(untitled) (Advances in Applied Mathematics and Mechanics, 2022)
In this paper, the Discrete Least Squares Meshless (DLSM) method is developed to determine crack-tip fields. In DLSM, the problem domain and its boundary are discretized by unrelated field nodes used to introduce the shape functions by the moving least-squares (MLS) interpolant. This method aims to minimize the sum of squared residuals of the governing differential equations at any nodal point. Since high-continuity shape functions are used, some necessary treatments, including the visibility criterion, diffraction, and transparency approaches, are employed in the DLSM to introduce strong discontinuities such as cracks. The stress extrapolation and J-integral methods are used to calculate stress intensity factors. Three classic numerical examples using three approaches to defining discontinuities in the irregular distribution of nodal points are considered to investigate the effectiveness of the DLSM method. The numerical tests indicated that the proposed method effectively employed the approaches to defining discontinuities to deal with discontinuous boundaries. It was also demonstrated that the diffraction approach obtained higher accuracy than the other techniques.