id	sid	tid	token	lemma	pos
cana-4140	1	1	communications	communication	NOUN
cana-4140	1	2	on	on	ADP
cana-4140	1	3	applied	apply	VERB
cana-4140	1	4	nonlinear	nonlinear	ADJ
cana-4140	1	5	analysis	analysis	NOUN
cana-4140	1	6	issn	issn	NOUN
cana-4140	1	7	:	:	PUNCT
cana-4140	1	8	1074	1074	NUM
cana-4140	1	9	-	-	PUNCT
cana-4140	1	10	133x	133x	NUM
cana-4140	1	11	vol	vol	NOUN
cana-4140	1	12	32	32	NUM
cana-4140	1	13	no	no	NOUN
cana-4140	1	14	.	.	NOUN
cana-4140	1	15	9(s	9(s	NUM
cana-4140	1	16	)	)	PUNCT
cana-4140	1	17	(	(	PUNCT
cana-4140	1	18	2025	2025	NUM
cana-4140	1	19	)	)	PUNCT
cana-4140	1	20	1312	1312	NUM
cana-4140	1	21	https://internationalpubls.com	https://internationalpubls.com	X
cana-4140	1	22	thermal	thermal	ADJ
cana-4140	1	23	stress	stress	NOUN
cana-4140	1	24	analysis	analysis	NOUN
cana-4140	1	25	of	of	ADP
cana-4140	1	26	two	two	NUM
cana-4140	1	27	dimensional	dimensional	ADJ
cana-4140	1	28	thermoelastic	thermoelastic	ADJ
cana-4140	1	29	problem	problem	NOUN
cana-4140	1	30	for	for	ADP
cana-4140	1	31	inhomogeneous	inhomogeneous	ADJ
cana-4140	1	32	half	half	ADJ
cana-4140	1	33	plane	plane	NOUN
cana-4140	1	34	shamal	shamal	PROPN
cana-4140	1	35	d.	d.	PROPN
cana-4140	1	36	nirde1	nirde1	PROPN
cana-4140	1	37	,	,	PUNCT
cana-4140	1	38	kirtiwant	kirtiwant	ADJ
cana-4140	1	39	p.	p.	PROPN
cana-4140	1	40	ghadle2	ghadle2	PROPN
cana-4140	1	41	,	,	PUNCT
cana-4140	1	42	aishwary	aishwary	PROPN
cana-4140	2	1	k.	k.	PROPN
cana-4140	2	2	ghadle3	ghadle3	PROPN
cana-4140	3	1	1,2department	1,2department	NUM
cana-4140	3	2	of	of	ADP
cana-4140	3	3	mathematics	mathematic	NOUN
cana-4140	3	4	,	,	PUNCT
cana-4140	3	5	dr	dr	PROPN
cana-4140	3	6	.	.	PROPN
cana-4140	3	7	babasaheb	babasaheb	PROPN
cana-4140	3	8	ambedkar	ambedkar	PROPN
cana-4140	3	9	marathwada	marathwada	PROPN
cana-4140	3	10	university	university	PROPN
cana-4140	3	11	,	,	PUNCT
cana-4140	3	12	chhatrapati	chhatrapati	NOUN
cana-4140	3	13	sambhajinagar	sambhajinagar	NOUN
cana-4140	3	14	431004(m.s.)-india	431004(m.s.)-india	NUM
cana-4140	3	15	.	.	PUNCT
cana-4140	4	1	3csmss	3csmss	NUM
cana-4140	4	2	,	,	PUNCT
cana-4140	4	3	chhatrapati	chhatrapati	NOUN
cana-4140	4	4	shahu	shahu	NOUN
cana-4140	4	5	college	college	PROPN
cana-4140	4	6	of	of	ADP
cana-4140	4	7	engineering	engineering	NOUN
cana-4140	4	8	,	,	PUNCT
cana-4140	4	9	chhatrapati	chhatrapati	NOUN
cana-4140	4	10	sambhajinagar-431002(m.s.)-india	sambhajinagar-431002(m.s.)-india	PROPN
cana-4140	4	11	,	,	PUNCT
cana-4140	4	12	1nirdeshamal@gmail.com	1nirdeshamal@gmail.com	NUM
cana-4140	4	13	,	,	PUNCT
cana-4140	4	14	2drkp.ghadle@gmail.com	2drkp.ghadle@gmail.com	NUM
cana-4140	4	15	,	,	PUNCT
cana-4140	4	16	3aishwaryghadle@gmail.com	3aishwaryghadle@gmail.com	PROPN
cana-4140	4	17	.	.	PUNCT
cana-4140	5	1	article	article	NOUN
cana-4140	5	2	history	history	NOUN
cana-4140	5	3	:	:	PUNCT
cana-4140	5	4	received	receive	VERB
cana-4140	5	5	:	:	PUNCT
cana-4140	5	6	12	12	NUM
cana-4140	5	7	-	-	SYM
cana-4140	5	8	01	01	NUM
cana-4140	5	9	-	-	PUNCT
cana-4140	5	10	2025	2025	NUM
cana-4140	5	11	revised	revise	VERB
cana-4140	5	12	:	:	PUNCT
cana-4140	5	13	15	15	NUM
cana-4140	5	14	-	-	NUM
cana-4140	5	15	02	02	NUM
cana-4140	5	16	-	-	PUNCT
cana-4140	5	17	2025	2025	NUM
cana-4140	5	18	accepted	accept	VERB
cana-4140	5	19	:	:	PUNCT
cana-4140	5	20	01	01	NUM
cana-4140	5	21	-	-	SYM
cana-4140	5	22	03	03	NUM
cana-4140	5	23	-	-	PUNCT
cana-4140	5	24	2025	2025	NUM
cana-4140	5	25	abstract	abstract	NOUN
cana-4140	5	26	:	:	PUNCT
cana-4140	5	27	this	this	DET
cana-4140	5	28	paper	paper	NOUN
cana-4140	5	29	develops	develop	VERB
cana-4140	5	30	a	a	DET
cana-4140	5	31	method	method	NOUN
cana-4140	5	32	for	for	ADP
cana-4140	5	33	analytically	analytically	ADV
cana-4140	5	34	solving	solve	VERB
cana-4140	5	35	plane	plane	NOUN
cana-4140	5	36	elasticity	elasticity	NOUN
cana-4140	5	37	and	and	CCONJ
cana-4140	5	38	thermo	thermo	NOUN
cana-4140	5	39	-	-	PUNCT
cana-4140	5	40	elasticity	elasticity	NOUN
cana-4140	5	41	problems	problem	NOUN
cana-4140	5	42	for	for	ADP
cana-4140	5	43	inhomogeneous	inhomogeneous	ADJ
cana-4140	5	44	half	half	ADJ
cana-4140	5	45	planes	plane	NOUN
cana-4140	5	46	.	.	PUNCT
cana-4140	6	1	with	with	ADP
cana-4140	6	2	the	the	DET
cana-4140	6	3	direct	direct	ADJ
cana-4140	6	4	integration	integration	NOUN
cana-4140	6	5	of	of	ADP
cana-4140	6	6	the	the	DET
cana-4140	6	7	equilibrium	equilibrium	NOUN
cana-4140	6	8	equation	equation	NOUN
cana-4140	6	9	,	,	PUNCT
cana-4140	6	10	the	the	DET
cana-4140	6	11	original	original	ADJ
cana-4140	6	12	problems	problem	NOUN
cana-4140	6	13	can	can	AUX
cana-4140	6	14	be	be	AUX
cana-4140	6	15	reduced	reduce	VERB
cana-4140	6	16	to	to	ADP
cana-4140	6	17	a	a	DET
cana-4140	6	18	set	set	NOUN
cana-4140	6	19	of	of	ADP
cana-4140	6	20	governing	govern	VERB
cana-4140	6	21	harmonic	harmonic	ADJ
cana-4140	6	22	equations	equation	NOUN
cana-4140	6	23	with	with	ADP
cana-4140	6	24	corresponding	corresponding	ADJ
cana-4140	6	25	boundary	boundary	ADJ
cana-4140	6	26	conditions	condition	NOUN
cana-4140	6	27	.	.	PUNCT
cana-4140	7	1	distribution	distribution	NOUN
cana-4140	7	2	of	of	ADP
cana-4140	7	3	young	young	ADJ
cana-4140	7	4	's	's	PART
cana-4140	7	5	modulus	modulus	NOUN
cana-4140	7	6	,	,	PUNCT
cana-4140	7	7	shearing	shearing	NOUN
cana-4140	7	8	modulus	modulus	NOUN
cana-4140	7	9	and	and	CCONJ
cana-4140	7	10	dimensionless	dimensionless	NOUN
cana-4140	7	11	stresses	stress	NOUN
cana-4140	7	12	are	be	AUX
cana-4140	7	13	illustrated	illustrate	VERB
cana-4140	7	14	numerically	numerically	ADV
cana-4140	7	15	and	and	CCONJ
cana-4140	7	16	shown	show	VERB
cana-4140	7	17	graphically	graphically	ADV
cana-4140	7	18	.	.	PUNCT
cana-4140	8	1	keywords	keyword	NOUN
cana-4140	8	2	:	:	PUNCT
cana-4140	8	3	thermal	thermal	ADJ
cana-4140	8	4	stress	stress	NOUN
cana-4140	8	5	,	,	PUNCT
cana-4140	8	6	isotropic	isotropic	NOUN
cana-4140	8	7	material	material	NOUN
cana-4140	8	8	,	,	PUNCT
cana-4140	8	9	inhomogeneous	inhomogeneous	ADJ
cana-4140	8	10	half	half	ADJ
cana-4140	8	11	plane	plane	NOUN
cana-4140	8	12	,	,	PUNCT
cana-4140	8	13	simple	simple	ADJ
cana-4140	8	14	iteration	iteration	NOUN
cana-4140	8	15	technique	technique	NOUN
cana-4140	8	16	,	,	PUNCT
cana-4140	8	17	integro	integro	ADJ
cana-4140	8	18	-	-	PUNCT
cana-4140	8	19	differential	differential	NOUN
cana-4140	8	20	equation	equation	NOUN
cana-4140	8	21	,	,	PUNCT
cana-4140	8	22	fourier	fourier	NOUN
cana-4140	8	23	transform	transform	VERB
cana-4140	8	24	1	1	NUM
cana-4140	8	25	.	.	PUNCT
cana-4140	9	1	introduction	introduction	NOUN
cana-4140	9	2	there	there	PRON
cana-4140	9	3	exist	exist	VERB
cana-4140	9	4	various	various	ADJ
cana-4140	9	5	methods	method	NOUN
cana-4140	9	6	for	for	ADP
cana-4140	9	7	analysis	analysis	NOUN
cana-4140	9	8	of	of	ADP
cana-4140	9	9	thermoelastic	thermoelastic	ADJ
cana-4140	9	10	problem	problem	NOUN
cana-4140	9	11	for	for	ADP
cana-4140	9	12	arbitrary	arbitrary	ADJ
cana-4140	9	13	inhomogeneous	inhomogeneous	ADJ
cana-4140	9	14	solids	solid	NOUN
cana-4140	9	15	with	with	ADP
cana-4140	9	16	boundary	boundary	ADJ
cana-4140	9	17	conditions	condition	NOUN
cana-4140	9	18	in	in	ADP
cana-4140	9	19	terms	term	NOUN
cana-4140	9	20	of	of	ADP
cana-4140	9	21	stresses	stress	NOUN
cana-4140	9	22	.	.	PUNCT
cana-4140	10	1	several	several	ADJ
cana-4140	10	2	analytical	analytical	ADJ
cana-4140	10	3	,	,	PUNCT
cana-4140	10	4	semi	semi	ADJ
cana-4140	10	5	-	-	ADJ
cana-4140	10	6	analytical	analytical	ADJ
cana-4140	10	7	approaches	approach	NOUN
cana-4140	10	8	were	be	AUX
cana-4140	10	9	developed	develop	VERB
cana-4140	10	10	for	for	ADP
cana-4140	10	11	solving	solve	VERB
cana-4140	10	12	the	the	DET
cana-4140	10	13	heat	heat	NOUN
cana-4140	10	14	conduction	conduction	NOUN
cana-4140	10	15	problems	problem	NOUN
cana-4140	10	16	.	.	PUNCT
cana-4140	11	1	explicit	explicit	ADJ
cana-4140	11	2	analytical	analytical	ADJ
cana-4140	11	3	solutions	solution	NOUN
cana-4140	11	4	are	be	AUX
cana-4140	11	5	restricted	restrict	VERB
cana-4140	11	6	to	to	ADP
cana-4140	11	7	simple	simple	ADJ
cana-4140	11	8	geometries	geometry	NOUN
cana-4140	11	9	but	but	CCONJ
cana-4140	11	10	these	these	PRON
cana-4140	11	11	are	be	AUX
cana-4140	11	12	well	well	ADV
cana-4140	11	13	organized	organize	VERB
cana-4140	11	14	computationally	computationally	ADV
cana-4140	11	15	.	.	PUNCT
cana-4140	12	1	exact	exact	ADJ
cana-4140	12	2	solutions	solution	NOUN
cana-4140	12	3	of	of	ADP
cana-4140	12	4	the	the	DET
cana-4140	12	5	inverse	inverse	ADJ
cana-4140	12	6	heat	heat	NOUN
cana-4140	12	7	conduction	conduction	NOUN
cana-4140	12	8	problems	problem	NOUN
cana-4140	12	9	are	be	AUX
cana-4140	12	10	significant	significant	ADJ
cana-4140	12	11	because	because	SCONJ
cana-4140	12	12	they	they	PRON
cana-4140	12	13	provide	provide	VERB
cana-4140	12	14	closed	closed	ADJ
cana-4140	12	15	form	form	NOUN
cana-4140	12	16	solution	solution	NOUN
cana-4140	12	17	for	for	ADP
cana-4140	12	18	heat	heat	NOUN
cana-4140	12	19	flux	flux	NOUN
cana-4140	12	20	in	in	ADP
cana-4140	12	21	terms	term	NOUN
cana-4140	12	22	of	of	ADP
cana-4140	12	23	temperature	temperature	NOUN
cana-4140	12	24	measurements	measurement	NOUN
cana-4140	12	25	.	.	PUNCT
cana-4140	13	1	in	in	ADP
cana-4140	13	2	this	this	DET
cana-4140	13	3	paper	paper	NOUN
cana-4140	13	4	we	we	PRON
cana-4140	13	5	extend	extend	VERB
cana-4140	13	6	the	the	DET
cana-4140	13	7	technique	technique	NOUN
cana-4140	13	8	to	to	PART
cana-4140	13	9	avoid	avoid	VERB
cana-4140	13	10	latter	latter	ADJ
cana-4140	13	11	complications	complication	NOUN
cana-4140	13	12	to	to	PART
cana-4140	13	13	represents	represent	VERB
cana-4140	13	14	solution	solution	NOUN
cana-4140	13	15	for	for	ADP
cana-4140	13	16	an	an	DET
cana-4140	13	17	elastic	elastic	ADJ
cana-4140	13	18	isotropic	isotropic	NOUN
cana-4140	13	19	material	material	NOUN
cana-4140	13	20	.	.	PUNCT
cana-4140	14	1	a.	a.	PROPN
cana-4140	14	2	hamoud	hamoud	PROPN
cana-4140	14	3	et	et	PROPN
cana-4140	14	4	al	al	PROPN
cana-4140	14	5	.	.	PUNCT
cana-4140	15	1	[	[	X
cana-4140	15	2	2	2	NUM
cana-4140	15	3	]	]	PUNCT
cana-4140	15	4	solved	solve	VERB
cana-4140	15	5	integro	integro	ADJ
cana-4140	15	6	-	-	PUNCT
cana-4140	15	7	differential	differential	NOUN
cana-4140	15	8	equations	equation	NOUN
cana-4140	15	9	by	by	ADP
cana-4140	15	10	using	use	VERB
cana-4140	15	11	numerical	numerical	ADJ
cana-4140	15	12	techniques	technique	NOUN
cana-4140	15	13	.	.	PUNCT
cana-4140	16	1	a.	a.	NOUN
cana-4140	16	2	yasinskyy	yasinskyy	PROPN
cana-4140	16	3	and	and	CCONJ
cana-4140	16	4	o.	o.	NOUN
cana-4140	16	5	ierokhova	ierokhova	PROPN
cana-4140	17	1	[	[	X
cana-4140	17	2	3	3	NUM
cana-4140	17	3	]	]	PUNCT
cana-4140	17	4	gives	give	VERB
cana-4140	17	5	optimization	optimization	NOUN
cana-4140	17	6	of	of	ADP
cana-4140	17	7	nonstationary	nonstationary	ADJ
cana-4140	17	8	thermal	thermal	ADJ
cana-4140	17	9	displacements	displacement	NOUN
cana-4140	17	10	in	in	ADP
cana-4140	17	11	a	a	DET
cana-4140	17	12	given	give	VERB
cana-4140	17	13	cross	cross	NOUN
cana-4140	17	14	section	section	NOUN
cana-4140	17	15	of	of	ADP
cana-4140	17	16	a	a	DET
cana-4140	17	17	half	half	ADJ
cana-4140	17	18	space	space	NOUN
cana-4140	17	19	in	in	ADP
cana-4140	17	20	the	the	DET
cana-4140	17	21	plane	plane	NOUN
cana-4140	17	22	strain	strain	NOUN
cana-4140	17	23	state	state	NOUN
cana-4140	17	24	.	.	PUNCT
cana-4140	18	1	b.	b.	PROPN
cana-4140	18	2	kalynyak	kalynyak	PROPN
cana-4140	18	3	et	et	PROPN
cana-4140	18	4	al	al	PROPN
cana-4140	18	5	.	.	PUNCT
cana-4140	19	1	[	[	X
cana-4140	19	2	4	4	X
cana-4140	19	3	]	]	PUNCT
cana-4140	19	4	studied	study	VERB
cana-4140	19	5	direct	direct	ADJ
cana-4140	19	6	and	and	CCONJ
cana-4140	19	7	inverse	inverse	NOUN
cana-4140	19	8	problems	problem	NOUN
cana-4140	19	9	of	of	ADP
