The size-dependent analysis of microplates via a newly developed shear deformation theory

This work deals with considering the small-scale effects on the static bending, vibrational behavior and buckling analysis of a simply supported microplate based on the newly developed shear deformation plate theory. This theory includes two unknown functions and meets the shear and couple-free conditions on the top and bottom surfaces of the plate without any shear correction factor. Hamilton’s principle and the modified couple stress theory are applied to obtain the governing equations and corresponding boundary conditions. Navier’s approach is used to analytically obtain the deflections, natural frequencies and critical buckling loads of the microplate. The reliability of the presented formulation in this paper is studied through comparison with previous existing data. It is revealed that the presented theory is comparable to the other shear deformation theories. Also, numerical results of this work demonstrate that the proposed theory predicts lower natural frequencies and critical buckling loads compared to the other theories because of the lower stiffness of the plate.