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P. Tong and T. Pian, “On the Convergence of the Finite Element Method for Problems with Singularity,” International Journal of Solids and Structures, Vol. 9, No. 3, 1973, pp. 313-321. doi:10.1016/0020-7683(73)90082-6

has been cited by the following article:

• TITLE: Extended Finite Element Modeling: Basic Review and Programming

  AUTHORS: Yazid Abdelaziz, K. Bendahane, A. Baraka

  KEYWORDS: X-FEM, Programming, Fracture, Cracks, LSM

  JOURNAL NAME: Engineering, Vol.3 No.7, July 29, 2011

  ABSTRACT: In this work, we have exposed a recent method for modeling crack growth without re-meshing. The main advantage of this method is its capability in modeling discontinuities independently, so the mesh is prepared without any considering the existence of discontinuities. The paper covers the formulation and implementation of XFEM, and discusses various aspects of the approach (enrichments functions, level set representation, numerical integration…). Numerical experiments show the effectiveness and robustness of the XFEM implementation.