IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i7p1162-d384844.html
   My bibliography  Save this article

Bending Analysis of Functionally Graded Nanoscale Plates by Using Nonlocal Mixed Variational Formula

Author

Listed:
  • Ashraf M. Zenkour

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
    Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt)

  • Zahra S. Hafed

    (Department of Mathematics, Faculty of Science, King Khaled University, Abha 21589, Saudi Arabia)

  • Ahmed F. Radwan

    (Department of Mathematics and Statistics, Higher Institute of Management and Information Technology, Nile for Science and Technology, Kafrelsheikh 33514, Egypt)

Abstract

This work is devoted to the bending analysis of functionally graded (FG) nano-scale plate by using the nonlocal mixed variational formula under simply supported edge conditions. According to Eringen’s nonlocal elasticity theory, the mixed formula is utilized in order to obtain the governing equations. The system of equations is derived by using the principle of virtual work. The governing equations include both the small and the mechanical effects. The impact of the small-scale parameter, aspect and thickness nano-scale plate ratios, and gradient index on the displacement and stresses are explored, numerically presented, and discussed in detail. Different comparisons are made to check the precision and validity of the bending outcomes obtained from the present analysis of FG nano-scale plates. Parametric examinations are then performed to inspect the impacts of the thickness of the plate on the by and large mechanical reaction of the practically evaluated plates. The displayed outcomes are valuable for the configuration procedures of keen structures and examination from materials.

Suggested Citation

  • Ashraf M. Zenkour & Zahra S. Hafed & Ahmed F. Radwan, 2020. "Bending Analysis of Functionally Graded Nanoscale Plates by Using Nonlocal Mixed Variational Formula," Mathematics, MDPI, vol. 8(7), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1162-:d:384844
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/7/1162/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/7/1162/
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Bekir Akgöz & Ömer Civalek, 2022. "Buckling Analysis of Functionally Graded Tapered Microbeams via Rayleigh–Ritz Method," Mathematics, MDPI, vol. 10(23), pages 1-13, November.
    2. Fatima Zohra Zaoui & Djamel Ouinas & Belkacem Achour & Mabrouk Touahmia & Mustapha Boukendakdji & Enamur R. Latifee & Ahmed A. Alawi Al-Naghi & Jaime Aurelio Viña Olay, 2022. "Mathematical Approach for Mechanical Behaviour Analysis of FGM Plates on Elastic Foundation," Mathematics, MDPI, vol. 10(24), pages 1-29, December.

    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:8:y:2020:i:7:p:1162-:d:384844. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.