cana-4140	19	10	thermomechanics	thermomechanic	NOUN
cana-4140	19	11	concerning	concern	VERB
cana-4140	19	12	the	the	DET
cana-4140	19	13	optimization	optimization	NOUN
cana-4140	19	14	and	and	CCONJ
cana-4140	19	15	identification	identification	NOUN
cana-4140	19	16	of	of	ADP
cana-4140	19	17	the	the	DET
cana-4140	19	18	thermal	thermal	NOUN
cana-4140	19	19	stressed	stress	VERB
cana-4140	19	20	state	state	NOUN
cana-4140	19	21	of	of	ADP
cana-4140	19	22	deformed	deform	VERB
cana-4140	19	23	solids	solid	NOUN
cana-4140	19	24	.	.	PUNCT
cana-4140	20	1	y.	y.	PROPN
cana-4140	20	2	tokovyy	tokovyy	PROPN
cana-4140	20	3	and	and	CCONJ
cana-4140	20	4	ma	ma	PROPN
cana-4140	20	5	.	.	PROPN
cana-4140	20	6	chien	chien	PROPN
cana-4140	20	7	-	-	PUNCT
cana-4140	20	8	ching	ching	PROPN
cana-4140	21	1	[	[	X
cana-4140	21	2	9	9	NUM
cana-4140	21	3	,	,	PUNCT
cana-4140	21	4	10,11	10,11	NUM
cana-4140	21	5	]	]	PUNCT
cana-4140	21	6	gives	give	VERB
cana-4140	21	7	an	an	DET
cana-4140	21	8	explict	explict	NOUN
cana-4140	21	9	form	form	NOUN
cana-4140	21	10	solution	solution	NOUN
cana-4140	21	11	to	to	ADP
cana-4140	21	12	the	the	DET
cana-4140	21	13	plane	plane	NOUN
cana-4140	21	14	elasticity	elasticity	NOUN
cana-4140	21	15	and	and	CCONJ
cana-4140	21	16	thermoelasticity	thermoelasticity	NOUN
cana-4140	21	17	problems	problem	NOUN
cana-4140	21	18	for	for	ADP
cana-4140	21	19	anisotropic	anisotropic	NOUN
cana-4140	21	20	and	and	CCONJ
cana-4140	21	21	inhomogeneous	inhomogeneous	ADJ
cana-4140	21	22	solids	solid	NOUN
cana-4140	21	23	and	and	CCONJ
cana-4140	21	24	find	find	VERB
cana-4140	21	25	out	out	ADP
cana-4140	21	26	analytical	analytical	ADJ
cana-4140	21	27	solutions	solution	NOUN
cana-4140	21	28	to	to	ADP
cana-4140	21	29	the	the	DET
cana-4140	21	30	2d	2d	PROPN
cana-4140	21	31	elasticity	elasticity	NOUN
cana-4140	21	32	and	and	CCONJ
cana-4140	21	33	thermoelasticity	thermoelasticity	NOUN
cana-4140	21	34	problems	problem	NOUN
cana-4140	21	35	for	for	ADP
cana-4140	21	36	inhomogeneous	inhomogeneous	ADJ
cana-4140	21	37	planes	plane	NOUN
cana-4140	21	38	and	and	CCONJ
cana-4140	21	39	half	half	ADJ
cana-4140	21	40	planes	plane	NOUN
cana-4140	21	41	.	.	PUNCT
cana-4140	22	1	this	this	DET
cana-4140	22	2	method	method	NOUN
cana-4140	22	3	was	be	AUX
cana-4140	22	4	established	establish	VERB
cana-4140	22	5	by	by	ADP
cana-4140	22	6	v.	v.	ADP
cana-4140	22	7	vigak	vigak	NOUN
cana-4140	23	1	[	[	X
cana-4140	23	2	7	7	NUM
cana-4140	23	3	]	]	PUNCT
cana-4140	23	4	.	.	PUNCT
cana-4140	24	1	this	this	DET
cana-4140	24	2	method	method	NOUN
cana-4140	24	3	was	be	AUX
cana-4140	24	4	already	already	ADV
cana-4140	24	5	applied	apply	VERB
cana-4140	24	6	to	to	PART
cana-4140	24	7	solve	solve	VERB
cana-4140	24	8	some	some	DET
cana-4140	24	9	direct	direct	ADJ
cana-4140	24	10	and	and	CCONJ
cana-4140	24	11	inverse	inverse	ADJ
cana-4140	24	12	boundary	boundary	ADJ
cana-4140	24	13	value	value	NOUN
cana-4140	24	14	problems	problem	NOUN
cana-4140	24	15	[	[	X
cana-4140	24	16	8	8	NUM
cana-4140	24	17	]	]	PUNCT
cana-4140	24	18	.	.	PUNCT
cana-4140	25	1	after	after	ADP
cana-4140	25	2	integrating	integrate	VERB
cana-4140	25	3	the	the	DET
cana-4140	25	4	differential	differential	ADJ
cana-4140	25	5	equilibrium	equilibrium	NOUN
cana-4140	25	6	equations	equation	NOUN
cana-4140	25	7	,	,	PUNCT
cana-4140	25	8	we	we	PRON
cana-4140	25	9	can	can	AUX
cana-4140	25	10	determine	determine	VERB
cana-4140	25	11	the	the	DET
cana-4140	25	12	relationship	relationship	NOUN
cana-4140	25	13	between	between	ADP
cana-4140	25	14	the	the	DET
cana-4140	25	15	stress	stress	NOUN
cana-4140	25	16	tensor	tensor	NOUN
cana-4140	25	17	component	component	NOUN
cana-4140	25	18	.	.	PUNCT
cana-4140	26	1	with	with	ADP
cana-4140	26	2	this	this	DET
cana-4140	26	3	technique	technique	NOUN
cana-4140	26	4	the	the	DET
cana-4140	26	5	governing	govern	VERB
cana-4140	26	6	equations	equation	NOUN
cana-4140	26	7	are	be	AUX
cana-4140	26	8	reduced	reduce	VERB
cana-4140	26	9	to	to	ADP
cana-4140	26	10	integro	integro	ADJ
cana-4140	26	11	-	-	PUNCT
cana-4140	26	12	differential	differential	NOUN
cana-4140	26	13	equation	equation	NOUN
cana-4140	26	14	for	for	ADP
cana-4140	26	15	stress	stress	NOUN
cana-4140	26	16	tensor	tensor	NOUN
cana-4140	26	17	component	component	NOUN
cana-4140	26	18	.	.	PUNCT
cana-4140	27	1	with	with	ADP
cana-4140	27	2	application	application	NOUN
cana-4140	27	3	of	of	ADP
cana-4140	27	4	simple	simple	ADJ
cana-4140	27	5	iteration	iteration	NOUN
cana-4140	27	6	method	method	NOUN
cana-4140	27	7	,	,	PUNCT
cana-4140	27	8	derived	derive	VERB
cana-4140	27	9	integral	integral	ADJ
cana-4140	27	10	equations	equation	NOUN
cana-4140	27	11	has	have	AUX
cana-4140	27	12	been	be	AUX
cana-4140	27	13	solved	solve	VERB
cana-4140	27	14	for	for	ADP
cana-4140	27	15	constructing	construct	VERB
cana-4140	27	16	the	the	DET
cana-4140	27	17	solution	solution	NOUN
cana-4140	27	18	in	in	ADP
cana-4140	27	19	explicit	explicit	ADJ
cana-4140	27	20	form	form	NOUN
cana-4140	27	21	expression	expression	NOUN
cana-4140	27	22	with	with	ADP
cana-4140	27	23	interdependence	interdependence	NOUN
cana-4140	27	24	of	of	ADP
cana-4140	27	25	elastic	elastic	ADJ
cana-4140	27	26	moduli	modulus	NOUN
cana-4140	27	27	communications	communication	NOUN
cana-4140	27	28	on	on	ADP
cana-4140	27	29	applied	apply	VERB
cana-4140	27	30	nonlinear	nonlinear	ADJ
cana-4140	27	31	analysis	analysis	NOUN
cana-4140	27	32	issn	issn	NOUN
cana-4140	27	33	:	:	PUNCT
cana-4140	27	34	1074	1074	NUM
cana-4140	27	35	-	-	PUNCT
cana-4140	27	36	133x	133x	NUM
cana-4140	27	37	vol	vol	NOUN
cana-4140	27	38	32	32	NUM
cana-4140	27	39	no	no	NOUN
cana-4140	27	40	.	.	NOUN
cana-4140	27	41	9(s	9(s	NUM
cana-4140	27	42	)	)	PUNCT
cana-4140	27	43	(	(	PUNCT
cana-4140	27	44	2025	2025	NUM
cana-4140	27	45	)	)	PUNCT
cana-4140	27	46	1313	1313	NUM
cana-4140	27	47	https://internationalpubls.com	https://internationalpubls.com	X
cana-4140	28	1	2	2	X
cana-4140	28	2	.	.	X
cana-4140	28	3	preliminary	preliminary	ADJ
cana-4140	28	4	in	in	ADP
cana-4140	28	5	this	this	DET
cana-4140	28	6	section	section	NOUN
cana-4140	28	7	,	,	PUNCT
cana-4140	28	8	we	we	PRON
cana-4140	28	9	collect	collect	VERB
cana-4140	28	10	some	some	DET
cana-4140	28	11	basic	basic	ADJ
cana-4140	28	12	definitions	definition	NOUN
cana-4140	28	13	that	that	PRON
cana-4140	28	14	will	will	AUX
cana-4140	28	15	be	be	AUX
cana-4140	28	16	important	important	ADJ
cana-4140	28	17	to	to	ADP
cana-4140	28	18	us	we	PRON
cana-4140	28	19	in	in	ADP
cana-4140	28	20	the	the	DET
cana-4140	28	21	sequel	sequel	NOUN
cana-4140	28	22	.	.	PUNCT
cana-4140	29	1	2.1	2.1	NUM
cana-4140	29	2	definition	definition	NOUN
cana-4140	29	3	a	a	DET
cana-4140	29	4	fourier	fourier	NOUN
cana-4140	29	5	transform	transform	NOUN
cana-4140	29	6	of	of	ADP
cana-4140	29	7	function	function	NOUN
cana-4140	29	8	f(x	f(x	PROPN
cana-4140	29	9	)	)	PUNCT
cana-4140	29	10	is	be	AUX
cana-4140	29	11	defined	define	VERB
cana-4140	29	12	as	as	ADP
cana-4140	29	13	[	[	X
cana-4140	29	14	6	6	NUM
cana-4140	29	15	]	]	X
cana-4140	29	16	:	:	PUNCT
cana-4140	29	17	f(ω	f(ω	PROPN
cana-4140	29	18	)	)	PUNCT
cana-4140	30	1	=	=	SYM
cana-4140	30	2	∫	∫	PROPN
cana-4140	31	1	f(x)e−iωxdx	f(x)e−iωxdx	NOUN
cana-4140	31	2	∞	∞	PROPN
cana-4140	32	1	−∞	−∞	NOUN
cana-4140	32	2	.	.	PUNCT
cana-4140	33	1	2.2	2.2	NUM
cana-4140	33	2	definition	definition	NOUN
cana-4140	33	3	inverse	inverse	NOUN
cana-4140	33	4	fourier	fourier	NOUN
cana-4140	33	5	transform	transform	NOUN
cana-4140	33	6	of	of	ADP
cana-4140	33	7	function	function	NOUN
cana-4140	33	8	f(x	f(x	PROPN
cana-4140	33	9	)	)	PUNCT
cana-4140	33	10	is	be	AUX
cana-4140	33	11	defined	define	VERB
cana-4140	33	12	as	as	ADP
cana-4140	33	13	[	[	X
cana-4140	33	14	12	12	NUM
cana-4140	33	15	]	]	X
cana-4140	33	16	:	:	PUNCT
cana-4140	33	17	f(x	f(x	PROPN
cana-4140	33	18	)	)	PUNCT
cana-4140	33	19	=	=	PUNCT
cana-4140	34	1	1	1	NUM
cana-4140	34	2	2π	2π	NUM
cana-4140	34	3	∫	∫	PROPN
cana-4140	34	4	f(ω)eiωxdx	f(ω)eiωxdx	X
cana-4140	34	5	∞	∞	PROPN
cana-4140	34	6	−∞	−∞	NOUN
cana-4140	34	7	.	.	PUNCT
cana-4140	35	1	3	3	X
cana-4140	35	2	.	.	X
cana-4140	35	3	problem	problem	NOUN
cana-4140	35	4	formulation	formulation	NOUN
cana-4140	35	5	consider	consider	VERB
cana-4140	35	6	an	an	DET
cana-4140	35	7	isotropic	isotropic	NOUN
cana-4140	35	8	inhomogeneous	inhomogeneous	ADJ
cana-4140	35	9	half	half	ADJ
cana-4140	35	10	plane	plane	NOUN
cana-4140	35	11	𝐷	𝐷	NOUN
cana-4140	35	12	=	=	PUNCT
cana-4140	35	13	{	{	PUNCT
cana-4140	35	14	(	(	PUNCT
cana-4140	35	15	𝑥	𝑥	NOUN
cana-4140	35	16	,	,	PUNCT
cana-4140	35	17	𝑦	𝑦	NOUN
cana-4140	35	18	)	)	PUNCT
cana-4140	35	19	∈	∈	PROPN
cana-4140	36	1	[	[	X
cana-4140	36	2	0	0	NUM
cana-4140	36	3	,	,	PUNCT
cana-4140	36	4	∞	∞	PROPN
cana-4140	36	5	)	)	PUNCT
cana-4140	36	6	×	×	NOUN
cana-4140	36	7	(	(	PUNCT
cana-4140	36	8	−∞	−∞	NOUN
cana-4140	36	9	,	,	PUNCT
cana-4140	36	10	∞	∞	PROPN
cana-4140	36	11	)	)	PUNCT
cana-4140	36	12	}	}	PUNCT
cana-4140	36	13	.	.	PUNCT
cana-4140	37	1	the	the	DET
cana-4140	37	2	problem	problem	NOUN
cana-4140	37	3	is	be	AUX
cana-4140	37	4	governed	govern	VERB
cana-4140	37	5	by	by	ADP
cana-4140	37	6	the	the	DET
cana-4140	37	7	equilibrium	equilibrium	NOUN
cana-4140	37	8	equation	equation	NOUN
cana-4140	37	9	[	[	X
cana-4140	37	10	8	8	NUM
cana-4140	37	11	]	]	PUNCT
cana-4140	37	12	,	,	PUNCT
cana-4140	37	13	∂σxx	∂σxx	NOUN
cana-4140	37	14	∂x	∂x	PROPN
cana-4140	37	15	+	+	CCONJ
cana-4140	37	16	∂σxy	∂σxy	SYM
cana-4140	37	17	∂y	∂y	NOUN
cana-4140	38	1	+	+	PUNCT
cana-4140	38	2	x	x	SYM
cana-4140	38	3	=	=	SYM
cana-4140	38	4	0	0	NUM
cana-4140	38	5	,	,	PUNCT
cana-4140	38	6	∂σxy	∂σxy	SYM
cana-4140	38	7	∂x	∂x	PROPN
cana-4140	38	8	+	+	CCONJ
cana-4140	38	9	∂σyy	∂σyy	NUM
cana-4140	38	10	∂y	∂y	NOUN
cana-4140	39	1	+	+	CCONJ
cana-4140	39	2	y	y	PROPN
cana-4140	39	3	=	=	SYM
cana-4140	39	4	0	0	PROPN
cana-4140	39	5	,	,	PUNCT
cana-4140	39	6	(	(	PUNCT
cana-4140	39	7	x	x	X
cana-4140	39	8	,	,	PUNCT
cana-4140	39	9	y	y	PROPN
cana-4140	39	10	)	)	PUNCT
cana-4140	39	11	∈	∈	PROPN
cana-4140	39	12	d.	d.	NOUN
cana-4140	39	13	(	(	PUNCT
cana-4140	39	14	1	1	NUM
cana-4140	39	15	)	)	PUNCT
cana-4140	39	16	strain	strain	NOUN
cana-4140	39	17	-	-	PUNCT
cana-4140	39	18	compatibility	compatibility	NOUN
cana-4140	39	19	equations	equation	NOUN
cana-4140	39	20	[	[	X
cana-4140	39	21	7	7	NUM
cana-4140	39	22	]	]	X
cana-4140	39	23	:	:	PUNCT
cana-4140	39	24	𝜕2𝜏𝑥𝑥	𝜕2𝜏𝑥𝑥	PROPN
cana-4140	39	25	𝜕𝑦2	𝜕𝑦2	PROPN
cana-4140	39	26	+	+	NUM
cana-4140	39	27	𝜕2𝜏𝑦𝑦	𝜕2𝜏𝑦𝑦	NOUN
cana-4140	39	28	𝜕𝑥2	𝜕𝑥2	NOUN
cana-4140	39	29	=	=	SYM
cana-4140	39	30	𝜕2𝜏𝑥𝑦	𝜕2𝜏𝑥𝑦	PROPN
cana-4140	39	31	𝜕𝑥𝜕𝑦	𝜕𝑥𝜕𝑦	NOUN
cana-4140	39	32	.	.	PUNCT
cana-4140	40	1	(	(	PUNCT
cana-4140	40	2	2	2	X
cana-4140	40	3	)	)	PUNCT
cana-4140	40	4	stressstrain	stressstrain	NOUN
cana-4140	40	5	relations	relation	NOUN
cana-4140	40	6	[	[	X
cana-4140	40	7	8	8	NUM
cana-4140	40	8	]	]	X
cana-4140	40	9	:	:	PUNCT
cana-4140	40	10	𝜏𝑥𝑥	𝜏𝑥𝑥	ADJ
cana-4140	40	11	=	=	SYM
cana-4140	40	12	1	1	NUM
cana-4140	40	13	𝐸∗	𝐸∗	NOUN
cana-4140	40	14	(	(	PUNCT
cana-4140	40	15	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
cana-4140	40	16	−	−	X
cana-4140	40	17	𝜗𝜎𝑦𝑦	𝜗𝜎𝑦𝑦	ADJ
cana-4140	40	18	−	−	PROPN
cana-4140	40	19	𝑐∗	𝑐∗	PROPN
cana-4140	40	20	+	+	CCONJ
cana-4140	40	21	𝛼∗𝑇(𝑥	𝛼∗𝑇(𝑥	PROPN
cana-4140	40	22	,	,	PUNCT
cana-4140	40	23	𝑦	𝑦	NOUN
cana-4140	40	24	)	)	PUNCT
cana-4140	40	25	)	)	PUNCT
cana-4140	40	26	,	,	PUNCT
cana-4140	40	27	(	(	PUNCT
cana-4140	40	28	3	3	X
cana-4140	40	29	)	)	PUNCT
cana-4140	40	30	𝜏𝑥𝑥	𝜏𝑥𝑥	NOUN
cana-4140	40	31	=	=	SYM
cana-4140	40	32	1	1	NUM
cana-4140	40	33	𝐸∗	𝐸∗	NOUN
cana-4140	40	34	(	(	PUNCT
cana-4140	40	35	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
cana-4140	40	36	−	−	X
cana-4140	40	37	𝜗𝜎𝑦𝑦	𝜗𝜎𝑦𝑦	ADJ
cana-4140	40	38	−	−	PROPN
cana-4140	40	39	𝑐∗	𝑐∗	PROPN
