Local Mesh Refinement for Displacement-Based and Equilibrium-Based Finite Elements

Abstract

In this paper, a local mesh refinement algorithm for the computation of elastoplastic structures is presented. The elastoplastic computation is performed using a dual analysis combining two approaches: displacement-based and equilibrium-based finite elements. The remeshing scheme is applied to 3D structures discretized with three-dimensional tetrahedral meshes. Thanks to the dual approach, it is possible to assess a global error term that quantifies the distance between the displacement-based solution and the equilibrium solution. The local mesh refinement is based on the evaluation of the contribution of each element to this global error. This process is repeated as long as the distance between the two dual solutions doesn’t respect an accepted tolerance. The method is illustrated on a real project steel assembly.