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Journal articles on the topic 'Boundary value problem of thermoelasticity'

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Published: 5 June 2025

Last updated: 2 August 2025

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1

YAKUBOV, YAKOV. "COMPLETENESS OF ROOT FUNCTIONS AND ELEMENTARY SOLUTIONS OF THE THERMOELASTICITY SYSTEM." Mathematical Models and Methods in Applied Sciences 05, no. 05 (1995): 587–98. http://dx.doi.org/10.1142/s0218202595000346.

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In this paper we prove the completeness of the root functions (eigenfunctions and associated functions) of an elliptic system (in the sense of Douglis-Nirenberg) corresponding to the thermoelasticity system with the Dirichlet boundary value condition. The problem is considered in a domain with a non-smooth boundary. Then an initial boundary value problem corresponding to the thermoelasticity system with the Dirichlet boundary value condition is considered. We find sufficient conditions that guarantee an approximation of a solution to the initial boundary value problem by linear combinations of

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2

Khaldjigitov, Abduvali, Umidjon Djumayozov, Zebo Khasanova, and Robiya Rakhmonova. "Study on coupled problems of thermoelasticity in Strains." E3S Web of Conferences 497 (2024): 02008. http://dx.doi.org/10.1051/e3sconf/202449702008.

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In the work, within the framework of the strain compatibility conditions of Saint-Venant, two equivalent dynamic boundary value problems of thermoelasticity with respect to strains are formulated. In the case of the first boundary value problem, the dynamic equations of thermoelasticity are obtained from the compatibility conditions, in the second case, instead of the first three equations of thermoelasticity, the equations of motion expressed with respect to deformations are considered. Discrete analogues of boundary value problems are constructed using the finite-difference method in the for

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3

Djumayozov, Umidjon, and Nigora Eshmanova. "Coupled Problem on Thermo-Elasticity in Strains for an Isotropic Parallelepiped." E3S Web of Conferences 497 (2024): 02016. http://dx.doi.org/10.1051/e3sconf/202449702016.

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This work is devoted to mathematical and numerical modeling of the coupled dynamic problem of thermoelasticity in deformations. A numerically related boundary value problem of thermoelasticity in deformations for a parallelepiped with the corresponding initial and boundary conditions is formulated and solved. Grid equations are constructed using the finite-difference method in the form of explicit and implicit schemes. In this case, the solution of the explicit scheme is reduced to recurrent relations with respect to deformations and temperature. In the case of implicit difference schemes, the

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4

Khaldjigitov, Abduvali, Umidjon Djumayozov, Zebo Khasanova, and Robiya Rakhmonova. "Numerical Solution of the Plane Problem of Thermo-Elasticity in Strains." E3S Web of Conferences 563 (2024): 02019. http://dx.doi.org/10.1051/e3sconf/202456302019.

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In the work, within the framework of the Saint-Venant compatibility conditions, two plane problems of thermoelasticity with respect to deformations are formulated. The closedness of boundary value problems is achieved by considering equilibrium equations on the boundary of a given region. Grid equations of thermoelastic problems are compiled using the finite-difference method and solved by the alternative method. The problem of a free thermoelastic rectangle located in a given temperature field is solved numerically. The validity of the formulated boundary value problems and the reliability of

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5

Belova, M. M., V. M. Goncharenko, and S. S. Protsenko. "Numerical method for solving a boundary-value problem of thermoelasticity." Journal of Soviet Mathematics 58, no. 5 (1992): 443–46. http://dx.doi.org/10.1007/bf01100071.

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6

Racke, Reinhard. "On the time-asymptotic behaviour of solutions in thermoelasticity." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 107, no. 3-4 (1987): 289–98. http://dx.doi.org/10.1017/s0308210500031164.

