The finite element discretized symplectic method for interface cracks

The method of symplectic series discretized by finite element is introduced for the stress analysis of structures having cracks at the interface of dissimilar materials. The crack is modeled by the conventional finite elements dividing into two regions: near and far fields. The unknowns in the far field are as usual. In the near field, a Hamiltonian system is established for applying the method of separable variables and the solutions are expanded in exact symplectic eigenfunctions. By performing a transformation from the large amount of finite element unknowns to a small set of coefficients of the symplectic expansion, the stress intensity factors, the displacements and stresses in the singular region are obtained simultaneously without any post-processing. The numerical results are obtained for various cracks lying at the bi-material interface, and are found to be in good agreement with the reference solutions for the interface crack problems. Some practical examples are also given.