Smooth Poly-Hypar Surface Structures: A new approach to design freeform surfaces by combining hyperbolic paraboloids

Abstract

This dissertation introduces smooth poly-hypar surfaces, a new category of freeform surfaces, which integrates architectural forms with structural efficiency and ease of construction. As a combination of hyperbolic paraboloids (hypars), a smooth poly-hypar surface is ruled locally, while globally appearing to be continuous freeform. It achieves structural stiffness through the double curved shape, ensures bending-free behavior by smoothly connecting adjacent hypars, meanwhile indicates a relatively easy fabrication method due to being locally ruled. Based on the special geometrical and structural properties of smooth poly-hypar surfaces, the research presented in this dissertation aims to solve a conflict between the freedom of forms and the technical constraints in freeform surface design. In investigating this, it explicates the structural principles lying behind smooth poly-hypar surfaces, presents both intuitive visualizations and precise evaluations of static behaviors, and explores an operative method to design double curved freeform surfaces, which enables structural considerations to be involved from the initial design stages. Moreover, this research also shows the potential to approximate other types of freeform surfaces with smooth poly-hypar surfaces, thereby simplifying complex geometries, optimizing structural efficiencies, and reducing construction difficulties. As an extension to existing research on hypars, this dissertation makes use of graphic statics to evaluate the behavior of hypars by finding a balancing point between complex mathematical calculations and oversimplified visualizations. It concludes that the behavior of an individual hypar can be considered as a combination of a wall and a shell, with reactions only along rulings and edges. Based on this, a new solution to resist the forces at the edges of a hypar arises, which replaces rigid edge beams, and thereby resulting smooth connections between adjacent hyaprs in poly-hypar surfaces. There are two primary preconditions to ensure the bending-free behavior and global equilibrium of smooth poly-hypar surfaces: the coplanarity principle and fully supported load paths. By respecting the coplanarity principle, hypars can be joined in such a way that all intersecting rulings and edges are coplanar. Thereby the interactions between adjacent hypars are always in plane without activating bending moments. The concept of load paths is also introduced to check the global equilibrium of smooth poly-hypar surfaces. Once all load paths are supported, a smooth poly-hypar surface turns from an abstract geometry into an efficient surface structure. By following the coplanarity principle and ensuring fully supported load paths, a general method to design smooth poly-hypar surfaces is presented in this dissertation. All smooth polyhypar surfaces can be dissolved into two basic prototypes. By free arrangement of these two prototypes, following an additive sequence, various smooth poly-hypar surfaces can be generated. Through the parametrizations of these two prototypes, a smooth poly-hypar surface becomes a parametric typology, which can continuously diverge into a collection of surfaces, adopting different design contexts. To testify the design method and explore architectural potentials, smooth poly-hypar surfaces were applied in various teaching and design tasks. In several case studies, low-tech construction methods were developed, both in light-weight grid shells as well as concrete shells. The results 4 clearly show the advantages of smooth poly-hypar surfaces in construction. As a modular system, a smooth poly-hypar surface can be prefabricated as individual hypar modules, then assembled on site. Benefiting from their structural stiffness and the property of being ruled surfaces, neither grid shells nor concrete shells require scaffolding or formwork during construction. As such, smooth poly-hypar surfaces can be seen as the mediators between architectural smoothness, structural efficiency and construction expediency.