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SynopsisWe consider initial boundary value problems for the equations of linear thermoelasticity in both bounded and unbounded domains and for both nonhomogeneous and anisotropic media. For bounded domains, it is shown that the unique solution of the problem is time-asymptotically equal to the solution of a particular initial boundary value problem which is obtained from a natural decomposition of the original initial data and which represents a (in general non-vanishing) time harmonic part. For the unbounded case similar results are obtained, but now in the sense of weak convergence which lea

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7

Bitsadze, Lamara. "Boundary Value Problems of Thermoelasticity for Porous Sphere and for A Space with Spherical Cavity." Brilliant Engineering 3, no. 1 (2021): 1–10. http://dx.doi.org/10.36937/ben.2022.4501.

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This article is concerned with the coupled linear quasi-static theory of thermoelasticity for porous materials under local thermal equilibrium. The system of equations is based on the constitutive equations, Darcy's law of the flow of a fluid through a porous medium, Fourier's law of heat conduction, the equations of equilibrium, fluid mass conservation and heat transfer. The system of governing equations is expressed in terms of displacement vector field, the change of volume fraction of pores, the change of fluid pressure in pore network and the variation of temperature of porous material. T

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8

Yuqiu, Zhao. "On plane displacement boundary value problem of quasi–static linear thermoelasticity." Applicable Analysis 56, no. 1-2 (1995): 117–29. http://dx.doi.org/10.1080/00036819508840314.

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9

Podil'chuk, Yu N., and A. M. Kirichenko. "Boundary-value problem of thermoelasticity in displacements for an elongated spheroid." Journal of Soviet Mathematics 66, no. 3 (1993): 2299–306. http://dx.doi.org/10.1007/bf01229600.

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10

Jiang, Song. "Global existence of smooth solutions in one-dimensional nonlinear thermoelasticity." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 115, no. 3-4 (1990): 257–74. http://dx.doi.org/10.1017/s0308210500020631.

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SynopsisWe consider the initial boundary value problem for the equations of one-dimensional nonlinear thermoelasticity in ℝ+; and prove a global existence-uniqueness theorem for small smooth data. The asymptotic behaviour is simultaneously obtained.

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11

Burchuladze, T., and Yu Bezhuashvili. "Three-Dimensional Boundary Value Problems of Elastothermodiffusion with Mixed Boundary Conditions." gmj 4, no. 3 (1997): 243–58. http://dx.doi.org/10.1515/gmj.1997.243.

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Abstract We investigate the basic boundary value problems of the connected theory of elastothermodiffusion for three-dimensional domains bounded by several closed surfaces when the same boundary conditions are fulfilled on every separate boundary surface, but these conditions differ on different groups of surfaces. Using the results of papers [Kupradze, Gegelia, Basheleishvili, and Burchuladze, Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity, North-Holland Publishing Company, 1979, Russian original, 1976–Mikhlin, Multi-dimensional singular integrals and

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12

Lychev, S. A., A. V. Manzhirov, and S. V. Joubert. "Closed solutions of boundary-value problems of coupled thermoelasticity." Mechanics of Solids 45, no. 4 (2010): 610–23. http://dx.doi.org/10.3103/s0025654410040102.

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13

Chiriţă, Stan. "On the final boundary value problems in linear thermoelasticity." Meccanica 47, no. 8 (2012): 2005–11. http://dx.doi.org/10.1007/s11012-012-9570-1.

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14

Zhao, Yuqiu, and Wei Lin. "On the plane stress boundary value problem of quasi-static linear thermoelasticity." Acta Mathematicae Applicatae Sinica 13, no. 4 (1997): 385–94. http://dx.doi.org/10.1007/bf02009547.

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15

Jiang, Song. "Rapidly decreasing behaviour of solutions in nonlinear 3-D-thermoelasticity." Bulletin of the Australian Mathematical Society 43, no. 1 (1991): 89–99. http://dx.doi.org/10.1017/s000497270002880x.

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In this paper we study the asymptotic behaviour, as |x| → ∞, of solutions to the initial value problem in nonlinear three-dimensional thermoelasticity in some weighted Sobolev spaces. We show that under some conditions, solutions decrease fast for each t as x tends to infinity. We also consider the possible extension of the method presented in this paper to the initial boundary value problem in exterior domains.

