Meshfree radial point interpolation method for the vibration and buckling analysis of FG-GPLRC perforated plates under an in-plane loading

A meshfree radial point interpolation method (RPIM) based on a higher-order shear deformation theory (HSDT) is here developed to investigate the free vibration and buckling behavior of multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) perforated plates under an in-plane edge loading. The non-uniform initial stresses in the multilayer FG-GPLRC perforated plates are evaluated accurately by solving the equilibrium equations derived from the same approach. The mixed collocation-Lagrange multiplayer technique is employed to enforce the various boundary conditions. The multilayer FG-GPLRC plates are built up as perfectly-bonded composite layers reinforced with a uniform distribution of graphene platelets (GPLs), randomly oriented. Perforated plates with three different cut-out shapes are analyzed. Several numerical examples are provided to demonstrate the high performance, the fast convergence rate and the high accuracy of the proposed method. Then, we study the influence of different GPLs distribution patterns, GPLs weight fraction, shape and size of cut-outs on the free vibration and buckling behavior of the multilayer FG-GPLRC perforated plates under an in-plane edge loading.