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Abstract <p>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.</p>

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On the Issue of a Generalized Formulation of an Unsteady Problem of Coupled Thermoelasticity in Stresses

  • 期刊论文

  • 发表日期：

    2026年6月15日

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  • E. V. Davidenko,
  • A. V. Zemskov,
  • D. V. Tarlakovskii

摘要

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.