On the issue of a generalized formulation of an unsteady problem of coupled thermoelasticity in stresses

E. V. Davidenko^a, A. V. Zemskov^ba, D. V. Tarlakovskii<sup>ba

a</sup> Moscow Aviation Institute (National Research University)
^b Lomonosov Moscow State University

Abstract: The paper a problem formulation of unsteady thermoelasticity in stresses are considered. General equations of compatibility of deformations in stresses for an isotropic thermoelastic continuum in an arbitrary curvilinear coordinate system are obtained. These equations are generalizations of the Beltrami-Mitchell equations for the case of unsteady loads taking into account the finite velocity of heat flux propagation. The advantage of the proposed model when using numerical algorithms for solving initial-boundary value problems of coupled thermoelasticity based on the finite difference method is briefly analyzed. Fundamental solutions to one-dimensional problems of thermal elasticity in a Cartesian coordinate system are obtained.

Keywords: thermoelasticity, deformation compatibility equations, Beltrami-Mitchell equations, unsteady problems, continuum.

Received: 03.03.2025
Revised: 02.06.2025
Accepted: 09.06.2025

DOI: 10.20948/mm-2026-01-01