4	mechanics	mechanic	NOUN
ap-5981	300	5	125(4):435–442	125(4):435–442	NUM
ap-5981	300	6	,	,	PUNCT
ap-5981	300	7	1999	1999	NUM
ap-5981	300	8	.	.	PUNCT
ap-5981	301	1	doi:10.1061/(asce)0733	doi:10.1061/(asce)0733	VERB
ap-5981	301	2	-	-	PUNCT
ap-5981	301	3	9399(1999)125:4(435	9399(1999)125:4(435	NUM
ap-5981	301	4	)	)	PUNCT
ap-5981	301	5	.	.	PUNCT
ap-5981	302	1	509	509	NUM
ap-5981	302	2	http://dx.doi.org/10.1002/(sici)1096-9845(200002)29:2<159::aid-eqe895>3.0.co;2-1	http://dx.doi.org/10.1002/(sici)1096-9845(200002)29:2<159::aid-eqe895>3.0.co;2-1	PROPN
ap-5981	302	3	http://dx.doi.org/10.1002/(sici)1096-9845(200002)29:2<159::aid-eqe895>3.0.co;2-1	http://dx.doi.org/10.1002/(sici)1096-9845(200002)29:2<159::aid-eqe895>3.0.co;2-1	PROPN
ap-5981	302	4	http://dx.doi.org/10.1061/(asce)0733-9399(1999)125:4(435	http://dx.doi.org/10.1061/(asce)0733-9399(1999)125:4(435	PROPN
ap-5981	302	5	)	)	PUNCT
ap-5981	302	6	j.	j.	PROPN
ap-5981	302	7	schmidt	schmidt	PROPN
ap-5981	302	8	,	,	PUNCT
ap-5981	302	9	t.	t.	PROPN
ap-5981	302	10	janda	janda	PROPN
ap-5981	302	11	,	,	PUNCT
ap-5981	302	12	a.	a.	PROPN
ap-5981	302	13	zemanová	zemanová	PROPN
ap-5981	302	14	et	et	PROPN
ap-5981	302	15	al	al	PROPN
ap-5981	302	16	.	.	PROPN
ap-5981	303	1	acta	acta	PROPN
ap-5981	303	2	polytechnica	polytechnica	PROPN
ap-5981	303	3	time	time	PROPN
ap-5981	303	4	t	t	PROPN
ap-5981	303	5	[	[	X
ap-5981	303	6	s	s	X
ap-5981	303	7	]	]	X
ap-5981	303	8	di	di	X
ap-5981	303	9	sp	sp	ADP
ap-5981	303	10	la	la	PROPN
ap-5981	303	11	ce	ce	PROPN
ap-5981	303	12	m	m	PROPN
ap-5981	303	13	en	en	PROPN
ap-5981	303	14	t	t	PROPN
ap-5981	303	15	r	r	PROPN
ap-5981	303	16	(	(	PUNCT
ap-5981	303	17	t	t	PROPN
ap-5981	303	18	)	)	PUNCT
ap-5981	304	1	[	[	X
ap-5981	304	2	m	m	X
ap-5981	304	3	]	]	X
ap-5981	304	4	figure	figure	NOUN
ap-5981	304	5	5	5	NUM
ap-5981	304	6	.	.	PUNCT
ap-5981	305	1	snapshots	snapshot	NOUN
ap-5981	305	2	of	of	ADP
ap-5981	305	3	deformations	deformation	NOUN
ap-5981	305	4	of	of	ADP
ap-5981	305	5	a	a	DET
ap-5981	305	6	viscoelastic	viscoelastic	ADJ
ap-5981	305	7	cube	cube	NOUN
ap-5981	305	8	subjected	subject	VERB
ap-5981	305	9	to	to	PART
ap-5981	305	10	step	step	VERB
ap-5981	305	11	load	load	NOUN
ap-5981	305	12	.	.	PUNCT
ap-5981	306	1	[	[	X
ap-5981	306	2	4	4	X
ap-5981	306	3	]	]	X
ap-5981	306	4	l.	l.	PROPN
ap-5981	306	5	galuppi	galuppi	PROPN
ap-5981	306	6	,	,	PUNCT
ap-5981	306	7	g.	g.	PROPN
ap-5981	306	8	royer	royer	PROPN
ap-5981	306	9	-	-	PUNCT
ap-5981	306	10	carfagni	carfagni	PROPN
ap-5981	306	11	.	.	PUNCT
ap-5981	307	1	the	the	DET
ap-5981	307	2	design	design	NOUN
ap-5981	307	3	of	of	ADP
ap-5981	307	4	laminated	laminated	ADJ
ap-5981	307	5	glass	glass	NOUN
ap-5981	307	6	under	under	ADP
ap-5981	307	7	time	time	NOUN
ap-5981	307	8	-	-	PUNCT
ap-5981	307	9	dependent	dependent	ADJ
ap-5981	307	10	loading	loading	NOUN
ap-5981	307	11	.	.	PUNCT
ap-5981	308	1	international	international	ADJ
ap-5981	308	2	journal	journal	PROPN
ap-5981	308	3	of	of	ADP
ap-5981	308	4	mechanical	mechanical	ADJ
ap-5981	308	5	sciences	science	NOUN
ap-5981	308	6	68:67–75	68:67–75	PROPN
ap-5981	308	7	,	,	PUNCT
ap-5981	308	8	2013	2013	NUM
ap-5981	308	9	.	.	PUNCT
ap-5981	309	1	doi:10.1016	doi:10.1016	PROPN
ap-5981	309	2	/	/	SYM
ap-5981	309	3	j.ijmecsci.2012.12.019	j.ijmecsci.2012.12.019	PROPN
ap-5981	309	4	.	.	PUNCT
ap-5981	310	1	[	[	X
ap-5981	310	2	5	5	NUM
ap-5981	310	3	]	]	PUNCT
ap-5981	310	4	a.	a.	NOUN
ap-5981	310	5	zemanová	zemanová	PROPN
ap-5981	310	6	,	,	PUNCT
ap-5981	310	7	j.	j.	PROPN
ap-5981	310	8	zeman	zeman	PROPN
ap-5981	310	9	,	,	PUNCT
ap-5981	310	10	m.	m.	PROPN
ap-5981	310	11	šejnoha	šejnoha	PROPN
ap-5981	310	12	.	.	PUNCT
ap-5981	311	1	comparison	comparison	NOUN
ap-5981	311	2	of	of	ADP
ap-5981	311	3	viscoelastic	viscoelastic	ADJ
ap-5981	311	4	finite	finite	NOUN
ap-5981	311	5	element	element	NOUN
ap-5981	311	6	models	model	NOUN
ap-5981	311	7	for	for	ADP
ap-5981	311	8	laminated	laminated	ADJ
ap-5981	311	9	glass	glass	NOUN
ap-5981	311	10	beams	beam	NOUN
ap-5981	311	11	.	.	PUNCT
ap-5981	312	1	international	international	ADJ
ap-5981	312	2	journal	journal	PROPN
ap-5981	312	3	of	of	ADP
ap-5981	312	4	mechanical	mechanical	ADJ
ap-5981	312	5	sciences	science	NOUN
ap-5981	312	6	131	131	NUM
ap-5981	312	7	-	-	SYM
ap-5981	312	8	132:380–395	132:380–395	NUM
ap-5981	312	9	,	,	PUNCT
ap-5981	312	10	2017	2017	NUM
ap-5981	312	11	.	.	PUNCT
ap-5981	313	1	doi:10.1016	doi:10.1016	PROPN
ap-5981	313	2	/	/	SYM
ap-5981	313	3	j.ijmecsci.2017.05.035	j.ijmecsci.2017.05.035	PROPN
ap-5981	313	4	.	.	PUNCT
ap-5981	314	1	[	[	X
ap-5981	314	2	6	6	NUM
ap-5981	314	3	]	]	PUNCT
ap-5981	314	4	a.	a.	NOUN
ap-5981	314	5	zemanová	zemanová	PROPN
ap-5981	314	6	,	,	PUNCT
ap-5981	314	7	j.	j.	PROPN
ap-5981	314	8	zeman	zeman	PROPN
ap-5981	314	9	,	,	PUNCT
ap-5981	314	10	t.	t.	PROPN
ap-5981	314	11	janda	janda	PROPN
ap-5981	314	12	,	,	PUNCT
ap-5981	314	13	m.	m.	PROPN
ap-5981	314	14	šejnoha	šejnoha	PROPN
ap-5981	314	15	.	.	PUNCT
ap-5981	314	16	layer	layer	NOUN
ap-5981	314	17	-	-	PUNCT
ap-5981	314	18	wise	wise	ADJ
ap-5981	314	19	numerical	numerical	ADJ
ap-5981	314	20	model	model	NOUN
ap-5981	314	21	for	for	ADP
ap-5981	314	22	laminated	laminated	ADJ
ap-5981	314	23	glass	glass	NOUN
