Calibrated and Interactive Modelling of Form-Active Hybrid Structures

Abstract

Form-active hybrid structures (FAHS) couple two or more different structural elements of low self weight and low or negligible bending flexural stiffness (such as slender beams, cables and membranes) into one structural assembly of high global stiffness. They offer high load-bearing capacity at a fraction of the weight of traditional building elements and do so with a clear aesthetic expression of force flow and equilibrium. The design of FAHS is limited by one significant restriction: the geometry definition, form-finding and structural analysis are typically performed in separate and bespoke software packages which introduce interruptions and data exchange issues in the modelling pipeline. The mechanical precision, stability and open software architecture of Kangaroo has facilitated the development of proof-of-concept modelling pipelines which tackle this challenge and enable powerful materially-informed sketching. Making use of a projection-based dynamic relaxation solver for structural analysis, explorative design has proven to be highly effective.

Full text

Proceedings of the IASS Annual Symposium 2016
“Spatial Structures in the 21st Century”
26–30 September, 2016, Tokyo, Japan
K. Kawaguchi, M. Ohsaki, T. Takeuchi (eds.)
Copyright © 2016 by Gregory Quinn, Anders Holden Deleuran, Daniel Piker, Cecilie Brandt-Olsen, Martin
Tamke, Mette Ramsgaard Thomsen, Christoph Gengnagel
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
Calibrated and Interactive Modelling of Form-Active Hybrid
Structures
Gregory QUINN1*, Anders Holden DELEURAN2*, Daniel PIKER3, Cecilie BRANDT-OLSEN4
Martin TAMKE2, Mette Ramsgaard THOMSEN2, Christoph GENGNAGEL1
1* Department for Structural Design and Technology (KET), Berlin University of Arts
Hardenbergstrasse 33, 10623 Berlin, Germany
quinn@udk-berlin.de
2 Centre for Information Technology and Architecture (CITA), Royal Danish Academy of Fine Arts
3Robert McNeel & Associates, England
4Department of Civil Engineering, The Technical University of Denmark
Abstract
Form-active hybrid structures (FAHS) couple two or more different structural elements of low self
weight and low or negligible bending flexural stiffness (such as slender beams, cables and
membranes) into one structural assembly of high global stiffness. They offer high load-bearing
capacity at a fraction of the weight of traditional building elements and do so with a clear aesthetic
expression of force flow and equilibrium. The design of FAHS is limited by one significant restriction:
the geometry definition, form-finding and structural analysis are typically performed in separate and
bespoke software packages which introduce interruptions and data exchange issues in the modelling
pipeline. The mechanical precision, stability and open software architecture of Kangaroo has
facilitated the development of proof-of-concept modelling pipelines which tackle this challenge and
enable powerful materially-informed sketching. Making use of a projection-based dynamic relaxation
solver for structural analysis, explorative design has proven to be highly effective.
Keywords: dynamic relaxation, form-active, hybrid structure, form-finding, calibrated modelling, assembly
topology
1. Form-Active Hybrid Structures (FAHS)
1.1. Definition & Modelling Challenges
In this context the term hybrid structure is used to describe a structure in which the internal forces are
assigned to materials or components to which they are best suited. The term form-active was coined
and popularised by Heino Engel in Structure Systems [1] and refers to structural systems whose shape
is determined and stabilized by elements in a single stress state (i.e. pure tension or compression).
Typically, traditional membrane structures are supported at their edges either by tensioned cables with
negligible bending stiffness or by edge beams/foundations with extremely high bending stiffness. In
FAHS, tensile elements (cables or membrane) are supported at their edges by actively-bent slender
rods. Edges with relatively low bending stiffness in combination with tensile elements of high stiffness
present a substantial computational challenge in terms of finding stiffness-dependent shapes which
feature large initial deformations from shaping. If designed well, FAHS can offer high global stiffness,
low self weight and complex spatial configurations from initially flat or straight components. The

