Heterogeneous Problems in Plane Thermoelasticity

Abstract

Within the framework of the linear theory of thermoelasticity, the heterogeneous problem associated with multiple inclusions, circularly cylindrical layered media and plane layered media is considered and solved in this paper. The number of inclusions and layers is arbitrary and the system is subjected to arbitrary loading (singularities). The solutions to heat conduction (or antiplane deformation) and thermoelasticity problems are derived by the heterogenization technique that allows us to write down the solution explicitly in terms of the solution of a corresponding homogeneous problem subjected to the same loading. A rapid convergent series solution for both the temperature (or antiplane displacement) and stress functions, which is expressed in terms of an explicit general term of the complex potential of the corresponding homogeneous problem, is obtained in an elegant form. Numerical results are provided for some particular examples to investigate the effect of material combinations and geometrical configurations on the interfacial stresses.