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16

Liu, Wensen, X. Markenscoff, and M. Paukshto. "The Cosserat Spectrum Theory in Thermoelasticity and Application to the Problem of Heat Flow Past a Rigid Spherical Inclusion." Journal of Applied Mechanics 65, no. 3 (1998): 614–18. http://dx.doi.org/10.1115/1.2789102.

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We apply the Cosserat Spectrum theory to boundary value problems in thermoelasticity and show the advantages of this method. The thermoelastic displacement field caused by a general heat flow around a spherical rigid inclusion is calculatedand the results show that the discrete Cosserat eigenfunctions converge fast and thus provide a practical method for solving three-dimensional problems in thermoelasticity. In the case of uniform heat flow, the solution is obtained analytically in closed form and a variational principle within the frame of the Cosserat Spectrum theory shows that the solution

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17

L., A. Alexeyeva* M. M. Ahmetzhanova. "STATIONARY OSCILLATIONS OF THERMOELASTIC ROD UNDER ACTION OF EXTERNAL DISTURBANCES." Global Journal of Engineering Science and Research Management 5, no. 2 (2018): 33–43. https://doi.org/10.5281/zenodo.1186513.

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The dynamics of a thermoelastic rod of finite length are studied under action of periodic external force and thermal sources. The model of connected thermoelasticity are used, taking into account the effect of temperature on the elastic deformation and stresses and as well as the effect of elastic deformation speed on the temperature field in the rod. Based on the method of generalized functions the analytical solutions of boundary value problems of the stationary vibration of a thermoelastic rod for various types of boundary conditions are constructed. The computer implementation of the bound

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18

Khomasuridze, N. "Effective Solution of a Class of Boundary Value Problems of Thermoelasticity in Generalized Cylindrical Coordinates." gmj 11, no. 3 (2004): 495–514. http://dx.doi.org/10.1515/gmj.2004.495.

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Abstract A class of static boundary value problems of thermoelasticity is effectively solved for bodies bounded by coordinate surfaces of generalized cylindrical coordinates ρ, α, 𝑧 (ρ, α are orthogonal curvilinear coordinates on the plane and 𝑧 is a linear coordinate). Besides in the Cartesian system of coordinates some boundary value thermoelasticity problems are separately considered for a rectangular parallelepiped. An elastic body occupying the domain Ω = {ρ 0 < ρ < ρ 1, α 0 < α < α 1, 0 < 𝑧 < 𝑧1}, is considered to be weakly transversally isotropic (the medium is weakly

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19

Burchuladze, T., and D. Burchuladze. "On Three-Dimensional Dynamic Problems of Generalized Thermoelasticity." gmj 5, no. 1 (1998): 25–48. http://dx.doi.org/10.1515/gmj.1998.25.

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Abstract Lord–Shulman's system of partial differential equations of generalized thermoelasticity [Green and Lindsay, J. Elasticity 2: 1–7, 1972] is considered, in which the finite velocity of heat propagation is taken into account by introducing a relaxation time constant. General aspects of the theory of boundary value and initial-boundary value problems and representation of solutions by series and quadratures are considered using the method of a potential.

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20

Almazmumy, Mariam, Huda Bakodah, Nawal Al-Zaid, Abdelhalim Ebaid, and Randolph Rach. "Approximate analytical solution for 1-D problems of thermoelasticity with dirichlet condition." Thermal Science 23, no. 1 (2019): 255–69. http://dx.doi.org/10.2298/tsci161217032a.

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This paper presents the solution of the initial boundary-value problem for the system of 1-D thermoelasticity using a new modified decomposition method that takes into accounts both initial and boundary conditions. The obtained solution is based on the generalized form of the inverse operator and is given in the form of a finite series. Also, some numerical experiments were presented to the both the effectiveness and the accuracy of the presented method.

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21

Gawinecki, Jerzy August. "Initial-boundary value problem in nonlinear hyperbolic thermoelasticity. Some applications in continuum mechanics." Dissertationes Mathematicae 407 (2002): 1–51. http://dx.doi.org/10.4064/dm407-0-1.

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22

Kaliev, I. A., and M. F. Mugafarov. "The third boundary value problem for the system of equations of linear thermoelasticity." Journal of Applied and Industrial Mathematics 2, no. 4 (2008): 501–7. http://dx.doi.org/10.1134/s1990478908040066.

