Green's function for a point heat source embedded in an infinite body with two circular elastic inclusions

Abstract

• The analytical continuation technique and the alternation method are used. • The derived series solution is rapidly convergent. • The interfacial normal stresses become negative with a higher temperature. • Our present proposed method is efficient and general. A general solution for a point heat source interacting with two circular inclusions embedded in an infinite solid is presented in this work. Based on the method of analytical continuation in conjunction with the alternating technique, the solutions to the heat conduction and thermoelastic problems are derived. A rapidly convergent series solution for both the temperature and stress field, which is expressed in terms of an explicit general term of the corresponding homogeneous complex potential, is obtained in an elegant form. As a numerical illustration, the constant contour values of the temperature and stresses are displayed to provide a better understanding of both heat and stress flows for different locations of a point heat source. Numerical results of interfacial stresses are also shown in graphic form and discussed in detail. The solution obtained in this study can be treated as Green's functions which enable us to formulate an integral equation for the crack problem associated with two circular inclusions.