Analogue and digital form-finding of bending rod structures

Proceedings of the International Association for Shell and Spatial Structures (IASS)

Symposium 2015, Amsterdam

Future Visions

17 - 20 August 2015, Amsterdam, The Netherlands

Analogue and digital form-finding of bending rod

structures

Ioanna SYMEONIDOU*

*Institute of Architecture and Media

Technische Universität Graz, Inffeldgasse 10/2 8010 Graz, Austria

[email protected]

Abstract

This paper presents a research on real-time shape exploration employing analogue and digital form-

finding of bending structures, which concluded with the testing of the proposed design process during

an intensive student workshop at Graz University of Technology. The aim was to experiment with

analogue and digital tools in parallel, informing design decisions. The experiments involved physical

form-finding following the tradition of Frei Otto at the Institute of Lightweight Structures in Stuttgart

as well as computational form-finding simulating bending behavior with the use of dynamic relaxation

of spring-particle systems (Kangaroo plugin for Rhino). By establishing feedback between digital

media and physical prototypes, the creative process was informed by the material characteristics and

structural properties; the aim was to utilize a parametric model not merely as a representational tool,

but as a tool for real-time shape exploration that embeds the physical behavior and interaction among

bending rods. While traditional architecture and engineering aims at the structural optimization of an

existing form, a dynamic form-finding system can lead to a real-time discovery of structural form

encouraging the morphogenesis of optimized structures.

Keywords: form-finding, analogue-digital, parametric design, bending structures, Kangaroo physics

simulation, design education

1. Introduction

Form-finding is a well-established method in architecture and engineering aiming to define the

optimal geometry with respect to the structural behavior for certain boundary conditions. There is a

long history of experimentation in this field, supported by scientific research and built examples. Frei

Otto was the pioneer to research, study and categorize these structures, together with his team at the

Institute for Lightweight Structures in Stuttgart. Their physical experiments and models have been

documented in the famous volumes of IL books; although most of the IL series were published in the

early 70s, which is much before the wide use of computational design in architecture, they remain an

Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam

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essential reading for computational designers of our times. As Nerdinger explains The form-finding

processes are those which, given a specified set of conditions and following the prevailing laws of

nature, give rise to visible forms and constructions under experimental conditions. As they take place

without human intervention, they are also termed autonomous formation processes” (Nerdinger [1]).

The work presented in this paper summarizes the research and design approach that was adopted

during an experimental design workshop which took place at Graz University of Technology in

November 2014. The workshop explored analogue and digital form-finding of bending rod structures.

The students’ work employed both analogue and digital tools, and aimed to inform the design process

through the knowledge gained at the intersection of the two media. The methodology was based on

lightweight structures research and form-finding of bending structures as it was studied by Frei Otto

and his team at ILEK, and documented in the book IL 31: Bamboo as a building material (Dunkelberg

[2]). Frei Otto refers to such constructions with the generic term “Curved Compression Rods”

referring to arches, grid shells and other structures “whose form is determined by installing curved –

and thus prestressed rods”.

2. Bending as a design tool

Though there is an extensive body of research in membrane structures and a plethora of student work

relating to tensile structures, bending has gained less attention within the academic community. The

aim of the workshop was to utilize bending behavior as a design tool for formal experimentation. A

system of bending rods, just as any other form-found structure tries to minimize its energy to span

between the given borders. Eventually, the material system settles in a stable configuration. Thus a

bending rod configuration is able to ‘compute’ form. De Landa describes it as an ‘analog search

algorithm’. Such design process embeds performance criteria leading to optimized configurations. A

physics engine, like Kangaroo, acts as a design decision support system, it assists architects to

increase their intuitive understanding of the structural behavior of geometrically complex forms. ‘The

environment educates the user as to the effects of forces on the form of structures and provides an

interactive form-finding’ (Kilian and Ochsendorf [3]).

During the first stage of the workshop the students undertook research on existing structures that

employ elastic bending and studied numerous examples of bending structures documented in the

bibliography. These would range from vernacular architecture, huts and bridges (Dunkelberg [2]) to

contemporary constructions like the Multihalle Manheim by Frei Otto (Nerdinger [1]) and the

Research Pavilions at the Institute for Computational Design in Stuttgard (Fleischmann and Menges

[4]) (Fleischmann and Menges[5]) (Krieg et al. [6]). Bending-active construction systems are widely

used for temporary or mobile shelters. Leinhart et al. [7] in their paper about active bending provide a

comprehensive list of constructions from primitive housing to contemporary pavilions.

