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Structural Engineering and Mechanics Volume 62, Number 6, June25 2017 , pages 695-702 DOI: https://doi.org/10.12989/sem.2017.62.6.695 |
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A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams |
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Hichem Bellifa, Kouider Halim Benrahou, Abdelmoumen Anis Bousahla, Abdelouahed Tounsi and S.R. Mahmoud
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| Abstract | ||
| In this work, a nonlocal zeroth-order shear deformation theory is developed for the nonlinear postbuckling behavior of nanoscale beams. The beauty of this formulation is that, in addition to including the nonlocal effect according to the nonlocal elasticity theory of Eringen, the shear deformation effect is considered in the axial displacement within the use of shear forces instead of rotational displacement like in existing shear deformation theories. The principle of virtual work together of the nonlocal differential constitutive relations of Eringen, are considered to obtain the equations of equilibrium. Closed-form solutions for the critical buckling load and the amplitude of the static nonlinear response in the postbuckling state for simply supported and clamped clamped nanoscale beams are determined. | ||
| Key Words | ||
| nanobeams; postbuckling; nonlocal elasticity | ||
| Address | ||
| Hichem Bellifa, Kouider Halim Benrahou, Abdelmoumen Anis Bousahla, Abdelouahed Tounsi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria Abdelmoumen Anis Bousahla, Abdelouahed Tounsi: Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes, Algeria Abdelmoumen Anis Bousahla: Centre Universitaire de Relizane, Algerie S.R. Mahmoud: Department of Mathematics, Faculty of Science, King Abdulaziz University, Saudi Arabia S.R. Mahmoud: Mathematics Department, Faculty of Science, University of Sohag, Egypt | ||