On $\Lambda$-Elastica

IF 0.5 Q4 PHYSICS, MATHEMATICAL

Journal of Geometry and Symmetry in Physics Pub Date : 2019-09-04 DOI:10.7546/jgsp-54-2019-13-35

S. Matsutani, Hiroshi Nishiguchi, K. Higashida, A. Nakatani, Hiroyasu Hamada

引用次数: 0

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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在$\Lambda$ -Elastica

在本文中，我们研究了从弹性体到块形弹性体的过渡，其连接点定义了铰链角$\phi_0$;我们指的是分段弹性材料$\Lambda_{\phi_0}$ -elastica或$\Lambda$ -elastica。弯曲梁实验中出现了过渡;我们逐渐压缩弹性梁，然后突然由于断裂，$\Lambda$ -elastica的形状出现。我们构建了一个数学理论来描述这种现象，并完全用椭圆$\zeta$ -函数来表示$\Lambda$ -弹性。利用数学理论，从能量的角度讨论了实验结果，并在数值上给出了$\Lambda$ -elastica的显式形状。这意味着本文为考虑断裂的弹性力学理论提供了一个新的研究方向。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Symmetry in Physics PHYSICS, MATHEMATICAL-

CiteScore

1.50

自引率

25.00%

发文量

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On \(\Lambda\)-Elastica

Abstract