An Element Decomposition Method for Three-Dimensional Solid Mechanics

Abstract

This paper proposes an element decomposition method (EDM) for elastic-static, free vibration and forced vibration analyses of three-dimensional solid mechanics. The problem domain is first discretized using eight-node hexahedral elements. Then, each hexahedron is further subdivided into a set of sub-tetrahedral cells, and the local strains in each sub-tetrahedron are obtained using linear interpolation functions. For each hexahedron, the strain of the whole element is the weighted average value of the local strains, which means only one integration point is adopted to establish the stiffness matrix. To cure the numerical instability of one-point quadrature and improve the accuracy, a variation gradient item is complemented by variance of the local strains. Numerical examples, including both benchmark and practical engineering cases, demonstrate that the present method possesses the following interesting properties compared with the traditional finite element method using the same mesh discretization (1) super accuracy and faster convergence rate; (2) higher computational efficiency; (3) more immune to mesh distortion.