Numerical Simulation of the Coupled Dynamic Problem of Thermoelasticity in Stresses
DOI:
https://doi.org/10.71310/pcam.6_70.2025.04Keywords:
thermoelasticity, stresses, deformations, explicit scheme, implicit scheme, displacementsAbstract
This article proposes a dynamic model of a coupled thermoelasticity problem under stress. A coupled boundary value problem is formulated, consisting of three differen tial equations for the stress and temperature tensor components, as well as a heat flux equation with corresponding initial and boundary conditions. Explicit and implicit finite difference equations are developed, solved by successive application of the sweep method along the coordinate axes and recurrence relations, respectively. The coupled dynamic thermoelasticity problem for an anisotropic rectangle under stress is solved numerically. A comparison of the results of explicit and implicit difference schemes demonstrates the reliability of the obtained numerical results and the validity of the proposed coupled dynamic boundary value problem of thermoelasticity under stress.
References
Youssef H.M., Al-Felali A.S. Generalized thermoelasticity problem of material subjected to thermal loading due to laser pulse // Applied Mathematics. – 2012. – Vol. 3. – P. 142-146.
Novatskiy V. Dinamicheskiye zadachi termouprugosti. – M.: Mir, 1970. – 256 s
Pobedrya B.Ye. Chislennyye metody v teorii uprugosti i plastichnosti. – M.: MGU, 1996. – 343 s.
Konovalov A.N. Resheniye zadach termouprugosti v napryazheniyakh. – Novosibirsk, 1979. – 92 s.
Samarskiy A.A., Nikolayev Ye.S. Metody resheniya setochnykh uravneniy. – M.: Nauka, 1978. – 592 s.
Khaldjigitov A.A., Kalandarov A.A., Djumayozov U.Z. Numerical modeling of coupled problems of thermo-plasticity on non-uniform meshes // AIP Conference Proceedings. – 2022. – Vol. 2686, Issue 1. – Art. 020007.
Kalandarov A.A., Khaldjigitov A.A., Atabayev K. Coupled plane problem of dynamic thermal elasticity in stresses // AIP Conference Proceedings. – 2024. – (International Conference: Mechanics, Earthquake Engineering, Machinery Building, Tashkent, May 27-29, 2024).
Kalandarov A.A., Dzhumayozov U.Z., Sagdullayeva D.A. Chislennoye modelirovaniye termouprugoplasticheskogo sostoyaniya izotropnogo parallelepipeda // Problemy vychislitel'noy i prikladnoy matematiki. – 2021. – №4(15). – C. 1-19.
Khaldzhigitov A.A., Kalandarov A.A., Dzhumayozov U.Z. Chislennoye modelirovaniye svyazannoy zadachi termouprugosti v deformatsiyakh // Problemy vychislitel'noy i prikladnoy matematiki. – 2023. – №6(53). – C. 114-122.
Andrianov I., Topol H. Compatibility conditions: number of independent equations and boundary conditions // Mechanics and Physics of Structured Media. – 2022. – P. 123-140. doi: http://dx.doi.org/10.1016/b978-0-32-390543-5.00011-6.
Abirov R.A., Khusanov B.E., Sagdullaeva D.A. Numerical modeling of the problem of indentation of elastic and elastic-plastic massive bodies // IOP Conference Series: Materials Science and Engineering. – 2020. – Vol. 971. – Art. 032017. doi: http://dx.doi.org/10.1088/1757-899X/971/3/032017.
Akhmedov A., Kholmanov N. Problems of the theory of elasticity in stresses // AIP Conference Proceedings. – 2022. – Vol. 2637, Issue 1. – P. 1-10. doi: http://dx.doi.org/10.1063/5.0119144.
Borodachev N.M. Three-dimensional problem of the theory of elasticity in strains // Strength of Materials. – 1995. – Vol. 27. – P. 296-299. doi: http://dx.doi.org/10.1007/bf02208501.
Borodachev N.M. About one approach in the solution of the 3D problem of elasticity in stresses // International Journal of Applied Mechanics. – 1995. – Vol. 31, Issue 12. – P. 38-44.
Borodachev N.M. An approach to solving the stress problem of elasticity // International Applied Mechanics. – 2006. – Vol. 42, Issue 7. – P. 744-748. doi: http://dx.doi.org/10.1007/s10778-006-0142-8.
Georgievski D.V., Pobedrya B.E. On the number of independent compatibility equations in the mechanics of a deformable solid // Journal of Applied Mathematics and Mechanics. – 2004. – Vol. 68, Issue 6. – P. 941-946.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 A.A. Kalandarov
This work is licensed under a Creative Commons Attribution 4.0 International License.
