Special inclusion elements for thermal analysis of composite materials

A novel fundamental solution based finite element method (HFS-FEM) is proposed to analyze heat conduction problem of two-dimensional composite materials. In the proposed method, a linear combination of fundamental solutions at source points is taken as intra-element trial functions to construct the interior temperature field. The required fundamental solution is established by the charge simulation method, which makes it possible to establish arbitrarily shaped inclusion elements. The frame temperature field is independently approximated by the conventional finite element interpolation function to enforce the continuity between neighboring elements. The domain integral is eliminated by applying the divergence theorem to the modified variational functional, which gives HFS-FEM great flexibility in mesh generation. To assess the performance of the proposed elements, numerical examples are conducted and comparisons are made between HFS-FEM and ABAQUS. Numerical results show that HFS-FEM can capture the discontinuity of inclusion and exhibits high efficiency.