A new shear deformation model with modified couple stress theory for microplates

In this paper, a new deformation plate theory including two unknown functions and taking into account shear deformations is proposed for static and dynamic analysis of microplates. This theory accounts for a power-law form of the transverse shear stresses across the thickness and satisfies both the shear and couple-free conditions on the upper and bottom surfaces of the plate. Based on this deformation plate theory and using the modified couple stress analysis, the governing equations and the related boundary conditions are derived simultaneously using Hamilton’s principle. These equations are used to investigate the effect of shear deformation on the static bending and vibration responses of a simply supported microplate. In order to evaluate the accuracy and ability of this deformation plate theory in capturing shear deformation effects, the obtained responses are compared to the other deformation theories. The results show that the deflection and natural frequency predicted by the proposed plate theory are comparable to those obtained using higher-order theories which have a higher number of unknown functions. When the aspect ratio of the plate is large enough (thin plates), the difference between the results obtained from different deformation theories diminishes as expected.