Mehran Ghorbani, Nima Noormohammadi, Bijan Boroomand

Computers & Mathematics with Applications

Abstract

We introduce a novel enrichment technique for the element free Galerkin (EFG) method to capture the infinite stress field around the crack or notch tip. The singular enrichment bases are built through a weighted residual application of the governing partial differential equation. A special mapping is used to adapt the bases with the singularities. These bases are used in a moving least squares approximation to enrich the smooth polynomial bases of the EFG within the singularity-dominated zone in an intrinsic approach. The novelty of the method is that no a priori knowledge of the analytical singularity order is required to reproduce the singular bases, but they are automatically built during the solution procedure. The diffraction technique has been used to model the discontinuity of the notch tip. The effect of various parameters, including the enriched region size, enrichment factors, nodal distribution and irregularities, has been examined. Validation of the method using available analytical solutions or finite element modeling, revealed that the proposed enrichment is quite effective and accurate for displacement and stress components.