Green's function approach to the nonlinear transient heat transfer analysis of functionally graded materials

This paper presents a Green's function approach to the solution of nonlinear transient heat transfer problem in a functionally graded material (FGM) object for the purpose of both the numerical analysis accuracy and computational efficiency. The Green's functions of transient heat transfer problem for a short hollow cylinder with power law functionally graded materials have been obtained analytically. The generalized expressions of the effective material properties in FGM are simplified based on micromechanical models (Voigt model and Mori-Tanaka model). The nonlinearity resulting from the temperature-dependent properties is resolved using the artificial parameter method. Two examples have been given to compare the effectiveness of the proposed Green's function approach with the finite element method (FEM), and the accuracy is satisfactory. This approach can become a cost-effective and accurate method for FGM structure design and risk assessment.