Modeling of functionally graded material assemblages using the hybrid boundary element method

The hybrid boundary element method was introduced in 1987. Since then, the method has been successfully applied to different problems of elasticity and potential, including time-dependent problems. This paper focuses on establishing the conceptual framework for applying the hybrid boundary element method to functionally graded materials. In particular, a recently derived fundamental solution is employed to model heat conduction in materials with exponentially varying thermal conductivity. Thus, the boundary-only feature of the method is preserved even with such spatially varying material property. Two numerical examples are given in terms of an efficient patch test for irregular regions submitted to high gradients.