A novel element-free Galerkin method with uniform background grid for extremely deformed problems

CMES - Computer Modeling in Engineering and Sciences

Volumn 40, Issue 2, 2009, Pages 175-199

  Chen, Wen Hwa ^a   Chi, Cheng Te ^b   Lee, Ming Hsiao ^b  

^a NATIONAL TSING HUA UNIVERSITY   (Taiwan)

^b NONE

Author keywords

Background Grid; Element Free Galerkin Method (EFGM); Extreme Deformation; Metal Forming

Indexed keywords

DEFORMATION; GALERKIN METHODS; METAL FORMING;

ELEMENT FREE GALERKIN METHODS; ELEMENT-FREE GALERKIN METHOD; INCREMENTAL FORMULATION; INTERPOLATION FUNCTION; MOVING BOUNDARIES; MOVING LEAST SQUARE APPROXIMATION; NODAL DISPLACEMENT; NUMERICAL INTEGRATIONS;

LEAST SQUARES APPROXIMATIONS;

EID: 76249131140     PISSN: 15261492     EISSN: 15261506     Source Type: Journal    
DOI: 10.3970/cmes.2009.040.175     Document Type: Article

References (46)

1. Atluri, S. N., Zhu, T. (1998): A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics, Computational Mechanics, Vol. 22, pp. 117-127.
2. Atluri, S. N. (2004): The Meshless Method (MLPG) for Domain & BIE Discretizations, 680 pages, Tech Science Press.
3. Atluri, S. N., Han, Z. D., Rajendran, A. M. (2004): A New Implementation of the Meshless Finite Volume Method, Through the MLPG "Mixed" Approach, CMES: Computer Modeling in Engineering & Sciences, Vol. 6, no. 6, pp. 491-513.
4. Atluri, S. N., Liu, H. T., Han, Z. D. (2006): Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method For Elasticity Problems,CMES: Computer Modeling in Engineering & Sciencess, Vol. 14, no.3, pp. 141-152.
5. Atluri, S. N., Liu, H. T., Han, Z. D. (2006): Meshless Local Petrov-Galerkin (MLPG) Mixed Finite Difference Method for Solid Mechanics, CMES: Computer Modeling in Engineering & Sciencess, Vol. 15, no.1, pp. 1-16.
6. Bathe, K. J. (1996): Finite element procedures, Prentice Hall.
7. Belytschko, T., Lu, Y. Y., Gu, L. (1994): Element-Free Galerkin Method, International Journal for Numerical Methods in Engineering, Vol. 37, pp. 229-256.
8. Chen, J. S., Pan, C., Wu, C.T., Liu, W.K. (1996): Reproducing Kernel Particle Methods for Large Deformation Analysis of Nonlinear Structures, Computer Methods in Applied Mechanics and Engineering, Vol. 139, pp. 195-227.
9. Chen, J. S., Pan, C., Wu, C.T. (1997): Large Deformation Analysis of Rubber Based on Reproducing Kernel Particle Methods, Computational Mechanics, Vol. 19, pp. 211-227.
10. Chen, W. H., and Yeh, J. T. (1988): Finite element analysis of finite deformation contact problems with Friction, Computers and Structures, Vol. 29, no. 3, pp. 423-436.
11. Chen, W. H., Tsai, P. (1989): Finite element analysis of an involute gear drive considering friction effects, Journal of Engineering for industry, Transaction of the ASME, Vol. 111, no. 1, pp. 94-100.
12. Chen, W. H., Guo, X. M. (2001): Element Free Galerkin Method for Three- Dimensional Structural Analysis, CMES: Computer Modeling in Engineering & Sciencess, Vol. 2, no. 4, pp. 497-508.
13. Chen, W. H., Chen, C. H. (2005): On Three-Dimensional Fracture Mechanics Analysis by an Enriched Meshless Method, CMES: Computer Modeling in Engineering & Sciencess, Vol. 8, no. 3, pp. 177-190.