Proceedings of the IASS Annual Symposium 2016
Spatial Structures in the 21st Century
2
most successful structures of this type are perhaps the conventional tent and umbrella. In literature
substantial work has been carried out on the design and analysis of FAHS [2]–[6]. However until now,
it has been difficult to design them freely in the digital environment because structural analysis had to
be carried out in a different program to that of the geometric design. The exploration and development
of FAHS is valuable because of their potential to improve the performance of buildings in terms of
efficiency of material usage.
The full potential of hybrid structures can only be unlocked with a tool which facilitates their design in
a geometrically flexible environment (e.g. Grasshopper) and which simultaneously provides
immediate feedback to the designer in terms of structural performance (e.g. Kangaroo). The
application potential of the modelling pipeline and simulation method presented in this paper reach far
beyond FAHS.
1.2. Demonstrator
The modelling and simulation methods presented in this paper were implemented at a ‘cluster’
organised by the authors at SmartGeometry 2016 in Gothenburg. In just two days, participants learned
how to use the digital tooling and designed a tower based on the principles of FAHS. The tower was
built in the subsequent two days. The 5.5m hybrid tower was made from GFRP rods of 6mm diameter
and restrained by 6mm wide polyester strapping bands. The tower weighed just 7kg and deflected
roughly 6mm under its self weight. It is claimed that a designer would not be able to develop and
generate the complex spatial geometry or the highly effective hybrid restraint of the tower using
existing means of sketching, modelling and analysis in such a short period of time. As such this hybrid
tower, and the speed with which it was designed and analysed, is presented as evidence of the
method’s success.
Figure 1: 5.5m tall FAHS tower designed and built in just three days using the documented method
demonstrating its success [photo: Marc Webb]
2. Physical Simulation
Since its inception in 2010, the Grasshopper plugin Kangaroo has become an established tool for the
architectural design community helping to realise many real and conceptual projects. Its functionality
has, until recently, largely been associated with simulations independent of, or using arbitrary,
material stiffness. However, the implementation of a projection based dynamic relaxation technique
and an improved damping scheme in the latest release of Kangaroo facilitate simulation of

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Spatial Structures in the 21st Century
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mechanically accurate structural behaviour with remarkable stability and speed. The details of the
Kangaroo plugin will not be explained here.
2.1. Implicit versus explicit
The Dynamic Relaxation (DR) method for solving physical simulations was first developed in the
1960s [7] and has since become established in many fields. In the built environment, DR is most
commonly associated with stiffness-independent (purely force based) membrane form-finding or with
the manipulation of architectural geometry (e.g. meshing, panelisation). In structural engineering the
preferred, and most common, method for structural analysis is the implicit Direct Stiffness (DS)
method which in most implementations features a full six degrees of freedom (DOF) at each node
(three translational and three rotational) which can accurately describe mechanical stresses and
displacements in a discretized continuum under the assumption of small deflections. If equilibrium is
being sought in a system where deflections are large, the stiffness matrix must be updated over
multiple iterations in a non-linear analysis which can be computationally demanding and often
unstable. A prerequisite for DS systems is that they must be statically determinate or indeterminate.
Mechanisms cause numerical instability and cannot be calculated.
DR on the other hand, does not require the computation and inversion of a global stiffness matrix, but
instead seeks equilibrium in each node explicitly and simultaneously by assigning mass, acceleration
and a method of damping to the nodes. This means that DR 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). This insensitivity to static
determinacy and large deformations (unlike DS) is highly suitable and forgiving in an experimental
and interactive design environment. Adding or subtracting structural elements on the fly and observing
the immediate impact they have on structural performance (e.g. deflections, stability and forces) can
be an illuminating experience for the designer.
2.2. Calibration
The Kangaroo solver is based on the manipulation of vertices with three DOF each. This has certain
implications on which mathematical models can be used for the simulation of structural behaviour. For
the modelling of beams in Kangaroo, axial and bending stiffness are defined by two separate goals
based on Hooke’s Law and the Barnes / Adriaenssens model [8] respectively. Since Kangaroo
minimises the total energy of the system it is possible to simulate accurate structural behaviour by
providing appropriate stiffness values as input for the goals. This is because the displacements of a
structure always follow the path that minimises the total potential energy.
The bending model defines bending radii on a plane of three sequential nodes and does not account for
orientation or anisotropy of cross sections. Nor is beam torsion accounted for. As such the beam
model is simple yet fast to compute. While more accurate 4 and 6 DOF solutions exist to describe
beam behaviour using DR [9], [10], their increased computational demands significantly reduce their
speed and hence suitability for this method which depends on fast and interactive feedback. When
building FAHS from very slender rods with circular cross sections with pinned connections, the
effects of section anisotropy and beam torsion are negligible.
2.3. K2Engineering Plugin
The latest Kangaroo release encourages the development of custom goals through an API which was
utilised to create a structurally calibrated extension called K2Engineering [11]. The main purpose of
this plugin is to offer a direct output of meaningful structural values that can be used to evaluate the
performance. Whilst it is possible (in most cases) to input appropriate stiffness values for the existing
goals and subsequently back-calculate the forces from the displacements, this approach has the
advantage of avoiding duplicate functionality, simplifying the process of mapping the results back to
the structure and making it more clear which properties are needed for the calibration and their correct

