On the Internal Enrichment Implementation for Non-Convex Paths, Discontinuities and Crack Problems

Abstract

Studies on the cracked plates have shown high variations in the stress values around the crack tip. On the other hand, micro-cracks are observed in man-made pieces. Thus, analysis of stress fields as well as displacement at the crack tip will be inevitable and very important. Mesh-free methods are new techniques that do not require applying the communication-based concept on what is presented in the finite element method. The discretization of the problem domain is done by a set of node points. In the present study, the Element-Free Galerkin (EFG) method was used to analyze the problems of linear elastic stress field in cracked bodies. Two important and essential measures (steps) were done for increasing the accuracy of the results obtained from the analysis of the problems. In the first step, the standard moving least squares shape function was enriched for capturing discontinuity, using some extra basis functions obtained from analytical solutions.  In the next step, some consideration was applied in the case of confronting non-convex paths and discontinuities. For this purpose, the diffraction method was used to generate suitable shape functions. Finally, the accuracy of the results and proper efficiency of the proposed extended EFG method were assessed by the standard problem analysis and the results of numerical analysis were compared with the theoretical results.