TY - JOUR
T1 - Map of a Bending Problem for Self-Similar Beams into the Fractal Continuum Using the Euler–Bernoulli Principle
AU - Ochoa, Didier Samayoa
AU - Adame, Lucero Damián
AU - Kryvko, Andriy
N1 - Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2022/5
Y1 - 2022/5
N2 - The bending of self-similar beams applying the Euler–Bernoulli principle is studied in this paper. A generalization of the standard Euler–Bernoulli beam equation in the F3dH continuum using local fractional differential operators is obtained. The mapping of a bending problem for a self-similar beam into the corresponding problem for a fractal continuum is defined. Displacements, rotations, bending moments and shear forces as functions of fractal parameters of the beam are estimated, allowing the mechanical response for self-similar beams to be established. An example of the structural behavior of a cantilever beam with a load at the free end is considered to study the influence of fractality on the mechanical properties of beams.
AB - The bending of self-similar beams applying the Euler–Bernoulli principle is studied in this paper. A generalization of the standard Euler–Bernoulli beam equation in the F3dH continuum using local fractional differential operators is obtained. The mapping of a bending problem for a self-similar beam into the corresponding problem for a fractal continuum is defined. Displacements, rotations, bending moments and shear forces as functions of fractal parameters of the beam are estimated, allowing the mechanical response for self-similar beams to be established. An example of the structural behavior of a cantilever beam with a load at the free end is considered to study the influence of fractality on the mechanical properties of beams.
KW - Euler–Bernoulli bending principle
KW - Menger sponge
KW - Sierpinski carpet
KW - fractal continuum
KW - self-similar beam
UR - http://www.scopus.com/inward/record.url?scp=85129742025&partnerID=8YFLogxK
U2 - 10.3390/fractalfract6050230
DO - 10.3390/fractalfract6050230
M3 - Artículo
AN - SCOPUS:85129742025
SN - 2504-3110
VL - 6
JO - Fractal and Fractional
JF - Fractal and Fractional
IS - 5
M1 - 230
ER -