Application of Natural Element Method in Numerical Simulation of Crack Propagation

The properties of interpolation of nodal data, ease of imposing essential boundary conditions, and the computational efficiency are some of the most important advantages of natural element method based on the non-Sibsonian interpolation over other meshless methods based on the moving least squares approximants. Accurate imposition of essential boundary conditions is accomplished directly by constructing vector of the displacement field by using non-Sibsonian interpolation method, which is based on the Voronoi diagram and its dual Delaunay tessellation. The discrete control equations of natural element method are developed by utilizing the variational principle of elastic theory and combining the natural element method with the theory of the linear elastic fracture mechanics. Without the connectivity information of elements, the burdensome remeshing, which is used in finite element method, is avoided in the present natural element method. The analysis of crack propagation is simplified dramatically. The numerical examples reveal the advantages and effectiveness of the present method.