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

Ting Cao, Toni Kotnik, Joseph Schwartz

Research output: Contribution to journalArticleScientificpeer-review

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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.
Original languageEnglish
Number of pages25
JournalNexus Network Journal
Publication statusE-pub ahead of print - 11 Aug 2022
MoE publication typeA1 Journal article-refereed


  • Surface structures
  • Freeform shells
  • Descriptive geometry
  • Hyperbolic paraboloids
  • Graphic statics


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