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Steel and Composite Structures Volume 18, Number 2, February 2015 , pages 425-442 DOI: https://doi.org/10.12989/scs.2015.18.2.425 |
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Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect |
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Fouzia Larbi Chaht, Abdelhakim Kaci, Mohammed Sid Ahmed Houari, Abdelouahed Tounsi, O. Anwar Bég and S.R. Mahmoud
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| Abstract | ||
| This paper addresses theoretically the bending and buckling behaviors of size-dependent nanobeams made of functionally graded materials (FGMs) including the thickness stretching effect. The size-dependent FGM nanobeam is investigated on the basis of the nonlocal continuum model. 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 model 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 sinusoidal variation of all displacements through the thickness without using shear correction factor. The material properties of FGM nanobeams are assumed to vary through the thickness according to a power law. The governing equations and the related boundary conditions are derived using the principal of minimum total potential energy. A Navier-type solution is developed for simply-supported boundary conditions, and exact expressions are proposed for the deflections and the buckling load. The effects of nonlocal parameter, aspect ratio and various material compositions on the static and stability responses of the FGM nanobeam are discussed in detail. The study is relevant to nanotechnology deployment in for example aircraft structures. | ||
| Key Words | ||
| nanobeam; nonlocal elasticity theory; bending; buckling; stretching effect; functionally graded materials; navier solution; aspect ratio | ||
| Address | ||
| (1) Fouzia Larbi Chaht, Abdelhakim Kaci, Abdelouahed Tounsi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; (2) Mohammed Sid Ahmed Houari, Abdelouahed Tounsi: Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, Faculté de Technologie, Département de génie civil, Algérie; (3) O. Anwar Bég: Gort Engovation- Propulsion, Nanomechanics and Biophysics, Southmere Avenue, Bradford, UK; (4) S.R. Mahmoud: Department of Mathematics, Faculty of Science, King Abdulaziz University, Saudi Arabia; (5) S.R. Mahmoud: Mathematics Department, Faculty of Science, University of Sohag, Egypt. | ||