Analysis of Crack Propagation

    Using Element-Free Galerkin Methods

    Jung Jin Ahn



This paper presents a crack propagation analysis algorithm in a steel structural component under cyclic fatigue loading using Element-Free Galerkin (EFG) methods. Moving least square interpolants are employed for shape function, in which domain of influence and exponential weight function are introduced. Lagrange multipliers are used to satisfy the essential boundary condition in EFG formulation since shape function does not satisfy kronecker delta condition. In order to perform a numerical integration in EFG formulation, a cell structure independent of the nodes is used.

   In EFG crack analysis, the effects of the discontinuity of crack and the singularity of crack tip are considered by numerical techniques. To avoid discontinuities of the shape functions in crack tip fields, the diffraction method based on the way light diffraction is used. Conservation integrals are used to directly evaluate the individual stress intensity factors for the mixed-mode crack problem in terms of known auxiliary solutions. The maximum circumferential stress theory is used to measure the direction of crack growth. Paris equation is used to measure the extension of fatigue crack growth. Successive iteration is adopted to solve Paris equation.

   The validity of the proposed algorithm is demonstrated by numerical examples of mixed mode crack propagation problem.


Key Word

Element-Free Galerkin Methods, Moving least square interpolants, domain of influence, weight function, diffractioni method, fatigue crack propation


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