presence is minimally impactful to the site which houses a historically-protected and decrepit stone tower from the. 1500's, as shown in Fig. 1. The design by ...
Physical and Numerical Prototyping for Integrated Bending- and Form-Active Textile Hybrid Structures
PHYSICAL AND NUMERICAL PROTOTYPING FOR INTEGRATED BENDING- AND FORM-ACTIVE TEXTILE HYBRID STRUCTURES Sean Ahlquist University of Michigan, Taubman College of Architecture and Urban Planning, Ann Arbor, USA Julian Lienhard University of Stuttgart, Institute for Building Structures and Structural Design, Stuttgart, Germany Jan Knippers University of Stuttgart, Institute for Building Structures and Structural Design, Stuttgart, Germany Achim Menges University of Stuttgart, Institute for Computational Design, Stuttgart, Germany INTRODUCTION This paper describes research for the development and implementation of a functionally and structurally intricate textile hybrid architecture, entitled M1, built in Monthoiron, France as a part of the La Tour de l’Architecte complex. The term textile hybrid stands for the mutual exchange of structural action between bending- and form-active systems based on textile material behaviour. The implementation of such a structural logic is critical to this particular project as its presence is minimally impactful to the site which houses a historically-protected and decrepit stone tower from the 1500’s, as shown in Fig. 1. The design by Leonardo da Vinci employed an innovative buttressing system to structure the tower without a significant foundation. The buttresses have since been scavenged from the site, though the M1 structure seeks a minimal footprint to protect areas where traces of the original buttressing structure still exist.
Figure 1: Stone Tower and M1 Textile Hybrid at La Tour de l’Architecte, Monthoiron, France; (Photos and drawings provided by Christian Armbruster, 2011; Ahlquist and Lienhard, 2012) To explore the complexities for minimal site imposition, lightweight material deployment and spatial differentiation, a set of multi-scalar and multi-modal prototyping procedures are developed. In both physical and numerical simulation, data towards eventual full-scale implementation is cumulatively compiled and calibrated, interleaving aspects of topology, material specification, force distribution and geometry. This paper defines prototyping as the interplay between modes of design in physical form-finding, approximated simulation through spring-based methods, and finite element analysis to form, articulate and materialise the textile hybrid structure. A particular feature in the exchange between and within these modes of design is the consideration of geometric input as a critical variable in the formfinding of bending-active behaviour. MULTI-HIERARCHICAL TEXTILE HYBRID The M1 textile hybrid project is formed via a multi-hierarchical arrangement of glass-fibre reinforced polymer (GFRP) rods of varying cross-sectional dimensions which are structurally integrated with Polyester PVC membranes and 1
Physical and Numerical Prototyping for Integrated Bending- and Form-Active Textile Hybrid Structures
polyamide-based textiles. The primary structure, in Fig. 2a, is formed of a series of interleaved loops emerging from only three foundations at the boundary. The meta-scale bending-active structure morphs between gridshell-like moments and free-spans stabilized by the tensile membranes. A secondary system, in Fig. 2b, provides additional support through a series of interconnected cells embedded within the longest spanning region of the structure. Working to disintegrate the homogeneous nature of the textile membrane, the cells are differentiated in their form and orientation. The levels of hierarchy coalesce to form a clear span of up to eight meters with a total structure weighing only 60 kg, while simultaneously generating variation in all scales of the spatial architecture. Such articulation in behaviour and geometry is arrived at through an intricate exchange between various modes of formfinding. While the form-finding of tensile membrane structures considers stress harmoniously as an input variable, the form-finding of bending-active structures commonly results in varying stress distributions based on a comparatively large number of geometric and mechanical input variables. Therefore the process of form-finding in the development of bending-active and, furthermore, textile hybrid structures eschews the consideration of structural optimisation. Aligning all input variables to form a functioning equilibrium, which satisfies both mechanical behaviour and contextual constraints, becomes the challenge within the form-finding processes and overall design framework. Due to this unique combination of freedom and complexity, it is shown through this research that a single computational technique alone does not offer the necessary flexibility and insight for developing textile hybrid structures. Rather, the combination and integration of multiple modes and techniques of design into a structured framework is shown to be necessary for the exploration and rationalization of complex textile hybrid structures.
