Advances in nano research

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A new refined nonlocal beam theory accounting for effect of thickness stretching in nanoscale beams

  • Kheroubi, Boumediene (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Departement de Physique) ;
  • Benzair, Abdelnour (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Departement de Physique) ;
  • Tounsi, Abdelouahed (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Departement de Physique) ;
  • Semmah, Abdelwahed (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Departement de Physique)
  • Received : 2016.02.25
  • Accepted : 2016.10.28
  • Published : 2016.12.25
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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 (${\varepsilon}_z{\neq}0$) 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.

Keywords

Acknowledgement

Supported by : Algerian National Thematic Agency of Research in Science and Technology (ATRST), university of Sidi Bel Abbes (UDL SBA) in Algeria

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