Towards tangled finite element analysis over partially inverted hexahedral elements

TL;DR

This paper extends the tangled finite element method (TFEM) from 2D quadrilaterals to 3D hexahedral elements, enabling accurate analysis of tangled meshes with minimal modifications to existing FEM frameworks.

Contribution

The paper introduces an extension of TFEM to 3D hexahedral elements, addressing tangled meshes in 3D finite element analysis.

Findings

TFEM provides accurate results over tangled hexahedral elements.

Minimal changes are needed to integrate TFEM into existing FEM frameworks.

The method effectively handles tangled meshes during large deformation simulations.

Abstract

If a finite element mesh contains concave elements, it is said to tangled. Tangled meshes can occur during mesh generation, mesh optimization, and large deformation simulations, and will lead to erroneous results during finite element analysis. Recently, the authors introduced the tangled finite element method (TFEM) to accurately handle tangled 2D concave quadrilateral elements. In this paper, TFEM is extended to 3D hexahedral elements. We demonstrate that TFEM leads to accurate results over tangled hexahedral elements, requiring minimal changes to existing FEM framework.