Figure 2: Multi-hierarchical textile hybrid system; (Ahlquist and Lienhard, 2012) These modes of design, in prototyping through form-finding, include physical models, spring-based computational studies and finite element analysis. Via physical experiments, specifications of topology and approximations of geometry are derived. Through spring-based modelling, also referred to as mass-spring methods or particle systems, variation is generated in the interactions between bending resistance and tensile forces (Ahlquist et al 2013). In finite element analysis, fixed topological arrangements are inputs for exploration of specific mechanical relationships, force equilibria and further structural investigations (Lienhard et al 2012). Each avenue serves to advance and articulate design aspects of the textile hybrid while also establishing the degree of fidelity towards the overall design framework. PROTOTYPING FRAMEWORK FOR TEXTILE HYBRID SYSTEMS For designing a system formed of structural action, it can be decomposed into parameters of topology, structural forces, and materiality. Fig. 3 unravels these groups of parameters as they would be addressed within a spring-based modelling and simulation environment. Topology specifies the count, type and associations of all elements within the system. Force describes the primary internal stresses which the system will undergo, in this case tensile, compressive and bending actions. Materiality defines input parameters relevant to a material’s structural performance, while also translating values for computational or scaled behaviour into specific material definitions for fabrication and assembly. By distinguishing these parameters, particular relationships can be explored and exploited in their influence to material behaviour as it forms force-active spatial architectures (Ahlquist and Menges 2011). This research describes the relationship between these aspects of material behaviour and relevant modes of design in physical form-finding, springbased numerical methods, and simulation using finite element analysis.
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Physical and Numerical Prototyping for Integrated Bending- and Form-Active Textile Hybrid Structures
Physical Form-finding and Computational Means While physical form-finding provides agile means for studying relationships of materiality and structural action within a single model, there is a limitation for any such study to predict behaviour beyond its own specific arrangement and scale. With a homogeneous material description, bending-active behaviour is generally scale-able as long as the topological input is repeated (Levien 2009). To establish a vehicle for design search, an individual study must serve as a prototypical case, projecting a design space which implies a new vocabulary for form, performance and generative means (Coyne 1990). When integrating textile behaviour into a bending-active system, the extensibility of any one prototypical constructional model becomes further limited as the structural and spatial performance of the textile shifts greatly between scales.
Figure 3: Decomposition of material behaviour for spring-based modelling and simulation; (Ahlquist 2013) While the physical prototype projects a narrow set of parametric rules and material descriptions, it can be a resource in defining fundamental logics of topology, proportion and behaviour, for further computational exploration. In this research, computational explorations occur through two venues: modelling and simulation of relative material descriptions with spring-based numerical methods, and finite element analysis defining precise mechanical (material and force) relationships. Spring-based methods calculate force based upon linear elastic stress-strain relationships (Hooke’s Law of Elasticity); using a numerical integration method such as Euler or Runge-Kutta to approximate the equilibrium of multiple interconnected springs (Kilian and Oschendorf 2005). Such methods are deployed to primarily explore varied relationships between topology and force. Both conditions are easily manipulable during the process of spring-based form-finding, enabling immediacy for feedback and ability to extract how minute manipulations affect the overall system behaviour. A fundamental layer of this research is the continued development of a modelling environment, programmed in Processing (Java) with a particle-spring library, allowing for complex topologies and force descriptions to be initially generated then actively re-modelled through an interface. Finite element methods (FEM), on the other hand, contribute to forming complex equilibrium structures in defining the complete mechanical behaviour of the system. The given necessity for simulation of large elastic deformations in order to form-find bending-active structures poses no problem to modern nonlinear finite element analysis (Fertis 2006). However, software using FEM does not serve well as an expansive design environment, specifically for textile hybrid systems due to the inability to manipulate geometry and behaviour during the form-finding process. This necessitates the input data, for the pre-processing of the simulation, to be based upon the unrolled geometry of either physical formfinding or a computational environment such as the spring-based methods described above. Though, the advantage, as well as necessity, of FEM in the development of textile hybrids, lies in the possibility of a complete mechanical description of the system. Provided that form-finding solvers are included in the software, the possibility of freely combining shell, beam, cable, coupling and spring elements, enables FEM to simulate the exact physical properties of the system in an uninterrupted mechanical description. Such means allows the FEM environment to accomplish, in a single model, the complete scope of form-finding, analysis of performance under external loads, and, finally, the unrolling and patterning for fabrication.
