AN EXTENDED NATURAL ELEMENT METHOD FOR LINEAR ELASTIC FRACTURE PROBLEMS

In order to solve linear elastic fracture problems more effectively, an extended natural element method is proposed in this paper. Based on the ideas of partition of unity, enriched functions are added to the displacement mode of the natural element method in order to characterize the discontinuous displacement field along crack face and stress singularity around the crack tip. The level set method is employed to determine the crack surface and the crack tip region. The discrete linear equation of the equilibrium equation is derived by the virtual displacement principle. The shape function of the natural element method satisfies the Kronecker delta property and thus it is very convenient to impose the essential boundary conditions. The interaction integral method is then utilized to calculate the mixed-mode stress intensity factors. Several numerical examples are presented to demonstrate that the proposed method can deal with linear elastic fracture problems conveniently.