An extended cell-based smoothed discrete shear gap method(XCS-FEM-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.