单层石墨烯片的非线性板模型*

摘要

In the present paper, the kinematic equation of a monolayer graphene is proposed based on a plate theory, and the nonlinear elasticity stress-strain relations are obtained from experiments. The equation includes cubic and quintic nonlinearities. The bending produced when subjected to a concentrated force at the center of the plate and the static buckling arising from edge in-plane axial uniform loads are investigated using Ritz methods for a simply-supported rectangular plate. Results suggest that the plate theory with nonlinear constitutive equation may characterize the mechanical property of a monolayer graphene appropriately, and the quintic nonlinearities have a significant effect on the bending deformations of the graphene.%基于实验得到的非线性本构关系和板理论，本文建立了包含三次及五次非线性项的单层石墨烯片的板动力学模型。针对四边简支矩形板，使用Ritz法研究了在板中点作用集中力时的静力弯曲，以及边界均匀受力时的静力屈曲问题。结果显示，基于非线性本构关系的板模型能很好的描述单层石墨烯片的力学行为，而且模型中的五次非线性项对结构的弯曲变形有显著影响。