Optimum two-dimensional crack modeling in discrete least-squares meshless method by charged system search algorithm

Abstract

In this paper, a node adaptive rearrangement is presented based on the estimated error in various domains for some problems in the fracture mechanics by Discrete Least-Squares Meshless method (DLSM). This method is one of the approximate methods recently introduced and used in the various fields. The method is based on minimization of the least-squares functional with respect to the nodal parameters, and it uses moving least-squares method for calculating the shape functions. Due to the natural process of problem solving, after calculating the shape functions, the residuals are calculated and their values are considered as an objective function for rearrangement of the nodes. There are three popular methods for constructing shape functions in discontinuous domains, and here, the transparency method is utilized. Similar to other numerical methods, there are different procedures for refinement and improvement of the results; however, adaptive rearrangement can be employed without increasing the computational cost. In this paper, the Charged System Search (CSS) algorithm is used as a tool for adaptive rearrangement or repositioning process. Efficiency and effectiveness of the proposed adaptive rearrangement technique is tested by some benchmark two-dimensional crack examples with available analytical solution around crack tips.