ON THE BOUNDARY INTEGRAL FORMULATION OF THE PLANE THEORY OF THERMOELASTICITY (ANALYTICAL ASPECTS)

Abstract

The main purpose of this work is to present a formulation of the plane strain problem of thermoelasticity with heat sources for simply connected regions based on the combined use of the stress function and the boundary integral representation technique in terms of real functions. This is an alternative to the already existing boundary integral approach in displacements. The proposed formulation enables one to obtain closed-form analytical solutions for problems with simple geometries (as shown in the application) and is particularly well adapted to numerical approaches to the problem. Different thermal and mechanical boundary conditions are considered. A simple application for the circular boundary elucidates the mathematical complexity involved and the necessity of recurring to numerical treatments once the boundary deviates from being simple.