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units. The plugin currently contains a bar, cable, rod and support goal from which the axial forces,
reactions, shear and bending moments can be extracted. A number of additional components have
been developed to ease the modelling setup and further advance the structural output. These include a
number of different loads to quickly define realistic load scenarios, calculation of cross section
properties for circular and rectangular profiles, evaluation of displacements and summation of axial
and bending stresses. The plugin also focuses on the visualisation of forces (axial, shear and moments)
in relation to the three-dimensional geometry in order to obtain an intuitive understanding of the
structural behaviour and identify load paths without inspecting the specific values.
2.4. Augmented Reality Projection Board
In order to explain the structural principals of FAHS and to demonstrate the mechanical precision of
Kangaroo, an educational and interactive “projection board” was developed in parallel to the
modelling pipeline. The system allows users to create physical models of simple planar structural
systems (e.g. simply supported beam, cantilever, hanging chain, portal frame etc.) for which an
identical digital model exists in the simulation. The digital model is projected directly onto the
physical model such that when the physical model is subjected to loads, the deflections in the digital
projection correlate precisely. The physical model is augmented with additional visual information
such as plots of internal forces (bending moments, axial forces and shear) as well as reactions. The
graphical display of internal forces was scripted using native Grasshopper components as well as
custom Python scripts but could equally make use of the K2Engineering plugin. This educational AR
projection board was feasible only due to the speed of the Kangaroo solver and the flexibility of the
Grasshopper software environment.
Figure 2: Augmented reality projection board assisting in the teaching of structural behaviour and systems
powered by the Kangaroo solver.
Figure 3: Custom GUI and visualisation of internal and external forces. From left to right: bending moments,
axial force, shear force and reactions.

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3. Interactive Design Modelling Pipeline
3.1. Computational Design Modelling Pipelines
FAHS are designed and constructed by transforming stress-free linear and planar elements into an
assembly of curved elements through elastic bending of beams and tensioning of membranes/cables.
This process is similar whether using physical or computational modelling. As a modelling problem,
this is characterized by a high degree of interdependent behaviour, which adds complexity to the
existing challenges of designing form-active structures, making it difficult to model using off-the-shelf
software. This has resulted in the development of bespoke modelling pipelines which implement
various computational shaping and form-finding methods such as finite element modelling [12],
spring-based modelling [13], force-density methods [3] and projection-based methods [14]. These
pipelines have proven effective for modelling FAHS and have successfully automated central
processes such as shaping, form-finding, structural analysis and patterning. They however tend to
overlook the initial process of defining assemblies of elements and supports. That is, the topological
and geometrical definition of the assembly prior to the iterative shaping process. Where shaping
implies generating a FAHS appropriate shape and structural analysis the process of analysing the real
world behaviour of this shape. When employing a fixed inventory of structural elements, the definition
of how these are combined in an assembly becomes the primary design and modelling task. This
process is therefore a primary design driver when designing FAHS and is particularly significant in the
search for novel structural systems.
Figure 4: A modelling pipeline for shaping FAHS using Kangaroo for shaping (white) and an external FEA
package (SOFiSTiK) for structural analysis (black) previously commonly used by KET and CITA.
3.2. Exploratory Topology Modelling of Assemblies
Defining assembly geometry implies specifying topology and dimensions, i.e. defining element types,
their dimensions and how they connect in a network. This is performed either by directly modelling
the discrete geometries representing structural elements, or, by developing and integrating a
parametric model once an assembly topology is defined and can be encoded [14]. In either case, this
process is typically separate from the generative process of shaping the assembly. This has the effect
that the designer (or a search algorithm) is not allowed to add, remove or edit elements during shaping.
This prevents a feedback loop from occurring between assembly definition and shaping, preventing
the possibility of iteratively constructing or modifying assembly topology based on its currently
shaped state. This lock-in of assembly topology, or “body plan” [15], during shaping impedes on both
the creative and objective exploration of the shape space delineated by the inventory of the given
FAHS. Exploring topological design diversity implies interactively or exhaustively exploring the
connectivity of elements that define an assembly and searching for, fit candidates. When any change
in topology requires downstream processes to be reset and performed again, this becomes intractable.
Developing novel and unbiased FAHS therefore necessitates modelling pipelines that are more
conducive to exploring topological diversity. The research presented here aims to examine how to
achieve this by unlocking the body plan and enabling feedback to occur between assembly definition,
shaping and structural analysis in the FAHS modelling pipeline.

