Size-Dependent Green’s Function for Bending of Circular Micro Plates Under Eccentric Load

Abstract

In this paper, a Green’s function is developed for bending analysis of micro plates under an asymmetric load. In order to consider the length scale effect, the modified couple stress theory is used. This theory can accurately predict the behavior of micro structures. A thin micro plate is considered and therefore the classical plate theory is utilized. The size dependent governing equilibrium equation of a circular micro plate under an eccentric load is obtained by using the minimum total potential energy principle. This equation is a partial differential equation and it is hard to solve it for an arbitrary loading. A transformation of the coordinate system is introduced to obtain the asymmetric exact solution for deflection of circular micro-plates. By using the obtained size dependent Green’s function, the bending behavior of microplates under arbitrary loads can be easily defined. The results are presented for different asymmetric loads. Also, it is concluded that the length scale has a significant effect on bending of micro plates.