Though form-finding is an intuitive process and experimentation with analogue media leads to tacit

knowledge and experience with the material, there is a considerable knowledge gap in the

mathematical and computational understanging of the geometry of bending. Architect Marten

Nettelbladt has been experimenting with the geometry of bending and has created an important online

resource of experiments and observations concluding that all ‘elastic deformations’ follow the same

principals and therefore the same geometry (Nettelbladt [8]). Recent developments in Kangaroo

physics engine for interactive simulation, optimisation and form-finding within Grasshopper

(Parametric plugin for McNeel Rhinoceros), developed by Daniel Piker [9] can provide a very good


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approximation of bending geometry, and for this reason this tool was selected for the afoermentioned

workshop. This engine works in an iterative way calculating the interaction among predefined forces

like springs, bending resistance, pressure and gravity, and their repercussion on the geometry, until a

stable form is reached. Comparing the results obtained from the simulation to the physical models,

there is a very precise representation when simulating a single bending rod or a small set-up of

interacting rods. The digital experiments become more demanding when several interacting rods are in

play, adding to the complexity of the system. At the same time the physical form-finding experiments

revealed some unpredictable results that emerged from the self-organizational capacity of the system

to regulate and distribute forces to reach equilibrium.

In their paper, Active Bending, A Review on Structures where Bending is used as a Self-Formation

Process, the authors explain the differentiation of bending- active structures based on their design

approaches. They show three possible approaches: the behavior based approach, the geometry based

approach and the research that seeks to integrate the two. (Lienhard et al. [7]). In a behavior based

approach bending is studied intuitively; there is an empirical understanding of the geometry and

structural behavior. This involves several material tests, to test the limitations and the physical

properties. In a geometry based approach, the geometry is defined a priori through analytical methods

aiming to approximate the geometry of bending. There is an analysis of material limitations which are

calculated based on the curvature obtained through bending. In the integral approach there is a

combination of the above, the deformation due to elastic bending is studied through numerical form-

finding, aiming to an increased control of the geometry based on material behavior. The limitations

and the material properties are embedded in the analysis model. Lienhard et al. suggest that a

historical overview of built examples, would group the design approaches according to the analysis

tools available, reaching from empiric to analytical and finally, modern numerical analysis.

Nevertheless, despite the fact that is currently relatively easy to simulate complex bending behavior

through numerical analysis, the value of analogue form-finding experiments is still significant. The

computational tools are not introduced to completely substitute analogue form-finding methods, but to

complement them and enrich the design research. The two media cross-inform each other and aid

architects to take informed design decision. During the workshop it was seen that analogue media

proved more efficient with the gathering of qualitative characteristics and permitting design freedom,

while computational tools proved more efficient in the handling of big amounts of data and generally

quantitative characteristics. Therefore the aim of the workshop was to combine tools and

methodologies rather than referring to them as competing strategies for form exploration.

2.1. The set-up for analogue experiments

The analogue experiments were undertaken with stainless steel rods of 0.8 and 1 mm diameter as they

perform well in elastic bending and only in extreme bending configurations develop plastic

deformations. The physical models and material tests were documented and a first set of observations

provided a starting point for the study of the behavior of the structures. The models obtained from this

experimental stage were too complex to explain in simple mathematical rules, however it was obvious

that there are some internal physical rules that govern the obtained formations. Although the set-up

was relatively simple, the form-found structures in several cases were highly complex.

Having a very restricted variety of materials, that is stainless steel rods of certain length and diameter,

the design decisions mainly related to simple actions, such as, constraining the length of certain rods,


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imposing a predefined start tangent, forcing two rods to touch through a movable or fixed link, forcing

two rods to obtain the same tangent, bundling of rods and interlacing. No matter how simple the above

operations may sound, the combination of several of them within the same system can be a really

challenging task.

The aim of this set of form-finding experiments was to come up with a structure that is aesthetically

pleasing and structurally stable, so that it can be further developed into an architectural artefact. The

design brief was relatively free, ranging from small pavilions to shading devices and canopy schemes,

thus permitting flexibility, creativity and formal experimentation. This was an exploratory phase,

where physical models were used instead of sketches to highlight and communicate the design intent.

