Summary
In the present paper, we discuss the accuracy improvement for the free mesh method: a node based finite element technique. We propose here a scheme where the strain field is defined over clustered local elements in addition to the standard finite element displacement field. In order to determine the unknown parameter, the least square method or the Hellinger-Reissner Principle is employed. Through some bench mark examples, the proposed technique has shown excellent performances.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Zienkiewicz OC, Taylor RL (2000) The finite element method. Fifth edition, Butterworth Heinemann
Cook RD, Malkus DS, Plesha ME (1989) Concepts and applications of finite element analysis. Third edition, Wiley
Barth TJ, Griebel M, Keyes DE, Nieminen RM, Roose D, Schlick T (2003) Meshfree methods for partial differential equation. Springer-Verlag Berlin Heidelberg
Liu GR, Liu MB (2003) Smoothed Particle Hydrodynamics a meshfree particle method. World Scientific publishing
Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int J Num Meth Engng 37:229–256
Lu YY, Belytschko T, Gu L (1994) A new implementation of the element-free Galerkin Method. Comput Meth Appl Mech Engng 113:397–414
Liu WK, Jun S, Adee J, Belytischko T (1995) Reproducing kernel particle methods for structural dynamics. Int J Num Meth Engng 38:1655–1680
Liu WK, Li S, Belytschko T (1997) Moving least square kernel particle method Part 1: methodology and convergence. Comput Meth Appl Mech Engng 143:113–154
Yagawa G, Yamada T (1996) Free mesh method: a new meshless finite element method. Computational Mechanics 18:383–386
Yagawa G, Furukawa T (2000) Recent developments approaches for accurate free mesh method. Int J Num Meth Engng 47:1445–1462
Fujisawa T, Inaba M, Yagawa G (2003) Parallel computing of high-speed compressible flows using a node-based finite-element method. Int J Num Meth Engng 58:481–511
J. Imasato, Y. Sakai (2002) Application of 2-dimentional crack propagation problem using FMM. Advances in Meshfree and X-FEM Methods, Liu GR, editor, World-Scientific
Matsubara H, Iraha S, Tomiyama J, Yagawa G (2002) Application of 3D free mesh method to fracture analysis of concrete. Advances in Meshfree and X-FEM Methods, Liu GR, editor, World-Scientific
element including vertex rotations. JSCE J of Structural Mechanics and Earthquake Engineering 766(I–68):97–107
Tian R, Matsubara H, Yagawa G, Iraha S, Tomiyama J (2004) Accuracy improvement on free mesh method: a high performance quadratic tetrahe-dral/triangular element with only corners. Proc of the 2004 Sixth World Congress on Computational Mechanics (WCCM VI)
O.C. Zienkiewicz, K. Morgan (1983), Finite element and approximation, John Wiley & Sons
Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. PART 1: The recovery technique. Int J Num Meth Engng 33:1331–1364
Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. PART 2: Error estimates and adaptivity. Int J Num Meth Engng 33:1365–1382
Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery (SPR) and adaptive finite element refinement. Comput Meth Appl Mech Engng 101:207– 224
Babuska I, Rheinboldt WC (1978) A-posteriori error estimates for the finite element method. Int J Num Meth Engng 12:1597–1615
Washizu K (1968) Variational methods in elasticity and plasticity. Pergamon Press, New York
Timoshenko SP, Goodier JN (1987) Theory of elasticity. McGraw-Hill
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this chapter
Cite this chapter
Yagawa, G., Matsubara, H. (2007). Enriched Free Mesh Method: An Accuracy Improvement for Node-based FEM. In: Oñate, E., Owen, R. (eds) Computational Plasticity. Computational Methods in Applied Sciences, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6577-4_12
Download citation
DOI: https://doi.org/10.1007/978-1-4020-6577-4_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-6576-7
Online ISBN: 978-1-4020-6577-4
eBook Packages: EngineeringEngineering (R0)