IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i7p1081-d781194.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/7/1081/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/7/1081/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Alaa A. Abdelrahman & Mohamed S. Abdelwahed & Hani M. Ahmed & Amin Hamdi & Mohamed A. Eltaher, 2023. "Investigation of Size-Dependent Vibration Behavior of Piezoelectric Composite Nanobeams Embedded in an Elastic Foundation Considering Flexoelectricity Effects," Mathematics, MDPI, vol. 11(5), pages 1-31, February.
    3. Alaa A. Abdelrahman & Hussein A. Saleem & Gamal S. Abdelhaffez & Mohamed A. Eltaher, 2023. "On Bending of Piezoelectrically Layered Perforated Nanobeams Embedded in an Elastic Foundation with Flexoelectricity," Mathematics, MDPI, vol. 11(5), pages 1-24, February.
    4. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1081-:d:781194. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.