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

• Published in: International journal for numerical methods in engineering Vol. 94; no. 8; pp. 715 - 739
• Main Authors: Cazes, F., Meschke, G.
• Format: Journal Article
• Language: English
• Published: Chichester Blackwell Publishing Ltd 25.05.2013; Wiley
• Subjects: Exact sciences and technology; finite element methods; Fundamental areas of phenomenology (including applications); Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis. Scientific computation; Physics; Sciences and techniques of general use; Solid mechanics; solids; Structural and continuum mechanics; structures; Solid mechanics; Finite element method; Polyhedron; System with n degrees of freedom; Numerical integration; solids; Smoothing; finite element methods; Meshless method; Tetrahedral shape; structures; Modeling
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.4472

SUMMARYThe 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. Copyright © 2013 John Wiley & Sons, Ltd.