Isoropia: an Encompassing Approach for the Design, Analysis and Form-Finding of Bending-Active Textile Hybrids

Abstract

This paper discusses the design, simulation and construction of a bending-active textile hybrid structure commissioned to the authors as part of the 2018 Venice Biennale. The hybrid structure combines the flexibility and elastic properties of GFRP rods together with bespoke CNC knitted fabric, creating a subtle equilibrium of forces along the unfolding of the installation. Building on the knowledge developed by the authors on previous bending-active hybrid prototypes, the structure represents the latest effort in terms of integration of design analysis tools within a holistic and comprehensive workflow. This enables designers to step fluently from initial concept development and definition of overall shape to the final specification of the knitted membrane structure on loop level for digital fabrication. With particular emphasis on the simulation tools employed, the paper will focus on the most up-to-date computational technologies and numerical approaches that are currently being developed for the design and analysis of bending-active and textile hybrid structures. Specifically, three distinct environments were used to form-find and analyse the structural behaviour of the installation, these environments being Kangaroo (vector-based approach), Kiwi3d (Isogeometric Analysis) and SOFiSTiK (Finite Element Analysis). This all-encompassing approach provided the perfect platform to cross-benchmark the three different methods, highlighting the qualities of each one and providing valuable information on the most appropriate software within a certain stage of design.

Full text

Proceedings of the IASS Symposium 2018
Creativity in Structural Design
July 16-20, 2018, MIT, Boston, USA
Caitlin Mueller, Sigrid Adriaenssens (eds.)
Copyright © 2018 by Riccardo LA MAGNA, Valia FRAGKIA, Philipp LÄNGST, Julian LIENHARD, Rune NOËL,
Yuliya ŠINKE BARANOVSKAYA, Martin TAMKE, Mette RAMSGAARD THOMSEN
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
Isoropia: an Encompassing Approach for the Design, Analysis and
Form-Finding of Bending-Active Textile Hybrids
Riccardo LA MAGNA*, Valia FRAGKIA
b
, Philipp LÄNGST
a
, Julian LIENHARD
a
, Rune NOËL
b
,
Yuliya ŠINKE BARANOVSKAYA
b
, Martin TAMKE
b
, Mette RAMSGAARD THOMSEN
b
*str.ucture GmbH
Lindenspürstr. 32, 70176 Stuttgart
lamagna@str-ucture.com
a
str.ucture GmbH, Stuttgart
b
Centre for Information Technology and Architecture (CITA), KADK Copenhagen
Abstract
This paper discusses the design, simulation and construction of a bending-active textile hybrid structure
commissioned to the authors as part of the 2018 Venice Biennale. The hybrid structure combines the
flexibility and elastic properties of GFRP rods together with bespoke CNC knitted fabric, creating a
subtle equilibrium of forces along the unfolding of the installation. Building on the knowledge developed
by the authors on previous bending-active hybrid prototypes, the structure represents the latest effort in
terms of integration of design analysis tools within a holistic and comprehensive workflow. This enables
designers to step fluently from initial concept development and definition of overall shape to the final
specification of the knitted membrane structure on loop level for digital fabrication. With particular
emphasis on the simulation tools employed, the paper will focus on the most up-to-date computational
technologies and numerical approaches that are currently being developed for the design and analysis of
bending-active and textile hybrid structures. Specifically, three distinct environments were used to form-
find and analyse the structural behaviour of the installation, these environments being Kangaroo (vector-
based approach), Kiwi3d (Isogeometric Analysis) and SOFiSTiK (Finite Element Analysis). This all-
encompassing approach provided the perfect platform to cross-benchmark the three different methods,
highlighting the qualities of each one and providing valuable information on the most appropriate
software within a certain stage of design.
Keywords: bending-active, textile hybrids, form-finding, simulation, CNC knitting
Fig. 1. Scale model of the vaulted textile Fig. 2. Bespoke CNC knitted fabric

