Paper Title
Stress Driven Non Local Solutions for Axisymmetric Nano-Plates

Abstract
In the last years many efforts have been spent to capture small scale effects in nanostructures by using atomistic models, continuum models or hybrid models. In such frameworks, different non classical mechanics of continuum theories have been developed to take into account the atomistic discrete nature of the material at the nanoscale. Among these, it is relevant the non-local Eringen theory [1]. Starting from the Eringen model, some theories has been proposed to describe with greater accuracy the size-effects and overcome some paradoxes observed in the applications due to some models; again, in agreement with the shape of the solid, the nonlocal models has been applied to the mechanics of structures models (nano-beams, nano-plates). In this framework, the stress-driven nonlocal integral model (SDM) discussed by Romano et Barretta [2] allows to construct a mechanical model without internal mathematical contradictions by taking in to account some constraints on the displacement field which are required to obtain the exact solution of the integral field equation. In according with this model, in this study we investigate the mechanical response of an axisymmetric annular nano-plates by using the Kirchhoff plate theory. The elastodynamics problem for the nano-plate is described by the following sixth order ordinary differential equation in which the characteristic parameter L is introduced by the SDM to capture the size-dependent phenomena. The analytical solution is obtained in closed form by using hypergeometric and Meijer special functions. Some investigations on the scale parameter are presented and compared for different boundary conditions and transversal loading conditions of the nano-plate. The results show an increase of the stiffness with the increase of the size parameter with respect to the local model results. Comparisons with the corresponding numerical results obtained by [3] are in agreement with each other and suggest applying this theory to others nano-plate models and vibration analyses to furnish accurate suggestions in the design phase of nanostructures. Keywords - Stress-Driven Nonlocal Model; Kirchhoff Plates; Size Effects