An efficient midpoint and Richardson extrapolation-based rapid Quadrature for fracture problems using Radial Point Interpolation Method

An efficient numerical integration technique, namely the Element Midpoint(EM) Method, is successfully applied to meshless methods to solve the fracture problem, which is modeled using the Radial point interpolation method. The results were compared with standard (3 x 3) points Gauss quadrature and (6 x 6) points Gauss quadrature in 2D to validate the presented numerical methods. To demonstrate the efficiency and effectiveness of this method, four benchmark problems, Edge Crack, Center Crack, and Inclined Edge Crack problem under tensile load and Edge Crack problem under shear load, are considered to solve and further calculate Stress Intensity Factor (SIF). Based on the formulation and examples, a comparative study on accuracy and computational time has been presented to show the effectiveness of the integration technique against complex problems like fracture.