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Structural Engineering and Mechanics Volume 67, Number 5, September10 2018 , pages 527-544 DOI: https://doi.org/10.12989/sem.2018.67.5.527 |
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Effect of homogenization models on stress analysis of functionally graded plates |
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Sihame Ait Yahia, Lemya Hanifi Hachemi Amar, Zakaria Belabed and Abdelouahed Tounsi
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| Abstract | ||
| In this paper, the effect of homogenization models on stress analysis is presented for functionally graded plates (FGMs). The derivation of the effective elastic proprieties of the FGMs, which are a combination of both ceramic and metallic phase materials, is of most of importance. The majority of studies in the last decade, the Voigt homogenization model explored to derive the effective elastic proprieties of FGMs at macroscopic-scale in order to study their mechanical responses. In this work, various homogenization models were used to derive the effective elastic proprieties of FGMs. The effect of these models on the stress analysis have also been presented and discussed through a comparative study. So as to show this effect, a refined plate theory is formulated and evaluated. The number of unknowns and governing equations were reduced by dividing the transverse displacement into both bending and shear parts. Based on sinusoidal variation of displacement field trough the thickness, the shear stresses on top and bottom surfaces of plate were vanished and the shear correction factor was avoided. Governing equations of equilibrium were derived from the principle of virtual displacements. Analytical solutions of the stress analysis were obtained for simply supported FGM plates. The obtained results of the displacements and stresses were compared with those predicted by other plate theories available in the literature. This study demonstrates the sensitivity of the obtained results to different homogenization models and that the results generated may vary considerably from one theory to another. Finally, this study offers benchmark results for the multi-scale analysis of functionally graded plates. | ||
| Key Words | ||
| bending; stresses; FGM; plate theory; homogenization models | ||
| Address | ||
| Sihame Ait Yahia: 1) Departement de Genie Civil, Faculte des Sciences Appliquees, Universite Ibn Khaldoun, Tiaret, Algerie 2) Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria Lemya Hanifi Hachemi Amar: Laboratoire des Ressources Hydriques et Environnement, Universite Dr Tahar Moulay, BP 138 Cite En-Nasr 20000 Saida, Algerie 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 | ||