考虑表面效应的纳米矩形薄板挠度解析解  

Analytical Solution of Rectangular Plate Deflection with Surface Effects at Nanoscale

作　　者：姜礼鑫 曹高峰 林浩 

机构地区：[1]中国石油大学(华东)储运与建筑工程学院,山东青岛266580

出　　处：《吉首大学学报（自然科学版）》2015年第6期40-43,共4页Journal of Jishou University(Natural Sciences Edition)

基　　金：国家自然科学基金资助项目(11272357)

摘　　要：将表面弹性理论引入到纳米薄板承受外载荷的变形分析之中,根据薄板的小变形理论建立考虑表面效应的纳米薄板弹性微分方程.采用级数展开法,求出承受均布载荷的四边简支板、两对边承受正对称分布弯矩的四边简支板和两对边承受反对称分布弯矩的四边简支板的挠度解析解.Gurtin＇s theory on surface elasticity was introduced into the deformation analysis of a thin plate at nanoscale under external loads.With small deformation theory,the differential equation of the nanometer-sized thin plate with surface effects was established.Analytical solutions of the deflection of a plate were obtained through series expansions,including the quadrilateral simply supported plate under uniformly distributed load,the quadrilateral simply supported plate with symmetrically distributed bending moment on the two opposite sides,and the quadrilateral simply supported plate with dissymmetrically distributed bending moment on the two opposite sides.The influence of the surface effects on the deformation of the plate was demonstrated.

关 键 词：表面效应 Young-Laplace方程 表面残余应力 表面弹性 挠度 

分 类 号：O48[理学—固体物理]