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23

Abramenko, L. E., and V. P. Shevchenko. "The boundary-value problem of thermoelasticity for a spherical shell with local heating." Journal of Mathematical Sciences 84, no. 6 (1997): 1521–24. http://dx.doi.org/10.1007/bf02398813.

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24

Fil’shtinskii, Leonid, Marina Synah, and Tetiana Kirichok. "Time-harmonic boundary value problem of coupled thermoelasticity and related integral equations method." International Journal of Mechanical Sciences 115-116 (September 2016): 157–67. http://dx.doi.org/10.1016/j.ijmecsci.2016.06.017.

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25

Shlyakhin, D. A., and Zh M. Dauletmuratova. "Non-stationary coupled axisymmetric thermoelasticity problem for a rigidly fixed round plate." PNRPU Mechanics Bulletin, no. 4 (December 15, 2019): 191–200. http://dx.doi.org/10.15593/perm.mech/2019.4.18.

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A new closed solution is constructed for the axisymmetric dynamic problem of the classical (CTE) theory of thermoelasticity for a rigidly fixed circular isotropic plate in the case of a temperature change on its face surfaces (boundary conditions of the first kind). The mathematical formulation of the problem under consideration includes linear equations of thermal conductivity and equilibrium in a spatial setting, assuming that their inertial elastic characteristics can be neglected in the structures under study. In constructing a general solution of related non-self-conjugate equations, we u

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26

Racke, Reinhard. "Initial boundary value problems in one-dimensional non-linear thermoelasticity." Mathematical Methods in the Applied Sciences 10, no. 5 (1988): 517–29. http://dx.doi.org/10.1002/mma.1670100503.

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27

Khomasuridze, N. G. "A Class of Three-Dimensional Boundary-Value Problems of Thermoelasticity." International Applied Mechanics 41, no. 9 (2005): 1076–83. http://dx.doi.org/10.1007/s10778-006-0015-1.

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28

Svanadze, Merab. "Boundary Value Problems of the Theory of Thermoelasticity with Microtemperatures." PAMM 3, no. 1 (2003): 188–89. http://dx.doi.org/10.1002/pamm.200310368.

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29

Ailawalia, Praveen, and Suman Choudhary. "One-dimensional thermal shock problem for a semi-infinite semiconducting rod with hydrostatic initial stress." Structural Integrity and Life 25, no. 1 (2025): 60–65. https://doi.org/10.69644/ivk-2025-01-0060.

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The theory of generalised thermoelasticity is used to solve a boundary value problem of one-dimensional semi-infinite semiconducting rod with hydrostatic initial stress of length l. The left boundary of the rod is subjected to a sudden heat source. Normal mode analysis technique is applied to solve governing equations of the medium. The analytical expressions of displacement, carrier density, temperature distribution and stresses are obtained analytically. The numerical results are also presented graphically to show the effect of hydrostatic initial stress on the components.

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30

Marin, Marin, and Sorin Vlase. "Effect of internal state variables in thermoelasticity of microstretch bodies." Analele Universitatii "Ovidius" Constanta - Seria Matematica 24, no. 3 (2016): 241–57. http://dx.doi.org/10.1515/auom-2016-0057.

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AbstractFirst, we formulate the mixed initial boundary value problem in the theory of thermoelastic microstretch bodies having certain internal state variables. Then by using some approachable computing techniques and the known Gronwall's inequality we will prove that the presence of internal state variables do not influence the uniqueness of solution of the mixed problem.

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31

Duduchava, R., D. Natroshvili, and E. Shargorodsky. "Basic Boundary Value Problems of Thermoelasticity for Anisotropic Bodies with Cuts. II." gmj 2, no. 3 (1995): 259–76. http://dx.doi.org/10.1515/gmj.1995.259.

