Numerical Solution of the Plane Problem of Thermo-Elasticity in Strains

Abstract

In the work, within the framework of the Saint-Venant compatibility conditions, two plane problems of thermoelasticity with respect to deformations are formulated. The closedness of boundary value problems is achieved by considering equilibrium equations on the boundary of a given region. Grid equations of thermoelastic problems are compiled using the finite-difference method and solved by the alternative method. The problem of a free thermoelastic rectangle located in a given temperature field is solved numerically. The validity of the formulated boundary value problems and the reliability of the solution are justified by comparing the numerical results of the formulated boundary value problems regarding displacements and stresses.