Size-dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory

Abstract

Size-dependent models for bending, buckling, and vibration of functionally graded Kirchhoff and Mindlin plates are developed using a modified couple stress theory. The present models contain one material length scale parameter and can capture the size effect, geometric nonlinearity, and two-constituent material variation through the plate thickness. The equations of motion are derived from Hamilton’s principle based on a modified couple stress theory, the von Karman nonlinear strains, and the power law variation of the material through the thickness of the plate. Analytical solutions for deflection, buckling load, and frequency of a simply supported plate are presented to bring out the effect of the material length scale parameter on the bending, buckling, and vibration responses of microplates.