A Simple Automatic Hexahedron Mesh Generation and Polyhedral Smoothed Finite Element Method for Mechanics Problems

Abstract

A new fully automatic pure hexahedron mesh, called lotus mesh, generation technique of an arbitrary 2D/3D geometric domain and polyhedral smoothed finite element method (PSFEM) for efficient numerical simulation are presented. The lotus mesh algorithm is mainly based on the signed distance function (SDF) and the density function to generate nodes and control node density, respectively. We improved the generality of the SDF-based mesh method, realizing the meshing of 2D arbitrary polygons and 3D complex structures, and propose geometry-based adaptive meshing methods. In addition, to improve the stability and accuracy of lotus mesh, PSFEM based on smoothed finite method (SFEM) is proposed. Unlike the existing SFEM, this paper adopts an indirect way to calculate the stiffness matrix, which first calculates the transition matrix on the smoothed domain, and then maps it back to the real stiffness matrix through the transformation matrix, to address stiffness integral operation of the 3D complex polyhedron. Several demonstration examples are presented to verify the lotus mesh and its accuracy. • A fully automatic pure hexahedron mesh, lotus mesh, is proposed, whose algorithm structure is simple and easy to implement. • Mesh generation method based on signed distance function is improved to realize the meshing of 2D arbitrary polygons and 3D complex structures with geometry-based adaptivity. • Polyhedral smoothed finite element method is proposed, which has higher accuracy using lotus mesh than conventional finite element method.