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The small length scale effect for a non-local cantilever beam: a paradox solved

Challamel, N. and Wang, C. M. (2008) The small length scale effect for a non-local cantilever beam: a paradox solved. NANOTECHNOLOGY, 19 (34).

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Non-local continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with microstructures or nanostructures. This paper presents some simplified non-local elastic beam models, for the bending analyses of small scale rods. Integral-type or gradient non-local models abandon the classical assumption of locality, and admit that stress depends not only on the strain value at that point but also on the strain values of all points on the body. There is a paradox still unresolved at this stage: some bending solutions of integral-based non-local elastic beams have been found to be identical to the classical (local) solution, i.e. the small scale effect is not present at all. One example is the Euler-Bernoulli cantilever nanobeam model with a point load which has application in microelectromechanical systems and nanoelectromechanical systems as an actuator. In this paper, it will be shown that this paradox may be overcome with a gradient elastic model as well as an integral non-local elastic model that is based on combining the local and the non-local curvatures in the constitutive elastic relation. The latter model comprises the classical gradient model and Eringen's integral model, and its application produces small length scale terms in the non-local elastic cantilever beam solution.

Item Type:Article
Subjects:Material Science > Nanofabrication processes and tools
Engineering > Nanotechnology applications in civil engineering
Material Science > Nanostructured materials
ID Code:6310
Deposited By:IoN
Deposited On:17 Dec 2009 11:52
Last Modified:17 Dec 2009 11:52

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