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Mathematical Modeling and Analytical Solution of Thermoelastic Stability Problem of Functionally Graded Nanocomposite Cylinders within Different Theories

Author

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  • Mahmure Avey

    (Department of Mathematical Engineering, Graduate School, Istanbul Technical University, Istanbul 34469, Turkey
    Information Technology Research and Application Center of Consultancy Board of ITRAC Center, Istanbul Commerce University, Istanbul 34445, Turkey
    Analytical Information Resources Center, UNEC-Azerbaijan State Economic University, Baku 1001, Azerbaijan)

  • Nicholas Fantuzzi

    (Department of Civil, Chemical, Environmental, and Materials Engineering, University Bologna, 40126 Bologna, Italy)

  • Abdullah Sofiyev

    (Information Technology Research and Application Center of Consultancy Board of ITRAC Center, Istanbul Commerce University, Istanbul 34445, Turkey
    Department of Civil Engineering, Engineering Faculty, Suleyman Demirel University, Isparta 32260, Turkey
    Scientific Research Centers for Composition Materials, UNEC-Azerbaijan State Economic University, Baku 1001, Azerbaijan)

Abstract

Revolutionary advances in technology have led to the use of functionally graded nanocomposite structural elements that operate at high temperatures and whose properties depend on position, such as cylindrical shells designed as load-bearing elements. These advances in technology require new mathematical modeling and updated numerical calculations to be performed using improved theories at design time to reliably apply such elements. The main goal of this study is to model, mathematically and within an analytical solution, the thermoelastic stability problem of composite cylinders reinforced by carbon nanotubes (CNTs) under a uniform thermal loading within the shear deformation theory (ST). The influence of transverse shear deformations is considered when forming the fundamental relations of CNT-patterned cylindrical shells and the basic partial differential equations (PDEs) are derived within the modified Donnell-type shell theory. The PDEs are solved by the Galerkin method, and the formula is found for the eigenvalue (critical temperature) of the functionally graded nanocomposite cylindrical shells. The influences of CNT patterns, volume fraction, and geometric parameters on the critical temperature within the ST are estimated by comparing the results within classical theory (CT).

Suggested Citation

  • Mahmure Avey & Nicholas Fantuzzi & Abdullah Sofiyev, 2022. "Mathematical Modeling and Analytical Solution of Thermoelastic Stability Problem of Functionally Graded Nanocomposite Cylinders within Different Theories," Mathematics, MDPI, vol. 10(7), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1081-:d:781194
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    References listed on IDEAS

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    1. Giovanni Tocci Monaco & Nicholas Fantuzzi & Francesco Fabbrocino & Raimondo Luciano, 2021. "Trigonometric Solution for the Bending Analysis of Magneto-Electro-Elastic Strain Gradient Nonlocal Nanoplates in Hygro-Thermal Environment," Mathematics, MDPI, vol. 9(5), pages 1-22, March.
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    Cited by:

    1. Yunhe Zou & Yaser Kiani, 2023. "Vibrations of Nonlocal Polymer-GPL Plates at Nanoscale: Application of a Quasi-3D Plate Model," Mathematics, MDPI, vol. 11(19), pages 1-18, September.
    2. Krzysztof Kamil Żur & Jinseok Kim & Junuthula N. Reddy, 2022. "Special Issue of Mathematics : Analytical and Numerical Methods for Linear and Nonlinear Analysis of Structures at Macro, Micro and Nano Scale," Mathematics, MDPI, vol. 10(13), pages 1-2, June.
    3. Doaa Atta & Ahmed E. Abouelregal & Fahad Alsharari, 2022. "Thermoelastic Analysis of Functionally Graded Nanobeams via Fractional Heat Transfer Model with Nonlocal Kernels," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    4. Mahmure Avey & Nicholas Fantuzzi & Abdullah H. Sofiyev, 2023. "Analytical Solution of Stability Problem of Nanocomposite Cylindrical Shells under Combined Loadings in Thermal Environments," Mathematics, MDPI, vol. 11(17), pages 1-21, September.

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