Shaping hybrids – Form finding of new material systems

Abstract

Form-finding processes are an integral part of structural design. Because of their limitations, the classic approaches to finding a form – such as hanging models and the soap-film analogy – play only a minor role. The various possibilities of digital experimentation in the context of structural optimisation create new options for the designer generating forms, while enabling control over a wide variety of parameters. A complete mapping of the mechanical properties of a structure in a continuum mechanics model is possible but so are simplified modelling strategies which take into account only the most important properties of the structure, such as iteratively approximating to a solution via representations of kinematic states. Form finding is thus an extremely complex process, determined both by the freely selected parameters and by design decisions.

Keywords

Bending active form finding hybrid structures simulation textile architecture

Form finding as inductive–deductive method

Form finding as an inductive–deductive method, and thus as a scientifically supported experiment in the generation of forms, fascinated architects and engineers during the 20th century and led to a variety of ways of developing architectural applications and approaches based on scientific methodologies. Well-known examples are Antoni Gaudí’s hanging models for Colònia Güell in Barcelona, Heinz Isler’s membrane models for thin-walled shell constructions and the diverse productions of Frei Otto and his team at the Institute for Lightweight Structures.¹ Simplifying somewhat, it is possible to define two classic methods for the invention of form: soap-film models and hanging models.² Up until the 1970s, spatial designs were generated using these methods above all by means of physical experiments.

Hanging models

Hanging models are a traditional approach to find forms for arch and shell structures that dissipate external influences almost exclusively through compression and with little bending or distortion. In 1670, Robert Hooke recognised the connection between the freely hanging catenary under tensile stress and its reversal as a support line for arch and vault structures under compressive stress. The employment of scientific knowledge in the assessment of the stability of a real, large-scale building took place for the first time with Giovanni Poleni’s famous physical experiments of 1748, in which he analysed the dome of St. Peter’s Basilica in Rome (Figure 1). Suspension models were used several times in the 19th century in the design of singly and doubly curved constructions; the first to do this in Germany was Heinrich Hübsch,³ who designed several churches using this method. However, the logic of the supporting structure was not utilised in the architectural design of spaces. This was done by a canon of forms worked out entirely geometrically and used to disguise the load-bearing structure.

Figure 1.

Poleni’s sketch of Hooke’s analogy between an arch and a hanging chain and his analysis of the dome of Saint Peter in Rome (1748).

It was not until Antoni Gaudí’s hanging chain model – made from threads and suspended linen bags filled with birdshot for the church of the Güell workers’ settlement (Figure 2) – that a transformation was achieved that passed rigorously from constructive to architectural form. What was striking in Gaudí’s work was the complete mapping of the entire construction in a spatial and physical hanging model with a high degree of complexity.

Figure 2.

Antoni Gaudí’s hanging chain model for the stone church of Colònia Güell (1898).

In addition to the method of experimental modelling, Gaudí, like many others, also used graphic methods for generating forms and analysing arch constructions. When it comes to frame structures, both visually intuitive geometry-based approach and the soap-film analogy enable the designer to arrive at forms without a dependence on material. However, in contrast to rope and membrane structures under tensile stress, their use is limited in this case to low-ductility structures whose geometry follows a dominant load case, usually its own weight.

Computer-aided methods have also extended this approach into digital generation of complex spatial structures, thus enabling its applicability to modern planning and implementation processes. An example of this is the development of thrust network analysis.⁴ In recent years, the applicability and user-friendliness of this method have been consistently improved.⁵ The method was the basis for the realisation of the spectacular ‘Armadillo Vault’ at the 15th International Architecture Biennale in Venice in 2016.⁶ (Figure 3) In contrast to geometry-based methods, numerical simulations of hanging model experiments in continuum mechanics require the specification of material properties. Where a bend-free form is desired, complete nonlinear calculations become necessary on account of the large deformations. The material models used purely to generate form make it possible to define the distributions of stiffness and the form derivations that can follow from them.

Figure 3.

The Armadillo Vault by Block Research Group at the 15th International Architecture Biennale in Venice – © Iwan Baan.

