In this paper a Nth order nanoplate model is developed for the bending and buckling analysis of a graphene nanoplate based on a modified couple stress theory. The strain energy, external work and buckling equations are solved. Also using Hamilton’ principle, main and auxiliary equations of nano plate are obtained. The bending rates and dimensionless bending values under uniform surface traction and sinusoidal load, the dimensionless critical force under a uniaxial surface force in x direction are all obtained for various plate's dimensional ratios and material length scale to thickness ratios. The governing equations are numerically solved. The effect of material length scale, length, width and thickness of the nanoplate on the bending and buckling ratios are investigated and the results are presented and discussed in details. تفاصيل المقالة

In this paper, a Mindlin rectangular nanoplate model is developed for the bending and vibration analysis of a graphene nanoplate based on a modified couple stress theory. In order to consider the small scale effects, the modified couple stress theory, with one length scale parameter, is used. In modified couple stress theory, strain energy density is a function of strain tensor, curvature tensor, stress tensor and symmetric part of couple stress tensor. After obtaining the strain and kinetic energy, external work and substituting them in the Hamilton’s principle, the main and auxiliary equations of the nanoplate are obtained. Then, by manipulating the boundary conditions the governing equations are solved using Navier approach for bending and vibration of the nanoplate. The bending rates and dimensionless bending values under uniform surface traction and sinusoidal load and different mode frequencies are all obtained for various plate's dimensional ratios and material length scale to thickness ratios. The effect of material length scale, length, width and thickness of the nanoplate on the bending and vibration ratios are investigated and the results are presented and discussed in details. تفاصيل المقالة