Finite element method with 3D polyhedron-octree for the analysis of heat conduction and thermal stresses in composite materials

Applying the hybrid flux finite element method(HF-FEM) and hybrid thermal stress finite element method (HTS-FEM) is not prevalent in analyzing heat conduction and thermal stresses in particle-reinforced composite materials. Most of the research on this technique is confined to two-dimensional problems. This paper proposes the HF-FEM and HTS-FEM, based on 3D polyhedron-octree, to calculate the steady-state heat conduction and thermal stress of particle-reinforced composites. In addition, this paper presents a method for partitioning spherical particle-reinforced materials into polyhedron-octree elements, each of which contains only one type of material. Each element is divided into multiple Delaunay tetrahedrons, and hammer integration is used to perform the integrals. Additionally, this paper presents a technique to construct the heat flux function for polyhedral elements, and the effectiveness of the above methods is demonstrated by comparing it to several numerical examples of traditional finite element methods.