Please wait a minute...
Chin. Phys. B, 2010, Vol. 19(12): 120202    DOI: 10.1088/1674-1056/19/12/120202
GENERAL Prev   Next  

A moving Kriging interpolation-based boundary node method for two-dimensional potential problems

Li Xing-Guo(李兴国), Dai Bao-Dong(戴保东), and Wang Ling-Hui(王灵卉)
Department of Engineering Mechanics, Taiyuan University of Science & Technology, Taiyuan 030024, China
Abstract  In this paper, a meshfree boundary integral equation (BIE) method, called the moving Kriging interpolation-based boundary node method (MKIBNM), is developed for solving two-dimensional potential problems. This study combines the BIE method with the moving Kriging interpolation to present a boundary-type meshfree method, and the corresponding formulae of the MKIBNM are derived. In the present method, the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker's delta property, then the boundary conditions can be imposed directly and easily. To verify the accuracy and stability of the present formulation, three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically.
Keywords:  meshfree method      moving Kriging interpolation method      boundary integral equation      boundary node method      potential problem  
Received:  28 June 2010      Revised:  05 August 2010      Accepted manuscript online: 
PACS:  0260  
  0270  
  1240Q  
Fund: Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 10902076), the Natural Science Foundation of Shanxi Province of China (Grant No. 2007011009), the Scientific Research and Development Program of the Shanxi Higher Education Institutions (Grant No. 20091131), and the Doctoral Startup Foundation of Taiyuan University of Science and Technology (Grant No. 200708).

Cite this article: 

Li Xing-Guo(李兴国), Dai Bao-Dong(戴保东), and Wang Ling-Hui(王灵卉) A moving Kriging interpolation-based boundary node method for two-dimensional potential problems 2010 Chin. Phys. B 19 120202

[1] Belytschko T, Krongauz Y, Organ D, Fleming M and Krysl P 1996 Comput. Methods Appl. Mech. Eng. 139 3
[2] Zhang X, Liu Y and Ma S 2009 Advances in Mechanics 39 1 (in Chinese)
[3] Nayroles B, Touzot G and Villon P 1992 Comput. Mech. 10 307
[4] Belytschko T, Lu Y Y and Gu L 1994 Int. J. Numer. Meth. Eng. 37 229
[5] Atluri S N and Zhu T 1998 Comput. Mech. 22 117
[6] Liu G R and Gu Y T 2001 Int. J. Numer. Meth. Eng. 50 937
[7] Cheng Y M and Li J H 2005 Acta Phys. Sin. 54 4463 (in Chinese)
[8] Liew K M and Cheng Y M 2009 Comp. Meth. Appl. Mech. Eng. 198 3925
[9] Chen L and Cheng Y M 2008 Acta Phys. Sin. 57 1 (in Chinese)
[10] Chen L and Cheng Y M 2008 Acta Phys. Sin. 57 6047 (in Chinese)
[11] Zhang J M, Yao Z H and Li H 2002 Int. J. Numer. Meth. Eng. 53 751
[12] Ren H P, Cheng Y M and Zhang W 2009 Chin. Phys. B 18 4065
[13] Cheng Y M and Peng M J 2005 Sci. Chin. Ser. G: Phys. Mech. Astron. 48 641
[14] Cheng Y M, Liew K M and Kitipornchai S 2009 Int. J. Numer. Meth. Eng. 78 1258
[15] Peng M J and Cheng Y M 2009 Eng. Anal. Bound. Elem. 33 77
[16] Qin Y X and Cheng Y M 2006 Acta Phys. Sin. 55 3215 (in Chinese)
[17] Cheng Y M and Chen M J 2003 Acta Mech. Sin. 35 181 (in Chinese)
[18] Lancaster P and Salkauskas K 1981 Math. Comput. 37 141
[19] Mukherjee Y X and Mukherjee S 1997 Int. J. Numer. Meth. Eng. 40 797
[20] Kothnur V S, Mukherjee S and Mukherjee Y X 1999 Int. J. Solids Struc. 36 1129
[21] Zhu T, Zhang J D and Atluri S N 1998 Comput. Mech. 21 223
[22] Zhu T, Zhang J and Atluri S N 1998 Comput. Mech. 22 174
[23] Gu L 2003 Int. J. Numer. Meth. Eng. 56 1
[24] Zheng B J and Dai B D 2010 Acta Phys. Sin. 59 5182 (in Chinese)
[1] A meshless Galerkin method with moving least square approximations for infinite elastic solids
Li Xiao-Lin (李小林), Li Shu-Ling (李淑玲). Chin. Phys. B, 2013, 22(8): 080204.
[2] A new complex variable element-free Galerkin method for two-dimensional potential problems
Cheng Yu-Min (程玉民), Wang Jian-Fei (王健菲), Bai Fu-Nong (白福浓). Chin. Phys. B, 2012, 21(9): 090203.
[3] An improved interpolating element-free Galerkin method with nonsingular weight function for two-dimensional potential problems
Wang Ju-Feng (王聚丰), Sun Feng-Xin (孙凤欣), Cheng Yu-Min (程玉民). Chin. Phys. B, 2012, 21(9): 090204.
[4] A scaled boundary node method applied to two-dimensional crack problems
Chen Shen-Shen (陈莘莘), Li Qing-Hua (李庆华), Liu Ying-Hua (刘应华 ). Chin. Phys. B, 2012, 21(11): 110207.
[5] The complex variable meshless local Petrov–Galerkin method of solving two-dimensional potential problems
Yang Xiu-Li (杨秀丽), Dai Bao-Dong (戴保东), Zhang Wei-Wei (张伟伟). Chin. Phys. B, 2012, 21(10): 100208.
[6] An improved boundary element-free method (IBEFM) for two-dimensional potential problems
Ren Hong-Ping(任红萍), Cheng Yu-Min(程玉民), and Zhang Wu(张武). Chin. Phys. B, 2009, 18(10): 4065-4073.
No Suggested Reading articles found!