meshless method

In recently, several studies have been conducted to use meshless methods according to their advantages to investigate fracture mechanical problems. The utilization of meshless methods in fracture mechanics because of using continuous shape functions requires modification of the shape function near the discontinuity surface. In this paper, the discrete least squares Meshless method (DLSM) is used as truly meshless methods for solving the crack problems, by using discontinuities definition techniques. In the discrete least squares method, the problem domain discretization is performed by unrelated node points, for approximate the functions, used moving least squares shape function with high order of continuity. It also used the strong form of equations for discretizated the equations. The DLSM method is based on minimizing the squares of the residuals at a number of neighboring points of the main node. The boundary conditions are easily enforced by the penalty method. The visibility criterion, diffraction and transparency method are used to define the discontinuity. The performance of all three techniques is the same on the crack surfaces except near the crack tip. The efficiency and accuracy of applying each technique in the DLSM method are investigated by comparing the results of example modeling. Comparison of the results and the error rate of each technique indicate the high capability and accuracy of the proposed method for applying different techniques in cracked plate modeling. It has been shown that the diffraction method performs relatively better in dealing of discontinuous boundaries compared to the transparency and visibility criterion techniques.