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**Combined visibility and surrounding triangles method for simulation of crack discontinuities in meshless methods.**
*(English)*
Zbl 1264.74257

Summary: 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).

### MSC:

74R99 | Fracture and damage |

74S05 | Finite element methods applied to problems in solid mechanics |

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

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\textit{H. Pirali} et al., J. Appl. Math. 2012, Article ID 715613, 16 p. (2012; Zbl 1264.74257)

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