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Advances in Nano Research Volume 4, Number 4, December 2016 , pages 251-264 DOI: https://doi.org/10.12989/anr.2016.4.4.251 |
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A new refined nonlocal beam theory accounting for effect of thickness stretching in nanoscale beams |
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Boumediene Kheroubi, Abdelnour Benzair, Abdelouahed Tounsi
and Abdelwahed Semmah
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| Abstract | ||
| In this paper, a simple and refined nonlocal hyperbolic higher-order beam theory is proposed for bending and vibration response of nanoscale beams. The present formulation incorporates the nonlocal scale parameter which can capture the small scale effect, and it considers both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements across the thickness without employing shear correction factor. The highlight of this formulation is that, in addition to modeling the displacement field with only two unknowns, the thickness stretching effect (ez=/0) is also included in the present model. By utilizing the Hamilton\'s principle and the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanoscale beam are reformulated. Verification studies demonstrate that the developed theory is not only more accurate than the refined nonlocal beam theory, but also comparable with the higher-order shear deformation theories which contain more number of unknowns. The theoretical formulation proposed herein may serve as a reference for nonlocal theories as applied to the static and dynamic responses of complex-nanobeam-system such as complex carbon nanotube system. | ||
| Key Words | ||
| nonlocal theory; stretching effect; nanobeam | ||
| Address | ||
| Boumediene Kheroubi: Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Departement de Physique, BP 89 Cite Ben M\'hidi, 22000 Sidi Bel Abbes, Algeria Abdelnour Benzair: Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Departement de Physique, BP 89 Cite Ben M\'hidi, 22000 Sidi Bel Abbes, Algeria; Algerian National Thematic Agency of Research in Science and Technology (ATRST), Algeria Abdelouahed Tounsi: Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Departement de Physique, BP 89 Cite Ben M\'hidi, 22000 Sidi Bel Abbes, Algeria; Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; Algerian National Thematic Agency of Research in Science and Technology (ATRST), Algeria Abdelwahed Semmah: Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Departement de Physique, BP 89 Cite Ben M\'hidi, 22000 Sidi Bel Abbes, Algeria; Algerian National Thematic Agency of Research in Science and Technology (ATRST), Algeria | ||