Soap-film models

The soap-film principle is mainly used to derive forms for tension-only membrane structures. The freedom of the membrane to bend implies an optimal exploitation of the material, but at the same time creates an indissoluble link between the form and the flow of forces. Moreover, to stabilise the form, it is necessary to preload the anticlastically or synclastically curved surface. As a consequence, a fundamentally different strategy for deriving forms arises in comparison to other support systems. Boundary conditions and a selected state of stress generate a specific spatial form from a reference plane that may be selected at will but which in mathematical terms is clearly defined. This inverse approach – compared to the standard case of structural analysis – allows geometries to be derived without recourse to material properties. From a mathematical point of view, the question is related to the topic of minimal surfaces.⁷ Supported by the development of computer technology, different numerical methods have been established in the last 40 years for deriving forms for light surface structures: the force density method, its extension as dynamic relaxation (DR) and linearisation methods derived from continuum mechanics (finite elements method with the modified Newton–Raphson method or updated reference strategy). All these approaches are based on an iterative approximation to the equilibrium geometry of the given pre-stress state. In each procedure, the difference between the actual state of tension of the approximation and the nominal state differs. The updated reference strategy, which was rigorously formulated on the basis of continuum mechanics, reflects this iterative approach in its name. It enables the consideration of isotropic and anisotropic preloading and the explicit calculation of the load deviations from the nominal preload for anisotropically preloaded membranes.² The surface discretisation can be done in any finite element type (triangles, rectangles, etc.).

Form finding as an empirical process

Form finding in the architectural design process ultimately means a superposition of theoretical and empirical forms of knowledge that are linked by induction and deduction. In practice, this means a search for forms of hybrid structural systems that arise through an interaction between physical and digital experiments, geometrical and mathematical descriptions and also individual aesthetic experiences or considerations. In this interactive process of ‘hybrid modelling’, the tools that serve presentation are just as important as the tools that enable a sufficiently precise analysis of mechanical relationships. Methods such as structural optimisation offer a very large space for numerical experimentation, a space that includes the optimisation of cross-sections, forms and topologies. The basis for this lies in the various possibilities for the numerical simulation of nonlinear structural behaviour, which allow static and dynamic analyses of systems with large deformations or stability failures, as well as the consideration of deformation-dependent actions or the behaviours of nonlinear and anisotropic materials. This makes it possible to find and optimise forms for mixed systems consisting of membranes and highly elastic bending rods^8,9 or to develop form-adaptive systems.¹⁰

Form finding through structural optimisation

Numerical methods of structure optimisation are the most general procedures for determining an optimal structural form. Its properties are derived from undetermined number of state variables, optimisation variables, target functions and boundary conditions. One decisive element of a structure optimisation with many design parameters is sensitivity analysis. By varying the design variables, it determines the degree of change of the objective function(s) and boundary conditions involved in an optimisation problem. For a form-finding problem, these variables are typically the spatial coordinates of the control nodes of the design model, for example, finite element method (FEM) nodes or non-uniform rational B-spline (NURBS) control points in the case of isogeometric analysis (IGA). All the results of a structural analysis, such as displacements, stresses or natural frequencies are suited to being treated as target functions and boundary conditions. If the minimisation of strain energy is specified as the optimisation target and a predefined mass of the structure is given, then inefficient bending states can be reduced in the course of the optimisation process in favour of a load transfer via membrane stress states. Meanwhile a structural geometry is found that exhibits maximum rigidity and minimal bending, comparable to a hanging model.² The form-finding process for elastic (pre-stressed) grid shells differs from the traditional derivation of shell or membrane surface forms on account of the specification of target geometry. This target geometry can be defined geometrically or determined by a hanging model through a balancing of forces. The final form of the elastic lattice shell is an approximation of this ‘ideal’ geometry that depends on the flexural and axial rigidity of the rods and lattice topology.¹¹

Form-finding tools for textile hybrids

With a renewed interest in structural systems that employ form finding to achieve shape and equilibrium, new computational tools have been emerging and finding their way into the research and practicing community. In the following paragraph, a brief overview of the numerical approaches that have been used so far in the context of textile hybrids is presented.

Kangaroo

A DR-inspired solver, which has gained reasonable popularity in recent years due to its ease of use and speed. Currently in its second major rewritten version, it now follows the projection dynamics approach as developed by Bouaziz et al.^12–14

Inherently an explicit solver, equilibrium in each node is sought simultaneously by assigning mass, acceleration and damping of the nodes. This means that DR-based methods are insensitive to the static determinacy of the structural system such that mechanisms and large deformations are not an issue, provided the solver is able to remain stable (as is the case with Kangaroo).¹⁵

At the time of writing, the Kangaroo solver is based on the manipulation of vertices with three degrees of freedom (3DOF) and a 6DOF recently available. For the modelling of 3DOF beams in Kangaroo, axial and bending stiffness are defined by goals based on Hooke’s Law and the Barnes/Adriaenssens model, respectively.¹⁶ The bending model defines bending radii on a plane of three sequential nodes and does not account for orientation or anisotropy of cross-sections. As such, the beam model is simple and fast to compute.