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Physical and Numerical Prototyping for Integrated Bending- and Form-Active Textile Hybrid Structures
CELLULAR STRUCTURE: EXPLORING TOPOLOGICAL AND GEOMETRIC VARIATION Where bending action is triggered in a material system, certain geometric values become necessary inputs to the formfinding process. In simple terms, the length of the bending-active elements must be stated prior to the initiation of the form-finding process. In physical form-finding, geometry is inextricable from topology. The components, in their count, type, and associations, carry with them their material properties. This introduces a helpful constraint in managing the complexity of searching for states of form- and bending-active equilibria. In developing the cell strategy for the M1, the physical studies define a proportional geometric logic for the bending-active aspect of the system. The exact geometry of the multi-cell array is only realized when arranged within the interleaved macro-structure. As both the region within the meta-structure and the proportional rules of the individual cell are three-dimensionally complex, the spring-based modelling environment is well suited to explore the variation of geometric inputs arranging the meso-scale cellular textile hybrid system. Modelling and Active Manipulation of Material Behaviour Within the range of linear elastic material behaviour underlying the spring-based methods, a single spring element may compute tension or compression, and, in a combined arrangement, also bending action. Bending stiffness is simulated by adding positional constraint to the nodes (particles) that form a linear element. Three commonly known methods for simulating this behaviour are: crossover, vector position and vector normal (Provot 1995; Volino 2006; Adrianessens 2001). In modelling behaviour with springs, there is a unique consideration where certain springs define only a particular aspect of material behaviour, such as shear or bending stiffness, while others simulate the totality of behaviour and display the resultant material form, such as a surface geometry or linear bending element. In defining the tensile surface of a textile hybrid system, a mesh of springs both simulate the tensile condition, in warp, weft and shear behaviour, as well as define the material surface. In simulating bending stiffness, a linear array of springs implies the material condition of an elastic element, but the springs simulating constraint at the nodes do not have any geometric representation, as shown in Fig. 4. The flexibility in which a spring may drastically shift behaviour, between tension and compression, along with how relationships of geometry and behaviour can be more gradually tuned has been implemented as the foundation of the modelling environment programmed in Processing (Java). The key capacity in this particular mode of design is how the characterizations of behaviour can be manipulated, in topology and force description, during the effort of form-finding allowing freedom to define behaviour of different material make-up and composition.
Figure 4: Comparison of spring topology between simulating a surface and a linear element with bending stiffness; (Ahlquist 2013) Transferring Relational Logics from Physical Form-finding to Computational Exploration In the M1, the array of interconnected cells serve as secondary support to the overall structural system, while, more critically, providing a means for differentiating the spatial conditions underneath the primary membrane surface. The geometries of the bending rods are calibrated to act as stiffening struts spanning between the upper and lower level of the meta-scale bending-active network. Within the cellular structure, a series of tensioned textiles further stiffen the system and serve as the media for diffusing light. The fundamental relationships between the boundary condition for the cells, the structure of an individual cell and its relation to its neighbour are most readily represented in physical formfinding studies, as shown in Fig 5. Yet, due to the complexity of those combined conditions, specifying the geometry which successfully resolves all of those parameters and constraints is more readily accomplished in the spring-based environment where active manipulation of local and global behaviours is possible. 4
Physical and Numerical Prototyping for Integrated Bending- and Form-Active Textile Hybrid Structures
The spring-based modelling environment in Processing exposes variables related to the simulation of bending stiffness. Using the vector position method, the ratio of stiffness in the springs defining the linear beam elements to the degrees of constraint in the nodes can be varied to express differing amounts overall stiffness and curvature, thus implying different material properties. The lengths of the linear beam elements are exposed locally and globally enabling for the acute management of bending-active behaviour when multiple elements interconnect. These two capacities allow for initially simple topological and geometric arrangements to be formed into the complex relationships defined by the physical cell models and made suitable to the context of the interleaved bending-active structure, as shown in Fig. 6.
