Meccanica

, Volume 48, Issue 9, pp 2263–2270 | Cite as

Extended meshless method based on partition of unity for solving multiple crack problems

Article
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Abstract

An extended meshless method based on partition of unity was used in this study to simulate multiple cracks. The cracks are implicitly denoted by a jump in the displacement field function, which has nodes that have domains of influence completely segmented by cracks. Nodes whose domains of influence are partially segmented by cracks are extended by the crack tip singularity function. The influence domain of a node is independent of cracks so that the sparsity of the system equations should not be affected by cracks and the computing time should not increase with the effect of the cracks. Additionally, r −1/2 singularity can be accurately reproduced at the crack tip. Compared with the modified intrinsic enriched meshless method, our method has a higher computational efficiency and precision. Several numerical examples show that the extended meshless method based on partition of unity is feasible and effective in simulating multiple cracks.

Keywords

Extended meshless method Partition of unity Multiple cracks Stress intensity factors 
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Notes

Acknowledgements

The financial support of the work by the National Nature Science Foundation of China (Nos. 10972180, 61001156 and 51269024) and the National Key Basic Research Program of China (No. 2009CB724406) are gratefully acknowledged.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.School of Civil Engineering and ArchitectureXi’an University of TechnologyXi’anPeople’s Republic of China
  2. 2.School of Mathematics and Computer ScienceNingXia UniversityYinchuanPeople’s Republic of China

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