An interpolating boundary element-free method with nonsingular weight function for two-dimensional potential problems

International Journal of Computational Methods

Volumn 10, Issue 6, 2013, Pages

  Wang, Jufeng ^a,b   Wang, Jianfei ^a   Sun, Fengxin ^a,c   Cheng, Yumin ^a  

^a SHANGHAI UNIVERSITY   (China)

^b ZHEJIANG UNIVERSITY   (China)

^c NINGBO UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

improved interpolating boundary element free (IIBEF) method; improved interpolating moving least squares (IIMLS) method; Meshless method; moving least squares (MLS) approximation; potential problem

Indexed keywords

ELEMENT-FREE; MESH-LESS METHODS; MOVING LEAST SQUARES; MOVING LEAST SQUARES APPROXIMATION; POTENTIAL PROBLEMS;

BOUNDARY INTEGRAL EQUATIONS; COMPUTATIONAL MECHANICS; INTERPOLATION; TWO DIMENSIONAL;

BOUNDARY ELEMENT METHOD;

EID: 84877307992     PISSN: 02198762     EISSN: 17936969     Source Type: Journal    
DOI: 10.1142/S0219876213500436     Document Type: Article

References (43)

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., Lu, Y. Y. and Gu, L. [1994] "Element-free Galerkin methods," Int. J. Numer. Meth. Eng. 37, 229-256.
3. Belytschko, T., Krongauz, Y., Organ, D., Fleming, M. and Krysl, P. [1996] "Meshless method: An overview and recent developments," Comput. Meth. Appl. Mech. Eng. 139, 3-47. (Pubitemid 126382692)
4. Brebbia, C. A. and Wrobel, L. C. [1984] Boundary Element Techniques Theory and Applications in Engineering (Springer-Verlag, Berlin
5. Chati, M. K., Mukherjee, S. and Mukherjee, Y. X. [1999] "The boundary node method for three-dimensional linear elasticity," Int. J. Numer. Meth. Eng. 46, 1163-1184.
6. Chati, M. K. and Mukherjee, S. [2000] "The boundary node method for three-dimensional problems in potential theory," Int. J. Numer. Meth. Eng. 47, 1523-1547. (Pubitemid 30581168)
7. Cheng, R. and Cheng, Y. [2007] "The meshless method for solving the inverse heat conduction problem with a source parameter," Acta Physica Sinica 56, 5569-5574. (Pubitemid 350040990)
8. Cheng, Y., Peng, M. and Li, J. [2005] "The complex variable moving least-squares approximation and its application," Chinese J. Theoret. Appl. Mech. 37, 719-723.
9. Cheng, Y. and Peng, M. [2005] "Boundary element-free method for elastodynamics," Sci. China Series G: Phys. Mech. Astronomy 48, 641-657. (Pubitemid 43322615)
10. Gu, Y. T. and Liu, G. R. [2002] "A boundary point interpolation method for stress analysis of solids," Comput. Mech. 28, 47-54.
11. Gu, Y. T. and Liu, G. R. [2003a] "A boundary radial point interpolation method (BRPIM) for 2-D structural analyses," Struct. Eng. Mech. 15, 535-550.
12. Gu, Y. T. and Liu, G. R. [2003b] "Hybrid boundary point interpolation methods and their coupling with the element free Galerkin method," Eng. Anal. Bound. Elem. 27, 905-917.
13. Kaljevic, I. and Saigal, S. [1997] "An improved element free Galerkin formulation," Int. J. Numer. Meth. Eng. 40, 2953-2974. (Pubitemid 127748906)
14. Kitipornchai, S., Liew, K. M. and Cheng, Y. [2005] "A boundary element-free method (BEFM) for three-dimensional elasticity problems," Comput. Mech. 36, 13-20. (Pubitemid 40666684)
15. Kothnu, V. S., Mukherjee, S. and Mukherjee, Y. X. [1999] "Two dimensional linear elasticity by the boundary node method," Int. J. Solids Struct. 36, 1129-1147.
16. Lancaster, P. and Salkauskas, K. [1981] "Surfaces generated by moving least squares methods," Math. Comput. 37, 141-158.
17. Li, S. C. and Cheng, Y. [2005] "Enriched meshless manifold method for two-dimensional crack modeling," Theoret. Appl. Fract. Mech. 44, 234-248. (Pubitemid 43012922)
18. Liew, K. M., Ng, T. Y. and Wu, Y. C. [2002] "Meshfree method for large deformation analysis-a reproducing kernel particle approach," Eng. Struct. 24, 543-551. (Pubitemid 34452092)
19. Liew, K. M., Ren, J. and Reddy, J. N. [2005a] "Numerical simulation of thermomechanical behaviours of shape memory alloys via a non-linear mesh-free Galerkin formulation," Int. J. Numer. Meth. Eng. 63, 1014-1040. (Pubitemid 40865406)
