A cell-based smoothed discrete shear gap method (CS-DSG3) using triangular elements for static and free vibration analyses of shell structures

•CS-DSG3 for static and free vibration analyses of Mindlin shells is proposed.•Each triangular element in CS-DSG3 is divided into three sub-triangles.•CS-DSG3 improves the accuracy as well as the stability of the DSG3.

A cell-based smoothed discrete shear gap method (CS-DSG3) for static and free vibration analyses of Reissner–Mindlin shells is formulated by combining the cell-based strain smoothing technique with the discrete shear gap method (DSG3) using three-node triangular elements. In the CS-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the stabilized DSG3 is used to compute the strains and to avoid the transverse shear locking. Then the strain smoothing technique on whole of the triangular element is used to smooth the strains on these three sub-triangles. The CS-DSG3 hence not only overcomes the drawback of the DSG3 but also improves the accuracy as well as the stability of the DSG3. The numerical examples demonstrated that the CS-DSG3 is free of shear locking and achieves the high accuracy compared to other existing shell elements.