Independent cover meshless method using a polynomial approximation

In this paper, a novel independent cover meshless method (ICMM) is presented for the analyses of two dimensional linear elastic solids and the simulation of crack propagation. In the ICMM, the Delaunay criterion is employed to dynamically construct the non-overlapping independent nodal cover for each discrete node of analysis domain, and the virtual crack closure technique is used to calculate the stress intensity factors. The ICMM has the definite nodal cover (or nodal influence domain) and employs the general polynomial function to interpolate the nodal cover, which results in a simple formulation and numerical implementation, and facilitates the accurate numerical integration of the equilibrium equation and the enforcement of the boundary conditions. It well solves the problem of the general meshless methods interpolated by rational functions, and has a wide application prospective in practical engineering. Several representative numerical examples demonstrate the convergence, accuracy and robustness of the present method.