Hybrid fundamental-solution-based FEM for thermal analysis of cellular materials containing non-smooth holes

Abstract

A novel hybrid polygonal finite element is proposed for simulating the heat conduction in two-dimensional cellular materials based on the hybrid fundamental-solution-based finite element method (HFS-FEM). The proposed method assumes two independent temperature fields in the domain and boundary of the element, respectively. The intra-element temperature field is approximated by a combination of fundamental solutions satisfying the governing equation of the problem. The charge simulation method is introduced so that the required fundamental solution can be established for the domain with an arbitrarily-shaped hole. To satisfy the continuity condition between adjacent elements, a conforming frame temperature field is approximated by the conventional finite element interpolation functions. Combing two independent fields into the modified variational functional leads to the resultant finite element formulation avoiding the need for domain integration. Such boundary-type feature endows a great capability of constructing any polygonal element with different number of sides and makes a great flexibility in mesh generation. The accuracy and efficiency of HFS-FEM are demonstrated through three numerical examples which includes triangular, astroid and irregular hole elements.