Though it is straightforward to predict the behavior of the elements individually, their collective

behavior displays a substantial level of unpredictability as the system self-organizes for the given

forces and set-up.

As Achim Menges explains in his paper Behavior-based Computational Design Methodologies “the

design space is defined and constrained by material behavior, fabrication and production. This

understanding of design computation as a calibration between the virtual processes of generating form

and the physical becoming of material systems, should not be conceived as limiting the designer, but

rather as enabling the exploration of unknown points in the search space defined by the material itself”

(Menges [10])

The experimentation with stainless steel rods aimed primarily to highlight a morphological vocabulary

to be used in the workshop and derive performative geometric configurations. For scaling up the

system, to involve more parameters such as detailing, assembly and basic structural behavior, the

obvious choice would be to work with glass fiber rods or carbon fiber rods, in a medium scale set-up.

Full scale experiments with Glass Reinforced Polymer (GRP) rods have been undertaken by several

researchers, and documented in papers and work-in-progress reports (Symeonidou and Gupta [11],

Bessai [12]). Glass Reinforced Fiber is an anisotropic material with high Young modulus. When

casted in form of a rod, the fibers are aligned along the length giving the material high elastic strength

with flexibility to bend. It also attains a high elastic limit thus allowing to conduct experiments in

cases that stainless steel rods would get a permanent deformation (Symeonidou and Gupta [13]).

Figure 1: Loading tests of a single GRP element 9 mm with two fixed connections inducing a vertical

start tangent at both ends.


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In most of the experiments, torsional buckling and twist are present, but the circular cross section of

the rods does not indicate the amount of twist present in the structure. The form-finding of twisted

interlaced structures is further studied by EPFL group of Nabaei, Baverel and Weinand [14].

Departing from a rod approach, they further develop their simulation of linear panels of non-

equilateral cross section in order to control and visualize the twists and resolve intersections in case of

panels colliding while interlaced. According to the authors, interlacing adds to the structural resistance

of an object increasing its load bearing capacity. “Bending and twisting forces influence how the

interlaced relaxed geometry would look like. The fundamental interest of reproducing a pattern with

components resistant in bending and torsion (unlike tensile-only ones) is that the assembly will relax

into an actively curved geometry which can span over an architectural ambiance. This implies that the

geometry for an actively curved interlace of components with bending and torsional resistance has to

be form-found” (Nabaei et al. [14]).

Figure 2: Analogue form-finding model of stainless steel rods for a canopy scheme. There is tangency

constraint in the start and end of the bending rods as well as connection of rods in the middle of the

construction, with rods forced to self-organize obtaining a common tangency locally on the

connection point © Institute of Architecture and Media, TU Graz


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Figure 3: Analogue form-finding model of stainless steel rods for a car parking shading shelter.

Tangents are constrained on three points parallel to z axis in the start and end of the bending rods as

well as connection of rods in the middle of the construction, which are forced to obtain the same

tangency locally on the connection point © Institute of Architecture and Media, TU Graz

Figure 4: Analogue form-finding model of stainless steel rods for an urban installation. Continuous

loops are connected obtaining the same tangent locally and locking the entire structure in a stable

configuration © Institute of Architecture and Media, TU Graz


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2.2. The computational simulation of bending

In an attempt to computationally simulate bending behavior, as Achim Menges explains “there are no

simple mathematical equations which can describe the entirety of a surface defined by the equilibrium

of applied force – be it tensile, compressive, or pressurized” (Menges [10]).

Axel Kilian presented a computational methodology for form-finding as part of his research for the

development of CADenary software. Kilian’s methodology was based on spring-particle systems

which lies in the core of most simulations of that sort. As Kilian and Ochsendorf explain in their

paper, “particle-spring systems have been used extensively in cloth simulations and other graphics

problems, particularly for making realistic simulations for the animation of clothing and other

fabrics”(Kilian and Ochsendorf [3]). The idea behind the system is an algorithm that iteratively

computes forces, velocity and lengths of springs that behave according to Hooke’s Law.

Particle-spring systems are based on lumped masses (particles) which are connected by linear elastic

springs. Each spring is assigned a constant axial stiffness, a rest length, and a damping coefficient.

