An efficient boundary collocation scheme for transient thermal analysis in large-size-ratio functionally graded materials under heat source load

Abstract

This paper presents a boundary collocation scheme for transient thermal analysis in large-size-ratio functionally graded materials (FGMs) with heat source load. In the proposed scheme, Laplace transformation and the numerical inverse Laplace transformation (NILT) are implemented to avoid the troublesome time-stepping effect on numerical efficiency. The collocation Trefftz method (CTM) coupled with composite multiple reciprocity method is used to obtain the high accurate results in the solution of nonhomogeneous problems in Laplace-space domain. The extended precision arithmetic is introduced to overcome the ill-posed issues generated from the CTM simulation, the NILT process and the large-size-ratio FGM. Heuristic error analysis and numerical investigation are presented to demonstrate the effectiveness of the proposed scheme for transient thermal analysis. Several benchmark examples are considered under large-size-ratio FGMs with some specific spatial variations (quadratic, exponential and trigonometric functions). The proposed scheme is validated in comparison with known analytical solutions and COMSOL simulation.