ap-5981	314	24	plates	plate	NOUN
ap-5981	314	25	with	with	ADP
ap-5981	314	26	viscoelastic	viscoelastic	ADJ
ap-5981	314	27	interlayer	interlayer	NOUN
ap-5981	314	28	.	.	PUNCT
ap-5981	315	1	structural	structural	ADJ
ap-5981	315	2	engineering	engineering	NOUN
ap-5981	315	3	and	and	CCONJ
ap-5981	315	4	mechanics	mechanic	NOUN
ap-5981	315	5	65(4):369–380	65(4):369–380	NOUN
ap-5981	315	6	,	,	PUNCT
ap-5981	315	7	2018	2018	NUM
ap-5981	315	8	.	.	PUNCT
ap-5981	316	1	doi:10.12989	doi:10.12989	PROPN
ap-5981	316	2	/	/	SYM
ap-5981	316	3	sem.2018.65.4.369	sem.2018.65.4.369	PROPN
ap-5981	316	4	.	.	PUNCT
ap-5981	317	1	[	[	X
ap-5981	317	2	7	7	X
ap-5981	317	3	]	]	X
ap-5981	317	4	l.	l.	PROPN
ap-5981	317	5	andreozzi	andreozzi	PROPN
ap-5981	317	6	,	,	PUNCT
ap-5981	317	7	s.	s.	PROPN
ap-5981	317	8	b.	b.	PROPN
ap-5981	317	9	bati	bati	PROPN
ap-5981	317	10	,	,	PUNCT
ap-5981	317	11	m.	m.	NOUN
ap-5981	317	12	fagone	fagone	PROPN
ap-5981	317	13	,	,	PUNCT
ap-5981	317	14	et	et	PROPN
ap-5981	317	15	al	al	PROPN
ap-5981	317	16	.	.	PUNCT
ap-5981	317	17	dynamic	dynamic	ADJ
ap-5981	317	18	torsion	torsion	NOUN
ap-5981	317	19	tests	test	NOUN
ap-5981	317	20	to	to	PART
ap-5981	317	21	characterize	characterize	VERB
ap-5981	317	22	the	the	DET
ap-5981	317	23	thermo	thermo	NOUN
ap-5981	317	24	-	-	PUNCT
ap-5981	317	25	viscoelastic	viscoelastic	ADJ
ap-5981	317	26	properties	property	NOUN
ap-5981	317	27	of	of	ADP
ap-5981	317	28	polymeric	polymeric	ADJ
ap-5981	317	29	interlayers	interlayer	NOUN
ap-5981	317	30	for	for	ADP
ap-5981	317	31	laminated	laminated	ADJ
ap-5981	317	32	glass	glass	NOUN
ap-5981	317	33	.	.	PUNCT
ap-5981	318	1	construction	construction	NOUN
ap-5981	318	2	and	and	CCONJ
ap-5981	318	3	building	building	NOUN
ap-5981	318	4	materials	material	NOUN
ap-5981	318	5	65:1–13	65:1–13	NUM
ap-5981	318	6	,	,	PUNCT
ap-5981	318	7	2014	2014	NUM
ap-5981	318	8	.	.	PUNCT
ap-5981	319	1	doi:10.1016	doi:10.1016	PROPN
ap-5981	319	2	/	/	SYM
ap-5981	319	3	j.conbuildmat.2014.04.003	j.conbuildmat.2014.04.003	PROPN
ap-5981	319	4	.	.	PUNCT
ap-5981	320	1	[	[	X
ap-5981	320	2	8	8	NUM
ap-5981	320	3	]	]	X
ap-5981	320	4	y.	y.	PROPN
ap-5981	320	5	shitanoki	shitanoki	PROPN
ap-5981	320	6	,	,	PUNCT
ap-5981	320	7	s.	s.	PROPN
ap-5981	320	8	bennison	bennison	PROPN
ap-5981	320	9	,	,	PUNCT
ap-5981	320	10	y.	y.	PROPN
ap-5981	320	11	koike	koike	PROPN
ap-5981	320	12	.	.	PUNCT
ap-5981	321	1	a	a	DET
ap-5981	321	2	practical	practical	ADJ
ap-5981	321	3	,	,	PUNCT
ap-5981	321	4	nondestructive	nondestructive	ADJ
ap-5981	321	5	method	method	NOUN
ap-5981	321	6	to	to	PART
ap-5981	321	7	determine	determine	VERB
ap-5981	321	8	the	the	DET
ap-5981	321	9	shear	shear	NOUN
ap-5981	321	10	relaxation	relaxation	NOUN
ap-5981	321	11	modulus	modulus	NOUN
ap-5981	321	12	behavior	behavior	NOUN
ap-5981	321	13	of	of	ADP
ap-5981	321	14	polymeric	polymeric	ADJ
ap-5981	321	15	interlayers	interlayer	NOUN
ap-5981	321	16	for	for	ADP
ap-5981	321	17	laminated	laminated	ADJ
ap-5981	321	18	glass	glass	NOUN
ap-5981	321	19	.	.	PUNCT
ap-5981	322	1	polymer	polymer	NOUN
ap-5981	322	2	testing	testing	NOUN
ap-5981	322	3	37:59–67	37:59–67	NUM
ap-5981	322	4	,	,	PUNCT
ap-5981	322	5	2014	2014	NUM
ap-5981	322	6	.	.	PUNCT
ap-5981	323	1	doi:10.1016	doi:10.1016	PROPN
ap-5981	323	2	/	/	SYM
ap-5981	323	3	j.polymertesting.2014.04.011	j.polymertesting.2014.04.011	PROPN
ap-5981	323	4	.	.	PUNCT
ap-5981	324	1	[	[	X
ap-5981	324	2	9	9	NUM
ap-5981	324	3	]	]	PUNCT
ap-5981	324	4	i.	i.	NOUN
ap-5981	324	5	mohagheghian	mohagheghian	PROPN
ap-5981	324	6	,	,	PUNCT
ap-5981	324	7	y.	y.	PROPN
ap-5981	324	8	wang	wang	PROPN
ap-5981	324	9	,	,	PUNCT
ap-5981	324	10	l.	l.	PROPN
ap-5981	324	11	jiang	jiang	PROPN
ap-5981	324	12	,	,	PUNCT
ap-5981	324	13	et	et	PROPN
ap-5981	324	14	al	al	PROPN
ap-5981	324	15	.	.	PUNCT
ap-5981	324	16	quasi	quasi	ADJ
ap-5981	324	17	-	-	ADJ
ap-5981	324	18	static	static	ADJ
ap-5981	324	19	bending	bending	NOUN
ap-5981	324	20	and	and	CCONJ
ap-5981	324	21	low	low	ADJ
ap-5981	324	22	velocity	velocity	NOUN
ap-5981	324	23	impact	impact	NOUN
ap-5981	324	24	performance	performance	NOUN
ap-5981	324	25	of	of	ADP
ap-5981	324	26	monolithic	monolithic	ADJ
ap-5981	324	27	and	and	CCONJ
ap-5981	324	28	laminated	laminated	ADJ
ap-5981	324	29	glass	glass	NOUN
ap-5981	324	30	windows	window	NOUN
ap-5981	324	31	employing	employ	VERB
ap-5981	324	32	chemically	chemically	ADV
ap-5981	324	33	strengthened	strengthen	VERB
ap-5981	324	34	glass	glass	NOUN
ap-5981	324	35	.	.	PUNCT
ap-5981	325	1	european	european	PROPN
ap-5981	325	2	journal	journal	PROPN
ap-5981	325	3	of	of	ADP
ap-5981	325	4	mechanics	mechanic	NOUN
ap-5981	325	5	–	–	PUNCT
ap-5981	325	6	a	a	DET
ap-5981	325	7	/	/	SYM
ap-5981	325	8	solids	solid	NOUN
ap-5981	325	9	63:165–186	63:165–186	NOUN
ap-5981	325	10	,	,	PUNCT
ap-5981	325	11	2017	2017	NUM
ap-5981	325	12	.	.	PUNCT
ap-5981	326	1	doi:10.1016	doi:10.1016	PROPN
ap-5981	326	2	/	/	SYM
ap-5981	326	3	j.euromechsol.2017.01.006	j.euromechsol.2017.01.006	PROPN
ap-5981	326	4	.	.	PUNCT
ap-5981	327	1	[	[	X
ap-5981	327	2	10	10	NUM
ap-5981	327	3	]	]	PUNCT
ap-5981	327	4	t.	t.	NOUN
ap-5981	327	5	hána	hána	NOUN
ap-5981	327	6	,	,	PUNCT
ap-5981	327	7	t.	t.	PROPN
