Analysis of a crack problem via RKPM and GRKPM and a note on particle volume

Abstract

Analysis of a crack problem via RKPM and GRKPM and a note on particle volume Mani Khezri1, Alireza Hashemian1, Hossein M. Shodja1,2,3 Summary Meshless methods using kernel approximation like reproducing kernel particle method (RKPM) and gradient RKPM (GRKPM) generally use a set of particles to discretize the subjected domain. One of the major steps in discretization procedure is determination of associated volumes particles. In a non-uniform or irregular configuration of particles, determination of these volumes comprises some difficulties. This paper presents a straightforward numerical method for determination of related volumes and conducts a survey on influence of different assumption about computing the volume for each particle. Stress intensity factor (SIF) as a major representing parameter in fracture of solids is calculated by employing meshless methods for an edge-cracked plate under first mode loading condition which is one of the benchmark problems in fracture mechanics. The obtained results are compared using an analysis in terms of dilation parameter.