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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
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    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).
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    Cited by:

    1. Didier Samayoa & Liliana Alvarez-Romero & José Alfredo Jiménez-Bernal & Lucero Damián Adame & Andriy Kryvko & Claudia del C. Gutiérrez-Torres, 2024. "Torricelli’s Law in Fractal Space–Time Continuum," Mathematics, MDPI, vol. 12(13), pages 1-13, June.
    2. Eduardo Reyes de Luna & Andriy Kryvko & Juan B. Pascual-Francisco & Ignacio Hernández & Didier Samayoa, 2024. "Generalized Kelvin–Voigt Creep Model in Fractal Space–Time," Mathematics, MDPI, vol. 12(19), pages 1-13, October.

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