ap-5981	327	8	janda	janda	PROPN
ap-5981	327	9	,	,	PUNCT
ap-5981	327	10	j.	j.	PROPN
ap-5981	327	11	schmidt	schmidt	PROPN
ap-5981	327	12	,	,	PUNCT
ap-5981	327	13	et	et	PROPN
ap-5981	327	14	al	al	PROPN
ap-5981	327	15	.	.	PROPN
ap-5981	327	16	experimental	experimental	PROPN
ap-5981	327	17	and	and	CCONJ
ap-5981	327	18	numerical	numerical	ADJ
ap-5981	327	19	study	study	NOUN
ap-5981	327	20	of	of	ADP
ap-5981	327	21	viscoelastic	viscoelastic	ADJ
ap-5981	327	22	properties	property	NOUN
ap-5981	327	23	of	of	ADP
ap-5981	327	24	polymeric	polymeric	ADJ
ap-5981	327	25	interlayers	interlayer	NOUN
ap-5981	327	26	used	use	VERB
ap-5981	327	27	for	for	ADP
ap-5981	327	28	laminated	laminated	ADJ
ap-5981	327	29	glass	glass	NOUN
ap-5981	327	30	:	:	PUNCT
ap-5981	327	31	determination	determination	NOUN
ap-5981	327	32	of	of	ADP
ap-5981	327	33	material	material	NOUN
ap-5981	327	34	parameters	parameter	NOUN
ap-5981	327	35	.	.	PUNCT
ap-5981	328	1	materials	material	NOUN
ap-5981	328	2	12(14):2241	12(14):2241	NUM
ap-5981	328	3	,	,	PUNCT
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ap-5981	328	5	.	.	PUNCT
ap-5981	329	1	doi:10.3390	doi:10.3390	NOUN
ap-5981	329	2	/	/	SYM
ap-5981	329	3	ma12142241	ma12142241	PROPN
ap-5981	329	4	.	.	PUNCT
ap-5981	330	1	[	[	X
ap-5981	330	2	11	11	NUM
ap-5981	330	3	]	]	PUNCT
ap-5981	330	4	r.	r.	PROPN
ap-5981	330	5	w.	w.	PROPN
ap-5981	330	6	clough	clough	PROPN
ap-5981	330	7	,	,	PUNCT
ap-5981	330	8	j.	j.	PROPN
ap-5981	330	9	penzien	penzien	PROPN
ap-5981	330	10	.	.	PUNCT
ap-5981	330	11	dynamics	dynamic	NOUN
ap-5981	330	12	of	of	ADP
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ap-5981	330	14	.	.	PUNCT
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ap-5981	331	2	&	&	CCONJ
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ap-5981	331	4	,	,	PUNCT
ap-5981	331	5	inc	inc	PROPN
ap-5981	331	6	,	,	PUNCT
ap-5981	331	7	berkeley	berkeley	PROPN
ap-5981	331	8	,	,	PUNCT
ap-5981	331	9	3rd	3rd	ADJ
ap-5981	331	10	edn	edn	NOUN
ap-5981	331	11	.	.	PUNCT
ap-5981	331	12	,	,	PUNCT
ap-5981	331	13	2003	2003	NUM
ap-5981	331	14	.	.	PUNCT
ap-5981	332	1	[	[	X
ap-5981	332	2	12	12	NUM
ap-5981	332	3	]	]	X
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ap-5981	332	6	,	,	PUNCT
ap-5981	332	7	et	et	PROPN
ap-5981	332	8	al	al	PROPN
ap-5981	332	9	.	.	PROPN
ap-5981	333	1	static	static	ADJ
ap-5981	333	2	and	and	CCONJ
ap-5981	333	3	free	free	ADJ
ap-5981	333	4	vibration	vibration	NOUN
ap-5981	333	5	analysis	analysis	NOUN
ap-5981	333	6	of	of	ADP
ap-5981	333	7	laminated	laminated	ADJ
ap-5981	333	8	glass	glass	NOUN
ap-5981	333	9	beam	beam	NOUN
ap-5981	333	10	on	on	ADP
ap-5981	333	11	viscoelastic	viscoelastic	ADJ
ap-5981	333	12	supports	support	NOUN
ap-5981	333	13	.	.	PUNCT
ap-5981	334	1	international	international	ADJ
ap-5981	334	2	journal	journal	PROPN
ap-5981	334	3	of	of	ADP
ap-5981	334	4	solids	solid	NOUN
ap-5981	334	5	and	and	CCONJ
ap-5981	334	6	structures	structure	NOUN
ap-5981	334	7	44(2526):8735–8750	44(2526):8735–8750	NUM
ap-5981	334	8	,	,	PUNCT
ap-5981	334	9	2007	2007	NUM
ap-5981	334	10	.	.	PUNCT
ap-5981	335	1	doi:10.1016	doi:10.1016	PROPN
ap-5981	335	2	/	/	SYM
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ap-5981	335	4	.	.	PUNCT
ap-5981	336	1	[	[	X
ap-5981	336	2	13	13	NUM
ap-5981	336	3	]	]	PUNCT
ap-5981	336	4	m.	m.	NOUN
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ap-5981	336	6	aenlle	aenlle	PROPN
ap-5981	336	7	,	,	PUNCT
ap-5981	336	8	f.	f.	PROPN
ap-5981	336	9	pelayo	pelayo	PROPN
ap-5981	336	10	.	.	PUNCT
ap-5981	337	1	frequency	frequency	PROPN
ap-5981	337	2	response	response	NOUN
ap-5981	337	3	of	of	ADP
ap-5981	337	4	laminated	laminated	ADJ
ap-5981	337	5	glass	glass	NOUN
ap-5981	337	6	elements	element	NOUN
ap-5981	337	7	:	:	PUNCT
ap-5981	337	8	analytical	analytical	ADJ
ap-5981	337	9	modeling	modeling	NOUN
ap-5981	337	10	and	and	CCONJ
ap-5981	337	11	effective	effective	ADJ
ap-5981	337	12	thickness	thickness	NOUN
ap-5981	337	13	.	.	PUNCT
ap-5981	338	1	applied	apply	VERB
ap-5981	338	2	mechanics	mechanic	NOUN
ap-5981	338	3	reviews	review	NOUN
ap-5981	338	4	65(2):020802–020802–13	65(2):020802–020802–13	NUM
ap-5981	338	5	,	,	PUNCT
ap-5981	338	6	2013	2013	NUM
ap-5981	338	7	.	.	PUNCT
ap-5981	339	1	doi:10.1115/1.4023929	doi:10.1115/1.4023929	NOUN
ap-5981	339	2	.	.	PUNCT
ap-5981	340	1	[	[	X
ap-5981	340	2	14	14	NUM
ap-5981	340	3	]	]	PUNCT
ap-5981	340	4	a.	a.	NOUN
ap-5981	340	5	zemanová	zemanová	PROPN
ap-5981	340	6	,	,	PUNCT
ap-5981	340	7	j.	j.	PROPN
ap-5981	340	8	zeman	zeman	PROPN
ap-5981	340	9	,	,	PUNCT
ap-5981	340	10	t.	t.	PROPN
ap-5981	340	11	janda	janda	PROPN
ap-5981	340	12	,	,	PUNCT
ap-5981	340	13	et	et	PROPN
ap-5981	340	14	al	al	PROPN
ap-5981	340	15	.	.	PROPN
ap-5981	341	1	on	on	ADP
ap-5981	341	2	modal	modal	ADJ
ap-5981	341	3	analysis	analysis	NOUN
ap-5981	341	4	of	of	ADP
ap-5981	341	5	laminated	laminated	ADJ
ap-5981	341	6	glass	glass	NOUN
ap-5981	341	7	:	:	PUNCT
ap-5981	341	8	usability	usability	NOUN
ap-5981	341	9	of	of	ADP
ap-5981	341	10	simplified	simplified	ADJ
ap-5981	341	11	methods	method	NOUN
ap-5981	341	12	and	and	CCONJ
ap-5981	341	13	enhanced	enhance	VERB
ap-5981	341	14	effective	effective	ADJ
