Modeling dynamic fracture in Kirchhoff plates and shells using the extended finite element method

In this study, the extended finite element method was used for modeling dynamic fracture in Kirchhoff plate and shell problems. A new set of tip functions was extracted from analytical solutions of Kirchhoff plates. The semi-discrete method was used to simulate the dynamic behavior. An unconditionally stable implicit Newmark scheme was used for temporal discretization. The performance of the code in simulation of dynamic behaviors was proved by solving several benchmark problems and comparing the obtained results with other numerical and analytical solutions. Also, the problem of cracked thin tubes under gaseous detonation loading was simulated by the dynamic XFEM code. The results were compared with analytical and other numerical solutions and the obtained results showed that the method has good capability for simulation of these problems.