Analyzing three-dimensional potential problems with the improved element-free Galerkin method

Computational Mechanics

Volumn 44, Issue 2, 2009, Pages 273-284

  Zhang, Zan ^a   Zhao, Peng ^b   Liew, K M ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b SHANDONG UNIVERSITY   (China)

Author keywords

3D Potential problem; Improved element free Galerkin (IEFG) method; Improved moving least squares (IMLS) approximation; Weighted orthogonal function

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL MECHANICS; GALERKIN METHODS; ORTHOGONAL FUNCTIONS; PARTIAL DIFFERENTIAL EQUATIONS; POISSON EQUATION;

ELEMENT FREE GALERKIN METHODS; ENGINEERING MATHEMATICS; IMPROVED ELEMENT FREE GALERKIN (IEFG) METHODS; IMPROVED MOVING LEAST-SQUARES APPROXIMATION; MOVING LEAST-SQUARES INTERPOLANTS; POTENTIAL PROBLEMS; THREE DIMENSIONAL POTENTIAL PROBLEM; WEIGHTED ORTHOGONAL FUNCTION;

LEAST SQUARES APPROXIMATIONS;

EID: 67349269526     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-009-0364-9     Document Type: Article

References (26)

1. T Belytschko Y Krongauz D Organ M Fleming P Krysl 1996 Meshless method: an overview and recent developments Comput Methods Appl Mech Eng 139 3 47 (Pubitemid 126382692)
2. B Nayroles G Touzot PG Villon 1992 Generalizing the finite element method: diffuse approximation and diffuse elements Comput Mech 10 307 318 (Pubitemid 23570159)
3. T Belytschko YY Lu L Gu 1994 Element-free Galerkin methods Int J Numer Methods Eng 37 229 256
4. Duarte CA, Oden JT (1995) Hp clouds-a meshless method to solve boundary-value problems. Technical report 95-05. Texas Institute for Computational and Applied Mathematics, University of Texas at Austin
5. KM Liew TY Ng X Zhao 2002 Harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells Comput Methods Appl Mech Eng 191 4141 4157
6. SN Atluri TL Zhu 1998 A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics Computat Mech 22 117 127 (Pubitemid 128620889)
7. WK Liu S Jun YF Zhang 1995 Reproducing kernel particle method Int J Numer Methods Fluids 20 1081 1106
8. WK Liu Y Chen RA Uras 1996 Generalized multiple scale reproducing kernel particle Comp Methods Appl Mech Eng 139 91 157 (Pubitemid 126382695)
9. WK Liu S Li T Belytschko 1997 Moving least square reproducing kernel method Part I: methodology and convergence Comp Methods Appl Mech Eng 143 113 154 (Pubitemid 127411648)
10. WK Liu YJ Chen 1995 Wavelet and multiple scale reproducing kernel methods Int J Numer Methods Fluids 21 901 931
11. KM Liew XL Chen 2004 Mesh-free radial basis function method for buckling analysis of non-uniformly loaded arbitrarily shaped shear deformable plates Comp Methods Appl Mech Eng 193 205 224 (Pubitemid 38086750)
12. KM Liew XL Chen 2004 Mesh-free radial point interpolation method for the buckling analysis of Mindlin plates subjected to in-plane point loads Int J Numer Methods Eng 60 1861 1877 (Pubitemid 38978686)
13. KM Liew XL Chen 2004 Buckling of rectangular Mindlin plates subjected to partial in-plane edge loads using the radial point interpolation method Int J Solids Struct 41 1677 1695 (Pubitemid 38149671)
14. KM Liew C Feng Y Cheng S Kitipornchai 2007 Complex variable moving least-squares method: a meshless approximation technique Int J Numer Meth Eng 70 46 70 (Pubitemid 46502359)
15. S Kitipornchai KM Liew Y Cheng 2005 A boundary element-free method (BEFM) for three-dimensional elasticity problems Comput Mech 36 13 20
16. KM Liew Y Cheng S Kitipornchai 2005 Boundary element-free method (BEFM) for two-dimensional elastodynamic analysis using Laplace transform Int J Numer Methods Eng 64 1610 1627 (Pubitemid 41716058)
17. YZ Sun Z Zhang S Kitipornchai KM Liew 2006 Analyzing the interaction between collinear interfacial cracks by an efficient boundary element-free method Int J Eng Sci 44 37 48 (Pubitemid 43177732)
18. KM Liew Y Cheng S Kitipornchai 2006 Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems Int J Numer Methods Eng 65 1310 1332 (Pubitemid 43224818)
19. KM Liew YQ Huang JN Reddy 2003 Moving least-squares differential quadrature method and its application to the analysis of shear deformable plates Int J Numer Methods Engineering 56 2331 2351 (Pubitemid 36533529)
20. KM Liew YQ Huang JN Reddy 2004 Alalysis of general shaped thin plates by the moving least-squares differential quadrature method Finite Elem Anal Des 40 1453 1474
21. YY Lu T Belytschko M Tabbara 1995 Element-free Galerkin method for wave propagation and dynamic fracture Comp Methods Appl Mech Eng 126 131 153
22. Z Zhang KM Liew YM Cheng 2008 Coupling of the improved element-free Galerkin and boundary element methods for 2D elasticity problems Eng Anal Bound Elem 32 100 107 (Pubitemid 350198871)
23. Z Zhang KM Liew YM Cheng YY Lee 2008 Analyzing 2D fracture problems with the improved element-free Galerkin method Eng Anal Bound Elem 32 241 250
24. Liu GR (2003) Mesh free methods: moving beyond the finite element method. CRC Press, Boca Raton
25. P Lancaster K Salkauskas 1981 Surface generated by moving least squares methods Math Comput 37 141 158
26. I Babuska JT Oden JK Lee 1977 Mixed-hybrid finite element approximations of second-order elliptic boundary-value problems Comp Methods Appl Mech Eng 11 175 206