Thermal Stress of an Infinite Elastic Region in Uniform Heat Flow and Containing Some Spherical Cavities : Part 1, Solution for the Case of Containing Three Spherical Cavities

Abstract

A method of solution to determining the thermal stress of an infinite elastic region under the conditions of linear thermoelasticity and containing some spherical cavities is illustrated by two examples for the problems containing two and three spherical cavities. The fundamental equations governing the temperature distribution in a solid are first derived and then the elastic stresses in the solid bodies under prescribed temperature distributions are determined to satisfy the boundary conditions on the peripheries of the cavities. The method consists of a general series form of stress function in spherical coordinates, and it can be developed for a variety of cavity numbers and sizes. In this paper, the illustration for three cavities is given, and the numerical results are reported.