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Abstract In the first part [Duduchava, Natroshvili and Shargorodsky, Georgian Math. J. 2: 123–140, 1985] of the paper the basic boundary value problems of the mathematical theory of elasticity for three-dimensional anisotropic bodies with cuts were formulated. It is assumed that the two-dimensional surface of a cut is a smooth manifold of an arbitrary configuration with a smooth boundary. The existence and uniqueness theorems for boundary value problems were formulated in the Besov () and Bessel-potential () spaces. In the present part we give the proofs of the main results (Theorems 7 and 8)

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32

Shivay, Om N., and Santwana Mukhopadhyay. "Some basic theorems on a recent model of linear thermoelasticity for a homogeneous and isotropic medium." Mathematics and Mechanics of Solids 24, no. 8 (2018): 2444–57. http://dx.doi.org/10.1177/1081286518762612.

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This paper investigates a thermoelasticity theory based on the recent heat conduction model proposed by Quintanilla ( Mech Res Commun 2011; 38: 355–360). Taylor’s expansion of this model leads to an interesting problem of heat conduction. Serious attention has been paid by researchers in the last few years to investigating various heat conduction models. We have considered this newly proposed model of heat conduction given by Quintanilla and employed for coupled thermoelastic problems. We derive the basic governing equations for a homogeneous and isotropic medium and aim to derive some importa

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33

Nikabadze, Mikhail U., Armine R. Ulukhanyan, Tamar Moseshvili, Ketevan Tskhakaia, Nodar Mardaleishvili, and Zurab Arkania. "On the Modeling of Five-Layer Thin Prismatic Bodies." Mathematical and Computational Applications 24, no. 3 (2019): 69. http://dx.doi.org/10.3390/mca24030069.

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Proceeding from three-dimensional formulations of initial boundary value problems of the three-dimensional linear micropolar theory of thermoelasticity, similar formulations of initial boundary value problems for the theory of multilayer thermoelastic thin bodies are obtained. The initial boundary value problems for thin bodies are also obtained in the moments with respect to systems of orthogonal polynomials. We consider some particular cases of formulations of initial boundary value problems. In particular, the statements of the initial-boundary value problems of the micropolar theory of K-l

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34

MARIN, M., S. VLASE, I. M. FUDULU, and G. PRECUP. ""On instability in the theory of dipolar bodies with two-temperatures"." Carpathian Journal of Mathematics 38, no. 2 (2022): 459–68. http://dx.doi.org/10.37193/cjm.2022.02.15.

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"In this paper we approach a generalized thermoelasticity theory based on a heat conduction equation in bodies with dipolar structure, the heat conduction depends on two distinct temperatures, the thermodynamic temperature and the conductive temperature. In our considerations the difference between two temperatures is highlighted by the heat supply. For the mixed initial boundary value problem defined in this context, we prove the uniqueness of a solution corresponding some specific initial and boundary conditions. Also, if the initial energy is negative or null, we prove that the solutions of

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35

Marin, M., A. Chirilă, L. Codarcea, and S. Vlase. "On vibrations in Green-Naghdi thermoelasticity of dipolar bodies." Analele Universitatii "Ovidius" Constanta - Seria Matematica 27, no. 1 (2019): 125–40. http://dx.doi.org/10.2478/auom-2019-0007.

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Abstract This study is concerned with the theory of thermoelasticity of type III proposed by Green and Naghdi, which is extended to cover the bodies with dipolar structure. In this context we construct a boundary value problem for a prismatic bar which is subjected to some harmonic in time vibrations. For the oscillations whose amplitudes have the frequency lower than a critical value, we deduce some estimates for describing the spatial behavior.

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36

Bitsadze, Lamara. "The Neumann Type Boundary Value Problem in the Theory of Thermoelasticity with Microtemperatures for a Plane with Circular Hole." Journal of Nature, Science & Technology 1, no. 3 (2021): 11–16. http://dx.doi.org/10.36937/janset.2021.003.003.

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This paper studies the linear theory of thermoelastic materials with inner structure whose particles,in addition to the classical displacement and temperature fields, possess microtemperatures. The present work considers the 2D equilibrium theory of thermoelasticity for solids with microtemperatures. This paper is devoted to the explicit solution of the Neumann type boundary value problem for an elastic plane, with microtemperatures having a circular hole. Special representations of the regular solutions of the considered equations are constructed by means of the elementary (harmonic, bi-harmo

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37

Левина, Любовь Владимировна, Виктор Борисович Пеньков, and Евгений Александрович Новиков. "Strict particular solutions of heat conductivity and thermoelasticity problems." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 1(51) (October 5, 2022): 115–26. http://dx.doi.org/10.37972/chgpu.2022.51.1.011.

