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Effect of variable elastic foundations on static behavior of functionally graded plates using sinusoidal shear deformation

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Abstract

In the present research, static analysis of functionally graded (FG) plates resting on variables elastic foundation and subjected to mechanical loads is examined using four variable shear deformation theories The present theory utilized an undefined integral to reduce the number of the unknown from five unknown, as such higher theory and first shear theory, to only four unknown, without needing a shear corrector coefficient. The elastic medium is assumed as two-parameter elastic foundation (Pasternak-Winkler) with considering a variation in the Winkler layer along of a side of the functionally graded plate; however, the shear layer of Pasternak is supposed to be constant. The material proprieties of FG plates are supposed to vary smoothly through-the-thickness direction according to the power-law distribution. The equilibrium equations of functionally graded plates resting on the elastic foundation are derived using the principle of the virtual work. The solution of simply supported FG plates resting on two-parameter elastic foundation is obtained by using technique of Navier. Numerical results and validation for functionally plates are presented, the accuracy of the present method to predict static behavior of functionally graded plates and the influence of variable elastic foundation on stress and displacement of functionally graded plates are shown.

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Authors and Affiliations

  1. Faculty of Civil Engineering and Architecture, Civil Engineering Department, University Hassiba Benbouali of Chlef, Ouled Fares, Algeria

    Mokhtar Nebab, Hassen Ait Atmane & Riadh Bennai

  2. Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Sidi Bel Abbès, Algeria

    Hassen Ait Atmane & Abdelouahed Tounsi

  3. Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, Dhahran, Eastern Province, 31261, Saudi Arabia

    Abdelouahed Tounsi

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  1. Mokhtar Nebab
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  2. Hassen Ait Atmane
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  4. Abdelouahed Tounsi
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Nebab, M., Ait Atmane, H., Bennai, R. et al. Effect of variable elastic foundations on static behavior of functionally graded plates using sinusoidal shear deformation. Arab J Geosci 12, 809 (2019). https://doi.org/10.1007/s12517-019-4871-5

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