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http://dx.doi.org/10.3795/KSME-A.2005.29.6.860

The Meshfree Method Based on the Least-Squares Formulation for Elasto-Plasticity  

Youn Sung-Kie (한국과학기술원 기계공학과)
Kwon Kie-Chan (한국원자력연구소 사용후핵연료기술개발부)
Publication Information
Transactions of the Korean Society of Mechanical Engineers A / v.29, no.6, 2005 , pp. 860-875 More about this Journal
Abstract
A new meshfree method for the analysis of elasto-plastic deformations is presented. The method is based on the proposed first-order least-squares formulation, to which the moving least-squares approximation is applied. The least-squares formulation for the classical elasto-plasticity and its extension to an incrementally objective formulation for finite deformations are proposed. In the formulation, the equilibrium equation and flow rule are enforced in least-squares sense, while the hardening law and loading/unloading condition are enforced exactly at each integration point. The closest point projection method for the integration of rate-form constitutive equation is inherently involved in the formulation, and thus the radial-return mapping algorithm is not performed explicitly. Also the penalty schemes for the enforcement of the boundary and frictional contact conditions are devised. The main benefit of the proposed method is that any structure of cells is not used during the whole process of analysis. Through some numerical examples of metal forming processes, the validity and effectiveness of the method are presented.
Keywords
LSMFM; Least-Squares; Meshfree Method; Elasto-Plasticity; Metal Forming;
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Times Cited By KSCI : 3  (Citation Analysis)
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1 Simo, J.C. and Hughes, T.J.R., 1989, Computational Inelasticity, Springer-Verlag, New York
2 Simo, J.C, Kennedy, J.G and Taylor, R.L., 1989, 'Complementary mixed finite element formulations for elastoplasticity,' Comput. Methods Appl. Mech. Engrg., Vol. 74, pp. 177-206   DOI   ScienceOn
3 Kwon, K.C. and Youn, S.K, 2004, 'The Least-Squares Meshfree Method for the Analysis of Rigid-Plastic Deformation,' Transactions of the KSME(A), Vol. 28, No. 12, pp. 2019-2031   과학기술학회마을   DOI
4 Cai, Z., Manteuffel, T.A., McCormick, S.P. and Parter, S.Y., 1998, 'First-order System Least Squares (FOSLS) for Planar Linear Elasticity: Pure Traction Problem,' SIAM J. Numer. Anal., Vol. 35, pp. 320-335   DOI   ScienceOn
5 Kwon, K.C., Park, S.H., Jiang, B.N. and Youn, S.K., 2003, 'The Least-Squares Meshfree Method for Solving Linear Elastic Problems,' Comput. Mech., Vol. 30,pp.196-211   DOI
6 Kwon, K.C., Park, S.H. and Youn, S.K., 2002, 'The Least-Squares Meshfree Method for Linear Elasticity,' Transactions of the KSME(A), Vol. 26, No. 11, pp. 2312-2321   과학기술학회마을   DOI
7 Lancaster, P. and Salkauskas, K., 1981, 'Surfaces Generated by Moving Least-Squares Methods,' Math. Comput., Vol. 37, pp. 141-158   DOI
8 Duarte, C.A. and Oden, J.T., 1995, 'Hp Clouds - A Meshless Method to Solve Boundary-Value Problems,' Technical Report 95-05, TICAM, University of Texas at Austin, 1995