cana-4140	40	40	+	+	CCONJ
cana-4140	40	41	𝛼∗𝑇(𝑥	𝛼∗𝑇(𝑥	PROPN
cana-4140	40	42	,	,	PUNCT
cana-4140	40	43	𝑦	𝑦	NOUN
cana-4140	40	44	)	)	PUNCT
cana-4140	40	45	)	)	PUNCT
cana-4140	40	46	,	,	PUNCT
cana-4140	40	47	(	(	PUNCT
cana-4140	40	48	4	4	X
cana-4140	40	49	)	)	PUNCT
cana-4140	40	50	𝜏𝑥𝑦	𝜏𝑥𝑦	NOUN
cana-4140	40	51	=	=	SYM
cana-4140	40	52	1	1	NUM
cana-4140	40	53	𝐺	𝐺	NOUN
cana-4140	40	54	𝜎𝑥𝑦.	𝜎𝑥𝑦.	X
cana-4140	40	55	(	(	PUNCT
cana-4140	40	56	5	5	NUM
cana-4140	40	57	)	)	PUNCT
cana-4140	40	58	where	where	SCONJ
cana-4140	40	59	σxx	σxx	NOUN
cana-4140	40	60	,	,	PUNCT
cana-4140	40	61	σxy	σxy	NOUN
cana-4140	40	62	,	,	PUNCT
cana-4140	40	63	σyy	σyy	VERB
cana-4140	40	64	are	be	AUX
cana-4140	40	65	the	the	DET
cana-4140	40	66	stress	stress	NOUN
cana-4140	40	67	tensor	tensor	NOUN
cana-4140	40	68	components	component	NOUN
cana-4140	40	69	and	and	CCONJ
cana-4140	40	70	τxx	τxx	PRON
cana-4140	40	71	,	,	PUNCT
cana-4140	40	72	τxy	τxy	NOUN
cana-4140	40	73	,	,	PUNCT
cana-4140	40	74	τyy	τyy	PROPN
cana-4140	40	75	are	be	AUX
cana-4140	40	76	the	the	DET
cana-4140	40	77	strain	strain	NOUN
cana-4140	40	78	tensor	tensor	NOUN
cana-4140	40	79	components	component	NOUN
cana-4140	40	80	.	.	PUNCT
cana-4140	41	1	g	g	NOUN
cana-4140	41	2	,	,	PUNCT
cana-4140	41	3	e	e	NOUN
cana-4140	41	4	,	,	PUNCT
cana-4140	41	5	ν	ν	NOUN
cana-4140	41	6	are	be	AUX
cana-4140	41	7	shear	shear	ADJ
cana-4140	41	8	modulus	modulus	NOUN
cana-4140	41	9	,	,	PUNCT
cana-4140	41	10	modulus	modulus	NOUN
cana-4140	41	11	of	of	ADP
cana-4140	41	12	elasticity	elasticity	NOUN
cana-4140	41	13	and	and	CCONJ
cana-4140	41	14	poisson	poisson	NOUN
cana-4140	41	15	’s	’s	PART
cana-4140	41	16	ratio	ratio	NOUN
cana-4140	41	17	respectively	respectively	ADV
cana-4140	41	18	and	and	CCONJ
cana-4140	41	19	α	α	PRON
cana-4140	41	20	is	be	AUX
cana-4140	41	21	the	the	DET
cana-4140	41	22	coefficient	coefficient	NOUN
cana-4140	41	23	of	of	ADP
cana-4140	41	24	thermal	thermal	ADJ
cana-4140	41	25	expansion	expansion	NOUN
cana-4140	41	26	.	.	PUNCT
cana-4140	42	1	x	x	X
cana-4140	43	1	=	=	PUNCT
cana-4140	43	2	x	x	SYM
cana-4140	43	3	(	(	PUNCT
cana-4140	43	4	x	x	NOUN
cana-4140	43	5	,	,	PUNCT
cana-4140	43	6	y	y	PROPN
cana-4140	43	7	)	)	PUNCT
cana-4140	43	8	,	,	PUNCT
cana-4140	43	9	y	y	PROPN
cana-4140	43	10	=	=	SYM
cana-4140	43	11	y	y	PROPN
cana-4140	43	12	(	(	PUNCT
cana-4140	43	13	x	x	PROPN
cana-4140	43	14	,	,	PUNCT
cana-4140	43	15	y	y	NOUN
cana-4140	43	16	)	)	PUNCT
cana-4140	43	17	are	be	AUX
cana-4140	43	18	the	the	DET
cana-4140	43	19	stress	stress	ADJ
cana-4140	43	20	dimensional	dimensional	ADJ
cana-4140	43	21	projections	projection	NOUN
cana-4140	43	22	of	of	ADP
cana-4140	43	23	body	body	NOUN
cana-4140	43	24	forces	force	NOUN
cana-4140	43	25	in	in	ADP
cana-4140	43	26	the	the	DET
cana-4140	43	27	abscissa	abscissa	NOUN
cana-4140	43	28	and	and	CCONJ
cana-4140	43	29	co	co	NOUN
cana-4140	43	30	-	-	NOUN
cana-4140	43	31	ordinate	ordinate	NOUN
cana-4140	43	32	.	.	PUNCT
cana-4140	44	1	for	for	SCONJ
cana-4140	44	2	plane	plane	NOUN
cana-4140	44	3	strains	strain	NOUN
cana-4140	44	4	𝐸∗	𝐸∗	NOUN
cana-4140	44	5	=	=	NOUN
cana-4140	44	6	1	1	NUM
cana-4140	44	7	1−𝜗2	1−𝜗2	NUM
cana-4140	44	8	,	,	PUNCT
cana-4140	44	9	𝜗∗	𝜗∗	NOUN
cana-4140	44	10	=	=	SYM
cana-4140	44	11	𝜗	𝜗	PROPN
cana-4140	44	12	1−𝜗2	1−𝜗2	NUM
cana-4140	44	13	,	,	PUNCT
cana-4140	44	14	𝛼∗	𝛼∗	PROPN
cana-4140	45	1	=	=	PUNCT
cana-4140	45	2	𝛼(1	𝛼(1	NOUN
cana-4140	45	3	−	−	PROPN
cana-4140	45	4	𝜗	𝜗	NOUN
cana-4140	45	5	)	)	PUNCT
cana-4140	45	6	,	,	PUNCT
cana-4140	45	7	𝑐∗	𝑐∗	PROPN
cana-4140	45	8	=	=	SYM
cana-4140	45	9	𝜗𝑐.	𝜗𝑐.	X
cana-4140	45	10	(	(	PUNCT
cana-4140	45	11	6	6	NUM
cana-4140	45	12	)	)	PUNCT
cana-4140	45	13	for	for	ADP
cana-4140	45	14	plain	plain	ADJ
cana-4140	45	15	strain	strain	NOUN
cana-4140	45	16	,	,	PUNCT
cana-4140	45	17	𝐸∗	𝐸∗	NOUN
cana-4140	45	18	=	=	SYM
cana-4140	45	19	𝐸	𝐸	PROPN
cana-4140	45	20	,	,	PUNCT
cana-4140	45	21	𝜗∗	𝜗∗	NOUN
cana-4140	45	22	=	=	SYM
cana-4140	45	23	𝜗	𝜗	NOUN
cana-4140	45	24	,	,	PUNCT
cana-4140	45	25	𝛼∗	𝛼∗	NOUN
cana-4140	45	26	=	=	SYM
cana-4140	45	27	𝛼	𝛼	PROPN
cana-4140	45	28	,	,	PUNCT
cana-4140	45	29	𝑐∗	𝑐∗	PROPN
cana-4140	45	30	=	=	PUNCT
cana-4140	45	31	𝑐.	𝑐.	NOUN
cana-4140	45	32	(	(	PUNCT
cana-4140	45	33	7	7	NUM
cana-4140	45	34	)	)	PUNCT
cana-4140	45	35	according	accord	VERB
cana-4140	45	36	to	to	ADP
cana-4140	45	37	hook	hook	NOUN
cana-4140	45	38	's	's	PART
cana-4140	45	39	law	law	NOUN
cana-4140	45	40	,	,	PUNCT
cana-4140	46	1	𝐸𝑐	𝐸𝑐	PROPN
cana-4140	46	2	=	=	PUNCT
cana-4140	46	3	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-4140	46	4	−	−	PROPN
cana-4140	47	1	𝜗(𝜎𝑧𝑧	𝜗(𝜎𝑧𝑧	PROPN
cana-4140	47	2	+	+	NUM
cana-4140	47	3	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-4140	47	4	)	)	PUNCT
cana-4140	48	1	+	+	CCONJ
cana-4140	48	2	𝛼𝐸𝑇	𝛼𝐸𝑇	NUM
cana-4140	48	3	,	,	PUNCT
cana-4140	48	4	(	(	PUNCT
cana-4140	48	5	8)	8)	NUM
cana-4140	48	6	communications	communication	NOUN
cana-4140	48	7	on	on	ADP
cana-4140	48	8	applied	apply	VERB
cana-4140	48	9	nonlinear	nonlinear	ADJ
cana-4140	48	10	analysis	analysis	NOUN
cana-4140	48	11	issn	issn	NOUN
cana-4140	48	12	:	:	PUNCT
cana-4140	48	13	1074	1074	NUM
cana-4140	48	14	-	-	PUNCT
cana-4140	48	15	133x	133x	NUM
cana-4140	48	16	vol	vol	NOUN
cana-4140	48	17	32	32	NUM
cana-4140	48	18	no	no	NOUN
cana-4140	48	19	.	.	NOUN
cana-4140	48	20	9(s	9(s	NUM
cana-4140	48	21	)	)	PUNCT
cana-4140	48	22	(	(	PUNCT
cana-4140	48	23	2025	2025	NUM
cana-4140	48	24	)	)	PUNCT
cana-4140	48	25	1314	1314	NUM
cana-4140	48	26	https://internationalpubls.com	https://internationalpubls.com	X
cana-4140	49	1	c	c	X
cana-4140	49	2	=	=	SYM
cana-4140	49	3	constant	constant	ADJ
cana-4140	49	4	is	be	AUX
cana-4140	49	5	out	out	ADP
cana-4140	49	6	of	of	ADP
cana-4140	49	7	plane	plane	NOUN
cana-4140	49	8	strain	strain	NOUN
cana-4140	49	9	and	and	CCONJ
cana-4140	49	10	𝜎𝑧𝑧	𝜎𝑧𝑧	NOUN
cana-4140	49	11	is	be	AUX
cana-4140	49	12	the	the	DET
cana-4140	49	13	out	out	NOUN
cana-4140	49	14	of	of	ADP
cana-4140	49	15	plane	plane	NOUN
cana-4140	49	16	strain	strain	NOUN
cana-4140	49	17	and	and	CCONJ
cana-4140	49	18	𝑇	𝑇	PROPN
cana-4140	49	19	=	=	SYM
cana-4140	49	20	𝑇(𝑥	𝑇(𝑥	PROPN
cana-4140	49	21	,	,	PUNCT
cana-4140	49	22	𝑦	𝑦	NOUN
cana-4140	49	23	)	)	PUNCT
cana-4140	49	24	is	be	AUX
cana-4140	49	25	the	the	DET
cana-4140	49	26	temperature	temperature	NOUN
cana-4140	49	27	distribution	distribution	NOUN
cana-4140	49	28	.	.	PUNCT
cana-4140	50	1	we	we	PRON
cana-4140	50	2	impose	impose	VERB
cana-4140	50	3	tractions	traction	NOUN
cana-4140	50	4	at	at	ADP
cana-4140	50	5	the	the	DET
cana-4140	50	6	boundary	boundary	ADJ
cana-4140	50	7	𝜎𝑥𝑥|𝑥=0	𝜎𝑥𝑥|𝑥=0	NUM
cana-4140	50	8	=	=	SYM
cana-4140	50	9	−𝑝1(𝑦	−𝑝1(𝑦	PROPN
cana-4140	50	10	)	)	PUNCT
cana-4140	50	11	,	,	PUNCT
cana-4140	50	12	𝜎𝑥𝑦|𝑥=0	𝜎𝑥𝑦|𝑥=0	NUM
cana-4140	50	13	=	=	SYM
cana-4140	50	14	𝑞1(𝑦	𝑞1(𝑦	PROPN
cana-4140	50	15	)	)	PUNCT
cana-4140	50	16	.	.	PUNCT
cana-4140	51	1	(	(	PUNCT
cana-4140	51	2	9	9	X
cana-4140	51	3	)	)	PUNCT
cana-4140	51	4	assume	assume	VERB
cana-4140	51	5	that	that	SCONJ
cana-4140	51	6	,	,	PUNCT
cana-4140	51	7	as	as	ADP
cana-4140	51	8	|𝒚|	|𝒚|	PROPN
cana-4140	51	9	→	→	SYM
cana-4140	51	10	∞	∞	PROPN
cana-4140	51	11	the	the	DET
cana-4140	51	12	stresses	stress	NOUN
cana-4140	51	13	are	be	AUX
cana-4140	51	14	tending	tend	VERB
cana-4140	51	15	to	to	ADP
cana-4140	51	16	0	0	NUM
cana-4140	51	17	.	.	PUNCT
cana-4140	52	1	the	the	DET
cana-4140	52	2	steady	steady	ADJ
cana-4140	52	3	state	state	NOUN
cana-4140	52	4	temperature	temperature	NOUN
cana-4140	52	5	t	t	NOUN
cana-4140	52	6	(	(	PUNCT
cana-4140	52	7	x	x	NOUN
cana-4140	52	8	,	,	PUNCT
cana-4140	52	9	y	y	PROPN
cana-4140	52	10	)	)	PUNCT
cana-4140	52	11	can	can	AUX
cana-4140	52	12	be	be	AUX
cana-4140	52	13	found	find	VERB
cana-4140	52	14	from	from	ADP
cana-4140	52	15	the	the	DET
cana-4140	52	16	following	follow	VERB
cana-4140	52	17	heat	heat	NOUN
cana-4140	52	18	conduction	conduction	NOUN
cana-4140	52	19	equation	equation	NOUN
cana-4140	52	20	[	[	X
cana-4140	52	21	5	5	NUM
cana-4140	52	22	]	]	PUNCT
cana-4140	52	23	:	:	PUNCT
cana-4140	52	24	𝜕2𝑇	𝜕2𝑇	PROPN
cana-4140	52	25	𝜕𝑦2	𝜕𝑦2	PROPN
cana-4140	52	26	+	+	CCONJ
cana-4140	52	27	𝜕2𝑇	𝜕2𝑇	NOUN
cana-4140	52	28	𝜕𝑥2	𝜕𝑥2	NOUN
cana-4140	52	29	=	=	SYM
cana-4140	52	30	−𝑞(𝑥,𝑦	−𝑞(𝑥,𝑦	NOUN
cana-4140	52	31	)	)	PUNCT
cana-4140	52	32	𝐾	𝐾	NOUN
cana-4140	52	33	,	,	PUNCT
cana-4140	52	34	(	(	PUNCT
cana-4140	52	35	10	10	NUM
cana-4140	52	36	)	)	PUNCT
cana-4140	53	1	where	where	SCONJ
cana-4140	53	2	k	k	X
cana-4140	53	3	=	=	NOUN
cana-4140	53	4	constant	constant	ADJ
cana-4140	53	5	under	under	ADP
cana-4140	53	6	boundary	boundary	ADJ
cana-4140	53	7	conditions	condition	NOUN
cana-4140	53	8	employed	employ	VERB
cana-4140	53	9	at	at	ADP
cana-4140	53	10	boundary	boundary	ADJ
cana-4140	53	11	x=0	x=0	PROPN
cana-4140	53	12	.	.	PUNCT
cana-4140	54	1	the	the	DET
cana-4140	54	2	imposed	impose	VERB
cana-4140	54	3	boundary	boundary	ADJ
cana-4140	54	4	conditions	condition	NOUN
cana-4140	54	5	of	of	ADP
cana-4140	54	6	the	the	DET
cana-4140	54	7	given	give	VERB
cana-4140	54	8	problems	problem	NOUN
cana-4140	54	9	are	be	AUX
cana-4140	54	10	𝑇(𝑥	𝑇(𝑥	PROPN
cana-4140	54	11	,	,	PUNCT
cana-4140	54	12	𝑦	𝑦	NOUN
cana-4140	54	13	)	)	PUNCT
cana-4140	54	14	=	=	SYM
cana-4140	54	15	𝑇0(𝑦	𝑇0(𝑦	PROPN
cana-4140	54	16	)	)	PUNCT
cana-4140	54	17	𝑎𝑡	𝑎𝑡	ADP
cana-4140	54	18	𝑥	𝑥	NOUN
cana-4140	54	19	=	=	SYM
cana-4140	54	20	0	0	NUM
cana-4140	54	21	,	,	PUNCT
cana-4140	54	22	𝜕𝑇(𝑥,𝑦	𝜕𝑇(𝑥,𝑦	NOUN
cana-4140	54	23	)	)	PUNCT
cana-4140	54	24	𝜕𝑥	𝜕𝑥	NOUN
cana-4140	55	1	+	+	CCONJ
cana-4140	55	2	𝑎0t(x	𝑎0t(x	PROPN
cana-4140	55	3	,	,	PUNCT
cana-4140	55	4	y	y	PROPN
cana-4140	55	5	)	)	PUNCT
cana-4140	55	6	=	=	SYM
cana-4140	55	7	𝜑0(𝑦	𝜑0(𝑦	PROPN
cana-4140	55	8	)	)	PUNCT
cana-4140	55	9	,	,	PUNCT
cana-4140	55	10	at	at	ADP
cana-4140	55	11	x=0	x=0	PROPN
cana-4140	55	12	,	,	PUNCT
cana-4140	55	13	𝜕𝑇(𝑥,𝑦	𝜕𝑇(𝑥,𝑦	NOUN
cana-4140	55	14	)	)	PUNCT
cana-4140	55	15	𝜕𝑥	𝜕𝑥	NOUN
cana-4140	55	16	=	=	SYM
cana-4140	55	17	𝑏0	𝑏0	NOUN
cana-4140	55	18	,	,	PUNCT
cana-4140	55	19	at	at	ADP
cana-4140	55	20	x=0	x=0	PROPN
cana-4140	55	21	.	.	PUNCT
cana-4140	55	22	where	where	SCONJ
cana-4140	55	23	𝑎0	𝑎0	PROPN
cana-4140	55	24	,	,	PUNCT
cana-4140	55	25	𝑏0	𝑏0	PROPN
cana-4140	55	26	are	be	AUX
cana-4140	55	27	constant	constant	ADJ
cana-4140	55	28	and	and	CCONJ
cana-4140	55	29	𝑇0(𝑦	𝑇0(𝑦	NUM
cana-4140	55	30	)	)	PUNCT
cana-4140	55	31	,	,	PUNCT
cana-4140	55	32	𝜑0(𝑦	𝜑0(𝑦	PRON
cana-4140	55	33	)	)	PUNCT
cana-4140	55	34	are	be	AUX
cana-4140	55	35	given	give	VERB
cana-4140	55	36	functions	function	NOUN
cana-4140	55	37	.	.	PUNCT
cana-4140	56	1	4	4	NUM
cana-4140	56	2	.	.	NOUN
cana-4140	56	3	solution	solution	NOUN
cana-4140	56	4	formulations	formulation	NOUN
cana-4140	56	5	from	from	ADP
cana-4140	56	6	the	the	DET
cana-4140	56	7	physical	physical	ADJ
cana-4140	56	8	relation	relation	NOUN
cana-4140	56	9	of	of	ADP
cana-4140	56	10	(	(	PUNCT
cana-4140	56	11	3	3	NUM
cana-4140	56	12	,	,	PUNCT
cana-4140	56	13	4	4	NUM
cana-4140	56	14	,	,	PUNCT
cana-4140	56	15	5	5	NUM
cana-4140	56	16	)	)	PUNCT
cana-4140	56	17	and	and	CCONJ
cana-4140	56	18	the	the	DET
cana-4140	56	19	equilibrium	equilibrium	NOUN
cana-4140	56	20	equation	equation	NOUN
cana-4140	56	21	(	(	PUNCT
cana-4140	56	22	1	1	X
cana-4140	56	23	)	)	PUNCT
cana-4140	56	24	representing	represent	VERB
cana-4140	56	25	(	(	PUNCT
cana-4140	56	26	2	2	NUM
cana-4140	56	27	)	)	PUNCT
cana-4140	56	28	as	as	SCONJ
cana-4140	56	29	follows	follow	VERB
cana-4140	56	30	,	,	PUNCT
cana-4140	56	31	∆	∆	PROPN
cana-4140	56	32	[	[	PUNCT
cana-4140	56	33	𝜎	𝜎	PROPN
cana-4140	56	34	𝐸∗	𝐸∗	NOUN
cana-4140	56	35	+	+	CCONJ
cana-4140	56	36	𝛼∗𝑇	𝛼∗𝑇	NOUN
cana-4140	56	37	]	]	PUNCT
cana-4140	57	1	=	=	PUNCT
cana-4140	57	2	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
