Non-conforming generalized mixed element methods based on the volume coordinate system

Abstract

The computation accuracy of non-conforming isoparametric elements in the displacement finite element method remains suboptimal when confronted with serious mesh distortion. To improve this issue, the area coordinate system and the volume coordinate system method based on displacement were proposed in the last century. By adopting volume coordinates as local coordinates and integrating the advantages of the non-conforming mixed finite element method, which simultaneously handles displacement and stress boundary conditions, this paper proposes the Non-conforming Generalized Mixed Element Method based on the Volume Coordinate System (NGMVC). The local natural coordinates of the NGMVC maintain a linear relationship with the Cartesian coordinate system, ensuring insensitivity to mesh distortion. Moreover, the proposed method addresses the limitation that lacks stress analysis of the conventional univariate method. Consequently, it enhances the rationality of the finite element model and the accuracy of numerical results. In theory, the model is more rational and objective. The numerical results show that the NGMVC series elements have excellent stability and much superior accuracy compared to the conventional non-conforming displacement isoparametric elements when the mesh distortion is severe.