Initial Buckling Behavior of Elastically Supported Rectangular FGM Plate based on Higher Order Shear Deformation Theory via Spline RBF Method

In the present paper, the effect of aspect ratio on the initial buckling response of an elastically supported rectangular FGM plate, the thin plate spline radial basis function (RBF) method can be used. This method involves the use of a thin plate spline to interpolate the displacement field of the plate, allowing for accurate analysis of the plate's behavior. The higher-order shear deformation theory (HSDT) is used for the analysis of the FGM rectangular plate resting on two parameters of elastic foundation. The displacement field consists of five unknown variables and approximately parabolic distribution of the transverse stress profile through the plate thickness and tangential stress-free boundary conditions on the plate surface. The governing differential equations (GDEs) of the plate are developed in the framework of Hamilton’s principle. The thin plate spline radial basic function-based Meshfree method is used for discretizing the GDEs. To demonstrate the accuracy and efficacy of the present approach, the results obtained by the present approach are compared with the results given in the literature. The effect of various aspect ratios, grading index, span-to-thickness ratio, and two parameters of elastic foundations on the normalized buckling load is proposed. Some new results are also presented, which may be beneficial for future research works. The novelty of the present is the effects of aspect ratio on the elastically supported FGM plates.