On Bonded Circular Inclusions in Plane Thermoelasticity

Abstract

A general solution to the thermoelastic problem of a circular inhomogeneity in an infinite matrix is provided. The thermal loadings considered in this note include a point heat source located either in the matrix or in the inclusion and a uniform heat flow applied at infinity. The proposed analysis is based upon the use of Laurent series expansion of the corresponding complex potentials and the method of analytical continuation. The general expressions of the temperature and stress functions are derived explicitly in both the inclusion and the surrounding matrix. Comparison is made with some special cases such as a circular hole under remote uniform heat flow and a circular disk under a point heat source, which shows that the results presented here are exact and general.