An edge‐based smoothed finite element method for 3D analysis of solid mechanics problems

Abstract

The edge-based smoothed finite element method (ES-FEM) was proposed recently in Liu, Nguyen-Thoi, and Lam to improve the accuracy of the FEM for 2D problems. This method belongs to the wider family of the smoothed FEM for which smoothing cells are defined to perform the numerical integration over the domain. Later, the face-based smoothed FEM (FS-FEM) was proposed to generalize the ES-FEM to 3D problems. According to this method, the smoothing cells are centered along the faces of the tetrahedrons of the mesh. In the present paper, an alternative method for the extension of the ES-FEM to 3D is investigated. This method is based on an underlying mesh composed of tetrahedrons, and the approximation of the field variables is associated with the tetrahedral elements; however, in contrast to the FS-FEM, the smoothing cells of the proposed ES-FEM are centered along the edges of the tetrahedrons of the mesh. From selected numerical benchmark problems, it is observed that the ES-FEM is characterized by a higher accuracy and improved computational efficiency as compared with linear tetrahedral elements and to the FS-FEM for a given number of degrees of freedom.

A cell‐based smoothed finite element method with semi‐implicit CBS procedures for incompressible laminar viscous flows

“…The S‐FEM was firstly developed using strain smoothing techniques using quadrilateral (Q4) elements, and then many other types of novel ways of constructing smoothing domains was proposed. In general, S‐FEM can be classified, by the type of smoothing domains used, as cell‐based S‐FEM (CS‐FEM), edge‐based S‐FEM (ES‐FEM) for 2D problems, face‐based S‐FEM (FS‐FEM) for 3D problem, 3D–edge‐based S‐FEM (3D‐ES‐FEM), node‐based S‐FEM (NS‐FEM), and alpha S‐FEM . In these S‐FEMs, the ES‐FEM with 3‐node triangular elements and FS‐FEM with 4‐node tetrahedral elements are most preferred in solid mechanics, which is stable and much more accurate and robust than FEM using the same element.…”

F‐bar aided edge‐based smoothed finite element method using tetrahedral elements for finite deformation analysisof nearly incompressible solids

“…A combination of the F‐bar method and the face‐based S‐FEM (FS‐FEM) leads to F‐bar FS ‐FEM in the same fashion with only two adjacent elements at most. Considering ES‐FEM has better accuracy compared with FS‐FEM in 3D , we focus on F‐barES‐FEM in this paper.…”

Selective smoothed finite element methods for extremely large deformation of anisotropic incompressible bio‐tissues

“…In another point of view, this property of 3D-ES/NS-FEM-TET4 is also the cause of its good accuracy. Reference [26][27][28] also reported earlier are characteristics of 3D-ES-FEM-TET4, and they further tested the efficiency of 3D-ES- FEM-TET4, which is better than FS-FEM-TET4. 3D-ES/NS-FEM-TET4 should also inherit the batter efficiency than FS/NS-FEM-TET4 here.…”

“…However, spurious non-zero-energy eigen modes and temporal instabilities can arise, despite the fact that it is proven spatially stable (meaning that there is no spurious zero-energy modes) [18][19][20][21][22]. This temporal instability affects the solution of dynamics problems [25][26][27][28][29][30][31] and static large deformation problems [30]. Several techniques have been proposed to deal with the temporal instability of NS-FEM, such as˛-FEM [32,33] and the stabilized NS-FEM [29].…”