The improved element-free Galerkin method for two-dimensional elastodynamics problems

Engineering Analysis with Boundary Elements

Volumn 37, Issue 12, 2013, Pages 1576-1584

  Zhang, Zan ^a   Hao, S Y ^b   Liew, K M ^c   Cheng, Y M ^d  

^a EAST CHINA UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b LANZHOU JIAOTONG UNIVERSITY   (China)

^c CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^d SHANGHAI UNIVERSITY   (China)

Author keywords

Elastodynamics; Improved element free Galerkin (IEFG) method; Improved moving least squares (IMLS) approximation; Newmark algorithm; Penalty method; Weighted orthogonal function

Indexed keywords

ELASTO-DYNAMICS; IMPROVED ELEMENT FREE GALERKIN (IEFG) METHODS; IMPROVED MOVING LEAST-SQUARES APPROXIMATION; NEWMARK; PENALTY METHODS; WEIGHTED ORTHOGONAL FUNCTION;

APPROXIMATION ALGORITHMS; COMPUTATIONAL MECHANICS; INVERSE PROBLEMS; LEAST SQUARES APPROXIMATIONS; TWO DIMENSIONAL;

NUMERICAL METHODS;

EID: 84886287244     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2013.08.017     Document Type: Article

References (30)

1. ZJ Yang, and AJ. Deeks A frequency-domain approach for modeling transient elastodynamics using scaled boundary finite element method Computational Mechanics 40 2007 725 738 (Pubitemid 47000717)
2. T Belytschko, Y Krongauz, D Organ, and P. Krysl Meshless methods: an overview and recent developments Computer Methods in Applied Mechanics and Engineering 139 1996 3 47 (Pubitemid 126382692)
3. YY Lu, T Belytschko, and M. Tabbara Element-free Galerkin method for wave propagation and dynamic fracture Computer Methods in Applied Mechanics and Engineering 26 1995 131 153
4. T Belytschko, D Organ, and C. Gerlach Element-free Galerkin methods for dynamic fracture in concrete Computer Methods in Applied Mechanics and Engineering 187 2000 385 399
5. T Belytschko, and M. Tabbara Dynamic fracture using element free Galerkin method International Journal for Numerical Methods in Engineering 39 1996 923 938 (Pubitemid 126648105)
6. T Belytschko, YY Lu, L Gu, and M. Tabbara Element-free Galerkin method for static and dynamic fracture International Journal of Solids and Structures 32 1995 2547 2570
7. WK Liu, S Jun, S Li, J Adee, and T. Belytschko Reproducing kernel particle methods for structural dynamics International Journal for Numerical Methods in Engineering 38 1995 1655 1679
8. Ching HK. Solution of linear elastostatic and elastodynamic plane problems by the meshless local Petrov-Galerkin method. PhD dissertation, Blacksburg, Virginia; 2002.
9. YT Gu, and GR. Liu A meshless local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids Computational Mechanics 27 3 2001 188 198 (Pubitemid 32443981)
10. D Bueche, N Sukumar, and B. Moran Dispersive properties of the natural element method Computational Mechanics 25 2000 207 219 (Pubitemid 30593732)
11. S Li, Y Cheng, and S. Li Meshless manifold method for dynamic fracture mechanics Acta Physica Sinica 55 9 2006 4760 4766 (Pubitemid 44565920)
12. Y Cheng, and M. Peng Boundary element-free method for elastodynamics Science in China Series G: Physics, Mechanics and Astronomy 48 6 2005 641 657 (Pubitemid 43322615)
13. KM Liew, Y Cheng, and S. Kitipornchai Boundary element-free method (BEFM) for two-dimensional elastodynamic analysis using Laplace transform International Journal of Numerical Methods in Engineering 64 12 2005 1610 1627 (Pubitemid 41716058)
14. KM Liew, and Y. Cheng Complex variable boundary element-free method for two-dimensional elastodynamic problems Computer Methods in Applied Mechanics and Engineering 198 2009 3925 3933
15. L Chen, and YM. Cheng The complex variable reproducing kernel particle method for two-dimensional elastodynamics Chinese Physics B 19 9 2010 (090204-1-12)
16. Cheng Yumin, Wang Jianfei, and Li Rongxin The complex variable element-free Galerkin (CVEFG) method for two-dimensional elastodynamics problems International Journal of Applied Mechanics 4 4 2012 (1250042-1-23)
17. YY Lu, T Belytschko, and L.A Gu New implementation of the element free Galerkin method Computer Method in Applied Mechanics and Engineering 113 1994 397 414
18. Z Zhang, P Zhao, and KM. Liew Improved element-free Galerkin method for two-dimensional potential problems Engineering Analysis with Boundary Elements 33 2009 547 554
19. Z Zhang, P Zhao, and KM. Liew Analyzing three-dimensional potential problems with the improved element-free Galerkin method Computational Mechanics 44 2009 273 284
20. Z Zhang, D Li, Y Cheng, and KM. Liew The improved element-free Galerkin method for three-dimensional wave equation Acta Mechanica Sinica 28 3 2012 808 818
21. GR. Liu Mesh free methods: moving beyond the finite element method 2003 CRC Press LLC Boca Raton, FL
22. J. Dolbow, and T. Belytschko An introduction to programming the meshless element free Galerkin method Archives of Computational Methods in Engineering 5 1998 207 241
23. P Lancaster, and K. Salkauskas Surfaces generated by moving least-squares methods Mathematics Computation 37 1981 141 158
24. KM Liew, Y Cheng, and S. Kitipornchai Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems International Journal of Numerical Methods in Engineering 65 8 2006 1310 1332 (Pubitemid 43224818)
25. Y Cheng, KM Liew, and S. Kitipornchai Reply to 'Comments on 'Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems International Journal for Numerical Methods in Engineering 78 2009 1258 1260
26. P Krysl, and T. Belytschko Element-free Galerkin method: convergence of the continuous and discontinuous shape functions Computer Methods in Applied Mechanics and Engineering 148 1997 257 277 (Pubitemid 127407792)
27. HJ Chung, and T. Belytschko An error estimate in the EFG method Computational Mechanics 21 1998 91 100 (Pubitemid 128570272)
28. L Gavete, JL Cuesta, and A. Ruiz A procedure for approximation of the error in the EFG method International Journal for Numerical Methods in Engineering 53 2002 677 690 (Pubitemid 34039618)
29. L Gavete, and ML. Gavete A posteriori error approximation in EFG method International Journal for Numerical Methods in Engineering 58 2003 2239 2263 (Pubitemid 38039220)
30. L Gavete, and S. Faclon An error indicator for the element free Galerkin method European Journal of Mechanics A/Solids 20 2001 327 341 (Pubitemid 32257842)