FEM

Finite element analysis (FEA) is the de facto standard in the field of engineering simulation.¹⁷ Finite elements still are the most reliable tool for structural analysis, offering the complete picture of the situation and the most accurate mechanical description of the analysed system. The reliability of FEA has been proven in decades of research and real-world applications.

A matrix-based method, in its most common implementation, uses an implicit integration scheme to find the nodal displacements of the structure by solving a system of linear equations. For quasi-static problems, being the integration scheme implicit, the mass of the system and the acceleration of the nodes do not play a role, vastly simplifying the setup of the computational model. For most engineering problems one-dimensional (1D; beam) and two-dimensional (2D; shell) elements are generally sufficient to model all types of structural systems. In most finite elements codes, beam elements are formulated as Timoshenko beams, while shell elements follow the Reissner–Mindlin formulation, both of which provide second-order effects such as shearing of the cross-section, often disregarded in simplified formulations.¹⁸

Geometrical nonlinear finite elements are used for the computation of problems involving large deformations.¹⁹ Form finding represents a typical problem involving large displacements of the initial guess geometry. In computational terms, a temporary stiffness reduction is applied to the elements to be form found, leading to an equilibrium state which returns the final geometry. This is for the instance the method employed in the commercial code SOFiSTiK, which so far has been used extensively for the design and simulation of membrane architectures and textile hybrids.

IGA

IGA is a novel simulation approach first introduced by Hughes et al.²⁰ in 2005. Developing rapidly since then, it merges the mathematical description of geometric objects in computer-aided design (CAD) environments with the analysis model based on the FEM. The resulting rapid interaction between form generation and analysis opens up new potential for computer-aided structural design.

In CAD environments, a typical representation of free forms surfaces is realised by fitting trimmed NURBS patches together. By using the NURBS patches as a common basis for geometry description and structural calculation, the design and the analysis process are integrated and merged together,²¹ and unwanted geometric differences between the geometric design and the numerical structural analysis model can be avoided. This is realised by using the control points of NURBS patches as location for the basis functions which describe the mechanical behaviour of the structure in an analogous way to FEM.

IGA unveils significant potential in CAD and engineering, as it uses one consistent mathematical model description throughout architectural and engineering design phases skipping entirely the need of element discretisation. The IGA code Carat++, currently being developed by the team of the Chair of Structural Analysis at the Technical University of Munich (TUM), has recently been integrated into Rhino/Grasshopper in the plugin Kiwi3d.²² A promising tool for the design and analysis of textile hybrids, Kiwi3d integrates modules for geometrical linear and nonlinear analysis as well as cutting edge form-finding algorithms and building process routines directly embedded in the native NURBS definition of the model.

A test case: hybrid tower

The hybrid tower installation was conceived as a showcase project to investigate the potential of knitted fabric as structural membrane in combination with bending-active elements (Figure 4). The tower achieved its form and equilibrium state through the interaction between bending-active glass fibre-reinforced polymer (GFRP) rods and the external layer of knitted fabric. A hybrid structure due to the interaction of its two main components, bent GFRP rods and custom-made CNC knit, this hybrid action created a very light and yet stiff structure which balanced wind and other external actions through an interdependent combination of compression and tension elements.

Figure 4.

View of the hybrid tower project installed on the main square of the city of Guimarães.

For its development, the project involved researchers from Centre for Information Technology and Architecture (CITA) of the Royal Danish Academy of Fine Arts, KET (Chair of Structural Design and Technology) of the University of the Arts Berlin as well as A. Ferreira & Filhos (AFF), a textile company based near Oporto specialised in knitted items, in an interdisciplinary collaborative effort which touched upon multiple aspects, from design to simulation and fabrication.

Project description

Classic textile architecture employs membrane patches which are individually cut in patterns and later sewn or welded together to form the final shape. The requirement of pretensioning entails creating custom details on the membrane through pockets, patches, folds and loops that host the tensioning elements, in most cases cables or belts. By using knitted fabric as a structural membrane, all the details are easily embedded on the material itself as the final shapes are directly knitted using a CNC knitting machine. For this purpose, a custom interface between the design environment and the CNC production machines from Shima Seiki was developed by CITA and AFF (Figure 5). This interface enabled the direct creation of the machine code defining the knitting beds, the yarn carries and holding patterns, and thereby controlled the formation of the knitted textile and provided a direct control of the structure, material and shape.

Figure 5.

Detail of the knitted pockets and channels (left); computational pipeline for the production of CNC knitting machine compliant code (right).