ap-5981	341	15	thickness	thickness	NOUN
ap-5981	341	16	.	.	PUNCT
ap-5981	342	1	composites	composite	VERB
ap-5981	342	2	part	part	NOUN
ap-5981	342	3	b	b	NOUN
ap-5981	342	4	:	:	PUNCT
ap-5981	342	5	engineering	engineering	NOUN
ap-5981	342	6	151:92–105	151:92–105	NUM
ap-5981	342	7	,	,	PUNCT
ap-5981	342	8	2018	2018	NUM
ap-5981	342	9	.	.	PUNCT
ap-5981	343	1	doi:10.1016	doi:10.1016	PROPN
ap-5981	343	2	/	/	SYM
ap-5981	343	3	j.compositesb.2018.05.032	j.compositesb.2018.05.032	PROPN
ap-5981	343	4	.	.	PUNCT
ap-5981	344	1	[	[	X
ap-5981	344	2	15	15	NUM
ap-5981	344	3	]	]	X
ap-5981	344	4	o.	o.	PROPN
ap-5981	344	5	c.	c.	PROPN
ap-5981	344	6	zienkiewicz	zienkiewicz	PROPN
ap-5981	344	7	,	,	PUNCT
ap-5981	344	8	m.	m.	PROPN
ap-5981	344	9	watson	watson	PROPN
ap-5981	344	10	,	,	PUNCT
ap-5981	344	11	i.	i.	PROPN
ap-5981	344	12	p.	p.	PROPN
ap-5981	344	13	king	king	PROPN
ap-5981	344	14	.	.	PUNCT
ap-5981	345	1	a	a	DET
ap-5981	345	2	numerical	numerical	ADJ
ap-5981	345	3	method	method	NOUN
ap-5981	345	4	of	of	ADP
ap-5981	345	5	visco	visco	ADJ
ap-5981	345	6	-	-	ADJ
ap-5981	345	7	elastic	elastic	ADJ
ap-5981	345	8	stress	stress	NOUN
ap-5981	345	9	analysis	analysis	NOUN
ap-5981	345	10	.	.	PUNCT
ap-5981	346	1	international	international	ADJ
ap-5981	346	2	journal	journal	NOUN
ap-5981	346	3	of	of	ADP
ap-5981	346	4	mechanical	mechanical	ADJ
ap-5981	346	5	sciences	science	NOUN
ap-5981	346	6	10(10):807	10(10):807	NUM
ap-5981	346	7	–	–	PUNCT
ap-5981	346	8	827	827	NUM
ap-5981	346	9	,	,	PUNCT
ap-5981	346	10	1968	1968	NUM
ap-5981	346	11	.	.	PUNCT
ap-5981	347	1	doi:10.1016/0020	doi:10.1016/0020	PROPN
ap-5981	347	2	-	-	PUNCT
ap-5981	347	3	7403(68)90022	7403(68)90022	NOUN
ap-5981	347	4	-	-	PUNCT
ap-5981	347	5	2	2	NUM
ap-5981	347	6	.	.	PUNCT
ap-5981	348	1	[	[	X
ap-5981	348	2	16	16	NUM
ap-5981	348	3	]	]	PUNCT
ap-5981	348	4	z.	z.	PROPN
ap-5981	348	5	p.	p.	PROPN
ap-5981	348	6	bažant	bažant	PROPN
ap-5981	348	7	,	,	PUNCT
ap-5981	348	8	m.	m.	NOUN
ap-5981	348	9	jirásek	jirásek	NOUN
ap-5981	348	10	.	.	PUNCT
ap-5981	349	1	creep	creep	PROPN
ap-5981	349	2	and	and	CCONJ
ap-5981	349	3	hygrothermal	hygrothermal	ADJ
ap-5981	349	4	effects	effect	NOUN
ap-5981	349	5	in	in	ADP
ap-5981	349	6	concrete	concrete	ADJ
ap-5981	349	7	structures	structure	NOUN
ap-5981	349	8	,	,	PUNCT
ap-5981	349	9	vol	vol	NOUN
ap-5981	349	10	.	.	PROPN
ap-5981	349	11	225	225	NUM
ap-5981	349	12	of	of	ADP
ap-5981	349	13	solid	solid	ADJ
ap-5981	349	14	mechanics	mechanic	NOUN
ap-5981	349	15	and	and	CCONJ
ap-5981	349	16	its	its	PRON
ap-5981	349	17	applications	application	NOUN
ap-5981	349	18	.	.	PUNCT
ap-5981	350	1	springer	springer	NOUN
ap-5981	350	2	,	,	PUNCT
ap-5981	350	3	dordrecht	dordrecht	PROPN
ap-5981	350	4	,	,	PUNCT
ap-5981	350	5	2018	2018	NUM
ap-5981	350	6	.	.	PUNCT
ap-5981	351	1	doi:10.1007/978	doi:10.1007/978	PROPN
ap-5981	351	2	-	-	PUNCT
ap-5981	351	3	94	94	NUM
ap-5981	351	4	-	-	PUNCT
ap-5981	351	5	024	024	NUM
ap-5981	351	6	-	-	PUNCT
ap-5981	351	7	1138	1138	NUM
ap-5981	351	8	-	-	PUNCT
ap-5981	351	9	6	6	NUM
ap-5981	351	10	.	.	PUNCT
ap-5981	352	1	[	[	X
ap-5981	352	2	17	17	NUM
ap-5981	352	3	]	]	X
ap-5981	352	4	n.	n.	PROPN
ap-5981	352	5	m.	m.	PROPN
ap-5981	352	6	newmark	newmark	PROPN
ap-5981	352	7	.	.	PUNCT
ap-5981	353	1	a	a	DET
ap-5981	353	2	method	method	NOUN
ap-5981	353	3	of	of	ADP
ap-5981	353	4	computation	computation	NOUN
ap-5981	353	5	for	for	ADP
ap-5981	353	6	structural	structural	ADJ
ap-5981	353	7	dynamics	dynamic	NOUN
ap-5981	353	8	.	.	PUNCT
ap-5981	354	1	journal	journal	NOUN
ap-5981	354	2	of	of	ADP
ap-5981	354	3	the	the	DET
ap-5981	354	4	engineering	engineering	NOUN
ap-5981	354	5	mechanics	mechanic	NOUN
ap-5981	354	6	division	division	NOUN
ap-5981	354	7	85(3):67–94	85(3):67–94	NUM
ap-5981	354	8	,	,	PUNCT
ap-5981	354	9	1959	1959	NUM
ap-5981	354	10	.	.	PUNCT
ap-5981	355	1	[	[	X
ap-5981	355	2	18	18	NUM
ap-5981	355	3	]	]	X
ap-5981	355	4	c.	c.	PROPN
ap-5981	355	5	kane	kane	PROPN
ap-5981	355	6	,	,	PUNCT
ap-5981	355	7	j.	j.	PROPN
ap-5981	355	8	e.	e.	PROPN
ap-5981	355	9	marsden	marsden	PROPN
ap-5981	355	10	,	,	PUNCT
ap-5981	355	11	m.	m.	PROPN
ap-5981	355	12	ortiz	ortiz	PROPN
ap-5981	355	13	,	,	PUNCT
ap-5981	355	14	m.	m.	NOUN
ap-5981	355	15	west	west	PROPN
ap-5981	355	16	.	.	PUNCT
ap-5981	356	1	variational	variational	ADJ
ap-5981	356	2	integrators	integrator	NOUN
ap-5981	356	3	and	and	CCONJ
ap-5981	356	4	the	the	DET
ap-5981	356	5	newmark	newmark	PROPN
ap-5981	356	6	algorithm	algorithm	NOUN
ap-5981	356	7	for	for	ADP
ap-5981	356	8	conservative	conservative	ADJ
ap-5981	356	9	and	and	CCONJ
ap-5981	356	10	dissipative	dissipative	ADJ
ap-5981	356	11	mechanical	mechanical	ADJ
ap-5981	356	12	systems	system	NOUN
ap-5981	356	13	.	.	PUNCT
ap-5981	357	1	international	international	ADJ
ap-5981	357	2	journal	journal	PROPN
ap-5981	357	3	for	for	ADP
ap-5981	357	4	numerical	numerical	ADJ
ap-5981	357	5	methods	method	NOUN
ap-5981	357	6	in	in	ADP
ap-5981	357	7	engineering	engineer	VERB
ap-5981	357	8	49(10):1295–1325	49(10):1295–1325	PROPN
ap-5981	357	9	,	,	PUNCT
ap-5981	357	10	2000	2000	NUM
ap-5981	357	11	.	.	PUNCT
ap-5981	358	1	doi:10.1002/1097	doi:10.1002/1097	PROPN
ap-5981	358	2	-	-	PUNCT
