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Polynomial-exponential integral shear deformable theory for static stability and dynamic behaviors of FG-CNT nanobeams

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Abstract

In this work, we are interested in studying bending, buckling stability, and dynamic behaviors of functionally graded nanobeams reinforced by carbon nanotubes (FG-CNTRC) by a novel shear deformation theory. This model is simple and efficient based on the new polynomial-exponential integral shear deformation theory including the effect of size taking into account the effects of the Winkler–Pasternak elastic foundations. The polynomial-exponential transverse shear function is incorporated to better represent a new displacement field that includes indeterminate integral terms. It is presumed that the material possessions of FG-CNTRC are diverse along the thickness direction employing distinct four distributions of carbon nanotubes (NT-CNTs). The nonlocal elasticity offered by Eringen is used to involve size effects in this approach. The impacts of numerous factors such as the volume fraction of CNTs, the nonlocality, and the impacts of the elastic foundation on the response of the FG-CNTRC beams are examined.

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Authors and Affiliations

  1. Smart Structures Laboratory, University of Ain Témouchent, 46000, Ain Témouchent, Algeria

    Mokhtar Ellali

  2. Department of Civil Engineering, University Tahri Mohamed of Bechar, 08000, Bechar, Algeria

    Mokhtar Bouazza

  3. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, 21589, Jeddah, Saudi Arabia

    Ashraf M. Zenkour

  4. UMR 8107, Mechanics Laboratory of Lille, CNRS, University of Lille 1, 59655, Villeneuve d’Ascq, France

    Noureddine Benseddiq

  5. Laboratory of Materials and Hydrology (LMH), University of Sidi Bel Abbes, 22000, Sidi Bel Abbes, Algeria

    Mokhtar Bouazza

  6. Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh, 33516, Egypt

    Ashraf M. Zenkour

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  1. Mokhtar Ellali
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Software and draft preparation, ME, Methodology, supervision and writing-original, MB; writing—review and editing, AMZ; visualization and investigation, NB. All authors have read and agreed to the published version of the manuscript.

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Ellali, M., Bouazza, M., Zenkour, A.M. et al. Polynomial-exponential integral shear deformable theory for static stability and dynamic behaviors of FG-CNT nanobeams. Arch Appl Mech (2024). https://doi.org/10.1007/s00419-024-02582-w

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