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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 |
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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.
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Received: 26 April 2012
Revised: 20 June 2012
Accepted manuscript online:
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PACS:
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02.60.Cb
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(Numerical simulation; solution of equations)
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02.60.Lj
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(Ordinary and partial differential equations; boundary value problems)
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46.25.-y
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(Static elasticity)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11002054). |
Corresponding Authors:
Chen Shen-Shen
E-mail: chenshenshen@tsinghua.org.cn
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Cite this article:
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 2012 Chin. Phys. B 21 110207
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