Abstract：An effective and efficient method is presented to simulate 2D dynamic crack propagation problems without any remeshing. The unit decomposition function is constructed over a cracked region by using Shepard formula，visibility criteria and standard FEM shape functions. This set of unit decomposition function are discontinuous across crack lines. With self-defined functions，such as polynomials of any desired degree or asymptotic fields around crack tip，local approximation spaces on patches are built up. Then generalized shape functions are derived，and expected discontinuity is introduced into shape functions and accordingly to displacements field. This method can model fracture problem effectively and be combined with standard FEM procedure intrinsically，and it is called as generalized traditional method. In this method，expanded Newmark nonlinear method is used to solve the dynamic propagation process of crack，and the integral method over virtual extension domain based on energy balance is utilized to compute mixed mode stress intensity factors of static and dynamic fractures. At last，a new auxiliary function is proposed to raise accuracy of solution and improve numerical stability.
