A new hybrid smoothed FEM for static and free vibration analyses of Reissner–Mindlin Plates

A new smoothed finite element method (S-FEM) is proposed using hybrid smoothing operations based on nodes and edges of the mesh for static and free vibration analyses of plates governed by the Reissner–Mindlin plate theory. In the present approach, both the node-based smoothed finite element method (NS-FEM) and edge-based smoothed finite element method (ES-FEM) are utilized in a careful designed manner to overcome the shear locking. The formulations use 3-node triangular elements for easy automatic mesh creation, and linear interpolation functions are used for simplicity and robustness. The bending strains field are smoothed by the means of gradient smoothing technique over smoothing domains constructed by element edges, while the shear strains filed is smoothed based on the combination of NS-FEM and ES-FEM with a proper weightage controlled by a coefficient. A simple formula is developed for automatic selection of the coefficient by considering mesh size and thickness of the plate. For easy reference, the present technique is termed as NS+ES-FEM. The numerical examples demonstrate that the proposed method passes the shear-locking test and improves accuracy of the solution.