The hybrid boundary element method applied to functionally graded materials

The hybrid boundary element method has been successfully applied to various problems of elasticity and potential theory. This paper focuses on establishing the conceptual framework for applying the hybrid boundary element method to functionally graded materials. Several classes of fundamental solutions for problems of potential are derived. In particular, a recently developed 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 a patch test for irregular regions submitted to high gradients.