A face‐based smoothed finite element method (FS‐FEM) for 3D linear and geometrically non‐linear solid mechanics problems using 4‐node tetrahedral elements

Abstract

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.

RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)

“…In the other front of the development of numerical methods, Liu and Nguyen Thoi [39] have integrated the strain smoothing technique [40] into the finite element method (FEM) to create a series of smoothed FEMs (S-FEMs) such as cell/element-based smoothed FEM (CS-FEM) [41][42][43], node-based smoothed FEM (NS-FEM) [44][45][46], edge-based smoothed FEM (ES-FEM) [47,48], face-based smoothed FEM (FS-FEM) [49], and a group of alpha-FEM [50][51][52][53]. Each of these smoothed FEMs has different properties and has been used to produce desired solutions for a wide class of benchmark and practical mechanics problems.…”

Analysis of composite plates by a unified formulation-cell based smoothed finite element method and field consistent elements

“…By incorporating the strain smoothing technique into the finite element method (FEM), Liu et al, [26] have formulated a series of smoothed finite element methods (SFEM), named as cell-based SFEM (CS-FEM) [32,3], node-based SFEM [25], edge-based SFEM [24], facebased SFEM [31] and α-FEM [23]. Nguyen-Xuan et al, [33] employed CS-FEM for MindlinReissner plates.…”

Structural Topology Optimization Based on the Smoothed Finite Element Method

“…This new numerical method is rooted in meshless stabilized conforming nodal integration and exhibits a number of attractive properties such as good numerical stability and accuracy, excellent convergence rate, and insensitivity to volumetric locking and mesh distortion (Liu et al (2007)). The smoothed finite element method has been successfully applied to large variety of problems including 2D and 3D linear and nonlinear problems (Nguyen et al (2009)), dynamic analysis (Luong- Van et al (2014)), plate and shell structures ; Nguyen-Thanh et al (2008)). …”