Study on hybrid stress element of three-dimensional arbitrary polyhedron

In three-dimensional problems, regular tetrahedron, pentahedron, and hexahedron elements are used in standard finite element software. In practice, however, the three-dimensional model is irregular. Traditional regular elements cannot accurately describe model structure. The field function integral accuracy of traditional displacement finite elements is low, and the number of elements considerably affects the integral results. As the number of elements increases, the computational efficiency decreases as well. Therefore, based on the hybrid stress element method, this paper proposes a new numerical calculation element for three-dimensional problems–a three-dimensional arbitrary polyhedron element. The corresponding calculation scheme is the 3-Dimensional Voronoi Cell Finite Element Method (3DVCFEM). This paper first verifies the effectiveness of the scheme. The stress field model with a singular solution is further simulated, and the change rule of the number of stress terms is obtained. On this basis, 3DVCFEM is introduced into calculating octree elements to solve complex classification problems and difficult calculation of octree elements. Moreover, the efficiency of the octree elements is investigated.