Figure 5: Rules for bending-active cell structure; (Ahlquist, 2012)
Figure 6: Form-finding sequence for cells in spring-based modelling and simulation environment, programmed in Processing (Java) by Sean Ahlquist; (Ahlquist, 2012) INTERLEAVING STRUCTURE: DEVELOPING FORCE EQUILIBRIA The interleaving macro structure of the M1 exhibits how multiple modelling and simulation techniques 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 5
Physical and Numerical Prototyping for Integrated Bending- and Form-Active Textile Hybrid Structures
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. Resolving Geometry through Multiple Modes of Simulation Such freedoms afforded in physical form-finding are not readily available in computational analysis. While the springbased 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.
Figure 7: Sequence of form-finding for bending-active structure of the M1 using FEM software Sofistik; (Lienhard, 2012)
Figure 8: Comparison between physical form-finding model and computational model in Sofistik; (Photo by Ahlquist, 2013; Sofistik model by Lienhard, 2012) 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 6
Physical and Numerical Prototyping for Integrated Bending- and Form-Active Textile Hybrid Structures
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.
Figure 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.
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Physical and Numerical Prototyping for Integrated Bending- and Form-Active Textile Hybrid Structures
Figure 10: Topology map of GFRP rods for M1; (Ahlquist and Lienhard, 2012) 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.
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Physical and Numerical Prototyping for Integrated Bending- and Form-Active Textile Hybrid Structures
Figure 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. REFERENCES Adrianessens, S.M.L. and Barnes, M.R., 2001: Tensegrity spline beam and grid shell structures. Engineering Structures, 23 (2), pp. 29-36. Ahlquist, S. and Menges, A., 2011: Behavior-based Computational Design Methodologies – Integrative Processes for Force Defined Material Structures. In: Taron, J., Parlac, V., Kolarevic, B. and Johnson, J. (eds.) Proceedings of the 31st Annual Conference of the Association For Computer Aided Design In Architecture (ACADIA), Banff (Canada), October 2011, pp 82-89. Ahlquist, S., Lienhard, J., Knippers, J. and Menges, A., 2013: Exploring Material Reciprocities for Textile-Hybrid Systems as Spatial Structures. In: Stacey, M. (ed.) Prototyping Architecture: The Conference Paper, London, February 2013. London: Building Centre Trust, pp 187-210. 9
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Coyne, R.D., Rosenman, M.A., Radford, A.D., Balachandran, M. and Gero, J.S., 1990: Knowledge-Based Design Systems. Reading: Addison-Wesley Publishing Company. Levien, R. L. (2009) From spiral to spline, Dissertation, University of California, Berkeley. Kilian, A. and Ochsendorf, J., 2005: Particle-spring Systems for Structural Form Finding. Journal of the International Association for Shell and Spatial Structures, 46 (148), pp. 77-84. Fertis, D. G., 2006: Nonlinear Structural Engineering. With Unique Theories and Methods to Solve Effectively Complex Nonlinear Problems. Springer Berlin Heidelberg Lienhard, J., Ahlquist, S., Knippers, J., and Menges, A., 2012: Extending the Functional and Formal vocabulary of tensile membrane structures through the interaction with bending-active elements. In: [RE]THINKING lightweight structures, Proceedings of Tensinet Symposium, Istanbul, May 2013. (accepted, awaiting publication) Provot, X., 1995: Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior. In: Graphics Interface 95, Quebec, May 1995. pp 147-154. Volino, P. and Magnenat-Thalmann, N., 2006: Simple Linear Bending Stiffness in Particle Systems. In: Cani, M.P. and O’Brien, J. (eds.) Proceedings for Eurographics/ACM Siggraph Symposium on Computer Animation, Vienna, September 2006. Aire-la-Ville: Eurographics Association, pp. 101-105.
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