Hybrid Finite Element Method Based on Polygon-Quadtree Meshes for Heat Transfer and Thermal Elastic Analysis

A steady-state thermal hybrid element model is proposed to calculate particle-reinforced composites divided by an improved quadtree mesh. The functional of hybrid flux finite element method (HF-FEM) is constructed using the weighted residual method. This functional independently assumes a heat flux field in the cell domain and a temperature field along cell boundaries. The construction of a universal heat flux function is put forward, which is approximated by a complete polynomial, and the temperature at the cell boundary is obtained by linear interpolation. Also, the hybrid stress finite element method (HS-FEM) is constructed to solve the thermal stress. In this paper, an improved quadtree grid that can accurately describe the shape of elliptical inclusions is built. By comparing several numerical examples with the traditional FEM, it is demonstrated that the hybrid element of the thermal analysis proposed in this paper is practical.