cana-4140	57	3	2	2	NUM
cana-4140	57	4	𝑑2	𝑑2	NOUN
cana-4140	57	5	𝑑𝑥2	𝑑𝑥2	NOUN
cana-4140	57	6	(	(	PUNCT
cana-4140	57	7	1	1	NUM
cana-4140	57	8	𝐺	𝐺	NOUN
cana-4140	57	9	)	)	PUNCT
cana-4140	58	1	+	+	PUNCT
cana-4140	58	2	𝑑2𝑐∗	𝑑2𝑐∗	PROPN
cana-4140	58	3	𝑑𝑥2	𝑑𝑥2	NOUN
cana-4140	58	4	+	+	CCONJ
cana-4140	58	5	𝑑	𝑑	NOUN
cana-4140	58	6	𝑑𝑥	𝑑𝑥	VERB
cana-4140	58	7	(	(	PUNCT
cana-4140	58	8	1	1	NUM
cana-4140	58	9	𝐺	𝐺	NOUN
cana-4140	58	10	)	)	PUNCT
cana-4140	59	1	+	+	CCONJ
cana-4140	59	2	1	1	NUM
cana-4140	59	3	2𝐺	2𝐺	NOUN
cana-4140	59	4	[	[	PUNCT
cana-4140	59	5	𝜕𝑋	𝜕𝑋	X
cana-4140	59	6	𝜕𝑥	𝜕𝑥	X
cana-4140	59	7	+	+	CCONJ
cana-4140	59	8	𝜕𝑌	𝜕𝑌	X
cana-4140	59	9	𝜕𝑥	𝜕𝑥	X
cana-4140	59	10	]	]	PUNCT
cana-4140	59	11	.	.	PUNCT
cana-4140	60	1	(	(	PUNCT
cana-4140	60	2	12	12	NUM
cana-4140	60	3	)	)	PUNCT
cana-4140	60	4	to	to	PART
cana-4140	60	5	compute	compute	VERB
cana-4140	60	6	the	the	DET
cana-4140	60	7	total	total	ADJ
cana-4140	60	8	stress	stress	NOUN
cana-4140	60	9	𝜎	𝜎	PROPN
cana-4140	61	1	=	=	PUNCT
cana-4140	61	2	σxx	σxx	NOUN
cana-4140	61	3	+	+	CCONJ
cana-4140	61	4	σyy	σyy	VERB
cana-4140	61	5	in	in	ADP
cana-4140	61	6	terms	term	NOUN
cana-4140	61	7	of	of	ADP
cana-4140	61	8	𝜎𝑦𝑦.	𝜎𝑦𝑦.	X
cana-4140	61	9	we	we	PRON
cana-4140	61	10	use	use	VERB
cana-4140	61	11	the	the	DET
cana-4140	61	12	relation	relation	NOUN
cana-4140	61	13	,	,	PUNCT
cana-4140	61	14	∆𝜎𝑥𝑥	∆𝜎𝑥𝑥	PUNCT
cana-4140	61	15	=	=	SYM
cana-4140	61	16	𝜕2𝜎	𝜕2𝜎	NOUN
cana-4140	61	17	𝜕𝑦2	𝜕𝑦2	NOUN
cana-4140	61	18	−	−	PROPN
cana-4140	61	19	𝜕𝑋	𝜕𝑋	NOUN
cana-4140	61	20	𝜕𝑥	𝜕𝑥	X
cana-4140	61	21	+	+	CCONJ
cana-4140	61	22	𝜕𝑌	𝜕𝑌	PROPN
cana-4140	61	23	𝜕𝑥	𝜕𝑥	X
cana-4140	61	24	,	,	PUNCT
cana-4140	61	25	(	(	PUNCT
cana-4140	61	26	13	13	NUM
cana-4140	61	27	)	)	PUNCT
cana-4140	61	28	∆	∆	PROPN
cana-4140	61	29	denotes	denote	VERB
cana-4140	61	30	two	two	NUM
cana-4140	61	31	-dimensional	-dimensional	ADJ
cana-4140	61	32	laplace	laplace	NOUN
cana-4140	61	33	operator	operator	NOUN
cana-4140	61	34	.	.	PUNCT
cana-4140	62	1	to	to	PART
cana-4140	62	2	find	find	VERB
cana-4140	62	3	out	out	ADP
cana-4140	62	4	solution	solution	NOUN
cana-4140	62	5	for	for	ADP
cana-4140	62	6	problem	problem	NOUN
cana-4140	62	7	(	(	PUNCT
cana-4140	62	8	1	1	NUM
cana-4140	62	9	)	)	PUNCT
cana-4140	62	10	to	to	ADP
cana-4140	62	11	(	(	PUNCT
cana-4140	62	12	13	13	NUM
cana-4140	62	13	)	)	PUNCT
cana-4140	62	14	,	,	PUNCT
cana-4140	62	15	selecting	select	VERB
cana-4140	62	16	one	one	NUM
cana-4140	62	17	key	key	ADJ
cana-4140	62	18	stress	stress	NOUN
cana-4140	62	19	out	out	ADP
cana-4140	62	20	of	of	ADP
cana-4140	62	21	three	three	NUM
cana-4140	62	22	stress	stress	NOUN
cana-4140	62	23	components	component	NOUN
cana-4140	62	24	.	.	PUNCT
cana-4140	63	1	to	to	PART
cana-4140	63	2	find	find	VERB
cana-4140	63	3	out	out	ADP
cana-4140	63	4	the	the	DET
cana-4140	63	5	two	two	NUM
cana-4140	63	6	-dimensional	-dimensional	ADJ
cana-4140	63	7	stressed	stressed	ADJ
cana-4140	63	8	state	state	NOUN
cana-4140	63	9	,	,	PUNCT
cana-4140	63	10	the	the	DET
cana-4140	63	11	equation	equation	NOUN
cana-4140	63	12	of	of	ADP
cana-4140	63	13	continuity	continuity	NOUN
cana-4140	63	14	for	for	ADP
cana-4140	63	15	these	these	DET
cana-4140	63	16	regions	region	NOUN
cana-4140	63	17	,	,	PUNCT
cana-4140	63	18	written	write	VERB
cana-4140	63	19	for	for	ADP
cana-4140	63	20	the	the	DET
cana-4140	63	21	normal	normal	ADJ
cana-4140	63	22	stresses	stress	NOUN
cana-4140	63	23	𝜎𝑦𝑦	𝜎𝑦𝑦	VERB
cana-4140	63	24	integrating	integrate	VERB
cana-4140	63	25	equation	equation	NOUN
cana-4140	63	26	(	(	PUNCT
cana-4140	63	27	1	1	NUM
cana-4140	63	28	)	)	PUNCT
cana-4140	63	29	as	as	ADP
cana-4140	63	30	in	in	ADP
cana-4140	63	31	[	[	X
cana-4140	63	32	7	7	NUM
cana-4140	63	33	]	]	PUNCT
cana-4140	63	34	,	,	PUNCT
cana-4140	63	35	express	express	VERB
cana-4140	63	36	the	the	DET
cana-4140	63	37	stresses	stress	NOUN
cana-4140	63	38	𝜎𝑥𝑦	𝜎𝑥𝑦	NUM
cana-4140	63	39	in	in	ADP
cana-4140	63	40	terms	term	NOUN
cana-4140	63	41	of	of	ADP
cana-4140	63	42	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
cana-4140	63	43	,	,	PUNCT
cana-4140	63	44	𝜎𝑦𝑦.	𝜎𝑦𝑦.	X
cana-4140	63	45	4𝜎𝑦𝑦	4𝜎𝑦𝑦	NUM
cana-4140	63	46	=	=	SYM
cana-4140	63	47	𝑞1	𝑞1	PROPN
cana-4140	63	48	−	−	PROPN
cana-4140	63	49	∫	∫	PROPN
cana-4140	63	50	(	(	PUNCT
cana-4140	63	51	∂σyy	∂σyy	NUM
cana-4140	63	52	∂y	∂y	PROPN
cana-4140	63	53	+	+	NUM
cana-4140	63	54	y	y	NOUN
cana-4140	63	55	)	)	PUNCT
cana-4140	64	1	sgn(x	sgn(x	PROPN
cana-4140	64	2	−	−	PROPN
cana-4140	64	3	η)dη	η)dη	PROPN
cana-4140	64	4	−	−	PROPN
cana-4140	64	5	∫	∫	PROPN
cana-4140	64	6	(	(	PUNCT
cana-4140	64	7	∂σxx	∂σxx	NUM
cana-4140	64	8	∂x	∂x	PROPN
cana-4140	64	9	+	+	CCONJ
cana-4140	64	10	𝑋	𝑋	PROPN
cana-4140	64	11	)	)	PUNCT
cana-4140	64	12	𝑠𝑔𝑛(𝑦	𝑠𝑔𝑛(𝑦	PROPN
cana-4140	64	13	−	−	PROPN
cana-4140	64	14	𝜉)𝑑𝜉	𝜉)𝑑𝜉	PROPN
cana-4140	64	15	,	,	PUNCT
cana-4140	64	16	∞	∞	PROPN
cana-4140	64	17	−∞	−∞	ADP
cana-4140	64	18	∞	∞	PROPN
cana-4140	64	19	0	0	NUM
cana-4140	64	20	(	(	PUNCT
cana-4140	64	21	14	14	NUM
cana-4140	64	22	)	)	PUNCT
cana-4140	64	23	𝑠𝑔𝑛𝑥	𝑠𝑔𝑛𝑥	NOUN
cana-4140	64	24	=	=	SYM
cana-4140	64	25	{	{	PUNCT
cana-4140	64	26	−1	−1	NOUN
cana-4140	64	27	𝑥	𝑥	X
cana-4140	64	28	<	<	X
cana-4140	64	29	0	0	NUM
cana-4140	64	30	0	0	NUM
cana-4140	64	31	𝑥	𝑥	NOUN
cana-4140	64	32	=	=	SYM
cana-4140	64	33	0	0	NUM
cana-4140	64	34	1	1	NUM
cana-4140	64	35	𝑥	𝑥	NOUN
cana-4140	64	36	>	>	X
cana-4140	64	37	0	0	X
cana-4140	64	38	.	.	PUNCT
cana-4140	64	39	(	(	PUNCT
cana-4140	64	40	15	15	NUM
cana-4140	64	41	)	)	PUNCT
cana-4140	64	42	to	to	PART
cana-4140	64	43	find	find	VERB
cana-4140	64	44	out	out	ADP
cana-4140	64	45	the	the	DET
cana-4140	64	46	key	key	ADJ
cana-4140	64	47	stresses	stress	NOUN
cana-4140	64	48	,	,	PUNCT
cana-4140	64	49	using	use	VERB
cana-4140	64	50	integral	integral	ADJ
cana-4140	64	51	fourier	fourier	NOUN
cana-4140	64	52	transform	transform	NOUN
cana-4140	64	53	[	[	X
cana-4140	64	54	10	10	NUM
cana-4140	64	55	]	]	PUNCT
cana-4140	64	56	for	for	ADP
cana-4140	64	57	(	(	PUNCT
cana-4140	64	58	12	12	NUM
cana-4140	64	59	)	)	PUNCT
cana-4140	64	60	(	(	PUNCT
cana-4140	64	61	13	13	NUM
cana-4140	64	62	)	)	PUNCT
cana-4140	64	63	,	,	PUNCT
cana-4140	64	64	communications	communication	NOUN
cana-4140	64	65	on	on	ADP
cana-4140	64	66	applied	apply	VERB
cana-4140	64	67	nonlinear	nonlinear	ADJ
cana-4140	64	68	analysis	analysis	NOUN
cana-4140	64	69	issn	issn	NOUN
cana-4140	64	70	:	:	PUNCT
cana-4140	64	71	1074	1074	NUM
cana-4140	64	72	-	-	PUNCT
cana-4140	64	73	133x	133x	NUM
cana-4140	64	74	vol	vol	NOUN
cana-4140	64	75	32	32	NUM
cana-4140	64	76	no	no	NOUN
cana-4140	64	77	.	.	NOUN
cana-4140	64	78	9(s	9(s	NUM
cana-4140	64	79	)	)	PUNCT
cana-4140	64	80	(	(	PUNCT
cana-4140	64	81	2025	2025	NUM
cana-4140	64	82	)	)	PUNCT
cana-4140	64	83	1315	1315	NUM
cana-4140	64	84	https://internationalpubls.com	https://internationalpubls.com	X
cana-4140	64	85	(	(	PUNCT
cana-4140	64	86	𝑑2	𝑑2	NOUN
cana-4140	64	87	𝑑𝑥2	𝑑𝑥2	NOUN
cana-4140	64	88	−	−	PROPN
cana-4140	64	89	𝜔2	𝜔2	PROPN
cana-4140	64	90	)	)	PUNCT
cana-4140	64	91	[	[	PUNCT
cana-4140	64	92	𝜎	𝜎	PROPN
cana-4140	64	93	𝐸∗	𝐸∗	NOUN
cana-4140	64	94	+	+	CCONJ
cana-4140	64	95	𝛼∗𝑇	𝛼∗𝑇	NOUN
cana-4140	64	96	]	]	PUNCT
cana-4140	64	97	=	=	PUNCT
cana-4140	65	1	−	−	PROPN
cana-4140	65	2	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
cana-4140	65	3	2	2	NUM
cana-4140	65	4	(	(	PUNCT
cana-4140	65	5	𝜔2	𝜔2	PROPN
cana-4140	65	6	𝐺	𝐺	PROPN
cana-4140	65	7	)	)	PUNCT
cana-4140	65	8	−	−	PROPN
cana-4140	65	9	𝜔2𝑐∗2𝜋𝛿(𝜔	𝜔2𝑐∗2𝜋𝛿(𝜔	ADV
cana-4140	65	10	)	)	PUNCT
cana-4140	66	1	+	+	CCONJ
cana-4140	67	1	𝑖𝜔𝑋	𝑖𝜔𝑋	PRON
cana-4140	67	2	(	(	PUNCT
cana-4140	67	3	1	1	NUM
cana-4140	67	4	𝐺	𝐺	NOUN
cana-4140	67	5	)	)	PUNCT
cana-4140	67	6	+	+	CCONJ
cana-4140	67	7	1	1	NUM
cana-4140	67	8	2𝐺	2𝐺	NOUN
cana-4140	67	9	(	(	PUNCT
cana-4140	67	10	𝑖𝜔𝑋	𝑖𝜔𝑋	PROPN
cana-4140	67	11	+	+	CCONJ
cana-4140	67	12	𝑑𝑌	𝑑𝑌	ADJ
cana-4140	67	13	𝑑𝑦	𝑑𝑦	NOUN
cana-4140	67	14	)	)	PUNCT
cana-4140	67	15	,	,	PUNCT
cana-4140	67	16	(	(	PUNCT
cana-4140	67	17	16	16	NUM
cana-4140	67	18	)	)	PUNCT
cana-4140	67	19	𝑑2σxx	𝑑2σxx	VERB
cana-4140	67	20	𝑑𝑥2	𝑑𝑥2	NOUN
cana-4140	67	21	−	−	NOUN
cana-4140	67	22	𝜔2σxx	𝜔2σxx	NOUN
cana-4140	67	23	=	=	SYM
cana-4140	67	24	−𝜔𝜎	−𝜔𝜎	NOUN
cana-4140	67	25	−	−	PROPN
cana-4140	67	26	(	(	PUNCT
cana-4140	67	27	𝑖𝜔𝑋	𝑖𝜔𝑋	NOUN
cana-4140	67	28	−	−	PROPN
cana-4140	67	29	𝑑𝑌	𝑑𝑌	PROPN
cana-4140	67	30	𝑑𝑦	𝑑𝑦	NOUN
cana-4140	67	31	)	)	PUNCT
cana-4140	67	32	,	,	PUNCT
cana-4140	67	33	(	(	PUNCT
cana-4140	67	34	17	17	NUM
cana-4140	67	35	)	)	PUNCT
cana-4140	67	36	𝜎𝑥𝑥|𝑥=0	𝜎𝑥𝑥|𝑥=0	NUM
cana-4140	67	37	=	=	SYM
cana-4140	67	38	−𝑝1	−𝑝1	PROPN
cana-4140	67	39	,	,	PUNCT
cana-4140	67	40	𝜎𝑥𝑦|𝑥=0	𝜎𝑥𝑦|𝑥=0	NUM
cana-4140	67	41	=	=	SYM
cana-4140	67	42	𝑞1	𝑞1	PROPN
cana-4140	67	43	,	,	PUNCT
cana-4140	67	44	(	(	PUNCT
cana-4140	67	45	18	18	NUM
cana-4140	67	46	)	)	PUNCT
cana-4140	67	47	here	here	ADV
cana-4140	67	48	,	,	PUNCT
cana-4140	67	49	δ(ω	δ(ω	PROPN
cana-4140	67	50	)	)	PUNCT
cana-4140	67	51	is	be	AUX
cana-4140	67	52	the	the	DET
cana-4140	67	53	dirac	dirac	PROPN
cana-4140	67	54	delta	delta	NOUN
cana-4140	67	55	function	function	NOUN
cana-4140	67	56	.	.	PUNCT
cana-4140	68	1	this	this	DET
cana-4140	68	2	key	key	ADJ
cana-4140	68	3	stress	stress	NOUN
cana-4140	68	4	σxx	σxx	NOUN
cana-4140	68	5	should	should	AUX
cana-4140	68	6	satisfy	satisfy	VERB
cana-4140	68	7	the	the	DET
cana-4140	68	8	boundary	boundary	ADJ
cana-4140	68	9	condition	condition	NOUN
cana-4140	68	10	∂σxx	∂σxx	NOUN
cana-4140	68	11	∂y	∂y	NOUN
cana-4140	68	12	|𝑥=0	|𝑥=0	PROPN
cana-4140	68	13	=	=	PUNCT
cana-4140	68	14	−𝑖𝜔𝑞1̅̅̅	−𝑖𝜔𝑞1̅̅̅	NOUN
cana-4140	68	15	+	+	CCONJ
cana-4140	68	16	𝑋(0	𝑋(0	NOUN
cana-4140	68	17	)	)	PUNCT
cana-4140	68	18	.	.	PUNCT
cana-4140	69	1	(	(	PUNCT
cana-4140	69	2	19	19	NUM
cana-4140	69	3	)	)	PUNCT
cana-4140	69	4	here	here	ADV
cana-4140	69	5	,	,	PUNCT
cana-4140	69	6	ω	ω	PROPN
cana-4140	69	7	denotes	denote	VERB
cana-4140	69	8	integral	integral	ADJ
cana-4140	69	9	transform	transform	NOUN
cana-4140	69	10	parameter	parameter	NOUN
cana-4140	69	11	𝑖	𝑖	NOUN
cana-4140	69	12	=	=	PUNCT
cana-4140	69	13	√−1	√−1	PROPN
cana-4140	69	14	.	.	PUNCT
cana-4140	70	1	solving	solve	VERB
cana-4140	70	2	(	(	PUNCT
cana-4140	70	3	16	16	NUM
cana-4140	70	4	)	)	PUNCT
cana-4140	70	5	-(17	-(17	X
cana-4140	70	6	)	)	PUNCT
cana-4140	70	7	,	,	PUNCT
cana-4140	70	8	particular	particular	ADJ
cana-4140	70	9	solution	solution	NOUN
cana-4140	70	10	for	for	ADP
cana-4140	70	11	𝜎xx	𝜎xx	NOUN
cana-4140	70	12	from	from	ADP
cana-4140	70	13	equation	equation	NOUN
cana-4140	70	14	(	(	PUNCT
cana-4140	70	15	17	17	NUM
cana-4140	70	16	)	)	PUNCT
cana-4140	70	17	obtained	obtain	VERB
cana-4140	70	18	in	in	ADP
cana-4140	70	19	the	the	DET
cana-4140	70	20	form	form	NOUN
cana-4140	70	21	,	,	PUNCT
cana-4140	70	22	we	we	PRON
cana-4140	70	23	obtain	obtain	VERB
cana-4140	70	24	the	the	DET
cana-4140	70	25	expression	expression	NOUN
cana-4140	70	26	as	as	ADP
cana-4140	70	27	,	,	PUNCT
cana-4140	70	28	�	�	NOUN
cana-4140	70	29	̅	̅	NOUN
cana-4140	70	30	�	�	NOUN
cana-4140	70	31	xx	xx	NOUN
cana-4140	70	32	=	=	SYM
cana-4140	70	33	−𝑝1̅̅̅𝑒𝑥𝑝(−|𝜔|𝑥	−𝑝1̅̅̅𝑒𝑥𝑝(−|𝜔|𝑥	PROPN
cana-4140	70	34	)	)	PUNCT
cana-4140	71	1	+	+	NUM
cana-4140	71	2	|𝜔|	|𝜔|	NOUN
cana-4140	71	3	2	2	NUM
cana-4140	71	4	∫	∫	PROPN
cana-4140	71	5	𝜎(𝜉	𝜎(𝜉	PROPN
cana-4140	71	6	)	)	PUNCT
cana-4140	71	7	∞	∞	NUM
cana-4140	71	8	0	0	PUNCT
cana-4140	72	1	[	[	X
cana-4140	72	2	𝑒𝑥𝑝(−|𝜔||𝑥	𝑒𝑥𝑝(−|𝜔||𝑥	PROPN
cana-4140	72	3	−	−	PROPN
cana-4140	72	4	𝜉|	𝜉|	PROPN
cana-4140	72	5	)	)	PUNCT
cana-4140	72	6	−	−	PROPN
cana-4140	73	1	𝑒𝑥𝑝(−|𝜔||𝑥	𝑒𝑥𝑝(−|𝜔||𝑥	PROPN
cana-4140	73	2	+	+	PUNCT
cana-4140	73	3	𝜉|)]𝑑𝜉	𝜉|)]𝑑𝜉	ADJ
cana-4140	73	4	−	−	NUM
cana-4140	73	5	1	1	NUM
cana-4140	73	6	2|𝜔|	2|𝜔|	NUM
cana-4140	73	7	∫	∫	NOUN
cana-4140	73	8	(	(	PUNCT
cana-4140	73	9	𝑖	𝑖	NOUN
cana-4140	73	10	�	�	NOUN
