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Funicularity of conics
Acta Mechanica ( IF 2.3 ) Pub Date : 2021-06-11 , DOI: 10.1007/s00707-021-02987-6
Xavier Tellier , Cyril Douthe , Laurent Hauswirth , Olivier Baverel

Funicular structures can resist a given load with pure axial forces and therefore tend to use material very efficiently. One main challenge in their design is form finding, which often requires advanced numerical methods. In this article, we show analytically that a very common family of curves, conics, is funicular for a particular load case: a uniform radial load emanating from a focus. The result is a generalization of the well-known funicularity of parabolas and arcs of circles, respectively, under uniform vertical load and constant normal pressure. It can be used to design self-stressed structures by hand without the need for calculations. Portions of conics can be combined to obtain original shapes.



中文翻译:

圆锥曲线的索道性

索道结构可以用纯轴向力抵抗给定的载荷,因此往往非常有效地使用材料。他们设计中的一个主要挑战是找形,这通常需要先进的数值方法。在这篇文章中,我们通过分析展示了一个非常常见的曲线族,圆锥曲线,对于特定载荷情况是缆索状的:从一个焦点发出的均匀径向载荷。结果是在均匀垂直载荷和恒定法向压力下分别对抛物线和圆弧的众所周知的缆索性进行了推广。它可用于手动设计自应力结构,无需计算。可以组合圆锥的部分以获得原始形状。

更新日期:2021-06-11
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