Study on coupled problems of thermoelasticity in Strains

Abstract

In the work, within the framework of the strain compatibility conditions of Saint-Venant, two equivalent dynamic boundary value problems of thermoelasticity with respect to strains are formulated. In the case of the first boundary value problem, the dynamic equations of thermoelasticity are obtained from the compatibility conditions, in the second case, instead of the first three equations of thermoelasticity, the equations of motion expressed with respect to deformations are considered. Discrete analogues of boundary value problems are constructed using the finite-difference method in the form of explicit and implicit schemes. The solution of explicit schemes is reduced to recurrent relations with respect to deformations and temperature. Implicit schemes are solved by sequential application of the elimination method. The validity of the formulated thermoelastic boundary value problems is substantiated by comparing the numerical results of the problem of a thermoelastic parallelepiped obtained by different methods, as well as solving a similar problem in displacements.