单层石墨烯片的非线性板模型  

A nonlinear plate theory for the monolayer graphene

作　　者：黄坤[1] 殷雅俊[2] 吴继业[3] 

机构地区：[1]昆明理工大学土木工程学院工程力学系,昆明650500 [2]清华大学航天航空学院工程力学系,北京100084 [3]南京工业大学力学部,南京211816

出　　处：《物理学报》2014年第15期314-319,共6页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11272175;11072125);江苏省自然科学基金(批准号:BK20130910)资助的课题~~

摘　　要：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.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.

关 键 词：单层石墨烯 非线性本构关系 板理论 RITZ法 

分 类 号：O469[理学—凝聚态物理]