A soft architecture requires new thinking in terms of detailing and assembly. Instead of a storey wise construction sequence, the structural skin of the tower was assembled on the ground as a large pre-stressed textile surface. This was subsequently rolled into shape, tensioned, transported horizontally to the site and finally erected into its vertical position. The 9-m high structure was so light that it could be carried by only six people. A set of puzzle joints was developed to ease the assembly of the tower (Figure 6). The connection elements were then attached to the GFRP rods after they slid through the appropriate channels. In this way, the sliding puzzle joints provided a solid connection between the rods. By resting on metal stoppers which were fixed to the rods in predefined locations, the joints were able to withstand vertical wind loads up to 50 kg each. This approach allowed for fast assembly and disassembly.

Figure 6.

Puzzle joint connection detail for the coupling of the GFRP rods.

The hybrid tower was on display for 3 months on the main square of the Portuguese town of Guimarães (Figure 7). Throughout this period, the tower successfully demonstrated the strength and high performance of bespoke knit material on a large scale and provided an exciting architectural intervention for the town, bringing a new experience of a translucent and haptic textile architecture into the old urban environment.

Figure 7.

Interior view of the connection of the skin layer.

Form finding and analysis

The relationship between skin and structure is of central importance in the field of architectural textiles, positioning the textile membrane either as a cladding skin or engaged in hybrid dependencies in which membrane and supporting scaffold act as an integral system. The latter requires a high degree of control and understanding of the membrane’s material behaviour as well as the interdependency between all the elements that constitute the structural system. For the planning of hybrid tower, new modelling practices were developed to capture this hybrid behaviour. A set of computational tools was devised to design and specify these material systems, starting from the global shape and its discretisation into patches, up to the automatic production of the knitting machine information and detailing of the connection elements.

For the design and development of the hybrid tower project, two parallel computational approaches were adopted. A lightweight modelling pipeline guided the design iterations of the installation and provided the team an agile tool to quickly test geometrical variations. The information emerging from the first pipeline was in turn used to set up the simulation model that provided detailed insight into the behaviour of the tower (Figure 8). This dual approach stems from ongoing research being developed by the authors over a series of prototypes and test cases. Computational design workflows on the generative and explorative track are generally associated to lightweight simulations, as only these can provide the necessary amount of iterations within reasonable calculation time. On the other hand, the analytical track is characterised by fewer feedback cycles, in which computational intensive simulations are used to provide accurate and precise answers at the cost of higher processing time.

Figure 8.

Flowchart of the computational design workflow in which lightweight simulation is used for the shaping process (white) and the subsequent analysis in FEA (black).²²

The term lightweight stems from computer science, where it describes an algorithm or language which has a small memory footprint or impact on the overall performance of a computational system. In architectural and engineering contexts, lightweight simulations are similarly characterised by minimal use of computational power so that quick design iterations can be achieved without sacrificing performance. This allows them to be directly integrated into the generative track and workflows of early design stages. The lightweight approach provides a level of accuracy and precision that is sufficient for taking fundamental design decisions, while operating on high levels of abstractions, assumptions and generalisations. The algorithms underlying lightweight simulations should encompass a wide range of concerns and solve simultaneously questions related to geometry, structure, assembly and fabrication,²³ thereby providing an integrated environment between design and structural feedback.

Heavyweight simulations are in contrast more accurate and precise, but as well computationally intensive, specialised in scope and demanding in terms of knowledge about the design, geometry, materials and so on. A typical representative is FEA, which as seen in the previous chapter employs a matrix-based method for the solution of the equations of equilibrium and the associated stresses of the structural members as a result of forces, boundary conditions and material properties. Despite the computational overhead that derives from the more complex formulation of the mechanical properties of the system, this approach allows to form find and analyse structures in the most precise and accurate way possible.

For the hybrid tower, the goal solver Kangaroo2 was implemented both for describing form-finding behaviours, used during exploratory design where topology and dimensions are free, and for describing mechanically calibrated behaviours used during structural analysis feedback (Figure 9). The Kangaroo2 API enables designers and developers to integrate the solver and write custom goals with great freedom. Enabling both the development of the K2Engineering plugin and the interactive modelling pipeline¹⁴ where designers are free to handshake between the exploratory and structurally accurate modes of modelling at any time.

Figure 9.

Simulation steps of the hybrid tower in Kangaroo2.

The implementation of the K2 physics solver into the computational design model in Rhino/Grasshopper allowed for a real-time interaction between the early-stages design and the form finding of the structure. The ability to quickly customise the K2 simulation engine granted the necessary fluid design process. The general nature of the K2 engine allowed furthermore to represent and solve the many layers of design constraints in one modelling environment. This gave the opportunity to consider during the design process simultaneous parameters of shape, structure and behaviour, as the lightweight simulation provided feedback on the utilisation of the GFRP rods in terms of bending forces. This was possible as the rods, having a thin cross-section compared to their length, behave as a Bernoulli beam for which the bending moment is directly proportional to the curvature radius. Therefore, information on the material utilisation could be derived directly from the deformed geometry. An accurate FEA of the design and the behaviour of the overall structure under external loads was then performed in SOFiSTiK (Figure 10).

