Fractional Euler-Bernoulli Model
dimensional analysis and applications
DOI:
https://doi.org/10.5540/03.2025.011.01.0400Palabras clave:
Euler-Bernoulli, Timoshenko-Ehrenfest, ANSYS, solução fracionáriaResumen
A generalized fractional solution, presenting dimensional analysis, is proposed for the Euler-Bernoulli beam model in the case of a simply supported beam subjected to a uniformly distributed static load. This solution is used to evaluate and identify the shear effects, covered by the Timoshenko-Ehrenfest solution, as well as the effects on the deflection of the stress concentration in the supports of the aforementioned beam. The shear effects are evaluated by adjusting the parameter α incorporated in the fractional Euler-Bernoulli solution with the Timoshenko-Ehrenfest solution. The evaluation of the effects of supports is done by adjusting the fractional Euler-Bernoulli solution with the solution obtained from a linear analysis carried out in the ANSYS software. The adjustment, in both cases, is made by taking the maximum deflection as a reference.
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