Thin plate theory including surface effects

Abstract

In the paper, a general thin plate theory including surface effects, which can be used for size-dependent static and dynamic analysis of plate-like thin film structures, is proposed. This theory is a modification and generalization of the thin plate model in [Lim, C.W., He, L.H., 2004. Size-dependent nonlinear response of thin elastic films with nanoscale thickness. Int. J. Mech. Sci. 46, 1715–1726]. With the general theory, the governing equations of Kirchoff and Mindlin plate models including surface effects are derived, respectively. Some numerical examples are provided to verify the validities of the theory.