IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i16p3492-d1216276.html
   My bibliography  Save this article

Fractal Continuum Mapping Applied to Timoshenko Beams

Author

Listed:
  • Didier Samayoa

    (ESIME Zacatenco, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos, Mexico City 07738, Mexico)

  • Alexandro Alcántara

    (ESIME Zacatenco, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos, Mexico City 07738, Mexico)

  • Helvio Mollinedo

    (Engineering Department, Instituto Politécnico Nacional, UPIITA, Av. IPN, No. 2580, Col. La Laguna Ticoman, Gustavo A. Madero, Mexico City 07340, Mexico)

  • Francisco Javier Barrera-Lao

    (Facultad de Ingeniería, Universidad Autónoma de Campeche, Campus V, Av. Humberto Lanz, Col. ExHacienda Kalá, San Francisco de Campeche 24085, Mexico)

  • Christopher René Torres-SanMiguel

    (ESIME Zacatenco, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos, Mexico City 07738, Mexico)

Abstract

In this work, a generalization of the Timoshenko beam theory is introduced, which is based on fractal continuum calculus. The mapping of the bending problem onto a non-differentiable self-similar beam into a corresponding problem for a fractal continuum is derived using local fractional differential operators. Consequently, the functions defined in the fractal continua beam are differentiable in the ordinary calculus sense. Therefore, the non-conventional local derivatives defined in the fractal continua beam can be expressed in terms of the ordinary derivatives, which are solved theoretically and numerically. Lastly, examples of classical beams with different boundary conditions are shown in order to check some details of the physical phenomenon under study.

Suggested Citation

  • Didier Samayoa & Alexandro Alcántara & Helvio Mollinedo & Francisco Javier Barrera-Lao & Christopher René Torres-SanMiguel, 2023. "Fractal Continuum Mapping Applied to Timoshenko Beams," Mathematics, MDPI, vol. 11(16), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3492-:d:1216276
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/16/3492/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/16/3492/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Blaszczyk, Tomasz & Siedlecki, Jaroslaw & Sun, HongGuang, 2021. "An exact solution of fractional Euler-Bernoulli equation for a beam with fixed-supported and fixed-free ends," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    2. Balankin, Alexander S. & Mena, Baltasar, 2023. "Vector differential operators in a fractional dimensional space, on fractals, and in fractal continua," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    Full references (including those not matched with items on IDEAS)

    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. Li, Peiluan & Han, Liqin & Xu, Changjin & Peng, Xueqing & Rahman, Mati ur & Shi, Sairu, 2023. "Dynamical properties of a meminductor chaotic system with fractal–fractional power law operator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).

    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:11:y:2023:i:16:p:3492-:d:1216276. 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.