A Mesh Adaptive Procedure for Large Increment Method

A posteriorih-version mesh adaptive procedure is presented in the framework of large increment method (LIM) for elastic problems. In this mesh adaptive strategy, the classical Zienkiewicz–Zhu (ZZ) error estimator is adopted and a first class h-adaptive mesh refinement procedure is implemented. A major advantage of the proposed mesh adaptive procedure is that the numerical results from the previous mesh can be utilized to obtain the initial solution for the new mesh. Two-dimensional (2D) examples show that this initial solution is much closer to the real solution than the minimum norm solution used in the original LIM and the revised method can converge faster than the original method.

[1]  Xi-la Liu,et al.  A Large Increment Method for Material Nonlinearity Problems , 1997 .

[2]  Saeed Shojaee,et al.  CRACK ANALYSIS IN ORTHOTROPIC MEDIA USING COMBINATION OF ISOGEOMETRIC ANALYSIS AND EXTENDED FINITE ELEMENT , 2014 .

[3]  J. Z. Zhu,et al.  Effective and practical h–p‐version adaptive analysis procedures for the finite element method , 1989 .

[4]  O. C. Zienkiewicz,et al.  A simple error estimator and adaptive procedure for practical engineerng analysis , 1987 .

[5]  Adi Ben-Israel,et al.  Generalized inverses: theory and applications , 1974 .

[6]  Daniel N. Wilke,et al.  Relaxed error control in shape optimization that utilizes remeshing , 2013 .

[7]  Katsumi Yamazaki,et al.  Adaptive finite element meshing at each iterative calculation for electromagnetic field analysis of rotating machines , 2008 .

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

[9]  Guohua Liu,et al.  An h-hierarchical adaptive scaled boundary finite element method for elastodynamics , 2011 .

[10]  Gary F. Dargush,et al.  Flexibility-based large increment method for analysis of elastic-perfectly plastic beam structures , 2005 .

[11]  Patrice Coorevits,et al.  Alternative mesh optimality criteria for h-adaptive finite element method , 2004 .

[12]  Wolfgang Ehlers,et al.  h‐Adaptive FE methods applied to single‐ and multiphase problems , 2002 .

[13]  Amjad J. Aref,et al.  Framework for Finite-Element–Based Large Increment Method for Nonlinear Structural Problems , 2001 .

[14]  R. Krishna Kumar,et al.  Simulation of cold forging using contact and practical adaptive meshing algorithms , 2000 .

[15]  Gary F. Dargush,et al.  Development of the large increment method for elastic perfectly plastic analysis of plane frame structures under monotonic loading , 2005 .

[16]  Fatin F. Mahmoud,et al.  NONLINEAR ANALYSIS OF FRICTIONAL THERMO-VISCOELASTIC CONTACT PROBLEMS USING FEM , 2014 .

[17]  Boyce E. Griffith,et al.  Simulating the fluid dynamics of natural and prosthetic heart valves using the immersed boundary method , 2009 .

[18]  Gary F. Dargush,et al.  On the elastoplastic cyclic analysis of plane beam structures using a flexibility-based finite element approach , 2008 .

[19]  Guohua Liu,et al.  An adaptive scaled boundary finite element method by subdividing subdomains for elastodynamic problems , 2011 .

[20]  L. Herrmann.  Laplacian-Isoparametric Grid Generation Scheme , 1976 .

[21]  P. Wriggers,et al.  Error estimation for crack simulations using the XFEM , 2012 .

[22]  Shoubin Dong,et al.  SIMULATION OF GROWTH AND DIVISION OF 3D CELLS BASED ON FINITE ELEMENT METHOD , 2014 .

[23]  D. Dibben,et al.  High accuracy torque calculation for a rotating machine using adaptive meshing , 2004 .

[24]  O. C. Zienkiewicz,et al.  Adaptive techniques in the finite element method , 1988 .

[25]  Houman Borouchaki,et al.  Adaptive remeshing in large plastic strain with damage , 2005 .

[26]  Guowei Ma,et al.  An adaptive mesh refinement method for a medium with discrete fracture network , 2014 .

[27]  Per-Olof Persson,et al.  A Simple Mesh Generator in MATLAB , 2004, SIAM Rev..

[28]  Marcelo Krajnc Alves,et al.  Layout optimization with h‐adaptivity of structures , 2003 .

[29]  M. Mukhopadhyay,et al.  Unification of stress intensity factor (SIF) extraction methods with an h-adaptive finite element scheme , 2001 .