A microstructure-dependent sinusoidal plate model based on the strain gradient elasticity theory

A new non-classical sinusoidal plate model is developed on the basis of modified strain gradient theory. This model takes into account the effects of shear deformation without any shear correction factors and also can capture the size effects due to additional material length scale parameters. The governing equations and corresponding boundary conditions for bending, buckling, and free vibration analysis of the microplate are derived by implementing Hamilton's principle. Analytical solutions based on the Fourier series solution are presented for simply supported square microplates. A detailed parametric study is performed to demonstrate the influences of thickness-to-length scale parameter ratio, length-to-thickness ratio, and shear deformation on deflection, critical buckling load, and fundamental frequencies of microplates. It is observed that the effect of shear deformation becomes more significant for smaller values of length-to-thickness ratio.