ap-5981	358	3	0207(20001210)49:10<1295::aidnme993>3.0.co;2	0207(20001210)49:10<1295::aidnme993>3.0.co;2	NUM
ap-5981	358	4	-	-	PUNCT
ap-5981	358	5	w.	w.	NOUN
ap-5981	358	6	[	[	X
ap-5981	358	7	19	19	NUM
ap-5981	358	8	]	]	X
ap-5981	358	9	b.	b.	PROPN
ap-5981	358	10	bourdin	bourdin	PROPN
ap-5981	358	11	,	,	PUNCT
ap-5981	358	12	g.	g.	PROPN
ap-5981	358	13	a.	a.	PROPN
ap-5981	358	14	francfort	francfort	PROPN
ap-5981	358	15	,	,	PUNCT
ap-5981	358	16	j.-j	j.-j	PROPN
ap-5981	358	17	.	.	PUNCT
ap-5981	359	1	marigo	marigo	PROPN
ap-5981	359	2	.	.	PUNCT
ap-5981	360	1	the	the	DET
ap-5981	360	2	variational	variational	ADJ
ap-5981	360	3	approach	approach	NOUN
ap-5981	360	4	to	to	ADP
ap-5981	360	5	fracture	fracture	NOUN
ap-5981	360	6	.	.	PUNCT
ap-5981	361	1	journal	journal	PROPN
ap-5981	361	2	of	of	ADP
ap-5981	361	3	elasticity	elasticity	NOUN
ap-5981	361	4	91(1	91(1	NOUN
ap-5981	361	5	-	-	PUNCT
ap-5981	361	6	3):5–148	3):5–148	NUM
ap-5981	361	7	,	,	PUNCT
ap-5981	361	8	2008	2008	NUM
ap-5981	361	9	.	.	PUNCT
ap-5981	362	1	doi:10.1007	doi:10.1007	VERB
ap-5981	362	2	/	/	SYM
ap-5981	362	3	s10659	s10659	NOUN
ap-5981	362	4	-	-	PUNCT
ap-5981	362	5	007	007	NUM
ap-5981	362	6	-	-	PUNCT
ap-5981	362	7	9107	9107	NUM
ap-5981	362	8	-	-	SYM
ap-5981	362	9	3	3	NUM
ap-5981	362	10	.	.	PUNCT
ap-5981	363	1	[	[	X
ap-5981	363	2	20	20	NUM
ap-5981	363	3	]	]	PUNCT
ap-5981	363	4	m.	m.	NOUN
ap-5981	363	5	buliga	buliga	PROPN
ap-5981	363	6	.	.	PUNCT
ap-5981	364	1	hamiltonian	hamiltonian	ADJ
ap-5981	364	2	inclusions	inclusion	NOUN
ap-5981	364	3	with	with	ADP
ap-5981	364	4	convex	convex	ADJ
ap-5981	364	5	dissipation	dissipation	NOUN
ap-5981	364	6	with	with	ADP
ap-5981	364	7	a	a	DET
ap-5981	364	8	view	view	NOUN
ap-5981	364	9	towards	towards	ADP
ap-5981	364	10	applications	application	NOUN
ap-5981	364	11	.	.	PUNCT
ap-5981	365	1	annals	annal	NOUN
ap-5981	365	2	of	of	ADP
ap-5981	365	3	the	the	DET
ap-5981	365	4	academy	academy	NOUN
ap-5981	365	5	of	of	ADP
ap-5981	365	6	romanian	romanian	ADJ
ap-5981	365	7	scientists	scientist	NOUN
ap-5981	365	8	series	series	NOUN
ap-5981	365	9	on	on	ADP
ap-5981	365	10	mathematics	mathematic	NOUN
ap-5981	365	11	and	and	CCONJ
ap-5981	365	12	its	its	PRON
ap-5981	365	13	applications	application	NOUN
ap-5981	365	14	1(2):228–251	1(2):228–251	NUM
ap-5981	365	15	,	,	PUNCT
ap-5981	365	16	2009	2009	NUM
ap-5981	365	17	.	.	PUNCT
ap-5981	366	1	510	510	NUM
ap-5981	366	2	http://dx.doi.org/10.1016/j.ijmecsci.2012.12.019	http://dx.doi.org/10.1016/j.ijmecsci.2012.12.019	PROPN
ap-5981	366	3	http://dx.doi.org/10.1016/j.ijmecsci.2017.05.035	http://dx.doi.org/10.1016/j.ijmecsci.2017.05.035	PROPN
ap-5981	366	4	http://dx.doi.org/10.12989/sem.2018.65.4.369	http://dx.doi.org/10.12989/sem.2018.65.4.369	PROPN
ap-5981	366	5	http://dx.doi.org/10.1016/j.conbuildmat.2014.04.003	http://dx.doi.org/10.1016/j.conbuildmat.2014.04.003	PROPN
ap-5981	366	6	http://dx.doi.org/10.1016/j.polymertesting.2014.04.011	http://dx.doi.org/10.1016/j.polymertesting.2014.04.011	NOUN
ap-5981	366	7	http://dx.doi.org/10.1016/j.euromechsol.2017.01.006	http://dx.doi.org/10.1016/j.euromechsol.2017.01.006	ADJ
ap-5981	366	8	http://dx.doi.org/10.3390/ma12142241	http://dx.doi.org/10.3390/ma12142241	NOUN
ap-5981	366	9	http://dx.doi.org/10.1016/j.ijsolstr.2007.07.009	http://dx.doi.org/10.1016/j.ijsolstr.2007.07.009	PROPN
ap-5981	366	10	http://dx.doi.org/10.1115/1.4023929	http://dx.doi.org/10.1115/1.4023929	PROPN
ap-5981	366	11	http://dx.doi.org/10.1016/j.compositesb.2018.05.032	http://dx.doi.org/10.1016/j.compositesb.2018.05.032	PROPN
ap-5981	366	12	http://dx.doi.org/10.1016/0020-7403(68)90022-2	http://dx.doi.org/10.1016/0020-7403(68)90022-2	PROPN
ap-5981	366	13	http://dx.doi.org/10.1007/978-94-024-1138-6	http://dx.doi.org/10.1007/978-94-024-1138-6	PROPN
ap-5981	366	14	http://dx.doi.org/10.1002/1097-0207(20001210)49:10<1295::aid-nme993>3.0.co;2-w	http://dx.doi.org/10.1002/1097-0207(20001210)49:10<1295::aid-nme993>3.0.co;2-w	PROPN
ap-5981	366	15	http://dx.doi.org/10.1002/1097-0207(20001210)49:10<1295::aid-nme993>3.0.co;2-w	http://dx.doi.org/10.1002/1097-0207(20001210)49:10<1295::aid-nme993>3.0.co;2-w	PROPN
ap-5981	366	16	http://dx.doi.org/10.1007/s10659-007-9107-3	http://dx.doi.org/10.1007/s10659-007-9107-3	PROPN
ap-5981	366	17	vol	vol	NOUN
ap-5981	366	18	.	.	PUNCT
ap-5981	367	1	60	60	NUM
ap-5981	367	2	no	no	INTJ
ap-5981	367	3	.	.	PUNCT
ap-5981	368	1	6/2020	6/2020	NUM
ap-5981	368	2	newmark	newmark	NOUN
ap-5981	368	3	algorithm	algorithm	NOUN
ap-5981	368	4	for	for	ADP
ap-5981	368	5	dynamic	dynamic	ADJ
ap-5981	368	6	analysis	analysis	NOUN
ap-5981	368	7	of	of	ADP
ap-5981	368	8	viscoelastic	viscoelastic	ADJ
ap-5981	368	9	materials	material	NOUN
ap-5981	368	10	[	[	X
ap-5981	368	11	21	21	NUM
ap-5981	368	12	]	]	X
ap-5981	368	13	b.	b.	PROPN
ap-5981	368	14	bourdin	bourdin	PROPN
ap-5981	368	15	,	,	PUNCT
ap-5981	368	16	c.	c.	PROPN
ap-5981	368	17	j.	j.	PROPN
ap-5981	368	18	larsen	larsen	PROPN
ap-5981	368	19	,	,	PUNCT
ap-5981	368	20	c.	c.	PROPN
ap-5981	368	21	l.	l.	PROPN
ap-5981	368	22	richardson	richardson	PROPN
ap-5981	368	23	.	.	PUNCT
ap-5981	369	1	a	a	DET
ap-5981	369	2	time	time	NOUN
ap-5981	369	3	-	-	PUNCT
ap-5981	369	4	discrete	discrete	ADJ