cana-4140	73	11	̅	̅	NOUN
cana-4140	73	12	�	�	NOUN
cana-4140	73	13	(𝜉	(𝜉	NOUN
cana-4140	73	14	)	)	PUNCT
cana-4140	73	15	−	−	PROPN
cana-4140	74	1	𝑑	𝑑	NOUN
cana-4140	74	2	�	�	PROPN
cana-4140	74	3	̅	̅	NOUN
cana-4140	74	4	�	�	PROPN
cana-4140	74	5	𝑑𝜉	𝑑𝜉	ADP
cana-4140	74	6	)	)	PUNCT
cana-4140	74	7	∞	∞	NOUN
cana-4140	74	8	0	0	PUNCT
cana-4140	75	1	[	[	X
cana-4140	75	2	𝑒𝑥𝑝(−|𝜔||𝑥	𝑒𝑥𝑝(−|𝜔||𝑥	PROPN
cana-4140	75	3	−	−	PROPN
cana-4140	75	4	𝜉|	𝜉|	PROPN
cana-4140	75	5	)	)	PUNCT
cana-4140	75	6	−	−	PROPN
cana-4140	76	1	𝑒𝑥𝑝(−|𝜔||𝑥	𝑒𝑥𝑝(−|𝜔||𝑥	PROPN
cana-4140	76	2	+	+	NUM
cana-4140	76	3	𝜉|)]𝑑𝜉	𝜉|)]𝑑𝜉	PROPN
cana-4140	76	4	,	,	PUNCT
cana-4140	76	5	(	(	PUNCT
cana-4140	76	6	20	20	NUM
cana-4140	76	7	)	)	PUNCT
cana-4140	76	8	which	which	PRON
cana-4140	76	9	satisfy	satisfy	VERB
cana-4140	76	10	integral	integral	ADJ
cana-4140	76	11	conditions	condition	NOUN
cana-4140	76	12	,	,	PUNCT
cana-4140	76	13	𝜔2	𝜔2	NOUN
cana-4140	76	14	∫	∫	NOUN
cana-4140	76	15	𝜎𝑒𝑥𝑝(−|𝜔|𝑥)𝑑𝜉	𝜎𝑒𝑥𝑝(−|𝜔|𝑥)𝑑𝜉	PROPN
cana-4140	76	16	=	=	SYM
cana-4140	76	17	−|𝜔|	−|𝜔|	NOUN
cana-4140	76	18	�	�	PROPN
cana-4140	76	19	̅	̅	NOUN
cana-4140	76	20	�	�	NOUN
cana-4140	76	21	∞	∞	PROPN
cana-4140	76	22	0	0	NUM
cana-4140	76	23	−	−	NUM
cana-4140	76	24	𝑖𝜔	𝑖𝜔	SYM
cana-4140	76	25	�	�	PROPN
cana-4140	76	26	̅	̅	NOUN
cana-4140	76	27	�	�	PROPN
cana-4140	76	28	−	−	NUM
cana-4140	76	29	𝑋(0	𝑋(0	NOUN
cana-4140	76	30	)	)	PUNCT
cana-4140	77	1	+	+	CCONJ
cana-4140	77	2	∫	∫	PROPN
cana-4140	77	3	(	(	PUNCT
cana-4140	77	4	𝑖	𝑖	NOUN
cana-4140	77	5	�	�	NOUN
cana-4140	77	6	̅	̅	NOUN
cana-4140	77	7	�	�	NOUN
cana-4140	77	8	(𝜉	(𝜉	NOUN
cana-4140	77	9	)	)	PUNCT
cana-4140	77	10	−	−	PROPN
cana-4140	77	11	𝑑	𝑑	NOUN
cana-4140	77	12	�	�	PROPN
cana-4140	77	13	̅	̅	NOUN
cana-4140	77	14	�	�	PROPN
cana-4140	77	15	𝑑𝜉	𝑑𝜉	ADP
cana-4140	77	16	)	)	PUNCT
cana-4140	77	17	∞	∞	NOUN
cana-4140	77	18	0	0	X
cana-4140	78	1	𝑒𝑥𝑝(−|𝜔|𝑥)𝑑𝜉.	𝑒𝑥𝑝(−|𝜔|𝑥)𝑑𝜉.	PROPN
cana-4140	78	2	(	(	PUNCT
cana-4140	78	3	21	21	NUM
cana-4140	78	4	)	)	PUNCT
cana-4140	78	5	analogously	analogously	ADV
cana-4140	78	6	,	,	PUNCT
cana-4140	78	7	we	we	PRON
cana-4140	78	8	construct	construct	VERB
cana-4140	78	9	solution	solution	NOUN
cana-4140	78	10	from	from	ADP
cana-4140	78	11	equation	equation	NOUN
cana-4140	78	12	(	(	PUNCT
cana-4140	78	13	17	17	NUM
cana-4140	78	14	)	)	PUNCT
cana-4140	78	15	to	to	ADP
cana-4140	78	16	equation	equation	NOUN
cana-4140	78	17	(	(	PUNCT
cana-4140	78	18	16	16	NUM
cana-4140	78	19	)	)	PUNCT
cana-4140	78	20	in	in	ADP
cana-4140	78	21	the	the	DET
cana-4140	78	22	form	form	NOUN
cana-4140	78	23	,	,	PUNCT
cana-4140	78	24	𝜎	𝜎	NOUN
cana-4140	78	25	=	=	X
cana-4140	78	26	𝐸∗	𝐸∗	NOUN
cana-4140	79	1	[	[	X
cana-4140	79	2	𝐴𝑒𝑥𝑝(−|𝜔|𝑥	𝐴𝑒𝑥𝑝(−|𝜔|𝑥	X
cana-4140	79	3	−	−	PROPN
cana-4140	79	4	𝛼∗	𝛼∗	PROPN
cana-4140	79	5	�	�	PROPN
cana-4140	79	6	̅	̅	NOUN
cana-4140	79	7	�	�	NOUN
cana-4140	79	8	−	−	NOUN
cana-4140	79	9	𝜋	𝜋	NOUN
cana-4140	79	10	|𝜔|	|𝜔|	NOUN
cana-4140	79	11	∫	∫	PROPN
cana-4140	79	12	𝑐∗(𝜉)𝑒𝑥𝑝(−|𝜔||𝑥	𝑐∗(𝜉)𝑒𝑥𝑝(−|𝜔||𝑥	NOUN
cana-4140	79	13	−	−	PROPN
cana-4140	80	1	𝜉|)𝑑𝜉	𝜉|)𝑑𝜉	NUM
cana-4140	80	2	+	+	NUM
cana-4140	80	3	1	1	NUM
cana-4140	80	4	2𝜔	2𝜔	NUM
cana-4140	80	5	∫	∫	NOUN
cana-4140	80	6	(	(	PUNCT
cana-4140	80	7	𝑋(𝜉	𝑋(𝜉	NOUN
cana-4140	80	8	)	)	PUNCT
cana-4140	80	9	𝐺(𝜉	𝐺(𝜉	NUM
cana-4140	80	10	)	)	PUNCT
cana-4140	80	11	+	+	CCONJ
cana-4140	80	12	1	1	NUM
cana-4140	80	13	2𝐺(𝜉	2𝐺(𝜉	NUM
cana-4140	80	14	)	)	PUNCT
cana-4140	80	15	(	(	PUNCT
cana-4140	80	16	𝑖𝜔	𝑖𝜔	X
cana-4140	80	17	�	�	PROPN
cana-4140	80	18	̅	̅	NOUN
cana-4140	80	19	�	�	NOUN
cana-4140	80	20	(𝜉	(𝜉	NOUN
cana-4140	80	21	)	)	PUNCT
cana-4140	80	22	−	−	PROPN
cana-4140	81	1	∞	∞	NUM
cana-4140	81	2	0	0	NUM
cana-4140	82	1	∞	∞	NUM
cana-4140	82	2	0	0	NUM
cana-4140	82	3	𝑑	𝑑	NOUN
cana-4140	82	4	�	�	PROPN
cana-4140	82	5	̅	̅	NOUN
cana-4140	82	6	�	�	PROPN
cana-4140	82	7	𝑑𝜉	𝑑𝜉	ADP
cana-4140	82	8	)	)	PUNCT
cana-4140	82	9	−	−	PROPN
cana-4140	82	10	1	1	NUM
cana-4140	82	11	4𝜔	4𝜔	NOUN
cana-4140	82	12	𝜎𝑥𝑥	𝜎𝑥𝑥	NOUN
cana-4140	82	13	𝐺(𝜉	𝐺(𝜉	NUM
cana-4140	82	14	)	)	PUNCT
cana-4140	82	15	)	)	PUNCT
cana-4140	83	1	𝑒𝑥𝑝(−|𝜔||𝑥	𝑒𝑥𝑝(−|𝜔||𝑥	PROPN
cana-4140	83	2	−	−	PUNCT
cana-4140	83	3	𝜉|	𝜉|	PROPN
cana-4140	83	4	)	)	PUNCT
cana-4140	83	5	]	]	PUNCT
cana-4140	84	1	𝑑𝜉	𝑑𝜉	ADP
cana-4140	84	2	,	,	PUNCT
cana-4140	84	3	(	(	PUNCT
cana-4140	84	4	22	22	NUM
cana-4140	84	5	)	)	PUNCT
cana-4140	84	6	where	where	SCONJ
cana-4140	84	7	,	,	PUNCT
cana-4140	84	8	a	a	PRON
cana-4140	84	9	is	be	AUX
cana-4140	84	10	the	the	DET
cana-4140	84	11	constant	constant	ADJ
cana-4140	84	12	of	of	ADP
cana-4140	84	13	integration	integration	NOUN
cana-4140	84	14	.	.	PUNCT
cana-4140	85	1	substitution	substitution	NOUN
cana-4140	85	2	of	of	ADP
cana-4140	85	3	the	the	DET
cana-4140	85	4	expression	expression	NOUN
cana-4140	85	5	(	(	PUNCT
cana-4140	85	6	20	20	NUM
cana-4140	85	7	)	)	PUNCT
cana-4140	85	8	into	into	ADP
cana-4140	85	9	(	(	PUNCT
cana-4140	85	10	22	22	NUM
cana-4140	85	11	)	)	PUNCT
cana-4140	85	12	yields	yield	NOUN
cana-4140	85	13	expression	expression	NOUN
cana-4140	85	14	of	of	ADP
cana-4140	85	15	the	the	DET
cana-4140	85	16	form	form	NOUN
cana-4140	85	17	,	,	PUNCT
cana-4140	85	18	𝜎	𝜎	NOUN
cana-4140	85	19	=	=	SYM
cana-4140	85	20	𝐸∗	𝐸∗	NOUN
cana-4140	86	1	[	[	X
cana-4140	86	2	𝜓	𝜓	X
cana-4140	86	3	−	−	PROPN
cana-4140	86	4	𝛼∗	𝛼∗	PROPN
cana-4140	86	5	�	�	PROPN
cana-4140	86	6	̅	̅	NOUN
cana-4140	86	7	�	�	NOUN
cana-4140	86	8	−	−	NOUN
cana-4140	86	9	𝜙1	𝜙1	NOUN
cana-4140	86	10	−	−	NOUN
cana-4140	86	11	1	1	NUM
cana-4140	86	12	8	8	NUM
cana-4140	86	13	∫	∫	NOUN
cana-4140	86	14	𝜎(𝜉1	𝜎(𝜉1	PROPN
cana-4140	86	15	∞	∞	PROPN
cana-4140	86	16	0	0	NUM
cana-4140	86	17	)	)	PUNCT
cana-4140	86	18	𝑁(𝑥	𝑁(𝑥	PROPN
cana-4140	86	19	,	,	PUNCT
cana-4140	86	20	𝜉1	𝜉1	PROPN
cana-4140	86	21	)	)	PUNCT
cana-4140	86	22	]	]	PUNCT
cana-4140	86	23	𝑑𝜉1	𝑑𝜉1	NOUN
cana-4140	86	24	.	.	PUNCT
cana-4140	87	1	(	(	PUNCT
cana-4140	87	2	23	23	NUM
cana-4140	87	3	)	)	PUNCT
cana-4140	87	4	where	where	SCONJ
cana-4140	87	5	,	,	PUNCT
cana-4140	87	6	𝑁(𝑥	𝑁(𝑥	PROPN
cana-4140	87	7	,	,	PUNCT
cana-4140	87	8	𝜉1	𝜉1	PROPN
cana-4140	87	9	)	)	PUNCT
cana-4140	87	10	=	=	SYM
cana-4140	87	11	∫	∫	PROPN
cana-4140	87	12	1	1	NUM
cana-4140	87	13	𝐺(𝜉1	𝐺(𝜉1	NOUN
cana-4140	87	14	)	)	PUNCT
cana-4140	87	15	∞	∞	NUM
cana-4140	87	16	0	0	NUM
cana-4140	88	1	𝑒𝑥𝑝(−|𝜔||𝑥	𝑒𝑥𝑝(−|𝜔||𝑥	PROPN
cana-4140	88	2	−	−	PROPN
cana-4140	88	3	𝜉|)𝑑𝜉1	𝜉|)𝑑𝜉1	NOUN
cana-4140	88	4	;	;	PUNCT
cana-4140	88	5	𝜓	𝜓	X
cana-4140	88	6	=	=	X
cana-4140	88	7	𝜋	𝜋	NOUN
cana-4140	88	8	𝜔	𝜔	PRON
cana-4140	88	9	∫	∫	NOUN
cana-4140	88	10	𝑐∗𝑒𝑥𝑝(−|𝜔||𝑥	𝑐∗𝑒𝑥𝑝(−|𝜔||𝑥	ADJ
cana-4140	88	11	−	−	PROPN
cana-4140	88	12	𝜉|)𝑑𝜉	𝜉|)𝑑𝜉	NUM
cana-4140	88	13	∞	∞	PROPN
cana-4140	88	14	0	0	NUM
cana-4140	88	15	;	;	PUNCT
cana-4140	88	16	𝜙1	𝜙1	NOUN
cana-4140	88	17	=	=	SYM
cana-4140	88	18	1	1	NUM
cana-4140	88	19	2𝜔	2𝜔	NUM
cana-4140	88	20	∫	∫	NOUN
cana-4140	88	21	𝑋(𝜉	𝑋(𝜉	NOUN
cana-4140	88	22	)	)	PUNCT
cana-4140	88	23	𝐺(𝜉	𝐺(𝜉	NOUN
cana-4140	88	24	)	)	PUNCT
cana-4140	88	25	𝜔	𝜔	PRON
cana-4140	88	26	0	0	NUM
cana-4140	89	1	+	+	CCONJ
cana-4140	89	2	1	1	NUM
cana-4140	89	3	𝐺(𝜉	𝐺(𝜉	NOUN
cana-4140	89	4	)	)	PUNCT
cana-4140	89	5	(	(	PUNCT
cana-4140	89	6	(	(	PUNCT
cana-4140	89	7	𝑖𝜔𝑋(𝜉	𝑖𝜔𝑋(𝜉	NOUN
cana-4140	89	8	)	)	PUNCT
cana-4140	89	9	+	+	CCONJ
cana-4140	89	10	𝑑	𝑑	PROPN
cana-4140	89	11	�	�	PROPN
cana-4140	89	12	̅	̅	NOUN
cana-4140	89	13	�	�	PROPN
cana-4140	89	14	𝑑𝜉	𝑑𝜉	ADP
cana-4140	89	15	)	)	PUNCT
cana-4140	89	16	.	.	PUNCT
cana-4140	90	1	following	follow	VERB
cana-4140	90	2	the	the	DET
cana-4140	90	3	solution	solution	NOUN
cana-4140	90	4	technique	technique	NOUN
cana-4140	90	5	[	[	X
cana-4140	90	6	7	7	NUM
cana-4140	90	7	]	]	PUNCT
cana-4140	90	8	,	,	PUNCT
cana-4140	90	9	construct	construct	VERB
cana-4140	90	10	the	the	DET
cana-4140	90	11	solution	solution	NOUN
cana-4140	90	12	to	to	ADP
cana-4140	90	13	the	the	DET
cana-4140	90	14	integral	integral	ADJ
cana-4140	90	15	equation	equation	NOUN
cana-4140	90	16	(	(	PUNCT
cana-4140	90	17	23	23	NUM
cana-4140	90	18	)	)	PUNCT
cana-4140	90	19	as	as	ADP
cana-4140	90	20	the	the	DET
cana-4140	90	21	limit	limit	NOUN
cana-4140	90	22	,	,	PUNCT
cana-4140	90	23	𝜎	𝜎	PROPN
cana-4140	90	24	=	=	PROPN
cana-4140	90	25	lim	lim	PROPN
cana-4140	90	26	𝑛→∞	𝑛→∞	NUM
cana-4140	90	27	𝜎𝑛.	𝜎𝑛.	VERB
cana-4140	90	28	we	we	PRON
cana-4140	90	29	can	can	AUX
cana-4140	90	30	solve	solve	VERB
cana-4140	90	31	(	(	PUNCT
cana-4140	90	32	23	23	NUM
cana-4140	90	33	)	)	PUNCT
cana-4140	90	34	,	,	PUNCT
cana-4140	90	35	by	by	ADP
cana-4140	90	36	simple	simple	ADJ
cana-4140	90	37	iteration	iteration	NOUN
cana-4140	90	38	method	method	NOUN
cana-4140	90	39	[	[	X
cana-4140	90	40	7	7	NUM
cana-4140	90	41	]	]	PUNCT
cana-4140	90	42	as	as	SCONJ
cana-4140	90	43	follows	follow	VERB
cana-4140	90	44	,	,	PUNCT
cana-4140	90	45	communications	communication	NOUN
cana-4140	90	46	on	on	ADP
cana-4140	90	47	applied	apply	VERB
cana-4140	90	48	nonlinear	nonlinear	ADJ
cana-4140	90	49	analysis	analysis	NOUN
cana-4140	90	50	issn	issn	NOUN
cana-4140	90	51	:	:	PUNCT
cana-4140	90	52	1074	1074	NUM
cana-4140	90	53	-	-	PUNCT
cana-4140	90	54	133x	133x	NUM
cana-4140	90	55	vol	vol	NOUN
cana-4140	90	56	32	32	NUM
cana-4140	90	57	no	no	NOUN
cana-4140	90	58	.	.	NOUN
cana-4140	90	59	9(s	9(s	NUM
cana-4140	90	60	)	)	PUNCT
cana-4140	90	61	(	(	PUNCT
cana-4140	90	62	2025	2025	NUM
cana-4140	90	63	)	)	PUNCT
cana-4140	90	64	1316	1316	NUM
cana-4140	90	65	https://internationalpubls.com	https://internationalpubls.com	X
cana-4140	91	1	𝜎𝑛	𝜎𝑛	NOUN
cana-4140	91	2	=	=	PUNCT
cana-4140	91	3	𝐸∗	𝐸∗	NOUN
cana-4140	91	4	[	[	X
cana-4140	91	5	𝜓	𝜓	X
cana-4140	91	6	−	−	PROPN
cana-4140	91	7	𝛼∗	𝛼∗	PROPN
cana-4140	91	8	�	�	PROPN
cana-4140	91	9	̅	̅	NOUN
cana-4140	91	10	�	�	NOUN
cana-4140	91	11	−	−	NOUN
cana-4140	91	12	𝜙1	𝜙1	NOUN
cana-4140	91	13	−	−	NOUN
cana-4140	91	14	1	1	NUM
cana-4140	91	15	8	8	NUM
cana-4140	91	16	∫	∫	NOUN
cana-4140	92	1	𝜎𝑛−1(𝜉1	𝜎𝑛−1(𝜉1	PROPN
cana-4140	92	2	∞	∞	PROPN
cana-4140	92	3	0	0	NUM
cana-4140	92	4	)	)	PUNCT
cana-4140	92	5	𝑁(𝑥	𝑁(𝑥	PROPN
cana-4140	92	6	,	,	PUNCT
cana-4140	92	7	𝜉1	𝜉1	PROPN
cana-4140	92	8	)	)	PUNCT
cana-4140	92	9	]	]	PUNCT
cana-4140	93	1	𝑑𝜉1	𝑑𝜉1	NOUN
cana-4140	93	2	;	;	PUNCT
cana-4140	93	3	(	(	PUNCT
cana-4140	93	4	24	24	NUM
cana-4140	93	5	)	)	PUNCT
cana-4140	93	6	𝜎0	𝜎0	NOUN
cana-4140	93	7	=	=	SYM
cana-4140	93	8	0	0	NUM
cana-4140	93	9	,	,	PUNCT
cana-4140	93	10	𝑛	𝑛	NOUN
cana-4140	93	11	=	=	SYM
cana-4140	93	12	1	1	NUM
cana-4140	93	13	,	,	PUNCT
cana-4140	93	14	2	2	NUM
cana-4140	93	15	,	,	PUNCT
cana-4140	93	16	3	3	NUM
cana-4140	93	17	.	.	X
cana-4140	93	18	..	..	PUNCT
cana-4140	94	1	for	for	ADP
cana-4140	94	2	n	n	NOUN
cana-4140	94	3	=	=	SYM
cana-4140	94	4	1	1	NUM
cana-4140	94	5	iteration	iteration	NOUN
cana-4140	94	6	can	can	AUX
cana-4140	94	7	be	be	AUX
cana-4140	94	8	calculated	calculate	VERB
cana-4140	94	9	easily	easily	ADV
cana-4140	94	10	,	,	PUNCT
cana-4140	94	11	let	let	VERB
cana-4140	94	12	us	we	PRON
cana-4140	94	13	represent	represent	VERB
cana-4140	94	14	the	the	DET
cana-4140	94	15	expression	expression	NOUN
cana-4140	94	16	(	(	PUNCT
cana-4140	94	17	24	24	NUM
cana-4140	94	18	)	)	PUNCT
cana-4140	94	19	in	in	ADP
cana-4140	94	20	the	the	DET
cana-4140	94	21	form	form	NOUN
cana-4140	94	22	for	for	ADP
cana-4140	94	23	the	the	DET
cana-4140	94	24	n	n	PRON
cana-4140	94	25	th	th	X
cana-4140	94	26	iteration	iteration	NOUN
cana-4140	94	27	,	,	PUNCT
cana-4140	94	28	𝜎𝑛	𝜎𝑛	PRON
cana-4140	94	29	=	=	SYM
cana-4140	94	30	𝜎1	𝜎1	PROPN
cana-4140	94	31	+	+	CCONJ
cana-4140	94	32	�	�	NOUN
cana-4140	94	33	̅	̅	NOUN
cana-4140	94	34	�	�	NOUN
cana-4140	94	35	𝑛−1	𝑛−1	NUM
cana-4140	94	36	.	.	PUNCT
cana-4140	95	1	by	by	ADP
cana-4140	95	2	the	the	DET
cana-4140	95	3	substitution	substitution	NOUN
cana-4140	95	4	of	of	ADP
cana-4140	95	5	(	(	PUNCT
cana-4140	95	6	20	20	NUM
cana-4140	95	7	)	)	PUNCT
cana-4140	95	8	into	into	ADP
