Meshless method based on Shepard function and partition of unity for two-dimensional crack problems

A new Meshless method based on Shepard function and Partition of Unity (MSPU) is proposed for calculating crack SIFs (Stress Intensity Factors) and simulating crack propagation. Link elements are employed to connect the adjacent block elements inside and around the circle of a crack tip, and to solve the challenging problem of imposing essential boundary conditions for meshless methods. The proposed MSPU possesses the merits of concise interpolation formulation and simple numerical implementation, and shows many advantages over existing meshless methods. In this work, the virtual crack closure technique (VCCT) is used to capture the crack tip SIFs, and the crack propagation is determined based on the maximum circumferential stress criterion. Numerical examples of representative cracking problems indicate that the MSPU is of high accuracy, good stability and sufficient convergence rate in fracture analyses, and has a wide application prospective.