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Mathematical Problems in Engineering
Volume 2015, Article ID 495095, 8 pages
Research Article

A Fully Gradient Model for Euler-Bernoulli Nanobeams

1Department of Structures for Engineering and Architecture, Via Claudio 25, 80121 Naples, Italy
2Department of Civil and Mechanical Engineering, University of Cassino and Southern Lazio, Via G. Di Biasio 43, 03043 Cassino, Italy

Received 1 April 2015; Revised 31 August 2015; Accepted 2 September 2015

Academic Editor: Fumihiro Ashida

Copyright © 2015 Raffaele Barretta et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A fully gradient elasticity model for bending of nanobeams is proposed by using a nonlocal thermodynamic approach. As a basic theoretical novelty, the proposed constitutive law is assumed to depend on the axial strain gradient, while existing gradient elasticity formulations for nanobeams contemplate only the derivative of the axial strain with respect to the axis of the structure. Variational equations governing the elastic equilibrium problem of bending of a fully gradient nanobeam and the corresponding differential and boundary conditions are thus provided. Analytical solutions for a nanocantilever are given and the results are compared with those predicted by other theories. As a relevant implication of applicative interest in the research field of nanobeams used in nanoelectromechanical systems (NEMS), it is shown that displacements obtained by the present model are quite different from those predicted by the known gradient elasticity treatments.