关键词： 表面效应, Young-Laplace方程, 表面残余应力, 表面弹性, 挠度

Abstract: 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.

Key words: surface effect, young-laplace equation, surface residual stress, surface elasticity, deflection