Reconsiderations on boundary conditions of Kirchhoff micro-plate model based on a strain gradient elasticity theory

In the previous works, the boundary conditions of Kirchhoff micro-plate model are derived by only considering the cases of four-edge simply supported and/or four-edge clamped micro-plate, while it is invalid for the plates which have at least one free edge. The general boundary conditions as well as the governing equation of Kirchhoff micro-plate are re-derived based on a strain gradient elasticity theory. The general boundary conditions can degenerate into the corresponding ones of the classical continuum model. With the general boundary conditions, the deflection of some typical cases of plate are studied and discussed. Moreover, the effect of material length scale parameters on the deflection and the size effect of these plates are also discussed. The present work extends the former works to be a generalized one since the generalized boundary conditions may deal with different reasonable boundary conditions.