An n-sided polygonal edge-based smoothed finite element method (nES-FEM) for solid mechanics

• Published in: International journal for numerical methods in biomedical engineering Vol. 27; no. 9; pp. 1446 - 1472
• Main Authors: Nguyen-Thoi, T., Liu, G. R., Nguyen-Xuan, H.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.09.2011; Wiley
• Subjects: Convergence; edge-based smoothed finite element method (ES-FEM); Exact sciences and technology; Exact solutions; Finite element method; finite element method (FEM); Fundamental areas of phenomenology (including applications); Interpolation; Mathematical analysis; Mathematical models; node-based smoothed finite element method (NS-FEM); numerical methods; Physics; polygonal element; smoothed finite element methods (S-FEM); Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Solid mechanics; Averaging method; edge-based smoothed finite element method (ES-FEM); numerical methods; Triangular finite element; node-based smoothed finite element method (NS-FEM); finite element method (FEM); Modeling; Exact solution; Finite element method; Smoothing; polygonal element; Polynomial interpolation; Convergence rate; smoothed finite element methods (S-FEM); Polygon
• ISSN: 2040-7939; 2040-7947; 2040-7947
• DOI: 10.1002/cnm.1375

An edge‐based smoothed finite element method (ES‐FEM) using triangular elements was recently proposed to improve the accuracy and convergence rate of the existing standard finite element method (FEM) for the elastic solid mechanics problems. In this paper the ES‐FEM is further extended to a more general case, n‐sided polygonal edge‐based smoothed finite element method (nES‐FEM), in which the problem domain can be discretized by a set of polygons, each with an arbitrary number of sides. The simple averaging point interpolation method is suggested to construct nES‐FEM shape functions. In addition, a novel domain‐based selective scheme of a combined nES/NS‐FEM model is also proposed to avoid volumetric locking. Several numerical examples are investigated and the results of the nES‐FEM are found to agree well with exact solutions and are much better than those of others existing methods. Copyright © 2010 John Wiley & Sons, Ltd.