An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids

Abstract

This paper presents an edge-based smoothed finite element method (ES-FEM) to significantly improve the accuracy of the finite element method (FEM) without much changing to the standard FEM settings. The ES-FEM can use different shape of elements but prefers triangular elements that can be much easily generated automatically for complicated domains. In the ES-FEM, the system stiffness matrix is computed using strains smoothed over the smoothing domains associated with the edges of the triangles. Intensive numerical results demonstrated that the ES-FEM possesses the following excellent properties: (1) the ES-FEM model possesses a close-to-exact stiffness: it is much softer than the “overly-stiff” FEM and much stiffer than the “overly-soft” NS-FEM model; (2) the results are often found superconvergence and ultra-accurate: much more accurate than the linear triangular elements of FEM and even more accurate than those of the FEM using quadrilateral elements with the same sets of nodes; (3) there are no spurious non-zeros energy modes found and hence the method is also temporally stable and works well for vibration analysis and (4) the implementation of the method is straightforward and no penalty parameter is used, and the computational efficiency is better than the FEM using the same sets of nodes. In addition, a novel domain-based selective scheme is proposed leading to a combined ES/NS-FEM model that is immune from volumetric locking and hence works very well for nearly incompressible materials. These properties of the ES-FEM are confirmed using examples of static, free and forced vibration analyses of solids.