Proceedings of the IASS Symposium 2018
Creativity in Structural Design
2
1. Introduction
Bending-active hybrid structures (BAHS) (Fig. 1, Fig. 2) have been gathering growing interest within
the research community in the past years [1]. Combining the flexibility of bending elements with
tensioning membranes, very lightweight structures can be achieved in this way. These qualities of BAHS
make them perfectly suitable for quickly erecting large spanning canopies, shading systems and
temporary installations [2]. Besides these structural considerations, what has been drawing a
considerable number of researchers towards the topic is the increasing development of new
computational tools and approaches for the simulation of flexible systems. Based on the authors’
experience, three approaches (and associated software) have established themselves so far as the most
used and useful: Kangaroo, Kiwi3d and SOFiSTiK. Far from being competitors, each approach has
shown its strength and advantages at different stages of design and planning, each one complementing
and enriching the understanding of the system’s behaviour. In a benchmark conducted by the authors to
appear in this same issue of the proceedings [3], the three numerical approaches were compared for
accuracy against a simple example. The benchmark shown in the paper was specifically focused on the
accuracy of the results for the displacement of a simple cantilever beam. Major differences in the results
between the three approaches could be noticed for a small number of elements. As the elements
increased, the results converged towards the analytical solution. Despite the individual differences in
accuracy, each single software demonstrated pros and cons. Whilst the results of SOFiSTiK tend to be
extremely precise even at very low resolution, it is notoriously laborious to set up a complex modelling
environment. Kangaroo on the other hand, despite slightly less accurate results, presents a clear
advantage in terms of speed and modelling pipeline. Kiwi3d, almost at the intersection of both worlds,
combines accuracy at the cost of slightly higher overhead within an intuitive modelling environment
that relies on the native NURBS description of many CAD programmes.
Rather than mutually excluding each other, all three approaches were used in an all-encompassing
framework for the design and development of the extension of the Danish Pavilion for the 16
th
Architectural Biennale in Venice (Fig. 1, Fig. 2). Each stage of the design, analysis, dimensioning and
validation of results was performed with the appropriate program and the information cross-linked and
exchanged through the different levels of design, triggering modifications and adjustments based on the
intermediate results. Isoropia investigates the making of new computational modelling systems that
enable the rethinking of material practice in architecture, examining how design tools can integrate and
compose material simulations in design.
2. Description of computational methods
2.1. Kangaroo
A Dynamic Relaxation (DR) inspired solver, it 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. [4].
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.
At the time of writing, the Kangaroo solver is based on the manipulation of vertices with three degrees
of freedom (DOF) 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 [5]. 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.

Proceedings of the IASS Symposium 2018
Creativity in Structural Design
3
2.2. Kiwi3d
Kiwi3d, is a newly developed plugin for Grasshopper3d/Rhino3d, which enables to link Isogeometric
Analysis methods (IGA) as introduced by Hughes et al. [6] directly into CAD. IGA is a non-standard
discretization method for Finite Element Analysis (FEA). It uses Non-Uniform Rational B-Splines
(NURBS) as basis functions for the Finite Elements, which are commonly used for the geometry
description in CAD. Consequently, IGA allows to directly perform simulations on the NURBS-based
geometry model of CAD. Therefore, model reparameterization (commonly known as meshing) becomes
dispensable and allows to easily unify computational environment of design (CAD) and simulation
(FEA).
Further advantages are associated to isogeometric based simulation methods. In terms of modelling, the
parametrization for boundary conditions such as loads, supports and coupling entities is independent
from the geometry parametrization itself. Also, all CAD features are available e.g. for the derivation of
additional structural members.
As IGA-based simulation models consistently preserve the NURBS representation, it enables to model
consecutive simulations sequences in a consistent manner, such as required, when modelling additive
construction stages (Building Process Modelling).
Kiwi3d is developed at str.ucture GmbH. It wraps the FEM-kernel Carat++, which is proprietary
research at the Chair of Structural Analysis at the Technical University of Munich (Prof. Dr.-Ing. K.-U.
Bletzinger). It provides access to a broad variety of types of simulation, such as linear, non-linear
analysis as well as form-finding. The user can choose from finite element topologies, such as a shell and
membrane element (2D) as well as a beam and cable element (1D). The advanced features of the
implemented element formulations also allow to consider reference geometry configuration. This
implies that it is possible to persistently keep track of stress and displacements stages, as required in the
modelling of building processes. Application examples in this context can be found in [7][8][9].
2.3. SOFiSTiK
Finite Element Analysis is the de facto standard in the field of engineering simulation [10]. 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 it 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 (beam) and two-dimensional (shell) elements are generally sufficient to
model all types of structural systems. In most Finite Elements codes beam elements are formulated as
Timoshenko beams, whilst 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 [11].
Geometrical nonlinear Finite Elements are used for the computation of problems involving large
deformations [12]. 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. Recently, an Active Bending
module (ACTB) was implemented which automatically calculates the internal stress state from a curved
beam assuming that it was initially straight, making it possible to retrieve the bending forces directly
from the curved geometry of the element.

