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Article Dans Une Revue International Journal of Solids and Structures Année : 2023

Designing funicular grids with planar quads using i-liwein surfaces

Xavier Tellier
Cyril Douthe
Olivier Baverel
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Résumé

The design of curved structural building envelopes is challenging as it requires to account for a wide variety of constraints. In particular, the shape must be mechanically efficient, fabricable, and fit the site geometry. This article shows how a family of surfaces, called isotropic Linear Weingarten surfaces (nicknamed i-liwien), may fulfil all these constraints together, and be used as an intuitive design tool. We start by showing that these shapes are funicular for a uniform vertical load, and that principal stress lines form a conjugate net. This allows in particular for the design of gridshells with planar faces and low bending moments or for the design of self-stressed cable nets cladded by planar glass panels. We then propose a discrete model based on recent advances in discrete differential geometry. We use this model to propose a generation method from boundary curves with two additional control parameters. We demonstrate the shape potential on several examples. The application to shells, membranes, cable-nets and gridshells are discussed.
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Dates et versions

hal-04309298 , version 1 (27-11-2023)

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Xavier Tellier, Cyril Douthe, Olivier Baverel, Laurent Hauswirth. Designing funicular grids with planar quads using i-liwein surfaces. International Journal of Solids and Structures, 2023, 264, pp.112028. ⟨10.1016/j.ijsolstr.2022.112028⟩. ⟨hal-04309298⟩
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