14. Chen, W. H., Lee, M. S. (2005): On Three-Dimensional Electrostatical- structural Analysis Using Galerkin Meshless Method, The 29th National Conference on Theoretical and Applied Mechanics. Hsinchu, Taiwan, R.O.C., 16-17 December 2005.
15. Chen, W. F., Han, D. J. (1995): Plasticity for Structural Engineers, Gau Lih Book Co., Ltd.
16. Duarte, C. A., Oden, J. T. (1996a): H-p Clouds – An h-p Meshless Method, Numerical Methods for Partial Differential Equations, Vol. 12, pp. 673-705.
17. Duarte, C. A., Oden, J. T. (1996b): An h-p adaptive method using clouds, Computer Methods in Applied Mechanics and Engineering, Vol. 139, pp. 237-262.
18. Gu, Y.T., Wang, Q.X., Lam, K.Y. (2007): A meshless local Kriging method for large deformation analyses, Computer Methods in Applied Mechanics and Engineering, Vol. 196, no. 9-12, pp. 1673-1684.
19. Han, Z. D., Atluri, S. N. (2004): Meshless Local Petrov-Galerkin (MLPG) Approaches for Solving 3D Problems in Elasto-Statics, CMES: Computer Modeling in Engineering & Sciencess, Vol. 6, no. 2, pp. 169-188.
20. Han, Z. D., Rajendran, A. M., Atluri, S. N. (2005): Meshless Local Petrov-Galerkin (MLPG) Approaches for Solving Nonlinear Problems with Large Deformations and Rotations, CMES: Computer Modeling in Engineering & Sciencess, Vol. 10, no. 1, pp. 1-12.
21. Han, Z. D., Liu, H. T., Rajendran, A. M., Atluri, S. N. (2006): The Applications of Meshless Local Petrov-Galerkin (MLPG) Approaches in High-Speed Impact, Penetration and Perforation Problems, CMES: Computer Modeling in Engineering & Sciencess, Vol. 14, no. 2, pp. 119-128.
22. Hussler-Combe, U., Korn, C. (1998): An adaptive approach with the element-free Galerkin method, Computer Methods in Applied Mechanics and Engineering, Vol. 162, pp. 203-222.
23. Johnson, J.N., Owen, J.M. (2007): A Meshless Local Petrov-Galerkin Method for Magnetic Diffusion in Non-magnetic Conductors, CMES: Computer Modeling in Engineering & Sciencess, Vol. 22, no. 3, pp. 165-188.
24. Jarak, T., Soric, J. (2008): Analysis of rectangular square plates by the mixed Meshless Local Petrov-Galerkin (MLPG) approach, CMES: Computer Modeling in Engineering & Sciencess, Vol. 38, no. 3, pp. 231-261.
25. Jun, S., Im, S. (2000): Multiple-scale meshfree adaptivity for the simulation of adiabatic shear band formation, Computational Mechanics, Vol. 25, pp.257-266
26. Li, Q., Lee, K-M. (2006): An adaptive meshless method for magnetic field computation, IEEE Transactions on Magnetics, Vol. 42, no. 8, pp. 1996-2003.
27. Li, S., Atluri, S. N. (2008): The MLPG Mixed Collocation Method for Material Orientation and Topology Optimization of Anisotropic Solids and Structures, CMES: Computer Modeling in Engineering & Sciencess, Vol. 30, no.1, pp. 37-56.
28. Liu, H. T., Han, Z. D. Rajendran, A. M., Atluri, S. N. (2006): Computational Modeling of Impact Response with RD Damage Model and Meshless Local Petrov-Galerkin (MLPG) Approaches, Computers, Materials, & Continua, Vol. 4, no. 1, pp. 43-54.
29. Liu, Y. H., Chen, S. S., Li, J., Cen, Z. Z. (2008): A Meshless Local Natural Neighbour Interpolation Method Applied to Structural Dynamic Analysis, CMES: Computer Modeling in Engineering & Sciencess, Vol. 31, no.3, pp. 145-156.
30. Liu, W. K., Jun, S., Zhang, Y. F. (1995): Reproduction Kernel Particle methods, International Journal for Numerical Methods in Fluids, Vol. 20, pp. 1081-1106.
