A 3D brick element based on Hu-Washizu variational principle for mesh distortion

In order to improve the accuracy of the mixed element for irregular meshes, a penalty-equilibrating 3D-mixed element based on the Hu-Washizu variational principle has been proposed in this paper. The key idea in this work is to introduce a penalty term into the Hu-Washizu three-field functional, which can enforce the stress components to satisfy the equilibrium equations in a weak form. Compared with the classical hybrid and mixed elements, this technique can efficiently reduce the sensitivity of the element to mesh distortion. The reason for the better results of this penalty technique has been investigated by considering a simple 2D problem. From this investigation, it has been found that the penalty parameter here plays the role of a scaling factor to reduce the influence of the parasitic strain or stress, which is similar to the devised selective scaling factor proposed by Sze. Furthermore, compared with the hybrid stress element, the proposed element based on the three-field variational principle is more suitable for material non-linear analysis. Numerical examples have demonstrated the improved performance of the present element, especially in stress computation when FEM meshes are irregular.