Exploring three-dimensional edge-based smoothed finite element method based on polyhedral mesh to study elastic mechanics problems

基于多面体单元的三维ES-FEM理论研究

¹ School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
² National Key Laboratory of Science and Technology on Liquid Rocket Engine, Xi'an 710100, China

Received: 11 December 2020

Abstract

This paper established the three-dimensional edge-based smoothed finite element method(ES-FEM) based on polyhedral mesh, divided the smoothed domain, constructed the shape function and derived the geometric matrix and the stiffness matrix. The MATLAB software was used to prepare the corresponding computing programs, with which the paper studied the stress distribution of a hollow sphere model and a beam model under different numbers of polyhedral elements. The paper compared the calculation results from the conventional finite element methods(FEM) that use tetrahedral elements and hexahedral elements respectively in terms of stress relative error and energy relative error. The comparison results show that the three-dimensional ES-FEM based on polyhedral mesh has better precision and convergence than the conventional FEM and better adaptability to complex geometric structures.

摘要

建立了基于多面体单元的三维光滑边域有限元法（ES-FEM-Poly），包括多面体单元中光滑域的划分方法、形函数的构造，以及几何矩阵、刚度矩阵的推导。同时利用Matlab软件编制了相应的计算程序，研究了空心球模型和梁模型在不同数量多面体单元下的应力分布，与常规四面体单元和六面体单元有限元计算结果通过应力相对误差和能量相对误差进行比较。研究结果表明，基于多面体网格的三维光滑边域有限元法相比常规有限元法具有更好的精度和收敛性，且对于复杂的几何结构也有较好的适应性。