Assessment of RBFs Based Meshfree Method for the Vibration Response of FGM Rectangular Plate Using HSDT Model

Radial basis functions (RBFs) with modified radial distance are proposed for vibration analysis of functionally graded materials (FGM) rectangular plates. The displacement field with five variables higher-order shear deformation theory (HSDT) is considered. The governing differential equations (GDEs) and boundary conditions are obtained using Hamilton’s principle. The governing differential equations formulations are solved via strong-form solutions. The rectangular plates are analyzed in the framework of the RBF-based meshfree method. The novelty of the present modified method is to analyze the square and rectangular plates without changing the shape parameters. Here, the seventeen different RBFs are available in various literature to demonstrate the accuracy and efficiency of the present method in terms of the number of nodes and computational time. The results of several numerical examples have shown that the present modified RBF-based mesh-free method can lead to much more accurate solutions. Computational times of different RBFs are also analyzed.