cana-4140	95	9	(	(	PUNCT
cana-4140	95	10	23	23	NUM
cana-4140	95	11	)	)	PUNCT
cana-4140	95	12	,	,	PUNCT
cana-4140	95	13	we	we	PRON
cana-4140	95	14	obtain	obtain	VERB
cana-4140	95	15	,	,	PUNCT
cana-4140	95	16	𝜎	𝜎	NOUN
cana-4140	95	17	=	=	SYM
cana-4140	95	18	𝐸∗	𝐸∗	NOUN
cana-4140	96	1	[	[	X
cana-4140	96	2	𝜓	𝜓	X
cana-4140	96	3	+	+	CCONJ
cana-4140	96	4	𝑝1	𝑝1	NOUN
cana-4140	96	5	+	+	CCONJ
cana-4140	96	6	𝐴𝑒𝑥𝑝(−|𝑠|𝑥	𝐴𝑒𝑥𝑝(−|𝑠|𝑥	NOUN
cana-4140	96	7	−	−	PROPN
cana-4140	96	8	𝛼∗	𝛼∗	PROPN
cana-4140	96	9	�	�	PROPN
cana-4140	96	10	̅	̅	NOUN
cana-4140	96	11	�	�	PROPN
cana-4140	96	12	−	−	PROPN
cana-4140	96	13	𝜙2	𝜙2	NOUN
cana-4140	96	14	−	−	NOUN
cana-4140	96	15	1	1	NUM
cana-4140	96	16	8	8	NUM
cana-4140	96	17	∫	∫	NOUN
cana-4140	96	18	𝜎(𝜉1	𝜎(𝜉1	PROPN
cana-4140	96	19	∞	∞	PROPN
cana-4140	96	20	0	0	NUM
cana-4140	96	21	)	)	PUNCT
cana-4140	96	22	𝑁(𝑥	𝑁(𝑥	PROPN
cana-4140	96	23	,	,	PUNCT
cana-4140	96	24	𝜉1	𝜉1	PROPN
cana-4140	96	25	)	)	PUNCT
cana-4140	96	26	]	]	PUNCT
cana-4140	97	1	𝑑𝜉1	𝑑𝜉1	PROPN
cana-4140	97	2	,	,	PUNCT
cana-4140	97	3	(	(	PUNCT
cana-4140	97	4	25	25	NUM
cana-4140	97	5	)	)	PUNCT
cana-4140	97	6	𝐻𝑒𝑟𝑒	𝐻𝑒𝑟𝑒	PROPN
cana-4140	97	7	,	,	PUNCT
cana-4140	97	8	𝑁(𝑥	𝑁(𝑥	NOUN
cana-4140	97	9	,	,	PUNCT
cana-4140	97	10	𝜉1	𝜉1	PROPN
cana-4140	97	11	)	)	PUNCT
cana-4140	97	12	=	=	SYM
cana-4140	98	1	∫	∫	PROPN
cana-4140	98	2	1	1	NUM
cana-4140	98	3	𝐺(𝜉1	𝐺(𝜉1	NOUN
cana-4140	98	4	)	)	PUNCT
cana-4140	98	5	∞	∞	NOUN
cana-4140	98	6	0	0	PUNCT
cana-4140	99	1	[	[	X
cana-4140	99	2	[	[	X
cana-4140	99	3	𝑒𝑥𝑝(−|𝜔|(|𝜉	𝑒𝑥𝑝(−|𝜔|(|𝜉	NOUN
cana-4140	99	4	−	−	ADP
cana-4140	99	5	𝜉1|	𝜉1|	NOUN
cana-4140	99	6	+	+	NUM
cana-4140	99	7	|𝑥	|𝑥	NOUN
cana-4140	99	8	−	−	DET
cana-4140	99	9	𝜉1|	𝜉1|	PROPN
cana-4140	99	10	)	)	PUNCT
cana-4140	99	11	−	−	PROPN
cana-4140	100	1	𝑒𝑥𝑝(−|𝜔||𝜉	𝑒𝑥𝑝(−|𝜔||𝜉	PROPN
cana-4140	100	2	+	+	CCONJ
cana-4140	100	3	𝜉1||𝑦	𝜉1||𝑦	PROPN
cana-4140	100	4	+	+	CCONJ
cana-4140	100	5	𝜉1|	𝜉1|	NOUN
cana-4140	100	6	)	)	PUNCT
cana-4140	100	7	]	]	PUNCT
cana-4140	100	8	]	]	PUNCT
cana-4140	100	9	.	.	PUNCT
cana-4140	101	1	5	5	X
cana-4140	101	2	.	.	X
cana-4140	101	3	examples	example	NOUN
cana-4140	101	4	to	to	PART
cana-4140	101	5	find	find	VERB
cana-4140	101	6	the	the	DET
cana-4140	101	7	exact	exact	ADJ
cana-4140	101	8	solution	solution	NOUN
cana-4140	101	9	,	,	PUNCT
cana-4140	101	10	consider	consider	VERB
cana-4140	101	11	an	an	DET
cana-4140	101	12	example	example	NOUN
cana-4140	101	13	of	of	ADP
cana-4140	101	14	inhomogeneity	inhomogeneity	NOUN
cana-4140	101	15	,	,	PUNCT
cana-4140	101	16	let	let	VERB
cana-4140	101	17	𝑋	𝑋	PROPN
cana-4140	101	18	=	=	SYM
cana-4140	101	19	𝑌	𝑌	PROPN
cana-4140	101	20	=	=	SYM
cana-4140	101	21	𝑇	𝑇	PROPN
cana-4140	101	22	=	=	SYM
cana-4140	101	23	0	0	PROPN
cana-4140	101	24	,	,	PUNCT
cana-4140	101	25	𝐸	𝐸	NOUN
cana-4140	101	26	=	=	SYM
cana-4140	101	27	𝐸0𝑓(𝑥	𝐸0𝑓(𝑥	NOUN
cana-4140	101	28	)	)	PUNCT
cana-4140	101	29	,	,	PUNCT
cana-4140	101	30	𝑓(𝑥	𝑓(𝑥	NOUN
cana-4140	101	31	)	)	PUNCT
cana-4140	101	32	=	=	SYM
cana-4140	101	33	𝑒𝑥𝑝(𝑥4	𝑒𝑥𝑝(𝑥4	PROPN
cana-4140	101	34	)	)	PUNCT
cana-4140	101	35	,	,	PUNCT
cana-4140	101	36	𝐸0	𝐸0	NOUN
cana-4140	101	37	=	=	SYM
cana-4140	101	38	𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡	𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡	NOUN
cana-4140	101	39	,	,	PUNCT
cana-4140	101	40	𝑏	𝑏	PROPN
cana-4140	101	41	>	>	X
cana-4140	101	42	0	0	PUNCT
cana-4140	102	1	=	=	NUM
cana-4140	102	2	𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡	𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡	NOUN
cana-4140	102	3	from	from	ADP
cana-4140	102	4	(	(	PUNCT
cana-4140	102	5	20	20	NUM
cana-4140	102	6	)	)	PUNCT
cana-4140	102	7	,	,	PUNCT
cana-4140	102	8	we	we	PRON
cana-4140	102	9	obtain	obtain	VERB
cana-4140	102	10	required	require	VERB
cana-4140	102	11	thermal	thermal	ADJ
cana-4140	102	12	stresses	stress	NOUN
cana-4140	102	13	𝜎𝑥𝑥	𝜎𝑥𝑥	VERB
cana-4140	102	14	,	,	PUNCT
cana-4140	102	15	as	as	SCONJ
cana-4140	102	16	follows	follow	VERB
cana-4140	102	17	𝜎xx	𝜎xx	NOUN
cana-4140	102	18	=	=	SYM
cana-4140	102	19	−𝑝1̅̅̅𝑒𝑥𝑝(−|𝜔|𝑥	−𝑝1̅̅̅𝑒𝑥𝑝(−|𝜔|𝑥	PROPN
cana-4140	102	20	)	)	PUNCT
cana-4140	103	1	+	+	NUM
cana-4140	103	2	|𝜔|	|𝜔|	NOUN
cana-4140	103	3	2	2	NUM
cana-4140	103	4	∫	∫	PROPN
cana-4140	103	5	𝜎(𝜉	𝜎(𝜉	PROPN
cana-4140	103	6	)	)	PUNCT
cana-4140	103	7	∞	∞	NUM
cana-4140	103	8	0	0	PUNCT
cana-4140	104	1	[	[	X
cana-4140	104	2	𝑒𝑥𝑝(−|𝜔||𝑥	𝑒𝑥𝑝(−|𝜔||𝑥	PROPN
cana-4140	104	3	−	−	PROPN
cana-4140	104	4	𝜉|	𝜉|	PROPN
cana-4140	104	5	)	)	PUNCT
cana-4140	104	6	−	−	PROPN
cana-4140	105	1	𝑒𝑥𝑝(−|𝜔||𝑥	𝑒𝑥𝑝(−|𝜔||𝑥	PROPN
cana-4140	106	1	+	+	CCONJ
cana-4140	106	2	𝜉|)]𝑑𝜉.	𝜉|)]𝑑𝜉.	PROPN
cana-4140	106	3	from	from	ADP
cana-4140	106	4	(	(	PUNCT
cana-4140	106	5	25	25	NUM
cana-4140	106	6	)	)	PUNCT
cana-4140	106	7	𝜎	𝜎	NOUN
cana-4140	106	8	=	=	SYM
cana-4140	106	9	𝐸∗	𝐸∗	NOUN
cana-4140	107	1	[	[	X
cana-4140	107	2	𝜓	𝜓	X
cana-4140	107	3	+	+	CCONJ
cana-4140	107	4	𝑝1	𝑝1	NOUN
cana-4140	107	5	+	+	CCONJ
cana-4140	107	6	𝐴𝑒𝑥𝑝(−|𝑠|𝑥	𝐴𝑒𝑥𝑝(−|𝑠|𝑥	NOUN
cana-4140	107	7	−	−	PROPN
cana-4140	107	8	𝛼∗	𝛼∗	PROPN
cana-4140	107	9	�	�	PROPN
cana-4140	107	10	̅	̅	NOUN
cana-4140	107	11	�	�	PROPN
cana-4140	107	12	−	−	PROPN
cana-4140	107	13	𝜙2	𝜙2	NOUN
cana-4140	107	14	−	−	NOUN
cana-4140	107	15	1	1	NUM
cana-4140	107	16	8	8	NUM
cana-4140	107	17	∫	∫	NOUN
cana-4140	107	18	𝜎(𝜉1	𝜎(𝜉1	PROPN
cana-4140	107	19	∞	∞	PROPN
cana-4140	107	20	0	0	NUM
cana-4140	107	21	)	)	PUNCT
cana-4140	107	22	𝑁(𝑥	𝑁(𝑥	PROPN
cana-4140	107	23	,	,	PUNCT
cana-4140	107	24	𝜉1	𝜉1	PROPN
cana-4140	107	25	)	)	PUNCT
cana-4140	107	26	]	]	PUNCT
cana-4140	108	1	𝑑𝜉1	𝑑𝜉1	NOUN
cana-4140	108	2	.	.	PUNCT
cana-4140	109	1	consider	consider	VERB
cana-4140	109	2	the	the	DET
cana-4140	109	3	poisson	poisson	NOUN
cana-4140	109	4	’s	’s	PART
cana-4140	109	5	ratio	ratio	NOUN
cana-4140	109	6	µ=const	µ=const	ADP
cana-4140	109	7	.	.	PUNCT
cana-4140	110	1	by	by	ADP
cana-4140	110	2	the	the	DET
cana-4140	110	3	relation	relation	NOUN
cana-4140	110	4	between	between	ADP
cana-4140	110	5	young	young	PROPN
cana-4140	110	6	’s	’s	PART
cana-4140	110	7	and	and	CCONJ
cana-4140	110	8	shear	shear	ADJ
cana-4140	110	9	modulus	modulus	ADJ
cana-4140	110	10	latter	latter	NOUN
cana-4140	110	11	can	can	AUX
cana-4140	110	12	represent	represent	VERB
cana-4140	110	13	in	in	ADP
cana-4140	110	14	the	the	DET
cana-4140	110	15	form	form	NOUN
cana-4140	110	16	𝐸	𝐸	PROPN
cana-4140	110	17	=	=	SYM
cana-4140	110	18	𝐸0𝑓(𝑥)where	𝐸0𝑓(𝑥)where	NOUN
cana-4140	110	19	,	,	PUNCT
cana-4140	110	20	𝐺0	𝐺0	PROPN
cana-4140	110	21	=	=	SYM
cana-4140	110	22	𝐸0	𝐸0	ADJ
cana-4140	110	23	(	(	PUNCT
cana-4140	110	24	1	1	NUM
cana-4140	110	25	1+𝜇	1+𝜇	NUM
cana-4140	110	26	)	)	PUNCT
cana-4140	110	27	.	.	PUNCT
cana-4140	111	1	we	we	PRON
cana-4140	111	2	can	can	AUX
cana-4140	111	3	see	see	VERB
cana-4140	111	4	that	that	SCONJ
cana-4140	111	5	figure-1	figure-1	PROPN
cana-4140	111	6	indicates	indicate	VERB
cana-4140	111	7	the	the	DET
cana-4140	111	8	distribution	distribution	NOUN
cana-4140	111	9	of	of	ADP
cana-4140	111	10	µ(x	µ(x	NOUN
cana-4140	111	11	)	)	PUNCT
cana-4140	111	12	and	and	CCONJ
cana-4140	111	13	figure-2	figure-2	PRON
cana-4140	111	14	indicates	indicate	VERB
cana-4140	111	15	the	the	DET
cana-4140	111	16	distribution	distribution	NOUN
cana-4140	111	17	of	of	ADP
cana-4140	111	18	normal	normal	ADJ
cana-4140	111	19	stress	stress	NOUN
cana-4140	111	20	σyy	σyy	NOUN
cana-4140	111	21	,	,	PUNCT
cana-4140	111	22	σxy	σxy	NOUN
cana-4140	111	23	respectively	respectively	ADV
cana-4140	111	24	at	at	ADP
cana-4140	111	25	α=	α=	NOUN
cana-4140	111	26	1	1	NUM
cana-4140	111	27	,	,	PUNCT
cana-4140	111	28	1.5	1.5	NUM
cana-4140	111	29	,	,	PUNCT
cana-4140	111	30	2	2	NUM
cana-4140	111	31	respectively	respectively	ADV
cana-4140	111	32	.	.	PUNCT
cana-4140	112	1	we	we	PRON
cana-4140	112	2	conclude	conclude	VERB
cana-4140	112	3	that	that	DET
cana-4140	112	4	σxx,,σxy	σxx,,σxy	PROPN
cana-4140	112	5	,	,	PUNCT
cana-4140	112	6	𝜎are	𝜎are	VERB
cana-4140	112	7	independent	independent	ADJ
cana-4140	112	8	on	on	ADP
cana-4140	112	9	g	g	PROPN
cana-4140	112	10	and	and	CCONJ
cana-4140	112	11	depend	depend	VERB
cana-4140	112	12	on	on	ADP
cana-4140	112	13	poisson	poisson	PROPN
cana-4140	112	14	’s	’s	PART
cana-4140	112	15	ratio	ratio	NOUN
cana-4140	112	16	ν	ν	NOUN
cana-4140	112	17	which	which	PRON
cana-4140	112	18	vary	vary	VERB
cana-4140	112	19	with	with	ADP
cana-4140	112	20	x	x	NOUN
cana-4140	112	21	-	-	NOUN
cana-4140	112	22	coordinate	coordinate	NOUN
cana-4140	112	23	.	.	PUNCT
cana-4140	113	1	figure	figure	NOUN
cana-4140	113	2	1	1	NUM
cana-4140	113	3	:	:	PUNCT
cana-4140	113	4	distribution	distribution	NOUN
cana-4140	113	5	of	of	ADP
cana-4140	113	6	𝝁(𝒙	𝝁(𝒙	NOUN
cana-4140	113	7	)	)	PUNCT
cana-4140	114	1	𝒇𝒐𝒓	𝒇𝒐𝒓	NOUN
cana-4140	114	2	𝜶	𝜶	SYM
cana-4140	114	3	=	=	SYM
cana-4140	114	4	𝟏	𝟏	NUM
cana-4140	114	5	communications	communication	NOUN
cana-4140	114	6	on	on	ADP
cana-4140	114	7	applied	apply	VERB
cana-4140	114	8	nonlinear	nonlinear	ADJ
cana-4140	114	9	analysis	analysis	NOUN
cana-4140	114	10	issn	issn	NOUN
cana-4140	114	11	:	:	PUNCT
cana-4140	114	12	1074	1074	NUM
cana-4140	114	13	-	-	PUNCT
cana-4140	114	14	133x	133x	NUM
cana-4140	114	15	vol	vol	NOUN
cana-4140	114	16	32	32	NUM
cana-4140	114	17	no	no	NOUN
cana-4140	114	18	.	.	NOUN
cana-4140	114	19	9(s	9(s	NUM
cana-4140	114	20	)	)	PUNCT
cana-4140	114	21	(	(	PUNCT
cana-4140	114	22	2025	2025	NUM
cana-4140	114	23	)	)	PUNCT
cana-4140	114	24	1317	1317	NUM
cana-4140	114	25	https://internationalpubls.com	https://internationalpubls.com	X
cana-4140	114	26	figure	figure	NOUN
cana-4140	114	27	2	2	NUM
cana-4140	114	28	:	:	PUNCT
cana-4140	114	29	distribution	distribution	NOUN
cana-4140	114	30	of	of	ADP
cana-4140	114	31	𝝈𝒙𝒙	𝝈𝒙𝒙	PROPN
cana-4140	114	32	𝒇𝒐𝒓	𝒇𝒐𝒓	NOUN
cana-4140	114	33	𝜶	𝜶	NOUN
cana-4140	114	34	=	=	SYM
cana-4140	114	35	𝟏	𝟏	PROPN
cana-4140	114	36	,	,	PUNCT
cana-4140	114	37	𝟏.	𝟏.	X
cana-4140	114	38	𝟓	𝟓	NUM
cana-4140	114	39	,	,	PUNCT
cana-4140	114	40	𝟐	𝟐	NUM
cana-4140	114	41	6	6	NUM
cana-4140	114	42	.	.	PUNCT
cana-4140	114	43	conclusion	conclusion	NOUN
cana-4140	114	44	in	in	ADP
cana-4140	114	45	this	this	DET
cana-4140	114	46	manuscript	manuscript	NOUN
cana-4140	114	47	,	,	PUNCT
cana-4140	114	48	we	we	PRON
cana-4140	114	49	studied	study	VERB
cana-4140	114	50	an	an	DET
cana-4140	114	51	numerical	numerical	ADJ
cana-4140	114	52	approach	approach	NOUN
cana-4140	114	53	to	to	PART
cana-4140	114	54	solve	solve	VERB
cana-4140	114	55	the	the	DET
cana-4140	114	56	two	two	NUM
cana-4140	114	57	-	-	PUNCT
cana-4140	114	58	dimensional	dimensional	ADJ
cana-4140	114	59	problems	problem	NOUN
cana-4140	114	60	of	of	ADP
cana-4140	114	61	elasticity	elasticity	NOUN
cana-4140	114	62	and	and	CCONJ
cana-4140	114	63	thermoelasticity	thermoelasticity	NOUN
cana-4140	114	64	in	in	ADP
cana-4140	114	65	terms	term	NOUN
cana-4140	114	66	of	of	ADP
cana-4140	114	67	stresses	stress	NOUN
cana-4140	114	68	for	for	ADP
cana-4140	114	69	isotropic	isotropic	ADJ
cana-4140	114	70	material	material	NOUN
cana-4140	114	71	in	in	ADP
cana-4140	114	72	an	an	DET
cana-4140	114	73	inhomogeneous	inhomogeneous	ADJ
cana-4140	114	74	strip	strip	NOUN
cana-4140	114	75	which	which	PRON
cana-4140	114	76	is	be	AUX
cana-4140	114	77	infinite	infinite	ADJ
cana-4140	114	78	.	.	PUNCT
cana-4140	115	1	this	this	DET
cana-4140	115	2	approach	approach	NOUN
cana-4140	115	3	is	be	AUX
cana-4140	115	4	placed	place	VERB
cana-4140	115	5	on	on	ADP
cana-4140	115	6	the	the	DET
cana-4140	115	7	direct	direct	ADJ
cana-4140	115	8	integration	integration	NOUN
cana-4140	115	9	of	of	ADP
cana-4140	115	10	differential	differential	ADJ
cana-4140	115	11	equilibrium	equilibrium	NOUN
cana-4140	115	12	equations	equation	NOUN
cana-4140	115	13	.	.	PUNCT
cana-4140	116	1	this	this	DET
cana-4140	116	2	technique	technique	NOUN
