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Geomechanics and Engineering Volume 16, Number 3, October30 2018, pages 257-271 DOI: http://dx.doi.org/10.12989/gae.2018.16.3.257 |
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Investigation of influence of homogenization models on stability and dynamic of FGM plates on elastic foundations |
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Tewfik Mehala, Zakaria Belabed, Abdelouahed Tounsi and O. Anwar Bég
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| Abstract | ||
| In this paper, the effect of the homogenization models on buckling and free vibration is presented for simply supported functionally graded plates (FGM) resting on elastic foundation. The majority of investigations developed in the last decade, explored the Voigt homogenization model to predict the effective proprieties of functionally graded materials at the macroscopic-scale for FGM mechanical behavior. For this reason, various models have been used to derive the effective proprieties of FGMs and simulate thereby their effects on the buckling and free vibration of FGM plates based on comparative studies that may differ in terms of several parameters. The refined plate theory, as used in this paper, is based on dividing the transverse displacement into both bending and shear components. This leads to a reduction in the number of unknowns and governing equations. Furthermore the present formulation utilizes a sinusoidal variation of displacement field across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton\'s principle. Analytical solutions for the buckling and free vibration analysis are obtained for simply supported plates. The obtained results are compared with those predicted by other plate theories. This study shows the sensitivity of the obtained results to different homogenization models and that the results generated may vary considerably from one theory to another. Comprehensive visualization of results is provided. The analysis is relevant to aerospace, nuclear, civil and other structures. | ||
| Key Words | ||
| buckling; vibration; FGM; plate theory; elastic foundation; homogenization models | ||
| Address | ||
| Tewfik Mehala: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria Zakaria Belabed: 1.) Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria 2.) Department of Technology, Institute of Science and Technology, Center University of Naama, Algeria Abdelouahed Tounsi: 1.) Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria 2.) Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia O. Anwar Bég: Aeronautical and Mechanical Engineering, University of Salford, Newton Building, G77, The Crescent, Salford, M54WT, England, U.K. | ||