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Structural Engineering and Mechanics Volume 55, Number 4, August25 2015 , pages 743-763 DOI: https://doi.org/10.12989/sem.2015.55.4.743 |
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A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium |
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Khadidja Aissani, Mohamed Bachir Bouiadjra, Mama Ahouel
and Abdelouahed Tounsi
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| Abstract | ||
| This work presents a new nonlocal hyperbolic shear deformation beam theory for the static, buckling and vibration of nanoscale-beams embedded in an elastic medium. The present model is able to capture both the nonlocal parameter and the shear deformation effect without employing shear correction factor. The nonlocal parameter accounts for the small size effects when dealing with nanosize structures such as nanobeams. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanoscale-beam are obtained using Hamilton\'s principle. The effect of the surrounding elastic medium on the deflections, critical buckling loads and frequencies of the nanobeam is investigated. Both Winklertype and Pasternak-type foundation models are used to simulate the interaction of the nanobeam with the surrounding elastic medium. Analytical solutions are presented for a simply supported nanoscale-beam, and the obtained results compare well with those predicted by the other nonlocal theories available in literature. | ||
| Key Words | ||
| nonlocal theory; nanobeam; elastic medium | ||
| Address | ||
| Khadidja Aissani: Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, Faculté de Technologie, Département de Génie Cvil, Algérie Mohamed Bachir Bouiadjra: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria Mama Ahouel: Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria Abdelouahed Tounsi: Algerian National Thematic Agency of Research in Science and Technology (ATRST), Algeria | ||