A size-dependent functionally graded Reddy plate model based on a modified couple stress theory

Abstract

In this paper, a size-dependent model for bending and free vibration of functionally graded Reddy plate is developed. The present model accounts for both small scale and shear deformation effects in functionally graded microplates. The small scale effects are captured using the modified couple stress theory, while the shear deformation effects are included using the third-order shear deformation theory. The equations of motion and boundary conditions are derived from Hamilton’s principle. Analytical solutions are obtained for a simply supported plate. Numerical examples are presented to illustrate the effects of small scale on the responses of microplates. The results reveal that the inclusion of small scale effects results in an increase in plate stiffness, and consequently, leads to a reduction of deflection and an increase in frequency. Such small scale effects are significant when the plate thickness is small, but become negligible with increasing plate thickness.