Thermal analysis of a functionally graded coating/substrate system using the approximated transfer approach

As a heterogeneous material, functionally graded material (FGM) behaves as continuously changed material properties in certain directions from one composition to another, and hence it has received much more attention for biomedical applications and thermal protections to achieve innovative functions that conventional homogeneous material cannot accomplish. However, due to the particularly small thickness ratio of coating to substrate in practice, the conventional mesh discretization of the coating region is inefficient. To simplify the meshing procedure and increase the efficiency of analysis, the approximated transfer algorithm based on the concept of finite difference is developed for transferring boundary conditions applied on the coating surface to the interface of coating and substrate. As a result, only the substrate with transferred convection boundary conditions needs to be solved numerically, i.e., by the fundamental-solution based hybrid finite element method (HFS-FEM) with high accuracy and feasible polygonal element construction, in which only integrals along the element boundary are evaluated because of the application of fundamental solutions of the problem as kernel functions of interior approximated fields. Finally, numerical experiments including the single-layered, multi-layered and functionally graded coatings are carried out to verify the accuracy and applicability of the present method.