Coupled stress based formulation for static and dynamic analyses of a higher-order shear and normal deformable FG-GPL reinforced microplates

Abstract

In this paper, size-dependent static bending and also free and forced vibration analyses of composite microplates are studied based on the modified couple stress theory (MCST) and quasi-3D sinusoidal shear deformation theory. The composite microplate is composed of epoxy reinforced with functionally graded graphene nanoplatelets (GPLs). The governing equations are derived utilizing Hamilton's principle and are solved for simply supported microplate using Navier's approach. The accuracy of the presented solution is confirmed and the effects of various parameters on the static and dynamic deflections and natural frequencies of the microplate are investigated including material length scale parameter and surface area, thickness, mass fraction, and distribution pattern of the GPLs. Numerical results confirm that subjoining the GPLs to the polymer reduces the static and dynamic deflections of the microplates and increases the natural frequencies. It is concluded that to achieve the highest reduction in the static and dynamic deflections and the highest growth in the natural frequencies, it is more helpful to use the GPLs with the larger surface areas and put them as far as away from the neutral surface of the microplate.