Circular Nanoplate on Elastic Nanolayer under Axisymmetric Loading and Surface Effects

Abstract

Influence of surface energy on an interaction problem between a flexible circular nanoplate and a nanolayer is examined by using a variational formulation and the GM surface theory. The nanoplate is resting in smooth contact on the supporting nanolayer, and subjected to axisymmetric vertical loadings. The normal traction at the plate–layer interface is written in terms of generalized coordinates obtained from the flexibility equations derived from Green’s function and Hankel integral transform technique. A numerical solution scheme is then implemented into a computer code, and the convergence and accuracy of the proposed solution are verified with existing solutions. A set of numerical solutions is illustrated to present an impact of the surface energy effects on this interaction problem. Both deflection and bending moment of the nanoplate show a considerable dependence on the relative plate stiffness and the surface material properties, and demonstrate the size-dependent behaviors.