Three-dimensional exact analytical solutions of transversely isotropic plate under heat sources

Abstract

An accurate and efficient calculation method for the transversely isotropic thermoelastic plates plays an important role in exact design and quality control of the engineering structures. In this study, the three-dimensional (3D) thermal stress field of transversely isotropic plates under arbitrary heat source is obtained using Green’s function method. To achieve the purpose, the 3D Green’s function solutions of transversely isotropic plate under a point heat source are firstly derived based on the general solutions which are presented in potential functions. The concise harmonic potential functions are constructed in simple functions with undetermined constants by mirror image principle. Then, the Green’s functions are achieved by substituting the harmonic functions into the general solution. All temperature and stress components can be analytically expressed using simple functions which are convenient to use. The present method without simplifying assumption of dimensions has the applicability and reliability to analysis plate structures with arbitrarily thickness. Numerical calculations show the good convergence and high efficiency of the method. This study presents a high precision and efficiency predesign method for the thermos elastic plate structures. The numerical results provide theoretical guideline for the accurate design and quality control of plate structures.