An improved local boundary integral equation method for two-dimensional potential problems

International Journal of Applied Mechanics

Volumn 2, Issue 2, 2010, Pages 421-436

  Dai, Baodong ^a   Cheng, Yumin ^b  

^a TAIYUAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b SHANGHAI UNIVERSITY   (China)

Author keywords

improved local boundary integral equation method; Improved moving least square approximation; local boundary integral equation; potential problem; weighted orthogonal basis function

Indexed keywords

LOCAL BOUNDARY INTEGRAL EQUATION METHODS; LOCAL BOUNDARY INTEGRAL EQUATIONS; MOVING LEAST SQUARE APPROXIMATION; POTENTIAL PROBLEMS; WEIGHTED ORTHOGONAL BASIS FUNCTIONS;

BOUNDARY INTEGRAL EQUATIONS; COMPUTATIONAL EFFICIENCY; EFFICIENCY; FINITE ELEMENT METHOD; FUNCTIONALLY GRADED MATERIALS; NUMERICAL METHODS; ORTHOGONAL FUNCTIONS; REAL VARIABLES; TWO DIMENSIONAL;

LEAST SQUARES APPROXIMATIONS;

EID: 83455207970     PISSN: 17588251     EISSN: 1758826X     Source Type: Journal    
DOI: 10.1142/S1758825110000561     Document Type: Article

References (27)

1. Atluri, S. N., Sladek, J., Sladek, V. and Zhu, T. [2000] "The local boundary integral equation (LBIE) and its meshless implementation for linear elasticity," Comput. Mech. 25, 180-198. (Pubitemid 30593734)
2. Belytschko, T., Krongauz, Y., Organ, D., Fleming, M. and Krysl, P. [1996] "Meshless methods: An overview and recent developments," Comput. Meth. Appl. Mech. Eng. 139, 3-47. (Pubitemid 126382692)
3. Elhassan Boudaia, Lahbib Bousshine, Gery de Saxce and Ali Chaaba [2009] "A meshless method analysis of elasto-plastic contact problems with friction," Int. J. Appl. Mech. 1, 631-645.
4. Cheng, Y. M. and Peng, M. J. [2005] "Boundary element-free method for elastodynamics," Sci. China Ser. G Phys. Mech. Astron. 48, 641-657.
5. Cheng, Y. M. and Li, J. H. [2006] "A complex variable meshless method for fracture problems," Sci. China Ser. G Phys. Mech. Astron. 49, 46-59.
6. Cheng, Y. M., Liew, K. M. and Kitipornchai, S. [2009] "Reply to 'Comments on Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems'," Int. J. Numer. Meth. Eng. 78, 1258-1260.
7. Lancaster, P. and Salkauskas, K. [1981] "Surfaces generated by moving least squares methods," Math. Comput. 37, 141-158.
8. Liew, K. M., Cheng, Y. M. and Kitipornchai, S. [2005] "Boundary element-free method (BEFM) for two-dimensional elastodynamic analysis using Laplace transform," Int. J. Numer. Meth. Eng. 64, 1610-1627. (Pubitemid 41716058)
9. Liew, K. M., Cheng, Y. M. and Kitipornchai, S. [2006] "Boundary element-free method and its application to two-dimensional elasticity problems," Int. J. Numer. Meth. Eng. 65, 1310-1332. (Pubitemid 43224818)
10. Liew, K. M., Feng, C., Cheng, Y. M. and Kitipornchai, S. [2007a] "Complex variable moving least-squares method: A meshless approximation technique," Int. J. Numer. Meth. Eng. 70, 46-70. (Pubitemid 46502359)
11. Liew, K. M., Cheng, Y. M. and Kitipornchai, S. [2007b] "Analyzing the 2D fracture problems via the enriched boundary element-free method," Int. J. Solids Struct. 44, 4220-4233. (Pubitemid 46483437)
12. Liew, K. M. and Cheng, Y. M. [2009] "Complex variable boundary element-free method for two-dimensional elastodynamic problems," Comput. Meth. Appl. Mech. Eng. 198, 3925-3933.
13. Liu, G. R. and Zhang, Y. [2009] "A novel scheme of strain-constructed point interpolation method for static and dynamic mechanics problems," Int. J. Appl. Mech. 1, 233-258.
14. Long, S. Y. [2002] "A research on the companion solution for a thin plate in the meshless local boundary integral equation method," Eng. Anal. Boundary Elements 26, 505-509.
15. Lu, Y. Y., Belytschko, T. and Gu, L. [1994] "A new implementation of the element-free Galerkin method," Comput. Meth. Appl. Mech. Eng. 113, 397-414.
16. Peng, M. J. and Cheng, Y. M. [2009a] "A boundary element-free method (BEFM) for two-dimensional potential problems," Eng. Anal. Boundary Elements 33, 77-82.
17. Peng, M. J., Liu, P. and Cheng, Y. M. [2009b] "The complex variable element-free Galerkin (CVEFG) method for two-dimensional elasticity problems," Int. J. Appl. Mech. 1, 367-385.
18. Ren, H. P., Cheng, Y. M. and Zhang, W. [2009] "An improved boundary element-free method (IBEFM) for two-dimensional potential problems," Chin. Phys. B 18, 4065-4073.
19. Sladek, J., Sladek, V. and Atluri, S. N. [2000] "Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties," Comput. Mech. 24, 456-462. (Pubitemid 30548304)
20. Sladek, J. and Sladek, V. [2003] "A meshless method for large deflection of plates," Comput. Mech. 30, 155-163.
21. Sladek, J., Sladek, V. and Keer, V. R. [2003a] "Meshless local boundary integral equation method for 2D elastodynamic problems," Int. J. Numer. Meth. Eng. 57, 235-249. (Pubitemid 36586570)
22. Sladek, J., Sladek, V. and Zhang, Ch. [2003b] "Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method," Comput. Mater. Sci. 28, 494-504.
23. Zhang, Z., Liew, K. M. and Cheng, Y. M. [2008a] "Coupling of the improved element-free Galerkin and boundary element methods for two-dimensional elasticity problems," Eng. Anal. Boundary Elements 32, 100-107. (Pubitemid 350198871)
24. Zhang, Z., Liew, K. M., Cheng, Y. M. and Lee, Y. Y. [2008b] "Analyzing 2D fracture problems with the improved element-free Galerkin method," Eng. Anal. Boundary Elements 32, 241-250.
25. Zhang, Z., Zhao, P. and Liew, K. M. [2009] "Improved element-free Galerkin method for two-dimensional potential problems," Eng. Anal. Boundary Elements 33, 547-554.
26. Zheng, C., Wu, S. C., Tang, X. H. and Zhang, J. H. [2008] "A meshfree poly-cell Galerkin (MPLG) approach for problems of elasticity and fracture," Comput. Model. Eng. Sci. 38, 149-178.
27. Zhu, T., Zhang, J. D. and Atluri, S. N. [1998] "A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach," Comput. Mech. 21, 223-235. (Pubitemid 128566412)