cana-4140	116	3	permits	permit	VERB
cana-4140	116	4	to	to	PART
cana-4140	116	5	construct	construct	VERB
cana-4140	116	6	analytical	analytical	ADJ
cana-4140	116	7	solution	solution	NOUN
cana-4140	116	8	for	for	ADP
cana-4140	116	9	interdependence	interdependence	NOUN
cana-4140	116	10	between	between	ADP
cana-4140	116	11	the	the	DET
cana-4140	116	12	elastic	elastic	ADJ
cana-4140	116	13	modulie	modulie	NOUN
cana-4140	116	14	of	of	ADP
cana-4140	116	15	an	an	DET
cana-4140	116	16	isotropic	isotropic	ADJ
cana-4140	116	17	material	material	NOUN
cana-4140	116	18	.	.	PUNCT
cana-4140	117	1	we	we	PRON
cana-4140	117	2	reduce	reduce	VERB
cana-4140	117	3	the	the	DET
cana-4140	117	4	governing	govern	VERB
cana-4140	117	5	integro	integro	ADJ
cana-4140	117	6	-	-	PUNCT
cana-4140	117	7	differential	differential	NOUN
cana-4140	117	8	equations	equation	NOUN
cana-4140	117	9	with	with	ADP
cana-4140	117	10	variable	variable	ADJ
cana-4140	117	11	coefficients	coefficient	NOUN
cana-4140	117	12	in	in	ADP
cana-4140	117	13	accordance	accordance	NOUN
cana-4140	117	14	with	with	ADP
cana-4140	117	15	compatibility	compatibility	NOUN
cana-4140	117	16	and	and	CCONJ
cana-4140	117	17	equilibrium	equilibrium	NOUN
cana-4140	117	18	equations	equation	NOUN
cana-4140	117	19	.	.	PUNCT
cana-4140	118	1	the	the	DET
cana-4140	118	2	calculation	calculation	NOUN
cana-4140	118	3	for	for	ADP
cana-4140	118	4	constructing	construct	VERB
cana-4140	118	5	the	the	DET
cana-4140	118	6	solution	solution	NOUN
cana-4140	118	7	can	can	AUX
cana-4140	118	8	be	be	AUX
cana-4140	118	9	also	also	ADV
cana-4140	118	10	applied	apply	VERB
cana-4140	118	11	to	to	PART
cana-4140	118	12	solve	solve	VERB
cana-4140	118	13	optimization	optimization	NOUN
cana-4140	118	14	problems	problem	NOUN
cana-4140	118	15	,	,	PUNCT
cana-4140	118	16	comparable	comparable	ADJ
cana-4140	118	17	inverse	inverse	NOUN
cana-4140	118	18	thermoelasticity	thermoelasticity	NOUN
cana-4140	118	19	problems	problem	NOUN
cana-4140	118	20	in	in	ADP
cana-4140	118	21	terms	term	NOUN
cana-4140	118	22	of	of	ADP
cana-4140	118	23	stresses	stress	NOUN
cana-4140	118	24	.	.	PUNCT
cana-4140	119	1	in	in	ADP
cana-4140	119	2	this	this	DET
cana-4140	119	3	method	method	NOUN
cana-4140	119	4	we	we	PRON
cana-4140	119	5	can	can	AUX
cana-4140	119	6	easily	easily	ADV
cana-4140	119	7	calculate	calculate	VERB
cana-4140	119	8	the	the	DET
cana-4140	119	9	stressed	stressed	ADJ
cana-4140	119	10	state	state	NOUN
cana-4140	119	11	in	in	ADP
cana-4140	119	12	an	an	DET
cana-4140	119	13	infinite	infinite	ADJ
cana-4140	119	14	strip	strip	NOUN
cana-4140	119	15	,	,	PUNCT
cana-4140	119	16	as	as	SCONJ
cana-4140	119	17	compare	compare	ADJ
cana-4140	119	18	to	to	ADP
cana-4140	119	19	solving	solve	VERB
cana-4140	119	20	such	such	ADJ
cana-4140	119	21	problem	problem	NOUN
cana-4140	119	22	in	in	ADP
cana-4140	119	23	terms	term	NOUN
cana-4140	119	24	of	of	ADP
cana-4140	119	25	displacement	displacement	NOUN
cana-4140	119	26	.	.	PUNCT
cana-4140	120	1	with	with	ADP
cana-4140	120	2	the	the	DET
cana-4140	120	3	help	help	NOUN
cana-4140	120	4	of	of	ADP
cana-4140	120	5	simple	simple	ADJ
cana-4140	120	6	iteration	iteration	NOUN
cana-4140	120	7	method	method	NOUN
cana-4140	120	8	,	,	PUNCT
cana-4140	120	9	we	we	PRON
cana-4140	120	10	have	have	AUX
cana-4140	120	11	solved	solve	VERB
cana-4140	120	12	these	these	DET
cana-4140	120	13	governing	govern	VERB
cana-4140	120	14	equations	equation	NOUN
cana-4140	120	15	.	.	PUNCT
cana-4140	121	1	this	this	DET
cana-4140	121	2	method	method	NOUN
cana-4140	121	3	gives	give	VERB
cana-4140	121	4	exact	exact	ADJ
cana-4140	121	5	analytical	analytical	ADJ
cana-4140	121	6	solutions	solution	NOUN
cana-4140	121	7	if	if	SCONJ
cana-4140	121	8	the	the	DET
cana-4140	121	9	shear	shear	NOUN
cana-4140	121	10	modulus	modulus	NOUN
cana-4140	121	11	is	be	AUX
cana-4140	121	12	reciprocal	reciprocal	ADJ
cana-4140	121	13	of	of	ADP
cana-4140	121	14	linear	linear	ADJ
cana-4140	121	15	function	function	NOUN
cana-4140	121	16	in	in	ADP
cana-4140	121	17	cartesian	cartesian	ADJ
cana-4140	121	18	coordinate	coordinate	NOUN
cana-4140	121	19	system	system	NOUN
cana-4140	121	20	for	for	ADP
cana-4140	121	21	corresponding	correspond	VERB
cana-4140	121	22	problems	problem	NOUN
cana-4140	121	23	.	.	PUNCT
cana-4140	122	1	direct	direct	ADJ
cana-4140	122	2	integration	integration	NOUN
cana-4140	122	3	method	method	NOUN
cana-4140	122	4	is	be	AUX
cana-4140	122	5	very	very	ADV
cana-4140	122	6	useful	useful	ADJ
cana-4140	122	7	technique	technique	NOUN
cana-4140	122	8	to	to	PART
cana-4140	122	9	solve	solve	VERB
cana-4140	122	10	the	the	DET
cana-4140	122	11	boundary	boundary	ADJ
cana-4140	122	12	value	value	NOUN
cana-4140	122	13	problems	problem	NOUN
cana-4140	122	14	.	.	PUNCT
cana-4140	123	1	since	since	SCONJ
cana-4140	123	2	,	,	PUNCT
cana-4140	123	3	application	application	NOUN
cana-4140	123	4	of	of	ADP
cana-4140	123	5	this	this	DET
cana-4140	123	6	method	method	NOUN
cana-4140	123	7	depend	depend	VERB
cana-4140	123	8	on	on	ADP
cana-4140	123	9	the	the	DET
cana-4140	123	10	direct	direct	ADJ
cana-4140	123	11	integration	integration	NOUN
cana-4140	123	12	of	of	ADP
cana-4140	123	13	the	the	DET
cana-4140	123	14	equilibrium	equilibrium	NOUN
cana-4140	123	15	equations	equation	NOUN
cana-4140	123	16	for	for	ADP
cana-4140	123	17	efficient	efficient	ADJ
cana-4140	123	18	analysis	analysis	NOUN
cana-4140	123	19	of	of	ADP
cana-4140	123	20	inhomogeneous	inhomogeneous	ADJ
cana-4140	123	21	solids	solid	NOUN
cana-4140	123	22	.	.	PUNCT
cana-4140	124	1	7	7	X
cana-4140	124	2	.	.	X
cana-4140	124	3	acknowledgement	acknowledgement	NOUN
cana-4140	124	4	the	the	DET
cana-4140	124	5	authors	author	NOUN
cana-4140	124	6	are	be	AUX
cana-4140	124	7	thankful	thankful	ADJ
cana-4140	124	8	to	to	ADP
cana-4140	124	9	council	council	PROPN
cana-4140	124	10	of	of	ADP
cana-4140	124	11	scientific	scientific	ADJ
cana-4140	124	12	and	and	CCONJ
cana-4140	124	13	industrial	industrial	ADJ
cana-4140	124	14	research	research	NOUN
cana-4140	124	15	(	(	PUNCT
cana-4140	124	16	csir	csir	PROPN
cana-4140	124	17	)	)	PUNCT
cana-4140	124	18	,	,	PUNCT
cana-4140	124	19	delhi	delhi	PROPN
cana-4140	124	20	for	for	ADP
cana-4140	124	21	awarding	award	VERB
cana-4140	124	22	the	the	DET
cana-4140	124	23	research	research	NOUN
cana-4140	124	24	fellowship	fellowship	NOUN
cana-4140	124	25	09/809	09/809	NOUN
cana-4140	124	26	-	-	PUNCT
cana-4140	124	27	0028(2021)-emr	0028(2021)-emr	PROPN
cana-4140	124	28	.	.	PUNCT
cana-4140	125	1	references	reference	NOUN
cana-4140	125	2	[	[	X
cana-4140	125	3	1	1	NUM
cana-4140	125	4	]	]	PUNCT
cana-4140	125	5	a.	a.	NOUN
cana-4140	125	6	rychahivskyy	rychahivskyy	PROPN
cana-4140	125	7	and	and	CCONJ
cana-4140	125	8	y.	y.	PROPN
cana-4140	125	9	tokovyy	tokovyy	PROPN
cana-4140	125	10	:	:	PUNCT
cana-4140	125	11	correct	correct	ADJ
cana-4140	125	12	analytical	analytical	ADJ
cana-4140	125	13	solutions	solution	NOUN
cana-4140	125	14	to	to	ADP
cana-4140	125	15	the	the	DET
cana-4140	125	16	thermoelasticity	thermoelasticity	NOUN
cana-4140	125	17	problems	problem	NOUN
cana-4140	125	18	in	in	ADP
cana-4140	125	19	a	a	DET
cana-4140	125	20	semi	semi	ADJ
cana-4140	125	21	plane	plane	NOUN
cana-4140	125	22	,	,	PUNCT
cana-4140	125	23	journal	journal	NOUN
cana-4140	125	24	of	of	ADP
cana-4140	125	25	thermal	thermal	ADJ
cana-4140	125	26	stresses	stress	NOUN
cana-4140	125	27	,	,	PUNCT
cana-4140	125	28	vol	vol	NOUN
cana-4140	125	29	.	.	PROPN
cana-4140	125	30	31	31	NUM
cana-4140	125	31	,	,	PUNCT
cana-4140	125	32	pp-1125	pp-1125	NOUN
cana-4140	125	33	-	-	PUNCT
cana-4140	125	34	1145	1145	NUM
cana-4140	125	35	,	,	PUNCT
cana-4140	125	36	2008	2008	NUM
cana-4140	125	37	.	.	PUNCT
cana-4140	126	1	[	[	X
cana-4140	126	2	2	2	NUM
cana-4140	126	3	]	]	PUNCT
cana-4140	126	4	a.	a.	NOUN
cana-4140	126	5	hamoud	hamoud	NOUN
cana-4140	126	6	,	,	PUNCT
cana-4140	126	7	n.	n.	PROPN
cana-4140	126	8	mohammed	mohammed	PROPN
cana-4140	126	9	,	,	PUNCT
cana-4140	126	10	k.	k.	PROPN
cana-4140	126	11	ghadle	ghadle	PROPN
cana-4140	126	12	and	and	CCONJ
cana-4140	126	13	s.	s.	PROPN
cana-4140	126	14	dhondge	dhondge	VERB
cana-4140	126	15	:	:	PUNCT
cana-4140	126	16	solving	solve	VERB
cana-4140	126	17	integro	integro	ADJ
cana-4140	126	18	-	-	PUNCT
cana-4140	126	19	differential	differential	NOUN
cana-4140	126	20	equations	equation	NOUN
cana-4140	126	21	by	by	ADP
cana-4140	126	22	using	use	VERB
cana-4140	126	23	numerical	numerical	ADJ
cana-4140	126	24	techniques	technique	NOUN
cana-4140	126	25	,	,	PUNCT
cana-4140	126	26	international	international	ADJ
cana-4140	126	27	journal	journal	NOUN
cana-4140	126	28	of	of	ADP
cana-4140	126	29	applied	apply	VERB
cana-4140	126	30	engineering	engineering	NOUN
cana-4140	126	31	research	research	NOUN
cana-4140	126	32	,	,	PUNCT
cana-4140	126	33	vol	vol	NOUN
cana-4140	126	34	.	.	PROPN
cana-4140	126	35	14	14	NUM
cana-4140	126	36	,	,	PUNCT
cana-4140	126	37	pp	pp	ADJ
cana-4140	126	38	.	.	PUNCT
cana-4140	127	1	3219	3219	NUM
cana-4140	127	2	-	-	SYM
cana-4140	127	3	3225	3225	NUM
cana-4140	127	4	,	,	PUNCT
cana-4140	127	5	2019	2019	NUM
cana-4140	127	6	.	.	PUNCT
cana-4140	128	1	[	[	X
cana-4140	128	2	3	3	NUM
cana-4140	128	3	]	]	PUNCT
cana-4140	128	4	a.	a.	NOUN
cana-4140	128	5	yasinskyy	yasinskyy	NOUN
cana-4140	128	6	and	and	CCONJ
cana-4140	128	7	o.	o.	NOUN
cana-4140	128	8	ierokhova	ierokhova	PROPN
cana-4140	128	9	:	:	PUNCT
cana-4140	128	10	optimization	optimization	NOUN
cana-4140	128	11	of	of	ADP
cana-4140	128	12	nonstationary	nonstationary	ADJ
cana-4140	128	13	thermal	thermal	ADJ
cana-4140	128	14	displacements	displacement	NOUN
cana-4140	128	15	in	in	ADP
cana-4140	128	16	a	a	DET
cana-4140	128	17	given	give	VERB
cana-4140	128	18	cross	cross	NOUN
cana-4140	128	19	section	section	NOUN
cana-4140	128	20	of	of	ADP
cana-4140	128	21	a	a	DET
cana-4140	128	22	half	half	ADJ
cana-4140	128	23	space	space	NOUN
cana-4140	128	24	in	in	ADP
cana-4140	128	25	the	the	DET
cana-4140	128	26	plane	plane	NOUN
cana-4140	128	27	strain	strain	NOUN
cana-4140	128	28	state	state	NOUN
cana-4140	128	29	,	,	PUNCT
cana-4140	128	30	journal	journal	NOUN
cana-4140	128	31	of	of	ADP
cana-4140	128	32	mathematical	mathematical	ADJ
cana-4140	128	33	sciences	sciences	PROPN
cana-4140	128	34	,	,	PUNCT
cana-4140	128	35	vol	vol	NOUN
cana-4140	128	36	.	.	PROPN
cana-4140	128	37	223	223	NUM
cana-4140	128	38	,	,	PUNCT
cana-4140	128	39	pp	pp	ADJ
cana-4140	128	40	.	.	PUNCT
cana-4140	128	41	140	140	NUM
cana-4140	128	42	-	-	SYM
cana-4140	128	43	147	147	NUM
cana-4140	128	44	,	,	PUNCT
cana-4140	128	45	2017	2017	NUM
cana-4140	128	46	.	.	PUNCT
cana-4140	129	1	[	[	X
cana-4140	129	2	4	4	X
cana-4140	129	3	]	]	PUNCT
cana-4140	129	4	b.	b.	NOUN
cana-4140	129	5	kalynyak	kalynyak	PROPN
cana-4140	129	6	,	,	PUNCT
cana-4140	129	7	y.	y.	PROPN
cana-4140	129	8	tokovyy	tokovyy	PROPN
cana-4140	129	9	and	and	CCONJ
cana-4140	129	10	a.	a.	NOUN
cana-4140	129	11	yasinskyy	yasinskyy	PROPN
cana-4140	129	12	:	:	PUNCT
cana-4140	129	13	direct	direct	ADJ
cana-4140	129	14	and	and	CCONJ
cana-4140	129	15	inverse	inverse	ADJ
cana-4140	129	16	problems	problem	NOUN
cana-4140	129	17	of	of	ADP
cana-4140	129	18	thermomechanics	thermomechanic	NOUN
cana-4140	129	19	concerning	concern	VERB
cana-4140	129	20	the	the	DET
cana-4140	129	21	optimization	optimization	NOUN
cana-4140	129	22	and	and	CCONJ
cana-4140	129	23	identification	identification	NOUN
cana-4140	129	24	of	of	ADP
cana-4140	129	25	the	the	DET
cana-4140	129	26	thermal	thermal	NOUN
cana-4140	129	27	stressed	stress	VERB
cana-4140	129	28	state	state	NOUN
cana-4140	129	29	of	of	ADP
cana-4140	129	30	deformed	deform	VERB
cana-4140	129	31	solids	solid	NOUN
cana-4140	129	32	,	,	PUNCT
