Asymptotic Gridshell

Type: Poster & Model
Year: 2016
Team: Denis Hitrec, Eike Schling
Office: Technische Universität München, Chair of Structural Design, Prof. Dr.-Ing. Rainer Barthel
Exhibition: Advances in Architectural Geometry 2016, ETH Zurich

ASYMPTOTIC GRIDSHELL
Using asymptotic lines to design curved support structures
Design proposal of a pavilion for the Structural Membranes Conference 2017 in Munich

Experimental Structures is a research studio held annually at the Chair of Structural Design, Technische Universität München. We are searching for methods to simplify the construction of double curved surfaces. Through physical and computational experiments we demonstrate new possibilities for an intelligent symbiosis of form, structure and fabrication.

Curvature of Lines on Surfaces
A line on a surface can have three types of curvature:
normal curvature, geodesic curvature and geodesic torsion
Imagine an ant walking along a surface. To follow the implied line, the ant must either walk up or downhill to follow the normal curvature; it could turn left or right to follow the geodesic curvature; or it must turn around the axis of the line to be able to stand with its legs straight on the surface – this is called the geodesic torsion. (Tang, Kilian, Bo, Wallner, Pottmann, AAG 2016)
By omitting one of the three curvature types we can create specific line networks, which have decisive advantages for the construction of curved support structures. Figure 1 shows the different types of curvature (left) and their related curve networks. Indicated in the boxes are the bending or twisting of profiles, necessary to construct such networks.

Fig.1: Shown above are specific line networks, which are based on a constant value k=0 of either their normal curvature, geodesic curvature or geodesic torsion. This has an influence on the constructibility, as indicated by the bending or twisting of the respective profiles.

Asymptotic Lines
At any point on an anticlastic surface there are two asymptotic directions. They are the direction of zero normal curvature. If we follow these directions, step by step, we can generate an asymptotic curve. This curve will only turn sideways (geodesic curvature), but never up or down (normal curvature).
Structural elements that run along asymptotic lines and are oriented orthogonally to the surface can be unrolled to become straight strips. This is a decisive advantage for fabrication and material efficiency. Furthermore, on a minimal surface, these „asymptotic strips“ always intersect at 90 degrees. This allows for a simplified construction with rectangular joints.

Fig. 2: Model of an anticlastic surface constructed with polystyrol strips, which stand orthogonal to the surface and run along asymptotic lines. All elements can be unrolled as straight strips. Modell: Jan-Ove Reindl & Eike Schling; Foto: Magdalena Jooß

Asymptotic Gridshell
Design proposal of a pavilion for the Structural Membranes Conference 2017 in Munich.The design takes a clipping of a repetitive, cubic Schwarz D minimal surface, to generate an expressive sculptural space. The support structure follows a curve network of asymptotic lines. All elements can be constructed out of straight strips with orthogonal nodes. Future research will investigate material use, structural performance and assembly methods for this new type of gridshell.

Fig. 3: Design process: Left: A minimal surface inscribed in 6 edges of a cubic cell. An asymptotic curve network can be constructed from only 5 individual elements; Middle: The Schwarz D surface is assembled from multiple cubic cells. Right: The design surface is a clipping of this Schwarz D surface.

Fig. 4: Design proposal for an Asymptotic Gridshell for the Structural Membranes Conference 2017 in Munich.
Design & Visualisation: Denis Hitrec

Fig. 5: Prototype model at scale 1:5. A network of asymptotic lines on a clipping of a minimal Schwarz D surface. The support structure was constructed from straight strips of beech veneer. All joints are identical and orthogonal. Model: Denis Hitrec; Foto: Magdalena Jooß