Springs generate a force when displaced from their rest length. External forces can be applied to the

particles, as in the case of gravitational acceleration. Each particle in the system has a position, a

velocity, and a variable mass, as well as a summarized vector for all the forces acting on it. A force in

the particle-spring system can be applied to a particle based on the force vector‘s direction and

magnitude (Symeonidou [15]). The simulation takes place according to the parameters set by the

designer, and the system eventually reaches equilibrium. The above process, known as dynamic

relaxation was introduced in the 1960s by Alistair Day [16] and is “a computation modeling, which

can be used for the form-finding of cable and fabric structures. The dynamic relaxation method is

based on a discretized continuum in which the mass is assumed to be lumped at given nodes. The

system oscillates about the equilibrium position under the influence of loads. The iterative process is

achieved by simulating a pseudo-dynamic process in time” (Lewis [17]).

Having acquired some intuitive understanding of bending behavior through the analogue experiments,

the students of the workshop experimented with computational approaches using Kangaroo plugin for

Rhino and Grasshopper. Kangaroo is a physics engine developed by Daniel Piker, comprising of a

collection of algorithms that computationally simulate some aspects of real-world physical behavior of

materials and objects. As Piker explains “one great advantage of physically based methods is that we

have a natural feel for them, and this intuitive quality lends itself well to the design process” (Piker

[9]). The biggest benefit of form-finding in Kangaroo, is that the designer can embed rapid simulation

in early design stages, without the need to script a dynamic relaxation routine and therefore he can

drive the design towards informed and optimized solutions. In Piker’s words, “through the application

of real-world physics we can make computational tools that really work with us to design in a way

that is both creative and practical”.

During the workshop the students used the newly incorporated hinge components, which means that

apart from the standard spring-particle parameters like rest length, spring force, damping, they would

define a rest angle for the hinges to be computed during dynamic relaxation. For the case of elastically

bending rods, the initial geometry is represented by a curve which is divided into a finite number of

line segments which will be introduced as springs with a fixed length and high spring stiffness (for

avoiding changes in the total length of the rod). The rest angle (the angle between the tangents of two

consecutive line segments) is set to 0, so that the natural tendency of the rod is to spring back to its

initial straight condition. As the overall length of a rod is not negotiated during the simulation, it is


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important to set the start and end conditions of the rod. The designer would decide the degrees of

freedom at the two ends of the rod, in the case of pinned connection, the end point of the spring would

be anchored to fixed xyz coordinates, whereas for simulating a fixed connection we would require to

define a start tangent. This would geometrically mean to set the first two control points of a degree 2

curve in the desired direction, or in the case of spring-particle systems with hinges, to set the position

of the first two particles as fixed for the desired tangent direction.

Figure 5: Digital form-finding model of two rods with constraint tangency parallel to z axis at start

and end points and a connection point in their mid-length where they self-organize through dynamic

relaxation and also obtain a common tangency locally

For simulating panels with bending and twist degrees of freedom Nabaei and the group from EPFL

adopted a nonlinear structural model and came up with a formulation to impose an interlacing pattern

as coupling constraints and perform collision detection/handling if required. The building block of the

specific family of structures in their study is the Euler Elastica. They further explore twisted Elastica

made from flexible panels while dealing with collision resolving using a pseudo-dynamic shell solver

in case interlace and twist boundary condition cause panel intersection. (Nabaei et al. [14]). Their

motivation is to develop a physics-based tool, adopting an approach that brings some extra features

into the existing particle-based form-finding like Kangaroo, offering the possibility to deal with

general rod and shell cross sections with usual elastic stiffness terms, instead of simplified spring

stiffness, enhancing twist degrees of freedom for rod deformation and improving the out-of-plane

bending behavior.

Having reviewed the currently available algorithms, it was decided to make use of the bending

functions in Kangaroo, due to the intuitive and seamless user interface, lack of complexity and


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abundance of online tutorials for our students to refer to. In the case of stainless steel rods of circular

diameter, the simulation was done for linear elements and thickness was applied to the resulting

geometry after equilibrium was found. Therefore we are not considering a realistic approximation of

real-life material elastic stiffness as the EPFL approach explained above, but an interactive tool for

informing initial design ideas.

Figure 6: Typical Grasshopper definition for digital form-finding with Kangaroo physics engine

2.3. Some observations in the intersection between analogue and digital media

The experimentation with physical models was a medium that embeds information on stiffness and the

amount of force that needs to be applied in order to achieve the desired bending geometry. As the

students were setting up the models literally “with their hands”, they subconsciously obtained the tacit

knowledge about material behavior and the way forces translate into geometry. The sequence of

assembly is also a crucial mater, especially when bundling or interlacing of rods takes place. Some of

the rods are stabilized when a new rod enters the configuration to lock the moveable parts in place.