ap-5981	369	5	model	model	NOUN
ap-5981	369	6	for	for	ADP
ap-5981	369	7	dynamic	dynamic	ADJ
ap-5981	369	8	fracture	fracture	NOUN
ap-5981	369	9	based	base	VERB
ap-5981	369	10	on	on	ADP
ap-5981	369	11	crack	crack	NOUN
ap-5981	369	12	regularization	regularization	NOUN
ap-5981	369	13	.	.	PUNCT
ap-5981	370	1	international	international	ADJ
ap-5981	370	2	journal	journal	NOUN
ap-5981	370	3	of	of	ADP
ap-5981	370	4	fracture	fracture	PROPN
ap-5981	370	5	168(2):133–143	168(2):133–143	NUM
ap-5981	370	6	,	,	PUNCT
ap-5981	370	7	2011	2011	NUM
ap-5981	370	8	.	.	PUNCT
ap-5981	371	1	doi:10.1007	doi:10.1007	VERB
ap-5981	371	2	/	/	SYM
ap-5981	371	3	s10704	s10704	NOUN
ap-5981	371	4	-	-	PUNCT
ap-5981	371	5	010	010	NUM
ap-5981	371	6	-	-	PUNCT
ap-5981	371	7	9562	9562	NUM
ap-5981	371	8	-	-	PUNCT
ap-5981	371	9	x.	x.	NOUN
ap-5981	372	1	[	[	X
ap-5981	372	2	22	22	NUM
ap-5981	372	3	]	]	PUNCT
ap-5981	372	4	a.	a.	NOUN
ap-5981	372	5	bedford	bedford	PROPN
ap-5981	372	6	.	.	PUNCT
ap-5981	373	1	hamilton	hamilton	PROPN
ap-5981	373	2	’s	’s	PART
ap-5981	373	3	principle	principle	NOUN
ap-5981	373	4	in	in	ADP
ap-5981	373	5	continuum	continuum	ADJ
ap-5981	373	6	mechanics	mechanic	NOUN
ap-5981	373	7	.	.	PUNCT
ap-5981	374	1	pitman	pitman	NOUN
ap-5981	374	2	publishing	publishing	PROPN
ap-5981	374	3	,	,	PUNCT
ap-5981	374	4	boston	boston	PROPN
ap-5981	374	5	,	,	PUNCT
ap-5981	374	6	1985	1985	NUM
ap-5981	374	7	.	.	PUNCT
ap-5981	375	1	[	[	X
ap-5981	375	2	23	23	NUM
ap-5981	375	3	]	]	PUNCT
ap-5981	375	4	a.	a.	NOUN
ap-5981	375	5	mielke	mielke	PROPN
ap-5981	375	6	,	,	PUNCT
ap-5981	375	7	t.	t.	NOUN
ap-5981	375	8	roubíček	roubíček	NOUN
ap-5981	375	9	.	.	PUNCT
ap-5981	376	1	rate	rate	NOUN
ap-5981	376	2	-	-	PUNCT
ap-5981	376	3	independent	independent	ADJ
ap-5981	376	4	systems	system	NOUN
ap-5981	376	5	:	:	PUNCT
ap-5981	376	6	theory	theory	NOUN
ap-5981	376	7	and	and	CCONJ
ap-5981	376	8	application	application	NOUN
ap-5981	376	9	,	,	PUNCT
ap-5981	376	10	vol	vol	NOUN
ap-5981	376	11	.	.	PROPN
ap-5981	376	12	655	655	NUM
ap-5981	376	13	of	of	ADP
ap-5981	376	14	applied	apply	VERB
ap-5981	376	15	mathematical	mathematical	ADJ
ap-5981	376	16	sciences	science	NOUN
ap-5981	376	17	.	.	PUNCT
ap-5981	377	1	springer	springer	NOUN
ap-5981	377	2	,	,	PUNCT
ap-5981	377	3	new	new	PROPN
ap-5981	377	4	york	york	PROPN
ap-5981	377	5	,	,	PUNCT
ap-5981	377	6	2015	2015	NUM
ap-5981	377	7	.	.	PUNCT
ap-5981	378	1	doi:10.1007/978	doi:10.1007/978	NOUN
ap-5981	378	2	-	-	PUNCT
ap-5981	378	3	1	1	NUM
ap-5981	378	4	-	-	PUNCT
ap-5981	378	5	4939	4939	NUM
ap-5981	378	6	-	-	PUNCT
ap-5981	378	7	2706	2706	NUM
ap-5981	378	8	-	-	SYM
ap-5981	378	9	7	7	NUM
ap-5981	378	10	.	.	PUNCT
ap-5981	379	1	[	[	X
ap-5981	379	2	24	24	NUM
ap-5981	379	3	]	]	PUNCT
ap-5981	379	4	j.	j.	PROPN
ap-5981	379	5	schmidt	schmidt	PROPN
ap-5981	379	6	,	,	PUNCT
ap-5981	379	7	t.	t.	PROPN
ap-5981	379	8	janda	janda	PROPN
ap-5981	379	9	,	,	PUNCT
ap-5981	379	10	a.	a.	PROPN
ap-5981	379	11	zemanová	zemanová	PROPN
ap-5981	379	12	,	,	PUNCT
ap-5981	379	13	et	et	PROPN
ap-5981	379	14	al	al	PROPN
ap-5981	379	15	.	.	PUNCT
ap-5981	380	1	source	source	NOUN
ap-5981	380	2	codes	code	NOUN
ap-5981	380	3	for	for	ADP
ap-5981	380	4	preprint	preprint	NOUN
ap-5981	380	5	newmark	newmark	NOUN
ap-5981	380	6	algorithm	algorithm	NOUN
ap-5981	380	7	for	for	ADP
ap-5981	380	8	dynamic	dynamic	ADJ
ap-5981	380	9	analysis	analysis	NOUN
ap-5981	380	10	with	with	ADP
ap-5981	380	11	maxwell	maxwell	PROPN
ap-5981	380	12	chain	chain	NOUN
ap-5981	380	13	model	model	NOUN
ap-5981	380	14	,	,	PUNCT
ap-5981	380	15	2019	2019	NUM
ap-5981	380	16	.	.	PUNCT
ap-5981	381	1	doi:10.5281	doi:10.5281	PROPN
ap-5981	381	2	/	/	SYM
ap-5981	381	3	zenodo.3531802	zenodo.3531802	PROPN
ap-5981	381	4	.	.	PUNCT
ap-5981	382	1	[	[	X
ap-5981	382	2	25	25	NUM
ap-5981	382	3	]	]	X
ap-5981	382	4	l.	l.	PROPN
ap-5981	382	5	petzold	petzold	PROPN
ap-5981	382	6	.	.	PUNCT
ap-5981	382	7	automatic	automatic	ADJ
ap-5981	382	8	selection	selection	NOUN
ap-5981	382	9	of	of	ADP
ap-5981	382	10	methods	method	NOUN
ap-5981	382	11	for	for	ADP
ap-5981	382	12	solving	solve	VERB
ap-5981	382	13	stiff	stiff	ADJ
ap-5981	382	14	and	and	CCONJ
ap-5981	382	15	nonstiff	nonstiff	NOUN
ap-5981	382	16	systems	system	NOUN
ap-5981	382	17	of	of	ADP
ap-5981	382	18	ordinary	ordinary	ADJ
ap-5981	382	19	differential	differential	ADJ
ap-5981	382	20	equations	equation	NOUN
ap-5981	382	21	.	.	PUNCT
ap-5981	383	1	siam	siam	PROPN
ap-5981	383	2	journal	journal	PROPN
ap-5981	383	3	on	on	ADP
ap-5981	383	4	scientific	scientific	ADJ
ap-5981	383	5	and	and	CCONJ
ap-5981	383	6	statistical	statistical	ADJ
ap-5981	383	7	computing	computing	NOUN
ap-5981	383	8	4(1):136–148	4(1):136–148	NOUN
ap-5981	383	9	,	,	PUNCT
ap-5981	383	10	1983	1983	NUM
ap-5981	383	11	.	.	PUNCT
ap-5981	384	1	doi:10.1137/0904010	doi:10.1137/0904010	NOUN
ap-5981	384	2	.	.	PUNCT
ap-5981	385	1	[	[	X
ap-5981	385	2	26	26	NUM
ap-5981	385	3	]	]	PUNCT
ap-5981	385	4	e.	e.	PROPN
ap-5981	385	5	jones	jones	PROPN
ap-5981	385	6	,	,	PUNCT
ap-5981	385	7	t.	t.	PROPN
ap-5981	385	8	oliphant	oliphant	PROPN
ap-5981	385	9	,	,	PUNCT
ap-5981	385	10	p.	p.	PROPN
ap-5981	385	11	peterson	peterson	PROPN
ap-5981	385	12	,	,	PUNCT