9 Jiang, B.N., 1998, The Least-Squares Finite Element Method - Theory and Applications in Computational Fluid Dynamics and Electromagnetics, Spring-Verlag, Berlin
10 Park, S.H. and Youn, S.K, 2001, 'Least-Squares Meshfree Methods and Integration Error,' Transactions of the KSME(A), Vol. 25, No. 10, pp. 1605-1612   과학기술학회마을
11 Park, S.H., Kwon, K.C. and Youn, S.K., 2003, 'A Study on the Convergence of Least-Squares Meshfree Method under Inaccurate Integration,' Int. J. Numer. Meth. Engng., Vol. 56, pp. 1397-1419   DOI   ScienceOn
12 Zhang, X., Liu, X.H., Song, K.Z. and Lu, M.W, 2001, 'Least-Squares Collocation Meshless Method,' Int. J. Numer. Meth. Engng., Vol. 51, pp. 1089-1100   DOI   ScienceOn
13 Chen, J.S., Yoon, S., Wang, H.P. and Liu, W.K., 2000, 'An Improved Reproducing Kernel Particle Method for Nearly Incompressible Finite Elasticity,' Comput. Methods Appl. Mech. Engrg., Vol. 181, pp. 117-145   DOI   ScienceOn
14 Chen, J.S., Wang, H.P., Yoon, S. and You, Y., 2000, 'Some Recent Improvement in Meshfree Methods for Incompressible Finite Elasticity Boundary Value Problems with Contact,' Comput. Mech., Vol. 25, pp. 137-156   DOI
15 Park, S.H. and Youn, S.K., 2001, 'The Least-Squares Meshfree Method,' Int. J. Numer. Meth. Engng., Vol. 52, pp. 997-1012   DOI   ScienceOn
16 Carpinteri, A., Ferro, G. and Ventura, G., 2002, 'The Partition of Unity Quadrature in Meshless Methods,' Int. J. Numer. Meth. Engng., Vol. 54, pp. 987-1006   DOI   ScienceOn
17 Chen, J.S., Wu, C.T., Yoon, S. and You, Y., 2001, 'A Stabilized Confonning Nodal Integration for Galerkin Mesh-free Methods,' Int. J. Numer. Meth. Engng., Vol. 50, pp. 435-466   DOI   ScienceOn
18 Dolbow, J. and Belytschko, T., 1999, 'Volumetric Locking in the Element Free Galerkin Method,' Int. J. Numer. Meth. Engng., Vol. 46, pp. 925-942   DOI   ScienceOn
19 Atluri, S.N. and Zhu, T., 1998, 'A New Meshless Local Petrov-Galerkin (MLPG) Approach in Computational Mechanics,' Comput. Mech., Vol. 22, pp.117-127   DOI
20 Dolbow, J. and Belytschko, T., 1999, 'Numerical Integration of the Galerkin Weak Form in Meshfree Methods,' Comput. Mech., Vol. 23, pp. 219-230   DOI
21 Yoon, S. and Chen, J.S., 2002, 'Accelerated Meshfree Method for Metal Forming Simulation,' Finite Elem. Anal. Des., Vol. 38, pp. 937-948   DOI   ScienceOn
22 Liew, K.M., Ng, T.Y. and Wu, Y.C., 2002, 'Meshfree Method for Large Deformation Analysis-A Reproducing Kernel Particle Approach,' Eng. Struet., Vol. 24, pp. 543-551   DOI   ScienceOn
23 Beissel, S. and Belytschko, T., 1996, 'Nodal Integration of the Element-Free Galerkin Method,' Comput. Methods Appl. Mech. Engrg., Vol. 139, pp. 49-74   DOI   ScienceOn
24 Chen, J.S., Pan, C., Wu, C.T. and Liu W.K., 1996, 'Reproducing Kernel Particle Methods for Large Deformation Analysis of Non-linear Structures,' Comput. Methods Appl. Meeh. Engrg., Vol. 139, pp. 195-227   DOI   ScienceOn
25 Li, S., Hao, W. and Liu, W.K., 2000, 'Numerical Simulations of Large Deformation of Thin Shell Structures using Meshfree Method,' Comput. Mech., Vol. 25, pp. 102-116   DOI
26 Chen, J.S., Pan, C., Rogue, C.M.O.L. and Wang H.P., 198, 'A Lagrangian Reproducing Kernel Particle Method for Metal Forming Analysis,' Comput. Mech., Vol. 22, pp. 289-307   DOI