A highly accurate brick element based on a three-field variational principle for elasto-plastic analysis

Abstract

In this paper, a penalty equilibrating 3-D mixed element based on a modified Hu–Washizu variational functional has been proposed to improve the accuracy of the elasto-plastic analysis for irregular meshes. In order to construct this element, a penalty term, which can enforce the stress components to satisfy the equilibrium equations in a weak form, is introduced into the Hu–Washizu three-field functional to “penalize” the false stress caused by the distorted meshes. The selection of the penalty factor has also been discussed in detail. Unlike traditional hybrid or mixed elements, the performance of this element is not so sensitive to mesh distortion. Furthermore, compared with hybrid stress elements, the proposed element based on the three-field variational principle is more suitable for material non-linear analysis. Numerical examples including elastic and elasto-plastic analyses have demonstrated the improved performance of the proposed element.