ap-5981	385	13	et	et	PROPN
ap-5981	385	14	al	al	PROPN
ap-5981	385	15	.	.	PROPN
ap-5981	385	16	scipy	scipy	PROPN
ap-5981	385	17	:	:	PUNCT
ap-5981	385	18	open	open	ADJ
ap-5981	385	19	source	source	NOUN
ap-5981	385	20	scientific	scientific	ADJ
ap-5981	385	21	tools	tool	NOUN
ap-5981	385	22	for	for	ADP
ap-5981	385	23	python	python	NOUN
ap-5981	385	24	,	,	PUNCT
ap-5981	385	25	2001–.	2001–.	NOUN
ap-5981	385	26	http://www.scipy.org	http://www.scipy.org	NOUN
ap-5981	385	27	,	,	PUNCT
ap-5981	385	28	[	[	X
ap-5981	385	29	accessed	access	VERB
ap-5981	385	30	january	january	PROPN
ap-5981	385	31	12	12	NUM
ap-5981	385	32	,	,	PUNCT
ap-5981	385	33	2021	2021	NUM
ap-5981	385	34	]	]	PUNCT
ap-5981	385	35	.	.	PUNCT
ap-5981	386	1	[	[	X
ap-5981	386	2	27	27	NUM
ap-5981	386	3	]	]	PUNCT
ap-5981	386	4	t.	t.	PROPN
ap-5981	386	5	j.	j.	PROPN
ap-5981	386	6	r.	r.	PROPN
ap-5981	386	7	hughes	hughes	PROPN
ap-5981	386	8	.	.	PUNCT
ap-5981	387	1	analysis	analysis	NOUN
ap-5981	387	2	of	of	ADP
ap-5981	387	3	transient	transient	ADJ
ap-5981	387	4	algorithms	algorithm	NOUN
ap-5981	387	5	with	with	ADP
ap-5981	387	6	particular	particular	ADJ
ap-5981	387	7	reference	reference	NOUN
ap-5981	387	8	to	to	ADP
ap-5981	387	9	stability	stability	NOUN
ap-5981	387	10	behavior	behavior	NOUN
ap-5981	387	11	.	.	PUNCT
ap-5981	388	1	in	in	ADP
ap-5981	388	2	t.	t.	PROPN
ap-5981	388	3	belytschko	belytschko	PROPN
ap-5981	388	4	,	,	PUNCT
ap-5981	388	5	t.	t.	PROPN
ap-5981	388	6	j.	j.	PROPN
ap-5981	388	7	r.	r.	PROPN
ap-5981	388	8	hughes	hughes	PROPN
ap-5981	388	9	(	(	PUNCT
ap-5981	388	10	eds	eds	PROPN
ap-5981	388	11	.	.	PUNCT
ap-5981	388	12	)	)	PUNCT
ap-5981	388	13	,	,	PUNCT
ap-5981	388	14	computational	computational	ADJ
ap-5981	388	15	methods	method	NOUN
ap-5981	388	16	for	for	ADP
ap-5981	388	17	transient	transient	ADJ
ap-5981	388	18	analysis	analysis	NOUN
ap-5981	388	19	,	,	PUNCT
ap-5981	388	20	chap	chap	NOUN
ap-5981	388	21	.	.	PUNCT
ap-5981	389	1	2	2	NUM
ap-5981	389	2	,	,	PUNCT
ap-5981	389	3	pp	pp	ADJ
ap-5981	389	4	.	.	PUNCT
ap-5981	390	1	67–155	67–155	NOUN
ap-5981	390	2	.	.	PUNCT
ap-5981	391	1	north	north	NOUN
ap-5981	391	2	-	-	PUNCT
ap-5981	391	3	holland	holland	PROPN
ap-5981	391	4	,	,	PUNCT
ap-5981	391	5	amsterdam	amsterdam	PROPN
ap-5981	391	6	,	,	PUNCT
ap-5981	391	7	1983	1983	NUM
ap-5981	391	8	.	.	PUNCT
ap-5981	392	1	[	[	X
ap-5981	392	2	28	28	NUM
ap-5981	392	3	]	]	PUNCT
ap-5981	392	4	a.	a.	NOUN
ap-5981	392	5	logg	logg	PROPN
ap-5981	392	6	,	,	PUNCT
ap-5981	392	7	k.-a	k.-a	PROPN
ap-5981	392	8	.	.	PUNCT
ap-5981	392	9	mardal	mardal	PROPN
ap-5981	392	10	,	,	PUNCT
ap-5981	392	11	g.	g.	PROPN
ap-5981	392	12	wells	wells	PROPN
ap-5981	392	13	(	(	PUNCT
ap-5981	392	14	eds	eds	PROPN
ap-5981	392	15	.	.	PUNCT
ap-5981	392	16	)	)	PUNCT
ap-5981	392	17	.	.	PUNCT
ap-5981	393	1	automated	automate	VERB
ap-5981	393	2	solution	solution	NOUN
ap-5981	393	3	of	of	ADP
ap-5981	393	4	differential	differential	ADJ
ap-5981	393	5	equations	equation	NOUN
ap-5981	393	6	by	by	ADP
ap-5981	393	7	the	the	DET
ap-5981	393	8	finite	finite	PROPN
ap-5981	393	9	element	element	NOUN
ap-5981	393	10	method	method	NOUN
ap-5981	393	11	:	:	PUNCT
ap-5981	393	12	the	the	DET
ap-5981	393	13	fenics	fenics	PROPN
ap-5981	393	14	book	book	NOUN
ap-5981	393	15	.	.	PUNCT
ap-5981	394	1	lecture	lecture	NOUN
ap-5981	394	2	notes	note	NOUN
ap-5981	394	3	in	in	ADP
ap-5981	394	4	computational	computational	ADJ
ap-5981	394	5	science	science	NOUN
ap-5981	394	6	and	and	CCONJ
ap-5981	394	7	engineering	engineering	NOUN
ap-5981	394	8	.	.	PUNCT
ap-5981	395	1	springer	springer	NOUN
ap-5981	395	2	-	-	PUNCT
ap-5981	395	3	verlag	verlag	PROPN
ap-5981	395	4	,	,	PUNCT
ap-5981	395	5	berlin	berlin	PROPN
ap-5981	395	6	heidelberg	heidelberg	PROPN
ap-5981	395	7	,	,	PUNCT
ap-5981	395	8	2012	2012	NUM
ap-5981	395	9	.	.	PUNCT
ap-5981	396	1	doi:10.1007/978	doi:10.1007/978	ADJ
ap-5981	396	2	-	-	PUNCT
ap-5981	396	3	3	3	NUM
ap-5981	396	4	-	-	PUNCT
ap-5981	396	5	642	642	NUM
ap-5981	396	6	-	-	PUNCT
ap-5981	396	7	23099	23099	NUM
ap-5981	396	8	-	-	SYM
ap-5981	396	9	8	8	NUM
ap-5981	396	10	.	.	PUNCT
ap-5981	397	1	[	[	X
ap-5981	397	2	29	29	NUM
ap-5981	397	3	]	]	PUNCT
ap-5981	397	4	m.	m.	NOUN
ap-5981	397	5	s.	s.	PROPN
ap-5981	397	6	alnæs	alnæs	PROPN
ap-5981	397	7	,	,	PUNCT
ap-5981	397	8	j.	j.	PROPN
ap-5981	397	9	blechta	blechta	PROPN
ap-5981	397	10	,	,	PUNCT
ap-5981	397	11	j.	j.	PROPN
ap-5981	397	12	hake	hake	PROPN
ap-5981	397	13	,	,	PUNCT
ap-5981	397	14	et	et	PROPN
ap-5981	397	15	al	al	PROPN
ap-5981	397	16	.	.	PUNCT
ap-5981	398	1	the	the	DET
ap-5981	398	2	fenics	fenics	PROPN
ap-5981	398	3	project	project	VERB
ap-5981	398	4	version	version	NOUN
ap-5981	398	5	1.5	1.5	NUM
ap-5981	398	6	.	.	PUNCT
ap-5981	399	1	archive	archive	NOUN
ap-5981	399	2	of	of	ADP
ap-5981	399	3	numerical	numerical	ADJ
ap-5981	399	4	software	software	PROPN
ap-5981	399	5	3(100	3(100	NUM
ap-5981	399	6	)	)	PUNCT
ap-5981	399	7	,	,	PUNCT
ap-5981	399	8	2015	2015	NUM
ap-5981	399	9	.	.	PUNCT
ap-5981	400	1	doi:10.11588	doi:10.11588	ADV
ap-5981	400	2	/	/	SYM
ap-5981	400	3	ans.2015.100.20553	ans.2015.100.20553	NOUN
ap-5981	400	4	.	.	PUNCT
ap-5981	401	1	[	[	X
ap-5981	401	2	30	30	NUM
ap-5981	401	3	]	]	PUNCT
ap-5981	401	4	t.	t.	PROPN
