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

• Published in: International journal for numerical methods in engineering Vol. 78; no. 3; pp. 324 - 353
• Main Authors: Nguyen-Thoi, T., Liu, G. R., Lam, K. Y., Zhang, G. Y.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 16.04.2009; Wiley
• Subjects: Computational techniques; Exact sciences and technology; face-based smoothed finite element method (FS-FEM); finite element method (FEM); Fundamental areas of phenomenology (including applications); Mathematical methods in physics; meshfree methods; numerical methods; Physics; smoothed finite element method (SFEM); smoothed technique; Solid mechanics; Structural and continuum mechanics; tetrahedral elements; Solid mechanics; Stiffness matrix; numerical methods; Tetrahedral shape; Displacement(deformation); smoothed finite element method (SFEM); face-based smoothed finite element method (FS-FEM); finite element method (FEM); Incompressible material; Modeling; Penalty method; Finite element method; meshfree methods; smoothed technique; Smoothing; Meshless method; tetrahedral elements
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2491

This 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. Copyright © 2008 John Wiley & Sons, Ltd.