thermoelasticity, decomposition of the problem of thermoelasticity, rigorous solution, particular solution of the Poisson equation, particular solution of an inhomogeneous boundary value problem, method of boundary states, MBS, support basis.

Boundary value problems for a linear thermoelastic isotropically homogeneous medium are considered. The state of the medium is subject to the Duhamel-Neumann equations. In the case when the characteristics of the stress-strain state (SSS) on the surface of the body are not related to temperature factors in the boundary conditions (BC), the problem is decomposed into a sequence of inhomogeneous problems of heat conduction and elasticity theory with a known correction of body forces in the equilibrium equations. Particular attention is paid to the method of constructing a particular solution to the problem of heat conduction. The Green’s function method presents particular solutions of such problems in a singular form, which, for an arbitrary geometric configuration of the body, does not allow us to write out a rigorous analytical solution. An approach is proposed that makes it possible to obtain a particular solution rigorously in the case of a regular description of heat sources by a polynomial of finite order. The trace of such a solution at the boundary makes it possible to correct the BC of the heat conduction problem and construct a numerical-analytical solution by means of the method of boundary states (MBS). A similar approach is implemented for a rigorous particular solution of the linear elasticity problem. The constructed temperature field makes a regular addition to the volume forces of the second step - the problem of the theory of elasticity. Its solution is also effectively built using the MBS. The combination of these two steps makes it possible to write out a strictly particular solution for problems of linear thermoelastics.

Levina Lyubov Vladimirovna,

Ph.D., Associate Professor, Lipetsk State Technical University, Lipetsk, Russia,

Penkov Viktor Borisovich,

Dr. Sci. Phys. and Math, Professor, Lipetsk State Technical University, Lipetsk, Russia,

Novikov Evgeny Aleksandrovich,

Graduate Student, Lipetsk State Technical University, Lipetsk, Russia.