IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i13p2350-d855919.html
   My bibliography  Save this article

Calculation of Critical Load of Axially Functionally Graded and Variable Cross-Section Timoshenko Beams by Using Interpolating Matrix Method

Author

Listed:
  • Renyu Ge

    (Key Laboratory for Mechanics, Anhui Polytechnic University, Wuhu 241000, China)

  • Feng Liu

    (Key Laboratory for Mechanics, Anhui Polytechnic University, Wuhu 241000, China)

  • Chao Wang

    (Key Laboratory for Mechanics, Anhui Polytechnic University, Wuhu 241000, China)

  • Liangliang Ma

    (Key Laboratory for Mechanics, Anhui Polytechnic University, Wuhu 241000, China)

  • Jinping Wang

    (Key Laboratory for Mechanics, Anhui Polytechnic University, Wuhu 241000, China)

Abstract

In this paper, the interpolation matrix method (IMM) is proposed to solve the buckling critical load of axially functionally graded (FG) Timoshenko beams. Based on Timoshenko beam theory, a set of governing equations coupled by the deflection function and rotation function of the beam are obtained. Then, the deflection function and rotation function are decoupled and transformed into an eigenvalue problem of a variable coefficient fourth-order ordinary differential equation with unknown deflection function. According to the theory of interpolation matrix method, the eigenvalue problem of the variable coefficient fourth-order ordinary differential equation is transformed into an eigenvalue problem of a set of linear algebraic equations, and the critical buckling load and the corresponding deflection function of the axially functionally graded Timoshenko beam can be calculated by the orthogonal triangular (QR) decomposition method, which is the most effective and widely used method for finding all eigenvalues of a matrix. The numerical results are in good agreement with the existing results, which shows the effectiveness and accuracy of the method.

Suggested Citation

  • Renyu Ge & Feng Liu & Chao Wang & Liangliang Ma & Jinping Wang, 2022. "Calculation of Critical Load of Axially Functionally Graded and Variable Cross-Section Timoshenko Beams by Using Interpolating Matrix Method," Mathematics, MDPI, vol. 10(13), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2350-:d:855919
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/13/2350/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/13/2350/
    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.

    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:13:p:2350-:d:855919. 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.