Mechanistic Models for Nanobeams with Surface Stress Effects
Publication: Journal of Engineering Mechanics
Volume 144, Issue 11
Abstract
In this paper, a mechanistic model for nanobeams with surface energy effects is developed by using a variational formulation. This work is motivated by the unusual response of nanocantilevers predicted by models based on the Young-Laplace equation for surface stress. The governing equation and boundary conditions derived from the variational methods are compared with the governing equations and boundary conditions used in the Young-Laplace models and other formulations. A key difference in the shear force boundary condition is noted. Analytical solutions for simply supported, cantilevered, and fixed-fixed beams are reexamined. It is shown that the unusual behavior of nanocantilevers predicted by the Young-Laplace models is due to the shear force boundary condition used. The current formulation leads to consistent solutions for beams under different boundary conditions.
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Acknowledgments
This work was supported in part by grants from the Natural Sciences and Engineering Research Council of Canada and the Thailand Research Fund (TRF). The authors acknowledge discussions with Dr. E. de Mesquita Neto (University of Campinas, Brazil) and Dr. A. Phani (University of British Columbia, Canada).
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Published In
Journal of Engineering Mechanics
Volume 144 • Issue 11 • November 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Apr 30, 2018
Accepted: Apr 30, 2018
Published online: Aug 24, 2018
Published in print: Nov 1, 2018
Discussion open until: Jan 24, 2019
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