In this paper, bending analysis of rectangular functionally graded nanoplates under a uniform transverse load has been considered based on the modified couple stress theory. Using Hamilton’s principle, governing equations are derived based on a higher-order shear deformation theory. The set of coupled equations are solved using the dynamic relaxation method combined with finite difference discretization technique for clamped and simply supported boundary conditions. Finally, the effects of aspect ratio, thickness-to-length ratio, boundary conditions, transverse load, and length scale parameter are studied in detail. The results showed that by rising the length scale-to-thickness ratio, the influence of the grading index on the deflection decreased.

在本文中，基于改进的耦合应力理论，已经考虑了矩形功能梯度纳米板在均匀横向载荷下的弯曲分析。使用汉密尔顿原理，基于高阶剪切变形理论推导了控制方程。结合方程组使用动态松弛方法结合有限差分离散化技术求解固定和简单支持的边界条件。最后，详细研究了长宽比，厚度与长度之比，边界条件，横向载荷和长度比例参数的影响。结果表明，通过增加长度标度/厚度比，分级指数对挠度的影响减小了。