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Рассматриваются краевые задачи для линейной термоупругой изотропнооднородной среды. Состояние среды подчинено уравнениям Дюамеля-Неймана. В случае, когда характеристики напряженно-деформированного состояния (НДС) на поверхности тела не связаны в граничных условиях (ГУ) с температурными факторами, задача декомпозируется на последовательность неоднородных задач теплопроводности и теории упругости с известной коррекцией объемных сил в уравнениях равновесия. Особое внимание обращено на способ построения частного решения задачи теплопроводности. Метод функций Грина представляет частные решения таки

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38

Marin, M., and E. M. Craciun. "Uniqueness results for a boundary value problem in dipolar thermoelasticity to model composite materials." Composites Part B: Engineering 126 (October 2017): 27–37. http://dx.doi.org/10.1016/j.compositesb.2017.05.063.

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39

Seremet, Victor, Guy Bonnet, and Tatiana Speianu. "New Poisson's Type Integral Formula for Thermoelastic Half-Space." Mathematical Problems in Engineering 2009 (2009): 1–18. http://dx.doi.org/10.1155/2009/284380.

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A new Green's function and a new Poisson's type integral formula for a boundary value problem (BVP) in thermoelasticity for a half-space with mixed boundary conditions are derived. The thermoelastic displacements are generated by a heat source, applied in the inner points of the half-space and by temperature, and prescribed on its boundary. All results are obtained in closed forms that are formulated in a special theorem. A closed form solution for a particular BVP of thermoelasticity for a half-space also is included. The main difficulties to obtain these results are in deriving of functions

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40

Nenakhov, E. V., and E. M. Kartashov. "Estimates of Temperature Stresses in Models of Dynamic Thermoelasticity." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 1 (100) (February 2022): 88–106. http://dx.doi.org/10.18698/1812-3368-2022-1-88-106.

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The study focuses on the mathematical models of the heat shock theory in terms of dynamic thermoelasticity and describes the constitutive relations for boundary value problems based on hyperbolic equations (the idea of local nonequilibrium of the heat transfer process), which underlie the investigated models. Boundary conditions of the first, second, and third kinds are presented in a generalized form for the corresponding types of thermal action on the boundary of a solid surface. Relying on operational solutions of the corresponding dynamic problems, the paper introduces a new approach to th

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41

Sladek, Jan, Vladimir Sladek, Michael Wünsche, and Choon Lai Tan. "Fracture Mechanics Analysis of Size-Dependent Piezoelectric Solids under a Thermal Load." Key Engineering Materials 754 (September 2017): 165–68. http://dx.doi.org/10.4028/www.scientific.net/kem.754.165.

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General 2D boundary value problems of piezoelectric nanosized structures with cracks under a thermal load are analyzed by the finite element method (FEM). The size-effect phenomenon observed in nanosized structures is described by the strain-gradient effect. The strain gradients are considered in the constitutive equations for electric displacement and the high-order stress tensor. For this model, the governing equations are derived with the corresponding boundary conditions using the variational principle. Uncoupled thermoelasticity is considered, thus, the heat conduction problem is analyzed

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42

Marin, M., S. Vlase, and I. M. Fudulu. "A result of instability for two-temperatures Cosserat bodies." Analele Universitatii "Ovidius" Constanta - Seria Matematica 30, no. 2 (2022): 179–92. https://doi.org/10.2478/auom-2022-0025.