cana-4140	129	33	journal	journal	NOUN
cana-4140	129	34	of	of	ADP
cana-4140	129	35	mathematical	mathematical	ADJ
cana-4140	129	36	science	science	NOUN
cana-4140	129	37	,	,	PUNCT
cana-4140	129	38	vol	vol	NOUN
cana-4140	129	39	.	.	PROPN
cana-4140	129	40	236	236	NUM
cana-4140	129	41	,	,	PUNCT
cana-4140	129	42	pp	pp	ADJ
cana-4140	129	43	.	.	PUNCT
cana-4140	130	1	21	21	NUM
cana-4140	130	2	-	-	SYM
cana-4140	130	3	34	34	NUM
cana-4140	130	4	,	,	PUNCT
cana-4140	130	5	2019	2019	NUM
cana-4140	130	6	.	.	PUNCT
cana-4140	131	1	communications	communication	NOUN
cana-4140	131	2	on	on	ADP
cana-4140	131	3	applied	apply	VERB
cana-4140	131	4	nonlinear	nonlinear	ADJ
cana-4140	131	5	analysis	analysis	NOUN
cana-4140	131	6	issn	issn	NOUN
cana-4140	131	7	:	:	PUNCT
cana-4140	131	8	1074	1074	NUM
cana-4140	131	9	-	-	PUNCT
cana-4140	131	10	133x	133x	NUM
cana-4140	131	11	vol	vol	NOUN
cana-4140	131	12	32	32	NUM
cana-4140	131	13	no	no	NOUN
cana-4140	131	14	.	.	NOUN
cana-4140	131	15	9(s	9(s	NUM
cana-4140	131	16	)	)	PUNCT
cana-4140	131	17	(	(	PUNCT
cana-4140	131	18	2025	2025	NUM
cana-4140	131	19	)	)	PUNCT
cana-4140	131	20	1318	1318	NUM
cana-4140	131	21	https://internationalpubls.com	https://internationalpubls.com	X
cana-4140	132	1	[	[	X
cana-4140	132	2	5	5	NUM
cana-4140	132	3	]	]	PUNCT
cana-4140	132	4	k.	k.	NOUN
cana-4140	132	5	ghadle	ghadle	PROPN
cana-4140	132	6	and	and	CCONJ
cana-4140	132	7	a.	a.	NOUN
cana-4140	132	8	adhe	adhe	PROPN
cana-4140	132	9	:	:	PUNCT
cana-4140	132	10	steady	steady	ADJ
cana-4140	132	11	state	state	NOUN
cana-4140	132	12	temperature	temperature	NOUN
cana-4140	132	13	analysis	analysis	NOUN
cana-4140	132	14	to	to	ADP
cana-4140	132	15	2d	2d	NOUN
cana-4140	132	16	elasticity	elasticity	NOUN
cana-4140	132	17	and	and	CCONJ
cana-4140	132	18	thermoelasticity	thermoelasticity	NOUN
cana-4140	132	19	problems	problem	NOUN
cana-4140	132	20	for	for	ADP
cana-4140	132	21	inhomogeneous	inhomogeneous	ADJ
cana-4140	132	22	solids	solid	NOUN
cana-4140	132	23	in	in	ADP
cana-4140	132	24	half	half	ADJ
cana-4140	132	25	plane	plane	NOUN
cana-4140	132	26	,	,	PUNCT
cana-4140	132	27	the	the	DET
cana-4140	132	28	journal	journal	NOUN
cana-4140	132	29	of	of	ADP
cana-4140	132	30	the	the	DET
cana-4140	132	31	korean	korean	ADJ
cana-4140	132	32	society	society	NOUN
cana-4140	132	33	for	for	ADP
cana-4140	132	34	industrial	industrial	ADJ
cana-4140	132	35	and	and	CCONJ
cana-4140	132	36	applied	applied	ADJ
cana-4140	132	37	mathematics	mathematic	NOUN
cana-4140	132	38	,	,	PUNCT
cana-4140	132	39	vol	vol	NOUN
cana-4140	132	40	.	.	PROPN
cana-4140	133	1	24	24	NUM
cana-4140	133	2	,	,	PUNCT
cana-4140	133	3	pp	pp	ADJ
cana-4140	133	4	.	.	PUNCT
cana-4140	134	1	93	93	NUM
cana-4140	134	2	-	-	SYM
cana-4140	134	3	102	102	NUM
cana-4140	134	4	,	,	PUNCT
cana-4140	134	5	2020	2020	NUM
cana-4140	134	6	.	.	PUNCT
cana-4140	135	1	[	[	X
cana-4140	135	2	6	6	NUM
cana-4140	135	3	]	]	PUNCT
cana-4140	135	4	s.	s.	PROPN
cana-4140	135	5	nirde	nirde	PROPN
cana-4140	135	6	and	and	CCONJ
cana-4140	135	7	k.	k.	PROPN
cana-4140	135	8	ghadle	ghadle	PROPN
cana-4140	135	9	:	:	PUNCT
cana-4140	135	10	two	two	NUM
cana-4140	135	11	dimensional	dimensional	ADJ
cana-4140	135	12	thermoelasticity	thermoelasticity	NOUN
cana-4140	135	13	problems	problem	NOUN
cana-4140	135	14	in	in	ADP
cana-4140	135	15	an	an	DET
cana-4140	135	16	inhomogeneous	inhomogeneous	ADJ
cana-4140	135	17	strip	strip	NOUN
cana-4140	135	18	with	with	ADP
cana-4140	135	19	application	application	NOUN
cana-4140	135	20	of	of	ADP
cana-4140	135	21	direct	direct	ADJ
cana-4140	135	22	integration	integration	NOUN
cana-4140	135	23	method	method	NOUN
cana-4140	135	24	,	,	PUNCT
cana-4140	135	25	journal	journal	NOUN
cana-4140	135	26	of	of	ADP
cana-4140	135	27	fractional	fractional	ADJ
cana-4140	135	28	calculus	calculus	NOUN
cana-4140	135	29	and	and	CCONJ
cana-4140	135	30	applications	application	NOUN
cana-4140	135	31	,	,	PUNCT
cana-4140	135	32	vol	vol	NOUN
cana-4140	135	33	.	.	PROPN
cana-4140	135	34	16	16	NUM
cana-4140	135	35	,	,	PUNCT
cana-4140	135	36	issue	issue	NOUN
cana-4140	135	37	1	1	NUM
cana-4140	135	38	,	,	PUNCT
cana-4140	135	39	no-2	no-2	X
cana-4140	135	40	,	,	PUNCT
cana-4140	135	41	jan	jan	PROPN
cana-4140	135	42	.	.	PROPN
cana-4140	135	43	2025	2025	NUM
cana-4140	135	44	.	.	PUNCT
cana-4140	136	1	[	[	X
cana-4140	136	2	7	7	X
cana-4140	136	3	]	]	X
cana-4140	136	4	v.	v.	ADP
cana-4140	136	5	vigak	vigak	NOUN
cana-4140	136	6	:	:	PUNCT
cana-4140	136	7	correct	correct	ADJ
cana-4140	136	8	solutions	solution	NOUN
cana-4140	136	9	of	of	ADP
cana-4140	136	10	plane	plane	NOUN
cana-4140	136	11	elastic	elastic	ADJ
cana-4140	136	12	problems	problem	NOUN
cana-4140	136	13	for	for	ADP
cana-4140	136	14	a	a	DET
cana-4140	136	15	half	half	ADJ
cana-4140	136	16	-	-	PUNCT
cana-4140	136	17	plane	plane	NOUN
cana-4140	136	18	,	,	PUNCT
cana-4140	136	19	int	int	NOUN
cana-4140	136	20	.	.	PUNCT
cana-4140	137	1	applied	apply	VERB
cana-4140	137	2	mechanics	mechanic	NOUN
cana-4140	137	3	,	,	PUNCT
cana-4140	137	4	vol	vol	NOUN
cana-4140	137	5	.	.	PROPN
cana-4140	137	6	40	40	NUM
cana-4140	137	7	,	,	PUNCT
cana-4140	137	8	pp	pp	ADJ
cana-4140	137	9	.	.	PUNCT
cana-4140	138	1	283	283	NUM
cana-4140	138	2	-	-	SYM
cana-4140	138	3	289	289	NUM
cana-4140	138	4	,	,	PUNCT
cana-4140	138	5	2004	2004	NUM
cana-4140	138	6	.	.	PUNCT
cana-4140	139	1	[	[	X
cana-4140	139	2	8	8	NUM
cana-4140	139	3	]	]	X
cana-4140	139	4	y.	y.	NOUN
cana-4140	139	5	tokovyy	tokovyy	PROPN
cana-4140	139	6	and	and	CCONJ
cana-4140	139	7	a.	a.	NOUN
cana-4140	139	8	rychahivskyyi	rychahivskyyi	NOUN
cana-4140	139	9	:	:	PUNCT
cana-4140	139	10	reduction	reduction	NOUN
cana-4140	139	11	of	of	ADP
cana-4140	139	12	plane	plane	NOUN
cana-4140	139	13	thermoelasticity	thermoelasticity	NOUN
cana-4140	139	14	problem	problem	NOUN
cana-4140	139	15	in	in	ADP
cana-4140	139	16	inhomogeneous	inhomogeneous	ADJ
cana-4140	139	17	strip	strip	NOUN
cana-4140	139	18	to	to	ADP
cana-4140	139	19	integral	integral	ADJ
cana-4140	139	20	volterra	volterra	NOUN
cana-4140	139	21	type	type	NOUN
cana-4140	139	22	equation	equation	NOUN
cana-4140	139	23	,	,	PUNCT
cana-4140	139	24	mathematical	mathematical	ADJ
cana-4140	139	25	modelling	modelling	NOUN
cana-4140	139	26	and	and	CCONJ
cana-4140	139	27	analysis	analysis	NOUN
cana-4140	139	28	,	,	PUNCT
cana-4140	139	29	vol	vol	NOUN
cana-4140	139	30	.	.	PROPN
cana-4140	139	31	10	10	NUM
cana-4140	139	32	,	,	PUNCT
cana-4140	139	33	pp	pp	ADJ
cana-4140	139	34	.	.	PUNCT
cana-4140	140	1	91	91	NUM
cana-4140	140	2	-	-	SYM
cana-4140	140	3	100	100	NUM
cana-4140	140	4	,	,	PUNCT
cana-4140	140	5	2005	2005	NUM
cana-4140	140	6	.	.	PUNCT
cana-4140	141	1	[	[	X
cana-4140	141	2	9	9	X
cana-4140	141	3	]	]	X
cana-4140	141	4	y.	y.	NOUN
cana-4140	141	5	tokovyy	tokovyy	PROPN
cana-4140	141	6	and	and	CCONJ
cana-4140	141	7	ma	ma	PROPN
cana-4140	141	8	.	.	PROPN
cana-4140	141	9	chien	chien	PROPN
cana-4140	141	10	-	-	PUNCT
cana-4140	141	11	ching	ching	PROPN
cana-4140	141	12	:	:	PUNCT
cana-4140	141	13	elastic	elastic	ADJ
cana-4140	141	14	analysis	analysis	NOUN
cana-4140	141	15	of	of	ADP
cana-4140	141	16	inhomogeneous	inhomogeneous	ADJ
cana-4140	141	17	solids	solid	NOUN
cana-4140	141	18	,	,	PUNCT
cana-4140	141	19	journal	journal	NOUN
cana-4140	141	20	of	of	ADP
cana-4140	141	21	mechanics	mechanic	NOUN
cana-4140	141	22	,	,	PUNCT
cana-4140	141	23	vol	vol	NOUN
cana-4140	141	24	.	.	PROPN
cana-4140	141	25	35	35	NUM
cana-4140	141	26	,	,	PUNCT
cana-4140	141	27	pp	pp	ADJ
cana-4140	141	28	.	.	PUNCT
cana-4140	142	1	613	613	NUM
cana-4140	142	2	-	-	PUNCT
cana-4140	142	3	626	626	NUM
cana-4140	142	4	,	,	PUNCT
cana-4140	142	5	2019	2019	NUM
cana-4140	142	6	.	.	PUNCT
cana-4140	143	1	[	[	X
cana-4140	143	2	10	10	NUM
cana-4140	143	3	]	]	X
cana-4140	143	4	y.	y.	PROPN
cana-4140	143	5	tokovyy	tokovyy	PROPN
cana-4140	143	6	and	and	CCONJ
cana-4140	143	7	ma	ma	PROPN
cana-4140	143	8	.	.	PROPN
cana-4140	143	9	chien	chien	PROPN
cana-4140	143	10	-	-	PUNCT
cana-4140	143	11	ching	ching	PROPN
cana-4140	143	12	:	:	PUNCT
cana-4140	143	13	an	an	DET
cana-4140	143	14	explict	explict	NOUN
cana-4140	143	15	form	form	NOUN
cana-4140	143	16	solution	solution	NOUN
cana-4140	143	17	to	to	ADP
cana-4140	143	18	the	the	DET
cana-4140	143	19	plane	plane	NOUN
cana-4140	143	20	elasticity	elasticity	NOUN
cana-4140	143	21	and	and	CCONJ
cana-4140	143	22	thermoelasticity	thermoelasticity	NOUN
cana-4140	143	23	problems	problem	NOUN
cana-4140	143	24	for	for	ADP
cana-4140	143	25	anisotropic	anisotropic	NOUN
cana-4140	143	26	and	and	CCONJ
cana-4140	143	27	inhomogeneous	inhomogeneous	ADJ
cana-4140	143	28	solids	solid	NOUN
cana-4140	143	29	,	,	PUNCT
cana-4140	143	30	international	international	ADJ
cana-4140	143	31	journal	journal	NOUN
cana-4140	143	32	of	of	ADP
cana-4140	143	33	solid	solid	ADJ
cana-4140	143	34	structures	structure	NOUN
cana-4140	143	35	,	,	PUNCT
cana-4140	143	36	vol	vol	NOUN
cana-4140	143	37	.	.	PROPN
cana-4140	144	1	46	46	NUM
cana-4140	144	2	,	,	PUNCT
cana-4140	144	3	pp	pp	ADJ
cana-4140	144	4	.	.	PUNCT
cana-4140	145	1	38503859	38503859	NUM
cana-4140	145	2	,	,	PUNCT
cana-4140	145	3	2009	2009	NUM
cana-4140	145	4	.	.	PUNCT
cana-4140	146	1	[	[	X
cana-4140	146	2	11	11	NUM
cana-4140	146	3	]	]	X
cana-4140	146	4	y.	y.	PROPN
cana-4140	146	5	tokovyy	tokovyy	PROPN
cana-4140	146	6	and	and	CCONJ
cana-4140	146	7	ma	ma	PROPN
cana-4140	146	8	.	.	PROPN
cana-4140	146	9	chien	chien	PROPN
cana-4140	146	10	-	-	PUNCT
cana-4140	146	11	ching	ching	PROPN
cana-4140	146	12	:	:	PUNCT
cana-4140	146	13	analytical	analytical	ADJ
cana-4140	146	14	solutions	solution	NOUN
cana-4140	146	15	to	to	ADP
cana-4140	146	16	the	the	DET
cana-4140	146	17	2d	2d	PROPN
cana-4140	146	18	elasticity	elasticity	NOUN
cana-4140	146	19	and	and	CCONJ
cana-4140	146	20	thermoelasticity	thermoelasticity	NOUN
cana-4140	146	21	problems	problem	NOUN
cana-4140	146	22	for	for	ADP
cana-4140	146	23	inhomogeneous	inhomogeneous	ADJ
cana-4140	146	24	planes	plane	NOUN
cana-4140	146	25	and	and	CCONJ
cana-4140	146	26	half	half	ADJ
cana-4140	146	27	planes	plane	NOUN
cana-4140	146	28	,	,	PUNCT
cana-4140	146	29	archive	archive	NOUN
cana-4140	146	30	applied	apply	VERB
cana-4140	146	31	mechanics	mechanic	NOUN
cana-4140	146	32	,	,	PUNCT
cana-4140	146	33	vol	vol	NOUN
cana-4140	146	34	.	.	PROPN
cana-4140	146	35	79	79	NUM
cana-4140	146	36	,	,	PUNCT
cana-4140	146	37	pp	pp	ADJ
cana-4140	146	38	.	.	PUNCT
cana-4140	147	1	441–456	441–456	NUM
cana-4140	147	2	,	,	PUNCT
cana-4140	147	3	2009	2009	NUM
cana-4140	147	4	.	.	PUNCT
cana-4140	148	1	[	[	X
cana-4140	148	2	12	12	NUM
cana-4140	148	3	]	]	X
cana-4140	148	4	y.	y.	NOUN
cana-4140	148	5	tokovyy	tokovyy	PROPN
cana-4140	148	6	and	and	CCONJ
cana-4140	148	7	a.	a.	NOUN
cana-4140	148	8	rychahivskyy	rychahivskyy	NOUN
cana-4140	148	9	:	:	PUNCT
cana-4140	148	10	analytic	analytic	ADJ
cana-4140	148	11	solution	solution	NOUN
cana-4140	148	12	of	of	ADP
cana-4140	148	13	the	the	DET
cana-4140	148	14	plane	plane	NOUN
cana-4140	148	15	problem	problem	NOUN
cana-4140	148	16	of	of	ADP
cana-4140	148	17	the	the	DET
cana-4140	148	18	theory	theory	NOUN
cana-4140	148	19	of	of	ADP
cana-4140	148	20	elasticity	elasticity	NOUN
cana-4140	148	21	for	for	ADP
cana-4140	148	22	a	a	DET
cana-4140	148	23	nonuniform	nonuniform	ADJ
cana-4140	148	24	strip	strip	NOUN
cana-4140	148	25	,	,	PUNCT
cana-4140	148	26	materials	material	NOUN
cana-4140	148	27	science	science	NOUN
cana-4140	148	28	vol	vol	NOUN
cana-4140	148	29	.	.	PROPN
cana-4140	149	1	41	41	NUM
cana-4140	149	2	,	,	PUNCT
cana-4140	149	3	pp	pp	ADJ
cana-4140	149	4	.	.	PUNCT
cana-4140	150	1	114	114	NUM
cana-4140	150	2	-	-	SYM
cana-4140	150	3	116	116	NUM
cana-4140	150	4	,	,	PUNCT
cana-4140	150	5	2005	2005	NUM
cana-4140	150	6	.	.	PUNCT