Type: Conference Paper
Authors: Eike Schling, Martin Kilian, Hui Wang, Jonas Schikore, Helmut Pottmann
Published in: AAG 2018. Advances in Architectural Geometry. 1. Auflage. Wien: Klein Publishing, pp. 140–165
Editors: Lars Hesselgren, Karl-Gunnar Olsson, Axel Kilian, Samar Malek, Olga Sorkine-Hornung, Chris Williams
Office: Technische Universität München, Chair of Structural Design, Prof. Dr.-Ing. Rainer Barthel
The fabrication and construction of curved beams along freeform skins pose many challenges related to their individual and complex geometry. One strategy to simplify the fabrication process uses elastic deformation to construct curved beams from flat elements. Controlling the curvature of the design surface and beams has the additional potential to create repetitive building parts with beneficial beam orientation.
We aim for strained gridshells built entirely from straight or circular lamellas of the same radius and with orthogonal nodes. The lamellas are aligned normal to a reference surface enabling an elastic assembly via their weak axis and a local transfer of loads via their strong axis.
We show that the corresponding reference surfaces are of constant mean curvature and that the network of beams bisects principal curvature directions. We introduce a new discretization of these networks as quadrilateral meshes with spherical vertex stars and present a computational workflow for the design of such structures.
The geometric advantages of these networks were key for the fabrication and assembly of a prototype structure, the Asymptotic Gridshell. We describe the complete process from design to construction, presenting further insights on the symbiosis of geometry, fabrication and load-bearing behavior.
Keywords: curved support structures, CMC-surfaces, elastic deformation, developable surfaces, strained gridshell, asymptotic curves, minimal surfaces, FEM