Proceedings of the IASS Symposium 2018
Creativity in Structural Design
4
3. Form finding approaches
3.1. Kangaroo
Thanks to its speed and intuitiveness, Kangaroo was used as the main design platform for the installation.
The custom modelling pipeline developed by Deleuran [13] helped abstracting the design domain into
an array of topology assemblies (Fig. 3). The computational pipeline allows users to simply sketch
polygonal topology assemblies which in a subsequent form finding step relax into their equilibrium
position. This approach allowed to create a large series of designs iterations, giving the designers the
possibility to quickly explore topological variations and modify the geometry on the fly based on
structural, aesthetical and architectural requirements.
Fig. 3: Kangaroo design model of the canopy (top); topology assembly as a flat configuration (bottom left);
form found configuration of the initially flat assembly (bottom right).
3.2. Kiwi3d
The plugin Kiwi3d was used to evaluate form finding results, which were developed with Kangaroo,
with respect to displacements and stresses under common design load cases such as self-weight or wind
loads, while the erection process was also considered. Therefore, a parametric process was developed
which was integrated into the described design process.
The process itself contains 5 substeps, which will be described in the following by referring to a single
module, shown in Fig. 4.

Proceedings of the IASS Symposium 2018
Creativity in Structural Design
5
(1) (2) (3) (4)
(5) (6)
Fig. 4: Simulation Process of shape development as used for the global structure: (1) bending of rods, (2) relaxation
of rods, (3) adding of initial membrane geometry and form finding of membrane, (4) relaxation of membrane, (5)
application of wind load, (6) deflection under wind load.
The initial geometry setup (layout, orientation and length of rods and cables) was taken from the
Kangaroo model configuration:
1. The rods were form found by actively contracting the so-called X-cables (Fig. 4, (1)). During
the form finding process modified material properties are used, due to numeric reasons. An
initial imperfection is applied to the rod geometry.
2. In a relaxation step, the actual displacements and stresses considering the correct material
properties are evaluated (Fig. 4, (2)). The rod geometry for this second simulation is taken from
the deformed result model of the first simulation (Step 1). To consider the stresses which are
already applied (deformation from step 1 to step 2), the memorized stresses, a reference
geometry is assigned to the rods. This reference geometry is the undeformed (initial) geometry
of step 1 (straight rods). If the X-cables would be removed, the rods would snap back to their
initially straight configuration.
3. In the following step the initial geometry setup for the membrane is added to the model (standard
CAD operation) and a form finding simulation performed (Fig. 4, (3)). Again, the rods contain
a reference configuration to the initial geometry layout (step 1).
4. In the following step, a relaxation is applied to the membrane. (Fig. 4, (4)). The rods keep the
reference to step 1.

Proceedings of the IASS Symposium 2018
Creativity in Structural Design
6
5. An external wind load is applied. The membrane contains a reference to the form finding result
after relaxation (result of step 4) together with the defined internal prestress, while the bending
of the rods is considered via the reference to their configuration in step 1 (Fig. 4, (5)).
6. The deflected shape under wind load is shown (Fig. 4, (6)).
In the same way as described for the single module, the process was applied to the model of the global
pavilion structure, as shown in Fig. 5.
Fig. 5: Result of form finding for global geometry model, created using Kiwi3d and considering the individual
simulation steps of the erection process.
3.3. SOFiSTiK
The whole form finding process was reproduced in SOFiSTiK using the plugin STiKbug [14] to validate
the results and run detailed analysis of the structure. Compared to the two previous approaches, a fully-
fledged Finite Element simulation requires higher modelling accuracy, meaning longer pre-processing
time and fewer possibilities to explore an extensive array of variations. Nonetheless, the results achieved
through conventional FEA provide the deepest insight into the global behaviour of the structure, a
necessary aspect when considering safety and having to take into account building regulations. In Fig.
6 the maximum von Mises stress under wind pressure is shown for each GFRP rod of the canopy. This
analysis step was crucial to identify the critical areas of the elements and therefore prevent potential
failure.
Fig. 6: Maximum von Mises stress under wind pressure for each GFRP rod of the canopy calculated in SOFiSTiK.

Proceedings of the IASS Symposium 2018
Creativity in Structural Design
7
4. Isoropia - balance, equilibrium, stability
Fig. 7: Views of the Isoropia canopy for the Danish Pavilion at the 16
th
Venice Biennale 2018.
Isoropia was conceived as a lightweight canopy embracing the Danish Pavilion at the Giardini della
Biennale in Venice (Fig. 7). The installation is a finely tuned balance between tension and compression.
The cablenet is carefully tensioned until the correct configuration is reached, achieving a subtle state of
equilibrium between the bent rods and the tensioned cables. The knitted fabric patches spanning between
the bays actively restrain the buckling of the rods by keeping them constrained within their knitted
pockets. The cables further tension the fabric as their span is divided in several areas which are attached
directly to the textile. This creates a series of singular high-points in the fabric. In these areas
reinforcement patches are sewn on the fabric using the fabrication capabilities provided by CNC knitting
machines.
For the realisation of Isoropia 60 coupled GFRP rods were used with varying sections between
26x19 mm and 24.3x20.3 mm and an elastic modulus of 26000 MPa. The canopy makes use of Dyneema
cables for the external tensioning, edge cables as well as internal cables running through the patches.

