This paper presents a centre and edge crack analysis using meshless methods which is based on moving least squares (MLS) approximation. The unknown displacement function u(x) is approximated by moving least square approximation u h (x). These approximation are constructed by using a weight function which is based a monomial basis function and a set of non-constant coefficients. A subdivision that is similar to finite element method is used to provide a background mesh for numerical integration. An enriched EFG formulation with fracture problems is proposed to improve the solution accuracy for linear elastic fracture problem. The essential boundary conditions are enforced by Lagrange multipliers method. A code has been written in Matlab for the analysis of a crack tip. The obtained results of the developed EFG-code were compared to available experimental data and other numerical (exact methods and finite element method) methods.
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