A scaled boundary node method applied to two-dimensional crack problems

doi:10.1088/1674-1056/21/11/110207

中国物理B ›› 2012, Vol. 21 ›› Issue (11): 110207-110207.doi: 10.1088/1674-1056/21/11/110207

A scaled boundary node method applied to two-dimensional crack problems

陈莘莘^a, 李庆华^a, 刘应华^b

a College of Civil Engineering, Hunan University of Technology, Zhuzhou 412007, China;
b Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing 100084, China

收稿日期:2012-04-26 修回日期:2012-06-20 出版日期:2012-10-01 发布日期:2012-10-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11002054).

A scaled boundary node method applied to two-dimensional crack problems

Chen Shen-Shen (陈莘莘)^a, Li Qing-Hua (李庆华)^a, Liu Ying-Hua (刘应华 )^b

a College of Civil Engineering, Hunan University of Technology, Zhuzhou 412007, China;
b Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing 100084, China

Received:2012-04-26 Revised:2012-06-20 Online:2012-10-01 Published:2012-10-01
Contact: Chen Shen-Shen E-mail:chenshenshen@tsinghua.org.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11002054).

摘要/Abstract

摘要： A boundary-type meshless method called the scaled boundary node method (SBNM) is developed to directly evaluate the mixed mode stress intensity factors (SIFs) without extra post-processing. The SBNM combines the scaled boundary equations with the moving Kriging (MK) interpolation to retain the dimensionality advantage of the former and the meshless attribute of the latter. As a result, the SBNM requires only a set of scattered nodes on the boundary, and the displacement field is approximated by using the MK interpolation technique, which possesses the δ function property. This thus makes the developed method efficient and straightforward in imposing the essential boundary conditions, and no special treatment techniques are required. Besides, the SBNM works by weakening the governing differential equations in the circumferential direction and then solving the weakened equations analytically in the radial direction. Therefore, the SBNM permits an accurate representation of the singularities in the radial direction when the scaling center is located at the crack tip. Numerical examples using the SBNM for computing the SIFs are presented. Good agreements with available results in the literature are obtained.

关键词: meshless method, scaled boundary node method, moving Kriging interpolation, stress intensity factor

Abstract: A boundary-type meshless method called the scaled boundary node method (SBNM) is developed to directly evaluate the mixed mode stress intensity factors (SIFs) without extra post-processing. The SBNM combines the scaled boundary equations with the moving Kriging (MK) interpolation to retain the dimensionality advantage of the former and the meshless attribute of the latter. As a result, the SBNM requires only a set of scattered nodes on the boundary, and the displacement field is approximated by using the MK interpolation technique, which possesses the δ function property. This thus makes the developed method efficient and straightforward in imposing the essential boundary conditions, and no special treatment techniques are required. Besides, the SBNM works by weakening the governing differential equations in the circumferential direction and then solving the weakened equations analytically in the radial direction. Therefore, the SBNM permits an accurate representation of the singularities in the radial direction when the scaling center is located at the crack tip. Numerical examples using the SBNM for computing the SIFs are presented. Good agreements with available results in the literature are obtained.

Key words: meshless method, scaled boundary node method, moving Kriging interpolation, stress intensity factor

中图分类号: (Numerical simulation; solution of equations)

02.60.Cb

02.60.Lj (Ordinary and partial differential equations; boundary value problems) 46.25.-y (Static elasticity)

陈莘莘, 李庆华, 刘应华 . A scaled boundary node method applied to two-dimensional crack problems[J]. 中国物理B, 2012, 21(11): 110207-110207.

Chen Shen-Shen (陈莘莘), Li Qing-Hua (李庆华), Liu Ying-Hua (刘应华 ). A scaled boundary node method applied to two-dimensional crack problems[J]. Chin. Phys. B, 2012, 21(11): 110207-110207.

参考文献 29

[1]	Zhang X, Liu Y and Ma S 2009 Advances in Mechanics 39 1 (in Chinese)
[2]	Mukherjee Y X and Mukherjee S 1997 Int. J. Numer. Meth. Eng. 40 797
[3]	Kothnur V S, Mukherjee S and Mukherjee Y X 1999 Int. J. Solids Struc. 36 1129
[4]	Zhang J M, Yao Z H and Li H 2002 Int. J. Numer. Meth. Eng. 53 751
[5]	Zhang J M, Tanaka M and Matsumoto T 2004 Int. J. Numer. Meth. Eng. 59 1147
[6]	Miao Y, Wang Y H and Yu F 2005 Eng. Anal. Bound. Elem. 29 703
[7]	Yan F, Wang Y H, Miao Y and Tan F 2008 Acta Mech. Solida Sin. 21 267
[8]	Yan F, Wang Y H, Miao Y, Tham L G and Cheung Y K 2009 J. Sound Vib. 321 1036
[9]	Peng M J and Cheng Y M 2009 Eng. Anal. Bound. Elem. 33 77
[10]	Liew K M, Cheng Y M and Kitipornchai S 2007 Int. J. Solids Struct. 44 4220
[11]	Li X G, Dai B D and Wang L H 2010 Chin. Phys. B 19 120202
[12]	Chen W, Shen L J, Shen Z J and Yuan G W 2005 Eng. Anal. Bound. Elem. 29 756
[13]	Hon Y C and Chen W 2003 Int. J. Numer. Meth. Eng. 56 1931
[14]	Young D L, Chen K H and Lee C W 2005 J. Comput. Phys. 209 290
[15]	Song C and Wolf J 1997 Comput. Methods Appl. Mech. Eng. 147 329
[16]	Song C and Wolf J 2002 Comput. Struct. 80 183
[17]	Song C 2006 Int. J. Numer. Meth. Eng. 65 620
[18]	Liu J Y and Lin G 2007 China Ocean Eng. 21 293
[19]	Song C, Tin-Loi F and Gao W 2010 Eng. Fract. Mech. 77 2316
[20]	Deeks A J and Augarde C E 2005 Comput. Mech. 36 159
[21]	Gu L 2003 Int. J. Numer. Meth. Eng. 56 1
[22]	Zheng B J and Dai B D 2010 Acta Phys. Sin. 59 5182 (in Chinese)
[23]	Zheng B J and Dai B D 2011 Appl. Math. Comput. 218 563
[24]	Zhu P and Liew K M 2011 Compos. Struct. 93 2925
[25]	Bui Q T, Nguyen N M, Zhang Ch and Pham DAK 2011 Smart Mater. Struct. 20 1
[26]	Deeks A J and Wolf J P 2002 Comput. Mech. 28 489
[27]	Civelek M B and Erdogan F 1982 Int. J. Fract. 19 139
[28]	Kitagawa H and Yuuki R 1977 Trans. Jpn. Soc. Mech. Eng. 43 4354
[29]	Tsang D K L and Oyadiji S O 2008 Proc. R. Soc. A 464 2629

A scaled boundary node method applied to two-dimensional crack problems

A scaled boundary node method applied to two-dimensional crack problems

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