An extended cell-based smoothed discrete shear gap method (XCS-DSG3) for free vibration analysis of cracked Reissner-Mindlin shells

A cell-based smoothed discrete shear gap method (CS-FEM-DSG₃) was recently proposed and proven to be robust for free vibration analyses of Reissner-Mindlin shell. The method improves significantly the accuracy of the solution due to softening effect of the cell-based strain smoothing technique. In addition, due to using only three-node triangular elements generated automatically, the CS-FEM-DSG₃ can be applied flexibly for arbitrary complicated geometric domains. However so far, the CS-FEM-DSG₃ has been only developed for analyzing intact structures without possessing internal cracks. The paper hence tries to extend the CS-FEM-DSG₃ for free vibration analysis of cracked Reissner-Mindlin shells by integrating the original CS-FEM-DSG₃ with discontinuous and crack–tip singular enrichment functions of the extended finite element method (XFEM) to give a so-called extended cell-based smoothed discrete shear gap method (XCS-FEM-DSG₃). The accuracy and reliability of the novel XCS-FEM-DSG₃ for free vibration analysis of cracked Reissner-Mindlin shells are investigated through solving three numerical examples and comparing with commercial software ANSYS.