31. Liu, W. K., Jun, S. (1998): Multiple-scale reproducing kernel particle methods for large deformation problems, International Journal for Numerical Methods in Engineering, Vol. 41, pp. 1339-1362.
32. Nagashima, T. (2000): Development of a CAE system based on the node-by-node meshless method, Computer Methods in Applied Mechanics and Engineering, Vol. 187, pp.1-34.
33. Rabczuk, T., Belytschko, T. (2005): Adaptivity for structured meshfree particle methods in 2D and 3D, International Journal for Numerical Methods in Engineering, Vol. 63, no. 11, pp. 1559-1582.
34. Ren, J., Liew, K.M., Meguid, S. A. (2002): Modeling and simulation of the superelastic behaviour of shape memory alloys using the element-free Galerkin method,” International Journal of Mechanical Sciences, Vol. 44, pp. 2393-2413.
35. Rossi, R., Alves, M. K. (2007): On the analysis of an EFG method under large deformations and volumetric locking, Computational Mechanics, Vol. 39, no. 4, pp. 381-399.
36. Sageresan, N., Drathi, R. (2008): Crack Propagation in Concrete Using Meshless Method, CMES: Computer Modeling in Engineering & Sciencess, Vol. 32, no.2, pp. 103-112.
37. Sladek, J., Sladek, V., Wen, P. H., Aliabadi, M.H. (2006): Meshless Local Petrov-Galerkin (MLPG) Method for Shear Deformable Shells Analysis, CMES: Computer Modeling in Engineering & Sciencess, Vol. 13, no.2, pp. 103-117.
38. Sladek, J., Sladek, V., Tan, C.L., Atluri, S.N. (2008): Analysis of Transient Heat Conduction in 3D Anisotropic Functionally Graded Solids, by the MLPG Method, CMES: Computer Modeling in Engineering & Sciencess, Vol. 32, no.3, pp. 161-174.
39. Wen, P. H., Hon, Y. C. (2007): Geometrically Nonlinear Analysis of Reissner-Mindlin Plate by Meshless Computation, CMES: Computer Modeling in Engineering & Sciencess, Vol. 21, no.3, pp. 177-191.
40. Wong, S., Shie, Y. (2008): Large Deformation Analysis with Galerkin based Smoothed Particle Hydrodynamics, CMES: Computer Modeling in Engineering & Sciencess, Vol. 36, no.2, pp. 97-117.
41. Wu, X. H., Shen, S. P., Tao, W. Q. (2007): Meshless Local Petrov-Galerkin Collocation Method for Two-dimensional Heat Conduction Problems, CMES: Computer Modeling in Engineering & Sciencess, Vol. 22, no.1, pp. 65-76.
42. Xiong, S., Liu, W. K., Cao, J., Li, C.S., Rodrigues, J.M.C., Martins, P.A.F. (2005): Simulation of bulk metal forming processes using the reproducing kernel particle method, Computers and Structures, Vol. 83, no. 8-9, pp. 574-587.
43. Yeh, J. T. (1991): Three-Dimensional Finite Element Analysis of Contact Problems with Friction, Ph.D thesis, Department of Power Mechanical Engineering, National Tsing Hua University.
44. Yuan, W., Chen, Y., Gagalowicz, A., and Liu, K. (2008): Application of Meshless Local Petrov-Galerkin (MLPG) Method in Cloth Simulation, CMES: Computer Modeling in Engineering & Sciencess, Vol. 35, no. 2, pp. 133-154.
45. Zheng, C., Wu, S. C., Tang, X. H., Zhang, J. H. (2008): A meshfree poly-cell Galerkin (MPG) approach for problems of elasticity and fracture, CMES: Computer Modeling in Engineering & Sciencess, Vol. 38, no. 2, pp. 149-178.
46. Zhu, T., Atluri, S. N. (1998): A Modified Collocation Method and a Penalty Formulation for Enforcing the Essential Boundary Conditions in the Element Free Galerkin Method, Computational Mechanics, Vol. 21, pp. 211-222.