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2019 On $\Lambda$-Elastica
Shigeki Matsutani, Hiroshi Nishiguchi, Kenji Higashida, Akihiro Nakatani, Hiroyasu Hamada
J. Geom. Symmetry Phys. 54(none): 13-35 (2019). DOI: 10.7546/jgsp-54-2019-13-35

Abstract

In this paper, we investigate a transition from an elastica to a piece-wised elastica whose connected point defines the hinge angle $\phi_0$ and we call the piece-wised elastica $\Lambda_{\phi_0}$-elastica or $\Lambda$-elastica. Such transition appears in the bending beam experiment when an elastic beam is gradually compressed and at some moment suddenly due to the rupture, the shapes of $\Lambda$-elastica appear. We construct a mathematical theory to describe the phenomena and represent the $\Lambda$-elastica in terms of the elliptic $\zeta$-function completely. Using the mathematical theory, we discuss the experimental results from an energetic viewpoint and numerically show the explicit shape of $\Lambda$-elastica. It means that this paper provides a novel investigation on elastica theory with rupture.

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Shigeki Matsutani. Hiroshi Nishiguchi. Kenji Higashida. Akihiro Nakatani. Hiroyasu Hamada. "On $\Lambda$-Elastica." J. Geom. Symmetry Phys. 54 13 - 35, 2019. https://doi.org/10.7546/jgsp-54-2019-13-35

Information

Published: 2019
First available in Project Euclid: 5 January 2020

zbMATH: 07160716
MathSciNet: MR2642065
Digital Object Identifier: 10.7546/jgsp-54-2019-13-35

Rights: Copyright © 2019 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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