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Abstract In our study we consider a generalized thermoelasticity theory based on a heat conduction equation in micropolar bodies. Specifically, the heat conduction depends on two distinct temperatures, the conductive temperature and the thermodynamic temperature. In our analysis, the difference between the two temperatures is clear and is highlighted by the heat supply. After we formulate the mixed initial boundary value problem defined in this context, we prove the uniqueness of a solution corresponding some specific initial data and boundary conditions. Also, if the initial energy is negativ

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43

Podil'chuk, Yu N. "Some basic boundary value problems of thermoelasticity for a prolate spheroid." Soviet Applied Mechanics 22, no. 12 (1986): 1141–48. http://dx.doi.org/10.1007/bf01375811.

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44

Bitsadze, L., and George Jaiani. "Some basic boundary value problems of the plane thermoelasticity with microtemperatures." Mathematical Methods in the Applied Sciences 36, no. 8 (2012): 956–66. http://dx.doi.org/10.1002/mma.2652.

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45

Gawinecki, J. A. "Initial-boundary value problems in linear and nonlinear hyperbolic thermoelasticity theory." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 78, S3 (1998): 911–12. http://dx.doi.org/10.1002/zamm.19980781528.

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46

Alekseyeva, L. A., A. N. Dadayeva, and N. B. Zhanbyrbayev. "The method of boundary integral equations in unsteady boundary-value problems of uncoupled thermoelasticity." Journal of Applied Mathematics and Mechanics 63, no. 5 (1999): 803–8. http://dx.doi.org/10.1016/s0021-8928(99)00101-x.

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Duduchava, R., D. Natroshvili, and E. Shargorodsky. "Basic Boundary Value Problems of Thermoelasticity for Anisotropic Bodies with Cuts. I." gmj 2, no. 2 (1995): 123–40. http://dx.doi.org/10.1515/gmj.1995.123.

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Abstract The three-dimensional problems of the mathematical theory of thermoelasticity are considered for homogeneous anisotropic bodies with cuts. It is assumed that the two-dimensional surface of a cut is a smooth manifold of an arbitrary configuration with a smooth boundary. The existence and uniqueness theorems for boundary value problems of statics and pseudo-oscillations are proved in the Besov and Bessel-potential spaces by means of the classical potential methods and the theory of pseudodifferential equations on manifolds with boundary. Using the embedding theorems, it is proved that t

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Khusainov, Denys Ya, and Michael Pokojovy. "Solving the Linear 1D Thermoelasticity Equations with Pure Delay." International Journal of Mathematics and Mathematical Sciences 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/479267.

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We propose a system of partial differential equations with a single constant delayτ>0describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval ofR1. For an initial-boundary value problem associated with this system, we prove a well-posedness result in a certain topology under appropriate regularity conditions on the data. Further, we show the solution of our delayed model to converge to the solution of the classical equations of thermoelasticity asτ→0. Finally, we deduce an explicit solution representation for the delay problem.

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Kharashvili, Maia, and Ketevan Skhvitaridze. "Problem of Statics of the Linear Thermoelasticity of the Microstretch Materials with Microtemperatures for a Half-space." Works of Georgian Technical University, no. 2(520) (June 25, 2021): 202–19. http://dx.doi.org/10.36073/1512-0996-2021-2-202-219.

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We consider the statics case of the theory of linear thermoelasticity with microtemperatures and microstrech materials. The representation formula of differential equations obtained in the paper is expressed by the means of four harmonic and four metaharmonic functions. These formulas are very convenient and useful in many particular problems for domains with concrete geometry. Here we demonstrate an application of these formulas to the III type boundary value problem for a half-space. Uniqueness theorems are proved. Solutions are obtained in quadratures. 2010 Mathematics Subject Classificatio

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Feng, Yongping, and Junzhi Cui. "Multi-Scale and Finite Element Analysis of the Mixed Boundary Value Problem in a Perforated Domain under Coupled Thermoelasticity." Advanced Materials Research 9 (September 2005): 153–62. http://dx.doi.org/10.4028/www.scientific.net/amr.9.153.

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The two-scale asymptotic expression and error estimations based on two-scale analysis (TSA) are presented for the solution of the increment of temperature and the displacement of a composite structure with small periodic configurations under coupled thermoelasticity condition in a perforated domain. The two-scale coupled relation between the increment of temperature and displacement is established.The multi-scale finite element algorithms corresponding to TSA are described and numerical results are presented.

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