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Funicularity of conics

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Abstract

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.

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Funding

This work was supported by Labex MMCD (http://mmcd.univ-parisest.fr/).

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Authors and Affiliations

  1. Laboratoire Navier, Ecole des Ponts, CNRS, Université Gustave Eiffel, 77455, Champs-sur-Marne, France

    Xavier Tellier, Cyril Douthe & Olivier Baverel

  2. Laboratoire d’Analyse et de Mathématiques Appliquées, UPEC, CNRS, UGE, Champs-sur-Marne, France

    Xavier Tellier & Laurent Hauswirth

  3. GSA/ENS Architecture, Grenoble, France

    Olivier Baverel

Authors
  1. Xavier Tellier
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  2. Cyril Douthe
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  3. Laurent Hauswirth
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  4. Olivier Baverel
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Correspondence to Xavier Tellier.

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Tellier, X., Douthe, C., Hauswirth, L. et al. Funicularity of conics. Acta Mech 232, 3179–3191 (2021). https://doi.org/10.1007/s00707-021-02987-6

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  • DOI: https://doi.org/10.1007/s00707-021-02987-6

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