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

Jian Yang,Wei Xie,Zhiwei Zhang

doi:10.1051/jnwpu/20213940747

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.

Highlights

图 10 给出了梁模型应力相对误差随单边特征边长的收敛曲线。从图中可以看出, ES⁃FEM⁃Poly 的曲线明显低于 FEM⁃T4 和 FEM⁃H6,表明 ES⁃FEM⁃
Exploring three⁃dimensional edge⁃based smoothed finite element method based on polyhedral mesh to study elastic mechanics problems
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

Summary

Introduction

图 10 给出了梁模型应力相对误差随单边特征边长的收敛曲线。从图中可以看出, ES⁃FEM⁃Poly 的曲线明显低于 FEM⁃T4 和 FEM⁃H6,表明 ES⁃FEM⁃ 的计算精度显著高于 FEM⁃T4 和 FEM⁃H6。当 h = 0.5 m,即 lg( h)= -0.3 时,ES⁃FEM⁃Poly 的应力相对误差是 FEM⁃H6 的 1 / 4,是 FEM⁃T4 的 1 / 6。 [1] HUO S H, LIU G R, ZHANG J Q, et al A smoothed finite element method for octree⁃based polyhedral meshes with large num⁃ ber of hanging nodes and irregular elements[ J] .

Results

Conclusion