Static and free vibration analyses of plates on elastic foundation using a cell-based smoothed three-node mindlin plate element (CS-Min3)

A cell-based smoothed three-node Mindlin plate element (CS-MIN3) was recently proposed to improve the performance of the existing three-node Mindlin plate element (MIN3) for static and free vibration analyses of Mindlin plates. In this paper, the CSMIN3 is incorporated with spring systems for treating more complicated static and free vibration analyses of Mindlin plates on the elastic foundation. The plate-foundation system is modeled as a discretization of triangular plate elements supported by discrete springs at the nodal points representing the elastic foundation. The accuracy and reliability of the proposed method are verified by comparing with those of others available numerical results

Analyses of stiffened plates resting on the viscoelastic foundation subjected to a moving vehicle by a cell-based smoothed triangular plate element

Recently, a cell-based smoothed discrete shear gap method (CS-FEM-DSG3) based on the firstorder shear deformation theory (FSDT) was proposed for static and free vibration analyses of Mindlin plates. The CS-FEM-DSG3 uses three-node triangular elements that can be easily generated automatically for arbitrary complicated geometric domains. This paper further extends the CS-FEMDSG3 for static, free vibration, and dynamic response of the stiffened plate resting on viscoelastic foundation subjected to a moving vehicle. The viscoelastic foundation is modeled by discrete springs and dampers whereas the stiffened plate can be considered as the combination between the Mindlin plate and the Timoshenko beam elements. The moving vehicle is transformed into one concentrated load at its central point. Some numerical examples are investigated and numerical results show that the CS-FEMDSG3 overcomes shear-locking phenomena and has a fast convergence. The results also illustrate the good agreement of the CS-FEM-DSG3 for static and free vibration analyses of un-stiffened plate compared with the previous published methods. In addition, the numerical results for dynamic analysis of stiffened plates by the CS-FEM-DSG3 also show the expected property in which the deflection of the stiffened plate is much smaller than those of the un-stiffened plate