Effects of different loading on the bifurcation of annular elastic rods: theory vs. experiments

Matteo Gaibotti, Davide Bigoni, Arsenio Cutolo, Massimiliano Fraldi, Andrea Piccolroaz
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Abstract

The bifurcation problem of a circular Euler-Bernoulli rod subject to a uniform radial force distribution is investigated under three distinct loading conditions: (i.) hydrostatic pressure, (ii.) centrally-directed, and (iii.) dead load. Previous studies on this apparently 'familiar' structural problem have yielded controversial results, necessitating a comprehensive clarification. This study shows that results previously labelled as 'correct' or 'wrong' simply refer to different external constraints, whose presence becomes necessary only for the two latter loads, (ii.) and (iii.). Moreover, the paper presents the first experimental realization of a circular rod subjected to centrally-directed loads. The experimental findings align with the theoretical predictions and show the exploitation of a new type of load acting on a continuous structural element. The feasibility of this load is demonstrated through the use of inextensible cables and opens the way to applications in flexible robotics when cables are used for actuation.
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不同加载对环形弹性杆分叉的影响:理论与实验
在三种不同的加载条件下,研究了受均匀径向力分布作用的圆形欧拉-伯努利杆的分叉问题:(i.) 静水压力、(ii.) 中心定向和 (iii.) 死载荷。以前对这一看似 "熟悉 "的结构问题进行的研究得出了有争议的结果,因此有必要进行全面澄清。本研究表明,以前被称为 "正确 "或 "错误 "的结果仅仅是指不同的外部约束,只有后两种荷载(ii.)和(iii.)才需要外部约束。此外,本文首次在实验中实现了圆棒受中心定向载荷的作用。实验结果与理论预测相吻合,并显示了作用在连续结构元件上的新型载荷的利用。通过使用不可拉伸的缆绳,证明了这种负载的可行性,并为缆绳用于驱动时在柔性机器人技术中的应用开辟了道路。
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