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Smooth Poly-hypar Surface Structures: Freeform Shells Based on Combinations of Hyperbolic Paraboloids

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Abstract

This article presents a new approach to the design of freeform shells: smooth poly-hypar surface structures. As combinations of hyperbolic paraboloids (hypars), smooth poly-hypar surfaces are ruled locally while globally appearing to be continuous freeform. The double curvature of the individual hypar modules and the smooth connections (G1 degree) between them ensure global bending-free structural behavior, while the ruled geometrical property of these surfaces allows the relatively low cost of construction. In this article, the structural performance of smooth poly-hypar surface is calculated on two levels with vactor-based graphic statics: the distribution of internal forces within an individual hypar, and the combination of hypars. It also defines two geometrical constraints of a smooth poly-hypar surface—the coplanarity principle and load paths—which ensure the visual smoothness of the surface and limit only membrane forces transmitted within the global surface. Moreover, several built case studies are presented as applications of smooth poly-hypar surfaces in architectural design, which also show the ease of construction of this new type of double-curved freeform surface structures.

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Notes

  1. https://de-architects.com/Our-Lady-of-the-Miraculous-Medal-Church-Mexico-City.

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Acknowledgements

The authors would also like to thank Dr. Pierluigi D’Acunto, Alessandro Tellini, Prof. Zhang Hong, and Wang Yan for their supports and contributions to the manufacturing and assembly of construction prototypes mentioned in “Construction prototypes”. The fabrication of Hypar Pavilion is financed by Southeast University and ETH Zurich. The fabrication of Hypar Wave is funded by the architectural company GOA (Group of Architects). All images are by the authors unless otherwise noted.

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Authors and Affiliations

  1. Harbin Institute of Technology Shenzhen, University Town, Nanshan District, Shenzhen, 518055, China

    Ting Cao

  2. Aalto University, Otakaari 1B, 02150, Espoo, Finland

    Toni Kotnik

  3. ETH Zurich, Stefano-Franscini-Platz 1, 8093, Zurich, Switzerland

    Joseph Schwartz

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  1. Ting Cao
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  2. Toni Kotnik
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Correspondence to Ting Cao.

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Cao, T., Kotnik, T. & Schwartz, J. Smooth Poly-hypar Surface Structures: Freeform Shells Based on Combinations of Hyperbolic Paraboloids. Nexus Netw J 25, 439–463 (2023). https://doi.org/10.1007/s00004-022-00624-w

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