Statics analysis of N-order nanoplates using modified couple stress theory with the Navier s solution method

In this paper using the modified couple stress theory, to study the bending characteristics and buckling of N-order rectangular Nano plates with simply-supported boundary conditions was investigated. With the aim of considering the effects of small scales, the modified couple stress theory, which has only one parameter of length scale, was used. In the modified couple stress theory; the strain energy density is a function of the components of the strain tensor, curvature tensor, stress tensor and the symmetric part of the couple stress tensor. After obtaining the strain energy, external work, and buckling equation and placing them in the Hamilton s equation, the basic and auxiliary equations of the Nano plates were obtained. Then, by applying boundary and force conditions in the governing equations, the bending and buckling of the N-order rectangular Nano plates with thickness h and simply-supported conditions were explored. Moreover, the solution method was the Navier s solution.

Keywords:

Modified couple stress theory , N-order Nanoplates , Navier s solution method , Bending , Buckling.