A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams

Khadra Bouafia , Abdelhakim Kaci , Mohammed Sid Ahmed Houari , Abdelnour Benzair , Abdelouahed Tounsi

Abstract

In this paper, size dependent bending and free flexural vibration behaviors of functionally graded (FG) nanobeams are investigated using a nonlocal quasi-3D theory in which both shear deformation and thickness stretching effects are introduced. The nonlocal elastic behavior is described by the differential constitutive model of Eringen, which enables the present model to become effective in the analysis and design of nanostructures. The present theory incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect, and furthermore accounts for both shear deformation and thickness stretching effects by virtue of a hyperbolic variation of all displacements through the thickness without using shear correction factor. The material properties of FG nanobeams are assumed to vary through the thickness according to a power law. The neutral surface position for such FG nanobeams is determined and the present theory based on exact neutral surface position is employed here. The governing equations are derived using the principal of minimum total potential energy. The effects of nonlocal parameter, aspect ratio and various material compositions on the static and dynamic responses of the FG nanobeam are discussed in detail. A detailed numerical study is carried out to examine the effect of material gradient index, the nonlocal parameter, the beam aspect ratio on the global response of the FG nanobeam. These findings are important in mechanical design considerations of devices that use carbon nanotubes.

Key Words

nanobeam; nonlocal elasticity theory; bending; vibration; stretching effect; functionally graded materials

Address

Khadra Bouafia — Laboratoire de Modélisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes, Algeria
Abdelhakim Kaci — Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes, Faculte de Technologie, Département de genie civil, Algeria; Department of Civil Engineering and Hydraulics, University Dr. Taher Moulay of Saida, Algeria
Mohammed Sid Ahmed Houari — Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil, Algeria; Universite Mustapha Stambouli de Mascara, Department of Civil Engineering, Mascara, Algeria
Abdelnour Benzair — Laboratoire de Modélisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes, Algeria; Algerian National Thematic Agency of Research in Science and Technology (ATRST), Algeria
Abdelouahed Tounsi — Laboratoire de Modélisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes, Algeria; Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil, Algeria; Algerian National Thematic Agency of Research in Science and Technology (ATRST), Algeria

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