A shear deformation micro-plate model based on the most general form of strain gradient elasticity

In this study, a first order shear deformation micro-plate model based on strain gradient elasticity theory is developed. The most general form of Mindlinʹs linear isotropic strain gradient elasticity is employed and a general micro-plate formulation is obtained. The governing equations of motion and all possible boundary conditions are determined using the variational method. For some specific values of the gradient-based material parameters, the general plate formulation can be reduced to those based on simple forms of the strain gradient elasticity theory. Accordingly, a simple form of the plate formulation is introduced. To illustrate the behavior of a micro-plate predicted by the new plate formulation, the static bending and free vibration problems of a simply supported micro plate are investigated. Numerical results reveal that the plate defection decreases and natural frequencies increase remarkably when the plate thickness becomes comparable to its material length scale parameter. These size effects decrease or even diminish as the thickness of the plate is far greater than the material length scale parameter. It was also observed that the effects of shear deformation are more sensible at micro scales.