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: . doi:10.1088/0957-4484/19/34/345703

Author Challamel, N.
Wang, C. M.
Title The small length scale effect for a non-local cantilever beam: a paradox solved
Journal name Nanotechnology   Check publisher's open access policy
ISSN 0957-4484
Publication date 2008-08-27
Year available 2008
Sub-type Article (original research)
DOI 10.1088/0957-4484/19/34/345703
Open Access Status Not yet assessed
Volume 19
Issue 34
Total pages 7
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Language eng
Abstract 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.
Keyword Nanoscience & Nanotechnology
Materials Science, Multidisciplinary
Physics, Applied
Science & Technology - Other Topics
Materials Science
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Civil Engineering Publications
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Citation counts: TR Web of Science Citation Count  Cited 158 times in Thomson Reuters Web of Science Article | Citations
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