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Structural Engineering and Mechanics Volume 63, Number 5, September10 2017 , pages 683-689 DOI: https://doi.org/10.12989/sem.2017.63.5.683 |
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A refined hyperbolic shear deformation theory for bending of functionally graded beams based on neutral surface position |
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Nafissa Zouatnia, Lazreg Hadji and Amar Kassoul
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| Abstract | ||
| In this paper, a hyperbolic shear deformation theory is presented for bending analysis of functionally graded beams. This theory used in displacement field in terms of thickness co-ordinate to represent the shear deformation effects and does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The governing equations are derived by employing the virtual work principle and the physical neutral surface concept. A simply supported functionally graded beam subjected to uniformly distributed loads and sinusoidal loads are consider for detail numerical study. The accuracy of the present solutions is verified by comparing the obtained results with available published ones. | ||
| Key Words | ||
| functionally graded; Navier\'s solution; physical neutral surface; virtual work; sinusoidal loads | ||
| Address | ||
| Nafissa Zouatnia and Amar Kassoul : Department of Civil Engineering, Laboratory of Structures, Geotechnics and Risks (LSGR), Hassiba Benbouali University of Chlef, Algeria, BP 151, Hay Essalam, UHB Chlef, Chlef (02000), Algeria Lazreg Hadji : Department of Civil Engineering, Ibn Khaldoun University, BP 78 Zaaroura, 14000 Tiaret, Algeria | ||