Influence of Surface Stresses on the Deflection of Circular Nanoplate with Two-Parameter Elastic Substrate

Abstract

. This paper presents the influence of surface energy effects on the deflection of circular nanoplate with two - parameter elastic substrate. The governing equation for axisymmetric bending of the nanoplate, based on the Gurtin - Murdoch surface elasticity theory, resting on a Winkler - Pasternak elastic foundation is derived from a variational approach based on the concept of minimum total potential energy . The analytical general solution to the governing equation is then obtained in terms of the modified Bessel functions . Finally, closed - form solutions for deflections, bending moment and transverse shear in the nanoplate subjected to normally distributed loading are presented explicitly for the boundary conditions of simple, clamped, and free edges . A set of numerical solutions are selected to demonstrate the influence of surface material parameters and the substrate moduli on the deflection and bending moment profiles of a silicon nanoplate on Winkler Pasternak foundation. It is found that the nanoplate clearly shows size-dependent behaviors, and becomes stiffer with the existence of surface stresses.