A method for the solution of three-dimensional thermoelasticity problems for bodies with thin inclusions

We propose an efficient method for the approximate solution of a thermoelasticity problem for a three-dimensional body with a thin inclusion with smooth surface. The method is based on a new mathematical model of the inclusion that establishes the relationship between stresses, displacements, and temperature on its surfaces as well as on relations for finding distributions of stresses near the tip of the inclusion in terms of the stress intensity factors of the corresponding singular problem. As a result, the problem reduces to a system of singular integro-differential equations for the jumps of stresses and displacements on the surface of the inclusion. As an example, we consider the case of a spheroidal inclusion in an infinite body subjected to uniform heating.