In this study, we propose governing differential equations for beams, taking into account shear deformation, rotary inertia, locality, and surface stress effects. It is shown that the equation is both simpler and more consistent than the appropriate Bresse–Timoshenko equations extended to include locality and surface stress effects. The proposed equation contains 11 terms with respect to displacement versus 19 terms appearing in the equations that extend the Bresse–Timoshenko equations to include nonlocality and surface effects.
A Consistent Set of Nonlocal Bresse–Timoshenko Equations for Nanobeams With Surface Effects
Mines Paris Tech,
Centre des Matériaux,
CNRS UMR 7633, BP 87,
F-91003 Evry Cedex, France
Manuscript received December 14, 2011; final manuscript received January 21, 2013; accepted manuscript posted February 12, 2013; published online August 19, 2013. Assoc. Editor: Wei-Chau Xie.
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Elishakoff, I., and Soret, C. (August 19, 2013). "A Consistent Set of Nonlocal Bresse–Timoshenko Equations for Nanobeams With Surface Effects." ASME. J. Appl. Mech. November 2013; 80(6): 061001. https://doi.org/10.1115/1.4023630
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