Rethinking Prototyping

4 Cellular Structure: Exploring Topological and Geometric Variation

Where bending action is triggered in a material system, certain geometric values become necessary inputs to the form-finding 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.

4.1 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 simulates the tensile condition in warp, weft and shear behaviour, as well as defines 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 characterisations 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.

Fig. 4 Comparison of spring topology between simulating a surface and a linear element with bending stiffness (Ahlquist 2013)

4.2 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 form-finding 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.

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 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.

Fig. 5 Rules for bending-active cell structure (Ahlquist, 2012)

Fig. 6 Form-finding sequence for cells in spring-based modelling and simulation environment, programmed in Processing (Java) by Sean Ahlquist (Ahlquist, 2012)

5 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 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.

References

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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).

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From Shape to Shell: A Design Tool to Materialise FreeForm Shapes Using Gridshell Structures

Lionel du Peloux, Olivier Baverel, Jean-François Caron and Frederic Tayeb

Abstract This paper introduces and explains the design process of a gridshell in composite materials built in Paris in 2011 for the festival Soliday. A brief introduction presents the structural concept and the erection methodology employed. It explains why composite materials are relevant for such applications. Following this practical case, the whole process from 3D shape to real-shell is then detailed. Firstly, the shape is rationalized and optimized to smooth local curvature concentrations. Secondly, a specific computing tool is used to mesh the surface according to the compass method. This tool allows designers to look for optimal mesh orientations regarding the elements curvature. Finally, a full structural analysis is performed to find the relaxed shape of the grid and check its stability, strength and stiffness under loads. The authors conclude on the overall relevance of such structures.

Olivier Baverel

UR Navier, Ecole des Ponts ParisTech, Champs-sur-Marne, France

ENSAG, Grenoble, France

Jean-François Caron, Frederic Tayeb

UR Navier, Ecole des Ponts ParisTech, Champs-sur-Marne, France

Lionel du Peloux

UR Navier, Ecole des Ponts ParisTech, Champs-sur-Marne, France

T/E/S/S, Paris, France

1 Introduction

The emergence of gridshell structures – intensively studied by the German architect Frei Otto – is a major step in the development of complex shapes in AEC (Architecture, Engineering and Construction). Since the 1970s this structural concept has led to emblematic realizations (Mannheim [Happold and Lidell 1975], Downland [Harris et al 2003], Savill, Hanovre [Ban 2006]). They have shown that beyond their architectural potential, gridshells are well suitable for complex shape materialization because of their intrinsic geometric rationality.

However, the very few number of gridshells constructed up to now attests that they are quite tricky to design compared to standard buildings. Architects and engineers would face both demanding conceptual knowledge in 3D geometry, form-finding techniques, non-linear behaviour, large-scale deformations, permanent bending stresses, etc. and real lack of tools dedicated to their design.

This paper presents a computing tool based on Rhinoceros & Grasshopper that aims at meshing NURBS surfaces with the compass method. This tool also includes a one-way interface for GSA (a structural analysis software from Oasys) to perform the structural analysis of the resulting grid. Thereby, this tool introduces shape-driven design of gridshells. Following a case study – the construction of the first composite gridshell to host people – a methodology to design these shape-driven structures is proposed. Finally, future prospects to their development are discussed.

1.1 Gridshell: Concept, Erection Process, Materials
Concept

A gridshell is a structure, which behaves like a shell but is made of a grid. Thus, the material is not spread continuously as shells, but it is organized in a discrete grid pattern. Like shells, gridshells derive their stiffness from their double curvature shape. These structures can cross large spans with very few materials. They offer a rich and voluble lexicon to express blob-shapes.

Erection Process

Usually, the grid morphology is not trivial and leads to design numerous costly and complex joints. To overcome this issue, an original and innovative erection process was developed that takes advantage of the flexibility inherent to slender elements.

A regular planar grid made of long continuous linear members is built on the ground (Fig. 1). The elements are pinned together so the grid has no in-plane shear stiffness. Thus, the grid can accommodate large-scale deformations during erection (Fig. 2). Then the grid is bent elastically to its final shape (Fig. 3). Finally, the grid is frozen in the desired shape with a third layer of bracing members (Fig. 4). The grid becomes a shell and the structure’s stiffness is multiplied by about 15.

Fig. 1 Regular grid on the ground

Fig. 2 Grid erection

Fig. 3 Erected grid

Fig. 4 Grid triangulation

Material Flexibility for Structural Rigidity

Composite materials like glass fibre reinforced polymer (GFRP) could favourably replace wood in this case where both resistance and bending ability of the material is sought. Thus, the structure’s stiffness derives from its geometric curvature and not from the material’s intrinsic rigidity. Moreover, using synthetic materials free us from the painful problematic of wood joining and wood durability (Douthe, Caron and Baverel 2010).

High Tech & Low Cost

Though gridshells require high-tech design techniques, they seem to be a low-cost way to materialise non-standard morphologies (200€/m2), because of their geometric rationality. The project complexity is shifted upstream.