A meshfree method with gradient smoothing for free vibration and buckling analysis of a strain gradient thin plate

In this paper, a meshfree Galerkin approach is presented for analysis of free vibration and buckling of a strain gradient thin plate. A cubic moving least square or reproducing kernel approximation with C2 continuity is used to ensure convergence. Due to smoothness of the meshfree approximation, the only variable is the deflection of a thin plate. To improve the computational accuracy, a consistent integration scheme with gradient smoothing is introduced to construct stiffness and geometrical stiffness matrices. The effectiveness of such an approach is confirmed by numerical results, and it is superior to a standard Gauss integration based meshfree Galerkin method. Further, the influence of classical and high order boundary conditions is investigated on the natural frequencies and critical buckling loads of strain gradient thin plates