An Improved Cell-Based Smoothed Discrete Shear Gap Method (CS-DSG3) for Static and Dynamic Analyses of Reissner–Mindlin Plates

Abstract

The efficiency and accuracy of the cell-based smoothed discrete shear gap (CS-DSG3) are improved in simplifying the application process of the cell-based strain smoothing technique and redefining the stabilized parameter of Stenberg’s stabilization method, respectively. In the original CS-DSG3, both the smoothed bending strain and the smoothed shear strain are derived by the cell-based strain smoothing technique. This study proves that the smoothed bending strain matrix in the original CS-DSG3 is equal to the unsmoothed bending strain matrix. Theoretically, abandoning the bending strain smoothing operation can improve the efficiency while maintaining the accuracy of the original CS-DSG3. The introduction of Stenberg’s stabilization method can boost the accuracy of shear strain in the original CS-DSG3, whereas the relationships of the stabilized parameter in Stenberg’s stabilization method with the mesh density, the thickness–span ratio, and the boundary condition are still unclear. In this study, the range of the optimal stabilized parameter for different analyses and boundary conditions is determined through the static and dynamic analysis of the plate. The new stabilized parameter is applied to static analyses, free vibration analyses, and frequency response analyses for verification and comparison, which demonstrates that it can significantly improve the accuracy of the CS-DSG3.