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Structural Engineering and Mechanics Volume 69, Number 2, January10 2019 , pages 231-241 DOI: https://doi.org/10.12989/sem.2019.69.2.231 |
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An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models |
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Lazreg Hadji, Nafissa Zouatnia and Fabrice Bernard
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| Abstract | ||
| In this paper, a new higher order shear deformation model is developed for static and free vibration analysis of functionally graded beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. Different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. In addition, the effect of different micromechanical models on the bending and free vibration response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present higher-order shear deformation model, the equations of motion are derived from Hamilton\'s principle. Navier type solution method was used to obtain displacement, stresses and frequencies, and the numerical results are compared with those available in the literature. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, micromechanical models, mode numbers, and geometry on the bending and natural frequencies of imperfect FG beams. | ||
| Key Words | ||
| functionally graded materials; bending; free vibration; micromechanical models; porosity | ||
| Address | ||
| Lazreg Hadji: 1) Laboratory of Geomatics and Sustainable Development, Ibn Khaldoun University of Tiaret, Algeria 2) Department of Civil Engineering, Ibn Khaldoun University, BP 78 Zaaroura, 14000 Tiaret, Algeria Nafissa Zouatnia: 1) Department of Civil Engineering, Laboratory of Structures, Geotechnics and Risks (LSGR), Hassiba Benbouali University of Chlef, BP 151, Hay Essalam, UHB Chlef, Chlef (02000), Algeria 2) Department of Civil Engineering, Ibn Khaldoun University, BP 78 Zaaroura, 14000 Tiaret, Algeria Fabrice Bernard: University of Rennes, INSA Rennes, Laboratory of Civil Engineering and Mechanical Engineering, France | ||