Local adaptive refinement method applied to solid mechanics

Loic Daridon,Yann Monerie,Frédéric Perales,Eric Delaume

doi:10.24132/acm.2020.570

Abstract

A good spatial discretization is of prime interest in the accuracy of the Finite Element Method. This paper presents a new refinement criterion dedicated to an h-type refinement method called Conforming Hierarchical Adaptive Refinement MethodS (CHARMS) and applied to solid mechanics. This method produces conformally refined meshes and deals with refinement from a basis function point of view. The proposed refinement criterion allow adaptive refinement where the mesh is still too coarse and where a strain or a stress field has a large value or a large gradient. The sensitivity of the criterion to the value or to the gradient ca be adjusted. The method and the criteria are validated through 2-D test cases. One limitation of the h-adaptive refinement method is highlighted: the discretization of boundary curves.

Highlights

Higher accuracy in Finite Element Method (FEM) can be obtained by adjusting spatial resolution of domain discretization
The general idea is to construct a hierarchy of nested meshes, where at a given level of refinement each basis functions can be expressed as a linear combination of basis functions associated to the immediate finer or coarser mesh
This refinement method is here used with new refinement criterion and is validated through 2-D test cases

Summary

Introduction

Higher accuracy in Finite Element Method (FEM) can be obtained by adjusting spatial resolution of domain discretization. This method, initially developed in the framework of fluid mechanics [6, 16] and more recently applied to solid mechanics [10, 13], allows both (i) to preserve element shape quality while producing a conforming mesh and (ii) to perform local adaptive refinement and unrefinement This method deals with refinement from a basis function point of view and not from a geometrical point of view. The general idea is to construct a hierarchy of nested meshes, where at a given level of refinement each basis functions can be expressed as a linear combination of basis functions associated to the immediate finer or coarser mesh This refinement method is here used with new refinement criterion and is validated through 2-D test cases.

Refinement criteria

Role of power α

CHARMS refinement vs homogeneous refinement

Limitation: discretization of curved edge

Findings

Conclusions