中文摘要：

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.

英文摘要：

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.