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

In this study, a micro-scale Kirchhoff plate model based on the most general form of the linear isotropic strain gradient elasticity theory is developed. The governing equation of motion and corresponding boundary conditions are obtained using Hamilton’s principle. For some specific values of the gradient-based material parameters, the general plate formulation can be reduced to those based on some special forms of thestrain gradient elasticity theory. Accordingly, three different plate formulations are introduced. As an example, the static deformation and natural frequency problems of a rectangular plate with simply-supported boundaries are solved. In all cases, a decrease in the ratio of the plate thickness to the material length parameter results in the reduction of the lateral deflection and increase of the natural frequency of the micro-plate.

Keywords:

Strain gradient elasticity , Micro-plate , Kirchhoff model , Size effect