A High Order Continuation Method with a Weighted Least Squares Approach to Analysis Cracked Structures

In this study, we develop a method grounded in the Weighted Least Squares (WLS) approach to address two-dimensional nonlinear elasticity problems, focusing specifically on the analysis of cracked structures. We construct shape functions within a local support domain using the WLS approximation, which, when coupled with a High-Order Continuation method, allows for a strong problem formulation that circumvents the need for numerical integration and mesh generation. Moreover, we employ the J-integral to evaluate the singularity at the crack front. The proposed meshfree method's efficiency and accuracy is rigorously evaluated through numerical testing and compared against benchmark solutions.