On the forces that cable webs under tension can support and how to design cable webs to channel stresses

Abstract : In many applications of Structural Engineering the following question arises: given a set of forces f1, f2,. .. , fN applied at prescribed points x1, x2,. .. , xN , under what constraints on the forces does there exist a truss structure (or wire web) with all elements under tension that supports these forces? Here we provide answer to such a question for any configuration of the terminal points x1, x2,. .. , xN in the two-and three-dimensional case. Specifically, the existence of a web is guaranteed by a necessary and sufficient condition on the loading which corresponds to a finite dimensional linear programming problem. In two-dimensions we show that any such web can be replaced by one in which there are at most P elementary loops, where elementary means that the loop cannot be subdivided into subloops, and where P is the number of forces f1, f2,. .. , fN applied at points strictly within the convex hull of x1, x2,. .. , xN. In three-dimensions we show that, by slightly perturbing f1, f2,. .. , fN , there exists a uniloadable web supporting this loading. Uniloadable means it supports this loading and all positive multiples of it, but not any other loading. Uniloadable webs provide a mechanism for distributing stress in desired ways.
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Contributor : Pierre Seppecher <>
Submitted on : Thursday, July 18, 2019 - 3:20:35 PM
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Guy Bouchitté, Ornella Mattei, Graeme Milton, Pierre Seppecher. On the forces that cable webs under tension can support and how to design cable webs to channel stresses. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2019, 475 (2223), pp.20180781. ⟨10.1098/rspa.2018.0781⟩. ⟨hal-02188481⟩



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