Beam bending and Λ-fractional analysis

K.A. Lazopoulos; A.K. Lazopoulos; K.A. Lazopoulos; A.K. Lazopoulos

doi:10.3934/matersci.2023034

AIMS Materials Science

2023, Volume 10, Issue 4: 604-617. doi: 10.3934/matersci.2023034

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Beam bending and Λ-fractional analysis

K.A. Lazopoulos ^{1
,
,},
A.K. Lazopoulos ²

1.
14 Theatrou Str., Rafina, 19009 Greece
2.
Mathematical Sciences Department, Hellenic Army Academy, Vari, 16673 Greece

Received: 04 June 2023 Revised: 25 June 2023 Accepted: 27 June 2023 Published: 31 July 2023

Since the global stability criteria for Λ-fractional mechanics have been established, the Λ-fractional beam bending problem is discussed within that context. The co-existence of the phase phenomenon is revealed, allowing for elastic curves with non-smooth curvatures. The variational bending problem in the Λ-fractional space is considered. Global minimization of the total energy function of beam bending is necessarily applied. The variational Euler-Lagrange equation yields an equilibrium equation of the elastic curve, with the simultaneous possible corners being expressed by Weierstrass-Erdmann corner conditions.
- Λ-fractional derivative,
- Λ-fractional space,
- initial space,
- local stability,
- global stability,
- coexistence of phases,
- elastic curve,
- beam bending
Citation: K.A. Lazopoulos, A.K. Lazopoulos. Beam bending and Λ-fractional analysis[J]. AIMS Materials Science, 2023, 10(4): 604-617. doi: 10.3934/matersci.2023034

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Abstract

Since the global stability criteria for Λ-fractional mechanics have been established, the Λ-fractional beam bending problem is discussed within that context. The co-existence of the phase phenomenon is revealed, allowing for elastic curves with non-smooth curvatures. The variational bending problem in the Λ-fractional space is considered. Global minimization of the total energy function of beam bending is necessarily applied. The variational Euler-Lagrange equation yields an equilibrium equation of the elastic curve, with the simultaneous possible corners being expressed by Weierstrass-Erdmann corner conditions.

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