can be used at various scales to develop an intricate structural system. The development of a bending-active system goes hand in hand with its form-finding which in contrast to membrane structures includes the consideration of a large number of geometric and material input variables. The instant feedback of mechanical behaviour possible with the construction of a physical model is indispensable in finding ways for shortcutting forces in an intricate equilibrium system. Holding an elastically bent element in your hands directly shows the spring back tendency of the system and thereby supplies direct feedback for the position and orientation of necessary constraints. When interlocking multiple elements in a physical simulation, the moment of overlap is malleable and easily adjustable. Therefore, complex but harmoniously stressed equilibrium systems may be readily found through methods in physical form-finding.
5.1 Resolving Geometry through Multiple Modes of Simulation
Such freedoms afforded in physical form-finding are not readily available in computational analysis. While the spring-based vector position method allows for the simulation of elastic bending on already curved elements, the input geometry for finite element analysis is required to be straight or planar in order for shape and residual bending stresses to be simulated accurately. The form-finding sequence shown in Fig. 7 shows the transformation of individual straight elements into a network of interconnected leaves. The resultant bending-active geometry is compared to the scaled physical model, which provides the initial topological input as shown in Fig. 8. The geometric difference measured in relative length, was found to be smaller than 3%. In the case of both the meta-scale interleaved structure and meso-scale cellular structure, the precedent for the computational explorations and analysis was established through a physically feasible system.
Fig. 7 Sequence of form-finding for bending-active structure of the M1 using FEM software Sofistik (Lienhard, 2012)
Fig. 8 Comparison between physical form-finding model and computational model in Sofistik (Photo by Ahlquist, 2013; Sofistik model by Lienhard, 2012)
5.2 Designing the Complete Mechanical Behaviour
For the M1, the importance of generating the complete mechanical behaviour was exhibited in defining the final geometry of the entire system. In physical form-finding and spring-based modelling the results are approximations due respectively to their scalar nature and the relative calculations of material behaviour. In this case, the behaviour of the forces in the tensile surfaces resolves the geometry for critical cantilever conditions. Several iterations are explored to define the geometry of the free-spanning edge beam condition, whose position is only realized in the exact equilibrium of bending stiffness in the boundary rod and tensile stress in the upper and lower membrane surfaces as shown in Fig. 9. While this is only a single feature within the textile hybrid system, it can be explored efficiently as the topology generation and form-finding process is automated as a programmed routine within the FE software Sofistik.
Fig. 9 Form-finding of the brow condition for M1, with various membrane pre-stress ratios (Lienhard, 2012)
Element length is a critical consideration not only for the effort of form generation but also for the construction of an architecture that relies upon continuous and integrated structural behaviour. In typical building structures the joining of elements is solved at crossing nodes or points where the momentum curve passes through zero. Though in bending active structures the beam elements pass through the nodes with continuous curvature as defined by bending stress. Adjoining elements at these moments is unfavourable. Rather, the locations of low bending curvature are targeted as the moments for adjoining elements. For the M1 this defined the location of crossing nodes and total length of elements, as shown in Fig. 10, in order to assure positioning the joints at the locations of smallest bending stress and, at the same time, maximizing individual element lengths.
Fig. 10 Topology map of GFRP rods for M1 (Ahlquist and Lienhard, 2012)
6 Conclusion
This research establishes the coordinated means by which aspects of material behaviour can be explored in forming complex textile hybrid structures. The critical consideration is in the priority of prototyping constructional and behavioural logics through physical form-finding. In the two cases between the meta- and meso-scale textile hybrid systems though there is a difference in the application of the physical prototype to further study. As applied to computational exploration through spring-based methods the prototype is referential to a series of topological, geometric and material descriptions. On the other hand, in furthering the design through FEM the initial physical prototype defines literal parameters of topology and geometry. The behaviour is then more accurately reformed by engaging real material values, internal pre-stresses and external forces.
Because of the complexities inherent in engaging material behaviour as a design agent, the architectures formed are often based upon repeating modules whose differentiation is shaped by a singular relation of material make-up to structural behaviour. With the development of the M1 a design framework is proposed, which allows for the development of a structurally continuous system that is based upon the alignment of multiple differentiated agents in material, force and geometric constraints.
Fig. 11 Textile Hybrid M1 at La Tour de l’Architecte in Monthoiron, France, 2012 (Ahlquist and Lienhard, 2012)
Acknowledgements
The research on bending-active structures was developed through a collaboration between the Institute for Computational Design (ICD) and the Institute for Building Structures and Structural Design (ITKE) at the University of Stuttgart. The research from the ITKE is supported within the funding directive BIONA by the German Federal Ministry of Education and Research. The student team for the M1 Project was Markus Bernhard, David Cappo, Celeste Clayton, Oliver Kaertkemeyer, Hannah Kramer, Andreas Schoenbrunner. Funding of the M1 Project was provided by DVA Stiftung, The Serge Ferrari Group, Esmery Caron Structures, and Studiengeld zurück University of Stuttgart.
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