Crack Analysis by Using An Extended Meshfree Method and Cartesian Transformation Method without Creating Subdomains

Abstract

This paper investigates the fracture behavior of plates with through-thickness crack by using the extended concept of the Radial Point Interpolation Method (RPIM). The attractiveness of the RPIM shape functions is the satisfaction of the Kronecker delta property providing direct imposition of essential boundary conditions. In the extended concept, the jump in deflection and rotation fields caused by crack, also the stress singularity near the crack tip are described by adding enriched functions to the interpolation equation. Particularly, Heaviside function and asymptotic enriched function. For numerical integration, the Cartesian Transformation Method (CTM) is employed. No integration background cell is required in CTM, this technique transforms a domain integral into a boundary integral and a 1D integral. For analysis of discontinuous problems, in this study, the distribution of integration points is manipulated to avoid the discontinuity caused by crack segmentation. Therefore, no subdomains are required, unlike other reference CTM studies. To achieve that, a virtual boundary is introduced that represents the discontinuity such as holes or cracks. This also matches the concept of the extended approach that no explicit discontinuity exists in the geometry, instead, the discontinuity is modelled by mathematics equation. The Stress Intensity Factors (SIFs) of the cracked plate are evaluated through the interaction integral technique. The efficiency of the proposed method is illustrated through various numerical examples. The accuracy of the obtained results are compared with other available numerical solutions and analytical solutions.