Free vibration and buckling analyses of shear-deformable plates based on FSDT meshfree method

A meshfree method based on the reproducing kernel particle approximate is employed for the free vibration and buckling analyses of shear-deformable plates. In this approach, the first order Mindlin/Reissner plate theory (FSDT) is used, and the displacement shape functions are constructed using the reproducing kernel approximation satisfying the consistency condition. The essential boundary conditions are enforced by a transformation method. Numerical examples considering various aspect ratios, skew angles and boundary conditions are demonstrated to show the validity of the proposed method, and satisfactory results were obtained when comparisons are made with the exact and other available numerical results existing in the literature.