Stress oriented folded structures - an optimized light weight construction principle

• Applicants: Professor Dr. Leif Kobbelt; Professor Dr.-Ing. Martin Trautz
• Subject Area: Structural Engineering, Building Informatics and Construction Operation ; Image and Language Processing, Computer Graphics and Visualisation, Human Computer Interaction, Ubiquitous and Wearable Computing
• Term: from 2015 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 269321250

Geodesic domes with their facets composed of thin sheet metal are impressive representatives of the category spatial folding structures. Due to their spherical shape, their geometrical complexity can be controlled easily. Thanks to computer-graphic methods, parametric software and interface-techniques, nowadays spatial folding structures can be generated and structurally processed as freely shaped large scale forms. By adding spatial foldings and combining them with planar surface elements a light weight system can be generated, that uses these foldings and surfaces as its basic structure or its folded core. At the same time, this basic structure can be used to approximately determine a freely shaped form. Basic materials are thin, semi-finished goods like steel-sheet or fiber-reinforced plastics. Due to innovative forming techniques, these materials are foldable and can therefore be used to establish novel light weight constructions. Parameter studies with slab-like constructions in sandwich structure with planar covers, a folded core and a constant folding geometry prove their efficiency - a high bearing capacity at a light dead weight. It is to be expected, that these quality characteristics can be optimized by adapting the geometry of the folding construction to the loading of the dominant load case. While foldings with a constant folding geometry can be generated via standard cross-linking algorithms, the generation of load-oriented foldings requires at first the calculation of the main stress. Stress trajectories, which can be determined by the calculated vector field, form the basis for the tessellation and subsequent folding. In this process, the local adaption to the loading results solely from the variation of geometric parameters like the folding frequency and the height of the folding. For instance, areas with a high loading will have an elevated folding frequency and a greater folding height than less loaded areas. By calculating the main stress of the dominant load case as well as by analyzing the load-bearing capacity of the generated folding construction, geometrical and possible physical non-linearities need to be considered. All slab and folding elements are based upon nets made of primitive surfaces, which is a favorable precondition for an efficient implementation. However, to fabricate efficiently, it is advisable to minimize the number of geometrically different elements through anti-diversification-optimization. By slight deviations from the original geometry and tolerances in the contact areas of the folding elements, groups of similar building elements can be composed. This research application aims at analyzing the basic principles and fundamental technical characteristics of a load-oriented sheet-metal light weight system. The alternating development of computer-graphical and static-constructional contents necessitates the cooperation of architecture and computer sciences research units.

• DFG Programme: Research Grants