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Wind and Structures Volume 27, Number 4, October 2018 , pages 269-282 DOI: https://doi.org/10.12989/was.2018.27.4.269 |
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A refined quasi-3D hybrid-type higher order shear deformation theory for bending and Free vibration analysis of advanced composites beams |
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Mustapha Meradjah, Khaled Bouakkaz, Fatima Zohra Zaoui and Abdelouahed Tounsi
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| Abstract | ||
| In this paper, a new displacement field based on quasi-3D hybrid-type higher order shear deformation theory is developed to analyze the static and dynamic response of exponential (E), power-law (P) and sigmoïd (S) functionally graded beams. Novelty of this theory is that involve just three unknowns with including stretching effect, as opposed to four or even greater numbers in other shear and normal deformation theories. It also accounts for a parabolic distribution of the transverse shear stresses across the thickness, and satisfies the zero traction boundary conditions at beams surfaces without introducing a shear correction factor. The beam governing equations and boundary conditions are determined by employing the Hamilton\'s principle. Navier-type analytical solutions of bending and free vibration analysis are provided for simply supported beams subjected to uniform distribution loads. The effect of the sigmoid, exponent and power-law volume fraction, the thickness stretching and the material length scale parameter on the deflection, stresses and natural frequencies are discussed in tabular and graphical forms. The obtained results are compared with previously published results to verify the performance of this theory. It was clearly shown that this theory is not only accurate and efficient but almost comparable to other higher order shear deformation theories that contain more number of unknowns. | ||
| Key Words | ||
| functionally graded beam; free vibration; bending; stress; shear deformation theory; stretching effect | ||
| Address | ||
| Mustapha Meradjah: Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Département de génie Civil, Université de Sidi Bel Abbes, Faculté de Technologie, Algeria Khaled Bouakkaz: Département de Génie Civil, Université Ibn Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algeria Fatima Zohra Zaoui: Laboratory of numerical and experimental modeling of the mechanical phenomena, Department of Mechanical Engineering, Faculty of sciences and Technology, Ibn Badis University, Mostaganem 27000, Algeria Abdelouahed Tounsi: Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Département de génie Civil, Université de Sidi Bel Abbes, Faculté de Technologie, Algeria; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia; Material and Hydrology Laboratory, Department of Civil Engineering, University of Sidi Bel Abbes, Faculty of Technology, Algeria | ||