摘要
基于对Lenosky碳-碳共价键作用势连续化得到的单层石墨烯的势能和Hamilton原理,导出了单层石墨烯的动力学方程.使用该数学模型及Galerkin方法,研究了矩形单层石墨烯片的静力挠曲问题.结果显示,石墨烯片的几何尺寸较小时,弯曲刚度对结构的受力影响较大,可用板理论来描述;随着结构尺寸的增大,弯曲刚度的影响迅速降低;当矩形石墨烯片的短边尺寸大于10 nm时,可以忽略弯曲刚度对结构的影响,使用薄膜理论来描述单层石墨烯的力学性质.
In this paper, the equations of motion for a monolayer graphene are obtained by a continuum limit form of elastic energy of the Lenosky C--C covalent bond and Hamilton principle. Using the equations and Galerkin method the static bending of a rectangular monolayer graphene is investigated. It is found that the bending stiffness has a significant effect on the Mechanical Characteristics of the grapheme. The graphene may be described by a plate when the graphene size is small, but the effect of bending stiffness will quickly decrease accompanying the size increment of the graphene.When the short side dimension is greater than 10 nm for a rectangular monolayer graphene, the bending stiffness may be neglected and a thin film model is a good agreement with the monolayer graphene.
出处
《力学学报》
EI
CSCD
北大核心
2014年第6期905-910,共6页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金资助项目(11272175
11072125)~~
关键词
单层石墨烯
曲率弹性能
运动方程
板
薄膜
monolayer graphene,curvature elastic energy,equations of motion,plate,thin film
