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

*(English)*Zbl 1183.74299Summary: 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.

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74B05 | Classical linear elasticity |

##### Keywords:

numerical methods; meshfree methods; tetrahedral elements; smoothed technique; finite element method (FEM); smoothed finite element method (SFEM); face-based smoothed finite element method (FS-FEM)
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\textit{T. Nguyen-Thoi} et al., Int. J. Numer. Methods Eng. 78, No. 3, 324--353 (2009; Zbl 1183.74299)

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