The computational model on the other hand does not include the notion of assembly. The set-up of

rods is created as a diagram of relationships among rods, it is important to define what is connected to

what and which constraints are present in the system. When dynamic relaxation takes place, the

system oscillates around the equilibrium position until it finds a stable configuration. There are cases

where the obtained configuration looks “wrong” from an intuitive point of view, especially when a

physical experiment of similar constraints gives a different result. In such cases, sometimes it is

enough to impose artificially some movement to the system, in order to re-calculate all forces in play

and finally settle in a new stable position. Although assembly sequence cannot be simulated in the

given computational set-up, it was clearly seen in the computational experiments, that when


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simulating bending behavior, errors can occur when the user imposes the movement of the parts too

fast for the algorithm to re-calculate the forces and positions of the underlying spring-particle system.

Self-intersection of bending rods can also occur in the digital model, unless the designer imposes

certain collision constraint. The design of structures that implement elastic bending has always been

studied in an empirical experimental framework, from which it is understood that “in order to achieve

predictive design capability for force-active systems in real world situations, complementary physical

and computation models are necessary” (Bessai [12]).

3. Conclusions

Just as Otto’s soap-film experiments which are scaled material simulations utilized to mimic and test

full-scale system behavior, the piano wire experiments attempt to open up the repertoire for active

bending structures, in a series of scaled models that are indicative of the geometric behavior. This is

not to be seen as an in-depth study, because several structural parameters are omitted for the sake of

simplicity. The above approach is to be seen as a brainstorming tool for architects and does not require

specialized knowledge and advanced technical skills. However, the design process itself embeds

certain level of intelligence and optimization, which would not be achieved without analogue or

digital form-finding. From an educator’s point of view, the idea of actively engaging in a hands-on

exploratory process, both with analogue and digital media is extremely enriching for students for a

variety of reasons relating to perception, cognitive psychology and learning theories. In the majority

of his writings, MIT’s computer scientist, and educator Seymour Papert focuses on propagating the

idea of learning by actively constructing knowledge through the process of making and sharing both

the artefact and the knowledge (Papert [18], [19]). During the last decades there is a growing

acceptance of learning-by-making, it is broadly recognized that knowledge is a consequence of

experience and that the role of technology is significant in the construction of knowledge (Stager

[20]).

With relation to bending behaviour in particular, as Lienhard et al. explain, constant developments of

simulation tools and projects that exhibit active bending in various typological expressions, have by

no means exhausted their field of application. “There is a growing international number of scientists

committing themselves to research and development of design, material and simulation questions

related to bending-active structures” (Lienhard et al. [7]). The aim of this paper was to present an

overview of the techniques and methodologies investigated during “Bend the rules” workshop that

took place in November 2014 at the Institute of Architecture and Media at Graz University of

Technology. It addresses issues of design research through praxis, and design processes that

encourage creative design thinking towards an integral approach in architecture, which integrates

material behavior, functionality, material economy, aesthetics and optimized structural performance.

Acknowledgements

The author would like to acknowledge the contribution of Graz University of Technology students:

Brigitte Melek, Cordula Meiler, Csilla Huss, Daniel Plazza, Eva-Maria Merkl, El Basan Morina, Eleni

Chatzatoglou, Filip Luka Pejic, Luka Janko Janezic, Katrin Schegula, Kristina Schröder, Lukas

Andreas Zitterer, Markus Lammert, Matthias Assinger, Hoda Memaran, Stefan Neumann, Paul

Dominik Höber, Paul Christoph Lindheim, Sabrina Patricia Kullmaier, Sebastian Rapposch, Thomas

Kulmhofer and Mana Varzideh.


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Special thanks goes to all colleagues and student assistants at the Institute of Architecture and Media

for their continuous help and support. The results of the workshop are also documented in the

following web link: https://iam.tugraz.at/workshop14w/

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https://iam.tugraz.at/workshop14w/


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[15] I. Symeonidou, “Surface Nets: Digital - Material behaviour of a Hybrid Structure,” presented at

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Analogue and digital form-finding of bending rod structures

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