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Modelling and Simulation in Engineering
Volume 2016, Article ID 8574129, 9 pages
Research Article

Euler-Bernoulli Nanobeam Welded to a Compressible Semi-Infinite Substrate

1Department of Sciences and Methods for Engineering (DISMI), University of Modena and Reggio Emilia, Via Amendola 2, 42122 Reggio Emilia, Italy
2Department of Engineering Enzo Ferrari (DIEF), University of Modena and Reggio Emilia, Via P. Vivarelli 10, Int 27, 41125 Modena, Italy

Received 23 December 2015; Accepted 5 October 2016

Academic Editor: Julius Kaplunov

Copyright © 2016 Pietro Di Maida and Federico Oyedeji Falope. 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.


The contact problem of an Euler-Bernoulli nanobeam of finite length bonded to a homogeneous elastic half plane is studied in the present work. Both the beam and the half plane are assumed to display a linear elastic behaviour under infinitesimal strains. The analysis is performed under plane strain condition. Owing to the bending stiffness of the beam, shear and peeling stresses arise at the interface between the beam and the substrate within the contact region. The investigation allows evaluating the role played by the Poisson ratio of the half plane (and, in turn, its compressibility) on the beam-substrate mechanical interaction. Different symmetric and skew-symmetric loading conditions for the beam are considered, with particular emphasis to concentrated transversal and horizontal forces and couples acting at its edges. It is found that the Poisson ratio of the half plane affects the behaviour of the interfacial stress field, particularly at the beam edges, where the shear and peel stresses are singular.