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An iterative coupling between meshless methods to solve embedded crack problems. (English) Zbl 1403.74103
Summary: A truly meshless iterative coupling is presented to solve linear elastic fracture mechanic (LEFM) problems. The global domain of the problem is decomposed into sub-domains, where each one is addressed using an appropriate meshless method. The sub-domain which has embedded cracks is modeled by the method of fundamental solutions (MFS) with the help of the numerical Greens function (NGF) approach and the sub-domain without cracks is modeled by the meshless local Petrov-Galerkin (MLPG) procedure. By using the NGF approach the representation of the crack is automatically included. The specific computations of each meshless method are performed independently, coupled with an iterative renewal of variables procedure, restricted to interface unknowns, to achieve the final convergence. The iterative solution procedure presented yields good results as compared with the boundary element method and analytical solutions for stress intensity factor computations.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs
74B05 Classical linear elasticity
74R10 Brittle fracture
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