SUMMARYThis paper presents a novel face-based smoothed finite element method (FS-FEM) to improve the accuracy of the finite element method (FEM) for three-dimensional (3D) problems. The FS-FEM uses 4-node tetrahedral elements that can be generated automatically for complicated domains. In the FS-FEM, the system stiffness matrix is computed using strains smoothed over the smoothing domains associated with the faces of the tetrahedral elements. The results demonstrated that the FS-FEM is significantly more accurate than the FEM using tetrahedral elements for both linear and geometrically non-linear solid mechanics problems. In addition, a novel domain-based selective scheme is proposed leading to a combined FS/NS-FEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The implementation of the FS-FEM is straightforward and no penalty parameters or additional degrees of freedom are used. The computational efficiency of the FS-FEM is found better than that of the FEM.
In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements is formulated for static, free vibration and buckling analyses of Reissner-Mindlin plates. The discrete weak form of the NS-FEM is obtained based on the strain smoothing technique over smoothing domains associated with the nodes of the elements. The discrete shear gap (DSG) method together with a stabilization technique is incorporated into the NS-FEM to eliminate transverse shear locking and to maintain stability of the present formulation. A so-called node-based smoothed stabilized discrete shear gap method (NS-DSG) is then proposed. Several numerical examples are used to illustrate the accuracy and effectiveness of the present method.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.