A unified size-dependent plate theory for static bending and free vibration analyses of micro- and nano-scale plates based on the consistent couple stress theory

Based on the consistent couple stress theory (CCST), the authors develop a unified formulation of various shear deformation plate theories for static bending and free vibration analyses of simply-supported, micro-/nano-scale plates embedded in an elastic medium. The CCST-based classical plate theory (CPT), first-order shear deformation plate theory (SDPT), and Reddy's refined SDPT, as well as the CCST-based sinusoidal, exponential, and hyperbolic SDPTs can be obtained by assigning specific through-thickness distributions of the shear deformations into the unified formulation, and they are thus included as special cases of the unified consistent couple stress plate theory. The unified CCST-based plate theory is applied to static bending and free vibration analyses of simply-supported, functionally graded microplates (FGMPs) and multilayered graphene sheets (MLGSs) embedded in an elastic medium. The material length scale parameter, aspect ratio, and shear deformation effects on the deformation, stress, and frequency parameters of FGMPs and MLGSs are investigated. It is shown that the solutions for the deformation, the in-plane stress, and the frequency parameters of the FGMPs/MLGSs obtained using the MCST and the CCST are almost identical to each other. The material length scale parameter effects on static bending and free vibration behaviors of the FGMP/MLGS are significant.