Analytical solutions to a coated triangle hole embedded in an infinite plate under a remote uniform heat flow

Abstract

A general solution for a remote uniform heat flow interacting with a coated triangle hole embedded in an infinite plate is provided in this article. Based on the method of analytical continuation in conjunction with the alternation technique, the solutions to the heat conduction and thermoelastic problems are derived. A rapidly convergent series solution for both temperature and stress field is obtained in an elegant form which is expressed in terms of an explicit general form of the corresponding homogeneous complex potential. Numerical results of interfacial stresses are evaluated to provide a better understanding of an optimum design for various material properties and geometric parameters. The present proposed method can be further extended to deal with the corresponding thermoelastic problem with any shape of holes.