On the thermoelastic stresses of multiple interacting inhomogeneities

Abstract

An analytic solution is presented for the two-dimensional thermoelastic problem of multiple interacting circular inhomogeneities of different sizes and thermoelastic properties embedded in an isotropic elastic medium. Based upon the complex potentials of Muskhelishvili, the analytic solution is derived for the single circular inhomogeneity problem under arbitrary thermal loadings. The solution is then applied to the problem of an infinitely extended medium containing randomly located multiple inhomogeneities successively. This procedure leads to a series solution derived with perturbation technique. Study examples show the elegance and robustness of the present approach. The results reveal the dependence of the resulting thermal stresses upon the mismatch of the thermoelastic properties and the configuration of the inhomogeneities.