Size-dependent buckling and vibration analyses of GNP reinforced microplates based on the quasi-3D sinusoidal shear deformation theory

Based on the modified couple stress theory (MCST) and the quasi-3D sinusoidal shear deformation theory (SSDT), size-dependent mechanical buckling and free vibration analyses of microplates reinforced by functionally graded graphene nanoplatelets (FG-GNPs) are studied in this paper. The composite microplate is considered to be composed of epoxy reinforced by GNPs distributed along the thickness direction based on various symmetric and non-symmetric patterns. Effective material properties of the composite microplate are estimated based on the Halpin-Tsai model along with the rule of mixture and the set of governing equations are derived using Hamilton's principle. An exact solution is presented for simply supported microplates using Navier's method and effect of various parameters including aspect ratio and thickness of the microplate, material length scale parameter and width, thickness, total mass fraction and distribution of GNPs on the critical buckling load and natural frequencies are investigated.