Figure 10.

Finite element form finding and wind load analysis of the hybrid tower project.

The simulation of large elastic deformations, like in the case of bending-active and hybrid structures, does not pose a problem for modern nonlinear FEA, although available finite element programmes typically do not serve well as design environments. It is notoriously complex to organise a complete simulation setup for quick design explorations with almost any finite element programme. Despite the apparent complexity, recent advances and a wider availability of computational tools to the architectural and engineering community have been filling the gap between the two disciplines. In this way, a tighter interaction between early design developments and mechanical analysis feedback is becoming more commonplace in daily praxis, creating a direct link between the lightweight simulation properties of the early stages of design and the more complex tools for engineering analysis.

The advent of parametric tools initially geared towards the design community has been steadily trickling down to the engineering world, offering better environments to simulate, test and plan wider arrays of design variations. This paradigm shift is well reflected in typologies that actively employ the behaviour of materials as a form-giving strategy, the design of which is tightly coupled to a concurrent structural feedback.

The necessity and advantage of FEA in the development of the hybrid tower lies in the possibility of a thorough and 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. These include: mechanical material properties, asymmetrical and varying cross-sections, pre-stressing, eccentricities, coupling and interaction of individual components, nonlinear stress-stiffening effects, nonlinear simulation of stresses and deflections under external loads (e.g. wind and snow), patterning and compensation.

In the context of the hybrid tower, specific tools were employed to ease the communication between the design iterations performed in Kangaroo2 and the FEA platform. Working primarily in Rhino for the modelling and Grasshopper for the parametric organisation of the prototype, a direct exchange of data was achieved with the aid of the STiKbug plugin for Grasshopper. Currently under development,²⁴ STiKbug creates a direct link from the parametric modelling environment Grasshopper and the FEA software SOFiSTiK which was used for the analysis of the structure. The plugin enables a bidirectional flow of information to and from both software environments. In this way, the creation of input geometry can be seamlessly coupled to the output of the structural analysis and vice versa. This gave the researchers the opportunity to easily interact between seemingly separate software settings, besides elaborating and validating multiple design purposes supported by detailed structural feedback.

The communication between the two software environments happens in both directions by parsing and marshalling the data. The geometry information created in Rhino/Grasshopper is translated and parsed into SOFiSTiK friendly code which serves as the primary input for the finite element simulation. The flow of information in the opposite direction happens through marshalling of the C++ database of the results into .NET compliant classes. For each object in the database, a correspondent .NET object class exists, allowing for a seamless transition and flow of information to and from both environments. No additional translation of the information is required, as the plugin takes complete care of bridging the different data representation. In this way, the description of the system can be purely geometry based, rather than having to rely on platform-specific code representations.

In this way, the geometry of the tower emerging from the design iterations could be easily tested in terms of structural performance and external loading conditions such as horizontal and uplifting wind forces. In turn, the information gathered from the FEA runs in SOFiSTiK with the aid of STiKbug constantly informed the generation of the geometry and the development of the installation’s details.

Conclusion

This article discussed form finding as a shape-defining method for textile architectures along with typical strategies ranging from classic physical-based models to more advanced numerical methods. The focus of the article was set on the category of textile hybrids, a type of construction that employs the combined action of tensile membranes with bending-active elements. An overview of computational methods that have been adopted so far for their design and simulation was presented, along with a brief discussion on promising upcoming approaches that might redefine the way the CAD and computer-aided engineering (CAE) worlds interact.

The hybrid tower (Figure 11) project was then presented and discussed in the second part of the article. A textile hybrid prototype developed within an interdisciplinary research context, the design and engineering of the project required the development of ad hoc tools. Depending on the stage of development, whether design, simulation, analysis, validation or fabrication, this set of tools were conceived to enable a quick exchange of information between the different parties as well as creating an integrated design environment. In this way, feedback could flow between the different platforms, informing the design as well as the engineering and detailing of the project.

Figure 11.

View of the hybrid tower.

Due to the tight interaction between form and structure, textile hybrids provide the perfect setting to test and develop tools and strategies for the integration of design, engineering and fabrication. With the production of tools and their testing on prototypes, the long-term goal behind this ongoing research is to bridge the gap between disciplines and bring nearer these only apparently distinct aspects of project development.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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