ap-5981	401	5	li	li	PROPN
ap-5981	401	6	,	,	PUNCT
ap-5981	401	7	j.-j	j.-j	PROPN
ap-5981	401	8	.	.	PUNCT
ap-5981	402	1	marigo	marigo	PROPN
ap-5981	402	2	,	,	PUNCT
ap-5981	402	3	d.	d.	PROPN
ap-5981	402	4	guilbaud	guilbaud	PROPN
ap-5981	402	5	,	,	PUNCT
ap-5981	402	6	s.	s.	PROPN
ap-5981	402	7	potapov	potapov	PROPN
ap-5981	402	8	.	.	PUNCT
ap-5981	403	1	numerical	numerical	PROPN
ap-5981	403	2	investigation	investigation	NOUN
ap-5981	403	3	of	of	ADP
ap-5981	403	4	dynamic	dynamic	ADJ
ap-5981	403	5	brittle	brittle	ADJ
ap-5981	403	6	fracture	fracture	NOUN
ap-5981	403	7	via	via	ADP
ap-5981	403	8	gradient	gradient	ADJ
ap-5981	403	9	damage	damage	NOUN
ap-5981	403	10	models	model	NOUN
ap-5981	403	11	.	.	PUNCT
ap-5981	404	1	advanced	advanced	ADJ
ap-5981	404	2	modeling	modeling	NOUN
ap-5981	404	3	and	and	CCONJ
ap-5981	404	4	simulation	simulation	NOUN
ap-5981	404	5	in	in	ADP
ap-5981	404	6	engineering	engineering	NOUN
ap-5981	404	7	sciences	science	NOUN
ap-5981	404	8	3(1):26	3(1):26	NUM
ap-5981	404	9	,	,	PUNCT
ap-5981	404	10	2016	2016	NUM
ap-5981	404	11	.	.	PUNCT
ap-5981	405	1	doi:10.1186	doi:10.1186	PROPN
ap-5981	405	2	/	/	SYM
ap-5981	405	3	s40323	s40323	NOUN
ap-5981	405	4	-	-	PUNCT
ap-5981	405	5	016	016	NUM
ap-5981	405	6	-	-	PUNCT
ap-5981	405	7	0080	0080	NUM
ap-5981	405	8	-	-	PUNCT
ap-5981	405	9	x.	x.	NOUN
ap-5981	406	1	[	[	X
ap-5981	406	2	31	31	NUM
ap-5981	406	3	]	]	PUNCT
ap-5981	406	4	t.	t.	NOUN
ap-5981	406	5	roubíček	roubíček	NOUN
ap-5981	406	6	.	.	PUNCT
ap-5981	407	1	models	model	NOUN
ap-5981	407	2	of	of	ADP
ap-5981	407	3	dynamic	dynamic	ADJ
ap-5981	407	4	damage	damage	NOUN
ap-5981	407	5	and	and	CCONJ
ap-5981	407	6	phasefield	phasefield	NOUN
ap-5981	407	7	fracture	fracture	NOUN
ap-5981	407	8	,	,	PUNCT
ap-5981	407	9	and	and	CCONJ
ap-5981	407	10	their	their	PRON
ap-5981	407	11	various	various	ADJ
ap-5981	407	12	time	time	NOUN
ap-5981	407	13	discretisations	discretisation	NOUN
ap-5981	407	14	.	.	PUNCT
ap-5981	408	1	in	in	ADP
ap-5981	408	2	m.	m.	NOUN
ap-5981	408	3	hintermüller	hintermüller	NOUN
ap-5981	408	4	,	,	PUNCT
ap-5981	408	5	j.	j.	PROPN
ap-5981	408	6	f.	f.	PROPN
ap-5981	408	7	rodrigues	rodrigues	PROPN
ap-5981	408	8	(	(	PUNCT
ap-5981	408	9	eds	ed	NOUN
ap-5981	408	10	.	.	PUNCT
ap-5981	408	11	)	)	PUNCT
ap-5981	409	1	,	,	PUNCT
ap-5981	409	2	topics	topic	NOUN
ap-5981	409	3	in	in	ADP
ap-5981	409	4	applied	apply	VERB
ap-5981	409	5	analysis	analysis	NOUN
ap-5981	409	6	and	and	CCONJ
ap-5981	409	7	optimisation	optimisation	NOUN
ap-5981	409	8	,	,	PUNCT
ap-5981	409	9	pp	pp	ADP
ap-5981	409	10	.	.	PUNCT
ap-5981	410	1	363–396	363–396	NUM
ap-5981	410	2	.	.	PUNCT
ap-5981	411	1	springer	springer	NOUN
ap-5981	411	2	international	international	ADJ
ap-5981	411	3	publishing	publishing	NOUN
ap-5981	411	4	,	,	PUNCT
ap-5981	411	5	cham	cham	NOUN
ap-5981	411	6	,	,	PUNCT
ap-5981	411	7	2019	2019	NUM
ap-5981	411	8	.	.	PUNCT
ap-5981	412	1	511	511	NUM
ap-5981	412	2	http://dx.doi.org/10.1007/s10704-010-9562-x	http://dx.doi.org/10.1007/s10704-010-9562-x	PROPN
ap-5981	412	3	http://dx.doi.org/10.1007/978-1-4939-2706-7	http://dx.doi.org/10.1007/978-1-4939-2706-7	PROPN
ap-5981	412	4	http://dx.doi.org/10.5281/zenodo.3531802	http://dx.doi.org/10.5281/zenodo.3531802	X
ap-5981	412	5	http://dx.doi.org/10.1137/0904010	http://dx.doi.org/10.1137/0904010	PROPN
ap-5981	412	6	http://www.scipy.org	http://www.scipy.org	PROPN
ap-5981	412	7	http://dx.doi.org/10.1007/978-3-642-23099-8	http://dx.doi.org/10.1007/978-3-642-23099-8	PROPN
ap-5981	413	1	http://dx.doi.org/10.11588/ans.2015.100.20553	http://dx.doi.org/10.11588/ans.2015.100.20553	PROPN
ap-5981	413	2	http://dx.doi.org/10.1186/s40323-016-0080-x	http://dx.doi.org/10.1186/s40323-016-0080-x	PROPN
ap-5981	413	3	acta	acta	PROPN
ap-5981	413	4	polytechnica	polytechnica	PROPN
ap-5981	413	5	60(6):502–511	60(6):502–511	PROPN
ap-5981	413	6	,	,	PUNCT
ap-5981	413	7	2020	2020	NUM
ap-5981	413	8	1	1	NUM
ap-5981	413	9	introduction	introduction	NOUN
ap-5981	413	10	2	2	NUM
ap-5981	413	11	newmark	newmark	NOUN
ap-5981	413	12	method	method	NOUN
ap-5981	413	13	2.1	2.1	NUM
ap-5981	413	14	governing	governing	NOUN
ap-5981	413	15	equations	equation	NOUN
ap-5981	413	16	2.2	2.2	NUM
ap-5981	413	17	discretization	discretization	NOUN
ap-5981	413	18	3	3	NUM
ap-5981	413	19	variational	variational	ADJ
ap-5981	413	20	integrators	integrator	NOUN
ap-5981	413	21	3.1	3.1	NUM
ap-5981	413	22	variational	variational	ADJ
ap-5981	413	23	framework	framework	NOUN
ap-5981	413	24	3.2	3.2	NUM
ap-5981	413	25	discretization	discretization	NOUN
ap-5981	413	26	3.3	3.3	NUM
ap-5981	413	27	equivalence	equivalence	NOUN
ap-5981	413	28	to	to	ADP
ap-5981	413	29	newmark	newmark	PROPN
ap-5981	413	30	3.4	3.4	NUM
ap-5981	413	31	energy	energy	NOUN
ap-5981	413	32	balance	balance	NOUN
ap-5981	413	33	4	4	NUM
ap-5981	413	34	examples	example	NOUN
ap-5981	413	35	4.1	4.1	NUM
ap-5981	413	36	discrete	discrete	ADJ
ap-5981	413	37	problem	problem	NOUN
ap-5981	413	38	4.2	4.2	NUM
ap-5981	413	39	generalization	generalization	NOUN
ap-5981	413	40	5	5	NUM
ap-5981	413	41	conclusions	conclusion	NOUN
ap-5981	413	42	acknowledgements	acknowledgement	NOUN
ap-5981	413	43	references	reference	NOUN