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Structural Engineering and Mechanics Volume 64, Number 2, October25 2017 , pages 145-153 DOI: https://doi.org/10.12989/sem.2017.64.2.145 |
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A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams |
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Mohamed Zidi, Mohammed Sid Ahmed Houari, Abdelouahed Tounsi,
Aicha Bessaim, and S.R. Mahmoud
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| Abstract | ||
| In this article, a novel simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded (FG) beams is proposed. The beauty of this theory relies on its 2-unknowns displacement field as the Euler- Bernoulli beam theory, which is even less than the Timoshenko beam theory. A shear correction factor is, therefore, not needed. Equations of motion are obtained via Hamilton‟s principle. Analytical solutions for the bending and free vibration analysis are given for simply supported beams. Efficacy of the proposed model is shown through illustrative examples for bending and dynamic of FG beams. The numerical results obtained are compared with those of other higher-order shear deformation beam theory results. The results obtained are found to be accurate. | ||
| Key Words | ||
| a simple 2-unknown theory; bending; vibration; functionally graded beams | ||
| Address | ||
| Mohamed Zidi, Mohammed Sid Ahmed Houari, Abdelouahed Tounsi, Aicha Bessaim: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria S.R. Mahmoud: Department of Mathematics, Faculty of Science, King Abdulaziz University, Saudi Arabia | ||