Abstract Statement of an unsteady thermoelasticity problem in terms of stresses is considered. General equations of deformation compatibility in terms of stressaes for an isotropic thermoelastic medium 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 thermal elasticity problems in a Cartesian coordinate system are obtained.
Davidenko et al. (Mon,) studied this question.