Fractal Continuum Mapping Applied to Timoshenko Beams

Didier Samayoa, Alexandro Alcántara, Helvio Mollinedo, Francisco Javier Barrera-Lao and Christopher René Torres-SanMiguel ()
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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

Mathematics, 2023, vol. 11, issue 16, 1-12

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.

Keywords: Timoshenko beam; fractal beam; fractal calculus; fractional dimensions; transversal displacement (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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