Influence of boundary conditions on stiffness properties of a rectangular nanoplate

This paper presents the state equations of the large deflection of a plate in the framework of the classical nonlinear von Kármán theory with surface stresses taken into account. Unlike the original Gurtin-Murdoch model, the present model does not include any non-strain terms in the surface stress-strain relation. It is shown that the classical structure of the potential energy of a deformed nanoplate is preserved with the redefined elastic moduli, which contain the characteristics of a body and a surface, are introduced. This allows applying to nanoplates the known solutions and methods for macroplates. So the difference between the compressive buckling of a macroplate and of a nanoplate is put in evidence, as well as which factors influence this.