On multiple circular inclusions in plane thermoelasticity

Abstract

A general series solution to the problem of interacting circular inclusions in plane thermoelasticity is provided in this paper. Based upon the complex variable theory and the use of Laurent series expansion, the general expression of the stress functions is derived explicitly for the circular inclusion problem under remote uniform heat flow. By applying the use of the superposition, the problem dealing with any number of arbitrarily located inclusions can be then reduced to a set of linear algebraic equations which are solved with the aid of a perturbation technique. For illustrating the use of the present approach, an approximate closed form solution of the stress functions is derived explicitly for the problem containing two arbitrarily located inclusions. Numerical results of the interfacial stresses around a rigid circular inclusion or hoop stress along a circular hole due to the presence of an elastic inclusion are provided to demonstrate the dependence of the solution upon the pertinent parameters.