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Figure 5: The interactive Rhino/Grasshopper modelling and analysis pipeline in which assembly definition is an
iterative process and has feedback connections from shaping and analysis. A toggle enables the designer to
switch between shaping and calibrated modelling Kangaroo goals on the fly.
3.3. Assembly Definition
Assembly definition is based on a set of rules for how the designer is to construct the geometrical
representation of elements, a method for discretizing this geometry and methods for dynamically
coupling the Rhino document and the Grasshopper definition. Beams and cables are represented as
polylines, piecewise linear curves which may approximate continuous shapes. The designer draws
these as coarse polylines describing topology and initial dimensions. Implementing a layer naming
convention, these are automatically piped to Grasshopper on updates to the Rhino document
beam/cable layers. Here they are discretized by subdividing their edges into a user defined sub-edge
length. To enable the designer snapping to the discretized geometry, all vertices are automatically sent
back to the Rhino document as a locked point cloud. This modelling loop affords immediate and
precise definition of assemblies.
Figure 6: Definition/drawing of self-connecting beams. The rule for a non-periodic end-end connection is to
draw overlapping vertices at the connection, or, to have the incoming edges meet below a user specified angle.

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3.4. Representing and Solving Shaping Behaviours
Shaping has three sub-processes: defining, solving and refining standard Kangaroo goals. Defining
goals implies generating local Kangaroo goals along the discretized polylines that yield overall
element behaviour. A beam is represented by a goal for each edge maintaining its length and a goal for
each vertex and its neighbours which attempts to keep the angle formed by the three at 180 degrees.
Combining these goals enables accurate elastica behaviour. Cables are represented by edge-length
goals. Minimizing these, their shaping behaviour is similar to membrane shaping. If two elements
share vertices/edges they are connected at these sub-components. Goals are passed to the Kangaroo
solver which iteratively shapes the assembly until equilibrium. Any change in input (topological or
numerical) will trigger this solve-equilibrium loop. This enables the designer to interactively explore
shaped assembly topology and dimension element lengths by refining goals values.
Figure 7: Interactively defining topology and shaping an FAHS assembly with real-time shaping and
downstream bending analysis using our modelling pipeline
3.5. Shaped Assembly Geometry Analysis
Analytical methods are integrated downstream from shaping which provide the designer with real-
time visual and numerical feedback on the state of the shaped assembly. Cables are evaluated for
whether or not their polyline vertices are on a line, signifying whether the cable is under tension. For
beams a key geometric property with structural implications is the local bending radii along the
polyline. This value can be mapped to the bending stress, utilisation and reserve of the beam in
isolation of other load cases. The local radii are defined here as the radius of the circle constructed
through a polyline vertex and its two neighbours. This property is visualised in the viewport as
coloured/scaled vectors that also provide a visual representation of the bending orientation (see figures
6, 7 and 9).
3.6. Assembly Topology Analysis
Visually analysing assembly topology is difficult and provides no objective data from which to
differentiate assemblies and steer design space search. Methods are therefore integrated which
implement graphs as data structures for analysing and visualizing this. In discrete mathematics, a
graph is an abstract construct consisting of nodes, where some pairs of these are connected by edges.
Nodes describe the objects of a network and their properties, edges describe how nodes connect and
the properties of these connections. In our assembly graphs, nodes represent structural elements and
edges their physical connections. Nodes have two properties (element type and length) and edges have
two (where along the elements the connection occurs). The directed graph class of the NetworkX
Python module is implemented as the base representation. This enables us to arbitrarily add properties

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to nodes/edges, and to analyse assemblies for graph theoretical measures such as size, connectedness,
node degree, centrality and cycles. This graph is translated to DOT graph language notation and
compiled to an image using GraphViz which is rendered in the Rhino viewport. This occurs
automatically and enables the designer to visualise the topology using different graph layout
algorithms (hierarchical, force-directed etc.).
Figure 8: Hierarchical assembly graph analysis for the six construction steps presented in Figure 7. Beams are
black nodes, cables are white.
Figure 9: Screenshot of the Rhino/Grasshopper tower prototype described in section 1.2. During the final build,
additional floors were added. The modelling pipeline relies on the ability to quickly switch Rhino layers using
the status bar (below) and through exposing primary pipeline controls via the Grasshopper Remote Control Panel
(right)

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Acknowledgements
The authors would like to thank Will Pearson and Harri Lewis for their valuable contributions to this
work. The authors would also like to thank the participants of the SmartGeometry cluster.
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