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Steel and Composite Structures Volume 18, Number 2, February 2015 , pages 409-423 DOI: https://doi.org/10.12989/scs.2015.18.2.409 |
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A new simple shear and normal deformations theory for functionally graded beams |
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Mohamed Bourada, Abdelhakim Kaci, Mohammed Sid Ahmed Houari and Abdelouahed Tounsi
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| Abstract | ||
| In the present work, a simple and refined trigonometric higher-order beam theory is developed for bending and vibration of functionally graded beams. The beauty of this theory is that, in addition to modeling the displacement field with only 3 unknowns as in Timoshenko beam theory, the thickness stretching effect (εz ≠ 0) is also included in the present theory. Thus, the present refined beam theory has fewer number of unknowns and equations of motion than the other shear and normal deformations theories, and it considers also the transverse shear deformation effects without requiring shear correction factors. The neutral surface position for such beams in which the material properties vary in the thickness direction is determined. Based on the present refined trigonometric higher-order beam theory and the neutral surface concept, the equations of motion are derived from Hamilton's principle. Numerical results of the present theory are compared with other theories to show the effect of the inclusion of transverse normal strain on the deflections and stresses. | ||
| Key Words | ||
| functionally graded beam; a simple third-unknown theory; normal strain; neutral surface position | ||
| Address | ||
| (1) Mohamed Bourada, Abdelhakim Kaci, Mohammed Sid Ahmed Houari, Abdelouahed Tounsi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; (2) Abdelouahed Tounsi: Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil, Algeria. | ||