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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 715613, 16 pages
Research Article

Combined Visibility and Surrounding Triangles Method for Simulation of Crack Discontinuities in Meshless Methods

School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

Received 25 July 2012; Accepted 27 September 2012

Academic Editor: Khalida I. Noor

Copyright © 2012 H. Pirali et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper a combined node searching algorithm for simulation of crack discontinuities in meshless methods called combined visibility and surrounding triangles (CVT) is proposed. The element free Galerkin (EFG) method is employed for stress analysis of cracked bodies. The proposed node searching algorithm is based on the combination of surrounding triangles and visibility methods; the surrounding triangles method is used for support domains of nodes and quadrature points generated at the vicinity of crack faces and the visibility method is used for points located on the crack faces. In comparison with the conventional methods, such as the visibility, the transparency, and the diffraction method, this method is simpler with reasonable efficiency. To show the performance of this method, linear elastic fracture mechanics analyses are performed on number of standard test specimens and stress intensity factors are calculated. It is shown that the results are in good agreement with the exact solution and with those generated by the finite element method (FEM).