A modified model for simply supported ultrathin films

A modified model of simply supported ultrathin film for incorporating the surface effects and geometrically nonlinear conditions is proposed on basis of Kirchhoff's hypothesis. The governing equations and non-classical boundary conditions are derived via using Hamilton's principle. The residual membrane force and bending moment, in which the contributions of surface stresses and nonlinear terms are taken into account, are explicitly expatiated. Comparison between the modified model and conventional plate theory is also given. Using the simply supported bending strip-like film as an example, results indicate that the mechanical behaviors of the film are size-dependent when the thickness of the film is nanometer.