Polyhedral elements by means of node/edge‐based smoothed finite element method

Summary The node or edge based smoothed finite element method is extended to develop polyhedral elements that are allowed to have an arbitrary number of nodes or faces, and so retain a good geometric adaptability. The strain smoothing technique and implicit shape functions based on the linear point interpolation makes the element formulation simple and straightforward. The resulting polyhedral elements are free from the excessive zero-energy modes, and yield a robust solution very much insensitive to mesh distortion. Several numerical examples within the framework of linear elasticity demonstrate the accuracy and convergence behavior. The smoothed finite element methods based polyhedral elements in general yield solutions of better accuracy and faster convergence rate than those of the conventional finite element methods. This article is protected by copyright. All rights reserved.

[1]  Marc Duflot,et al.  A cell-based smoothed finite element method for three dimensional solid structures , 2012 .

[2]  Guirong Liu.  A GENERALIZED GRADIENT SMOOTHING TECHNIQUE AND THE SMOOTHED BILINEAR FORM FOR GALERKIN FORMULATION OF A WIDE CLASS OF COMPUTATIONAL METHODS , 2008 .

[3]  Somnath Ghosh,et al.  Extended Voronoi cell finite element model for multiple cohesive crack propagation in brittle materials , 2006 .

[4]  Glaucio H. Paulino,et al.  Unstructured polygonal meshes with adaptive refinement for the numerical simulation of dynamic cohesive fracture , 2014, International Journal of Fracture.

[5]  J. C. Simo,et al.  A CLASS OF MIXED ASSUMED STRAIN METHODS AND THE METHOD OF INCOMPATIBLE MODES , 1990 .

[6]  Lourenço Beirão da Veiga,et al.  Virtual Elements for Linear Elasticity Problems , 2013, SIAM J. Numer. Anal..

[7]  Guirong Liu,et al.  A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems , 2009 .

[8]  Glaucio H. Paulino,et al.  Honeycomb Wachspress finite elements for structural topology optimization , 2009 .

[9]  Somnath Ghosh,et al.  Three dimensional Voronoi cell finite element model for microstructures with ellipsoidal heterogeneties , 2004 .

[10]  Joseph E. Bishop,et al.  A displacement‐based finite element formulation for general polyhedra using harmonic shape functions , 2014 .

[11]  D. Malkus,et al.  Mixed finite element methods—reduced and selective integration techniques: a unification of concepts , 1990 .

[12]  Glaucio H. Paulino,et al.  Gradient correction for polygonal and polyhedral finite elements , 2015 .

[13]  K. Y. Dai,et al.  An n-sided polygonal smoothed finite element method (nSFEM) for solid mechanics , 2007 .

[14]  G. Y. Li,et al.  An edge-based smoothed tetrahedron finite element method (ES-T-FEM) for 3D static and dynamic problems , 2013 .

[15]  Markus H. Gross,et al.  A Finite Element Method on Convex Polyhedra , 2007, Comput. Graph. Forum.

[16]  Jae Hyuk Lim,et al.  An efficient scheme for coupling dissimilar hexahedral meshes with the aid of variable-node transition elements , 2013, Adv. Eng. Softw..

[17]  P. Milbradt,et al.  Polytope finite elements , 2008 .

[18]  Glaucio H. Paulino,et al.  On the Virtual Element Method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes , 2014 .

[19]  Dongwoo Sohn,et al.  A finite element scheme with the aid of a new carving technique combined with smoothed integration , 2013 .

[20]  Glaucio H. Paulino,et al.  Addressing Integration Error for Polygonal Finite Elements Through Polynomial Projections: A Patch Test Connection , 2013, 1307.4423.

[21]  T. Hughes.  Generalization of selective integration procedures to anisotropic and nonlinear media , 1980 .

[22]  Guirong Liu,et al.  An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids , 2009 .

[23]  Jiun-Shyan Chen,et al.  A stabilized conforming nodal integration for Galerkin mesh-free methods , 2001 .

[24]  K. Y. Dai,et al.  A Smoothed Finite Element Method for Mechanics Problems , 2007 .

[25]  Daniel W. Spring,et al.  Computational homogenization of the debonding of particle reinforced composites: The role of interphases in interfaces , 2015 .

[26]  Guirong Liu,et al.  Adaptive analysis using the node‐based smoothed finite element method (NS‐FEM) , 2011 .

[27]  Hung Nguyen-Xuan,et al.  An n‐sided polygonal edge‐based smoothed finite element method (nES‐FEM) for solid mechanics , 2010 .

[28]  Eugenio Oñate,et al.  The meshless finite element method , 2003 .

[29]  Guirong Liu,et al.  A face‐based smoothed finite element method (FS‐FEM) for 3D linear and geometrically non‐linear solid mechanics problems using 4‐node tetrahedral elements , 2009 .

[30]  J. C. Simo,et al.  Variational and projection methods for the volume constraint in finite deformation elasto-plasticity , 1985 .

[31]  Guirong Liu,et al.  ADDITIONAL PROPERTIES OF THE NODE-BASED SMOOTHED FINITE ELEMENT METHOD (NS-FEM) FOR SOLID MECHANICS PROBLEMS , 2009 .

[32]  F. Brezzi,et al.  Basic principles of Virtual Element Methods , 2013 .

[33]  Glaucio H. Paulino,et al.  Polygonal finite elements for finite elasticity , 2015 .

[34]  Glaucio H. Paulino,et al.  Reduction in mesh bias for dynamic fracture using adaptive splitting of polygonal finite elements , 2014 .