A smoothed enriched meshfree Galerkin method with two-level nesting triangular sub-domains for stress intensity factors at crack tips

Abstract

A smoothed enriched meshfree Galerkin method with two-level nesting triangular sub-domains (NSEMM) is presented for linear elastic fracture mechanics. In the present method, displacement fields are constructed by using the linear MLS approximation in linear region away from the crack tip and the enriched MLS approximation in enriched region around the crack tip respectively. To overcome the discontinuous problem of the coupling approximations and accelerate meshfree computations, two-level nesting triangular sub-domains based on the triangular background integration cells are designed and used to construct the smoothing strain. Each two-level nesting sub-domains includes the triangular background cell itself and four equal-area triangular sub-cells. The discretized system equations are created by the Generalized smoothed Galerkin (GS-Garlerkin) weak form and Richardson extrapolation method. The values of SIFs are evaluated by using the domain form of interaction integral. Numerical examples have been simulated to demonstrate the effectiveness and robustness of the present method for crack problems with complicated configurations, and very satisfactory results have been obtained. The NSEMM takes advantages of both EFGM and generalized strain smoothing technique such as lower computational cost, high accurate and easy to implementation.