A new symplectic analytical singular element for crack problems under dynamic loading condition

In this paper, the two-dimensional (2D) crack problem under dynamic loading condition is studied. Firstly, by the precise time domain expanding algorithm, the recursive formulation of the governing equation is derived, and the recursive equation can be solved by FEM. Then, a new Symplectic Analytical Singular Element (SASE) defined by the analytical symplectic eigen expanding terms is further developed for the investigated problem. The area near the crack tip is represented by using the SASE, while the other area is meshed by conventional elements. Taking advantage of the SASE, the crack problem can be solved with higher accuracy. Simultaneously, the dynamic stress intensity factors (DSIFs) can be obtained directly without any post processing through the relationship between the DSIFs and the eigen expanding coefficients. The numerical accuracy and stability is investigated carefully through the conducted numerical examples. It has been demonstrated that the proposed SASE for dynamic crack problem is effective and efficient.