Proceedings of the IASS Symposium 2018
Creativity in Structural Design
8
5. Conclusions
The realisation of the Isoropia canopy has proven to be an interesting challenge in terms of design and
simulation tools. A necessary requirement for the realisation of the project was to show that the canopy
could withstand the maximum wind loads blowing over Venice. Therefore, design intentions and
engineering prerequisites had to be brought together to mediate between different and often competing
requirements. To break down the workflow in an optimal way, different tools were chosen to be used at
different stages. This decision revealed itself to be beneficial for the speed of execution of the project,
as more refined tools were used only at a specific stage of development. In this way the design process
developed in Kangaroo was informed and steered by information provided by the middle stage of
analysis run in Kiwi3d, whereas a detailed analysis of the structural behaviour of the canopy occurred
at the latest stage of the development process with the use of SOFiSTiK. This “division of labour”
between software environments has proven to be particularly effective, pointing for the future towards
further integrated multi-stage design/analysis environments.
6. References
[1] S. Ahlquist, J. Lienhard, J. Knippers and A. Menges, “Physical and Numerical Prototyping for
Integrated Bending and Form-Active Textile Hybrid Structures,” Rethinking Prototyping,
proceedings of the 2013 Design Modelling Symposium, Berlin, Springer, 2013.
[2] S. Ahlquist, L. Ketcheson and C. Colombi, “Multisensory Architecture: The Dynamic Interplay of
Environment, Movement and Social Function,” Architectural Design, vol. 87, no. 2, pp. 90-99,
DOI: 10.1002/ad.2157, Mar. 2017.
[3] A. M. Bauer, P. Laengst, R. La Magna, J. Lienhard, D. Piker, G. Quinn, C. Gengnagel and K.-U.
Bletzinger, “Exploring Software Approaches in Simulating Bending Active Systems,” Proceedings
of the 2018 IASS Annual Symposium “Creativity in structural design”, Boston, 2018.
[4] S. Bouaziz, S. Martin, T. Liu, L. Kavan, and M. Pauly, “Projective dynamics: fusing constraint
projections for fast simulation,” ACM Trans. Graph. TOG, vol. 33, no. 4, p. 154, 2014.
[5] M. R. Barnes, S. Adriaenssens, and M. Krupka, “A novel torsion/bending element for dynamic
relaxation modeling,” Comput. Struct., vol. 119, pp. 60–67, Apr. 2013.
[6] T. J. R. Hughes, J. A. Cottrell, and Y. Bazilevs, “Isogeometric analysis: CAD, finite elements,
NURBS, exact geometry and mesh refinement,” Comput. Methods Appl. Mech. Eng., vol. 194, no.
39–41, pp. 4135–4195, Oct. 2005.
[7] P. Längst, A.M. Bauer, A. Michalski, and J. Lienhard, “The Potentials of Isogeometric Analysis
Methods in Integrated Design Processes,” Proceedings of the 2017 IASS Annual Symposium
“Interfaces: architecture. engineering. science”, Hamburg, 2017.
[8] A.M. Bauer, P. Längst, R. Wüchner, and K.-U. Bletzinger, “Isogeometric Analysis for Modeling
and Simulation of Building Processes,” Proceedings of the 2017 IASS Annual Symposium
“Interfaces: architecture. engineering. science”, Hamburg, 2017.
[9] A.M. Bauer, R. Wüchner, and K.-U. Bletzinger, “Isogeometric Analysis for Staged Construction
within Lightweight Design,” VIII International Conference on Textile Composites and Inflatable
Structures, Munich, 2017.
[10] S. Schleicher, A. Rastetter, R. La Magna, A. Schönbrunner, N. Haberbosch and J. Knippers, "Form-
Finding and Design Potentials of Bending-Active Plate Structures,” Modelling Behaviour,
proceedings of the 2015 Design Modelling Symposium, Berlin, Springer, 2015.
[11] K.J. Bathe. “Finite Element Procedures.” Prentice Hall, Upper Saddle River, New Jersey, 1996.
[12] C. Felippa. “Nonlinear Finite Element Methods.” Lecture material, University of Colorado,
Boulder, 2012.
[13] G. Quinn, A.H. Deleuran, D. Piker, C. Brandt-Olsen, M. Tamke, M.R. Thomsen, and C. Gengnagel,
“Calibrated and Interactive Modelling of Form-Active Hybrid Structures,” in Iass 2016 Tokyo
Symposium, 2016, pp. 1–9.
[14] J. Lienhard, C. Bergmann, R. La Magna, and J. Runberger, “A Collaborative Model for the Design
and Engineering of a Textile Hybrid Structure,” Proceedings of the 2017 IASS Annual Symposium
“Interfaces: architecture. engineering. science”, Hamburg, 2017.