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arXiv · 1909.01553

On $\Lambda$-Elastica

Shigeki Matsutani·Hiroshi Nishiguchi·Kenji Higashida·Akihiro Nakatani·Hiroyasu Hamada
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Abstract

In this paper, we investigate a transition from an elastica to a piece-wised elastica whose connected point defines the hinge angle $\phi_0$; we refer the piece-wised elastica $\Lambda_{\phi_0}$-elastica or $\Lambda$-elastica. The transition appears in the bending beam experiment; we compress elastic beams gradually and then suddenly due 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. 2019-09-04. On $\Lambda$-Elastica. https://arxiv.org/abs/1909.01553

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