20. Liew, K. M., Cheng, Y. and Kitipornchai, S. [2005b] "Boundary element-free method (BEFM) for two-dimensional elastodynamic analysis using Laplace transform," Int. J. Numer. Meth. Eng. 64, 1610-1627. (Pubitemid 41716058)
21. Liew, K. M., Cheng, Y. and Kitipornchai, S. [2006] "Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems," Int. J. Numer. Meth. Eng. 65, 1310-1332. (Pubitemid 43224818)
22. Liew, K. M., Cheng, Y. and Kitipornchai, S. [2007a] "Analyzing the 2D fracture problems via the enriched boundary element-free method," Int. J. Solids Struct. 44, 4220-4233. (Pubitemid 46483437)
23. Liew, K. M., Feng, C., Cheng, Y. and Kitipornchai, S. [2007b] "Complex variable moving least-squares method: A meshless approximation technique," Int. J. Numer. Meth. Eng. 70, 46-70. (Pubitemid 46502359)
24. Liu, G. R. and Gu, Y. T. [2000] "Coupling of element free Galerkin and hybrid boundary element methods using modified variational formulation," Comput. Mech. 26, 166-173.
25. Liu, G. R. and Gu, Y. T. [2004] "Boundary meshfree methods based on the boundary point interpolation methods," Eng. Anal. Bound. Elem. 28, 475-487.
26. Liu, Z. S., Harsono, E. and Swaddiwudhipong, S. [2009] "Material characterization based on instrumented and simulated indentation tests," Int. J. Appl. Mech. 1, 61-84.
27. Liu, Z. S., Hong, W., Suo, Z. G., Swaddiwudhipong, S. and Zhang, Y. W. [2010] "Modeling and simulation of buckling of polymeric membrane thin film gel," Comput. Mater. Sci. 49, 60-64.
28. Mukherjee, Y. X. and Mukherjee, S. [1997] "The boundary node method for potential problems," Int. J. Numer. Meth. Eng. 40, 797-815. (Pubitemid 127549025)
29. Netuzhylov, H. [2008] "Enforcement of boundary conditions in meshfree methods using interpolating moving least squares," Eng. Anal. Bound. Elem. 32, 512-516.
30. Ren, H., Cheng, Y. and Zhang, W. [2009] "An improved boundary element-free method (IBEFM) for two-dimensional potential problems," Chinese Phys. B 18, 4065-4073.
31. Ren, H., Cheng, Y. and Zhang, W. [2010] "An interpolating boundary element-free method (IBEFM) for elasticity problems," Sci. China Series G: Phys. Mech. Astronomy 53, 758-766.
32. Ren, H. and Cheng, Y. [2011] "The interpolating element-free Galerkin (IEFG) method for two-dimensional elasticity problems," Int. J. Appl. Mech. 3, 735-758.
33. Ren, H. and Cheng, Y. [2012] "The interpolating element-free Galerkin (IEFG) method for two-dimensional potential problems," Eng. Anal. Bound. Elem. 36, 873-880.
34. Shepard, D. [1968] "A two-dimensional interpolation function for irregularly spaced points," Proceeding of the 23rd ACM National Conference, 517-524.
35. Sladek, V., Sladek, J. and Atluri, S. N. [2000] "Numerical integration of singularities in meshless implementation of local boundary integral equations," Comput. Mech. 25, 394-403.
36. Thomas, M. and Christian, B. [2008] "New concepts for moving least squares: An interpolating non-singular weighting function and weighted nodal least squares," Eng. Anal. Bound. Elem. 32, 461-470.
37. Wang, J., Sun, F. and Cheng, R. [2010] "Element-free Galerkin method for a kind of KdV equation," Chinese Phys. B 19, 060201-1-060201-6.
38. Zhang, Z., Liew, K. M., Cheng, Y. and Li, Y. Y. [2008] "Analyzing 2D fracture problems with the improved element-free Galerkin method," Eng. Anal. Bound. Elem. 32, 241-250.
39. Zhang, J. M., Yao, Z. H. and Li, H. [2002] "A hybrid boundary node method," Int. J. Numer. Meth. Eng. 53, 751-763. (Pubitemid 34057170)
40. Zhang, J. M. and Tanaka, M. [2004] "Meshless analysis of potential problems in three dimensions with the hybrid boundary node method," Int. J. Numer. Meth. Eng. 41, 1147-1160.
41. Zhang, J. M. and Tanaka, M. [2008] "Fast HdBNM for large-scale thermal analysis of CNT-reinforced composites," Comput. Mech. 41, 777-787. (Pubitemid 351311848)
42. Zhang, J. M., Qin, X., Han, X. and Li, G. [2009] "A boundary face method for potential problems in three dimensions," Int. J. Numer. Meth. Eng. 80, 320-337.
43. Zhu, T., Zhang, J. and Atluri, S. N. [1999] "A meshless numerical method based on the local boundary integral equation (LBIE) to solve linear and non-linear boundary value problems," Eng. Anal. Bound. Elem. 23, 375-389.