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


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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.
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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,
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
, Philipp LÄNGST
, Rune NOËL
, Martin TAMKE
*str.ucture GmbH
Lindenspürstr. 32, 70176 Stuttgart
str.ucture GmbH, Stuttgart
Centre for Information Technology and Architecture (CITA), KADK Copenhagen
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
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
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
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
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
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
(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
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
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
4. Isoropia - balance, equilibrium, stability
Fig. 7: Views of the Isoropia canopy for the Danish Pavilion at the 16
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
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
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.
... This customizability not only influences the membrane form, but also enables the integration of external structural elements. Such strategies can be found in the domain of CNC-knitted membrane installations, as seen in the Hybrid Tower and Isoropia by the Centre for Information Technology and Architecture (CITA) [9,10]. In these examples, fabric membranes were fully fashioned and integrated with continuous channels. ...
... To minimize the weight of the membrane, single needle bed stitch patterns (versus double needle bed stitch patterns) were chosen. Piquet lacoste stitch pattern, which is formed by alternating between knit only rows and knittuck rows [10] (Fig. 7), was selected because the presence of tucks (as opposed to knit or miss stitches) reduces the course-wise (horizontal) shrinkage after knitting, resulting in a wider piece of fabric compared to other single needle bed stitch patterns. To minimize the amount of cutting and sewing required, the membrane was shaped during the knitting process using two methods. ...
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... Although scarce, examples of architectural designs and research work on knitted structures exist. For instance, the myTread and Lumen installations by Jenny Sabin (Sabin, 2013;Sabin et al., 2018), Isoropia and The Tower developed at the CITA -Centre for Information Technology and Architecture in Copenhagen (Deleuran et al., 2015;La Magna et al., 2018;Ramsgaard Thomsen et al., 2019), the Knit Tensegrity Shell project by Gupta et al. (2019) and Sean Ahlquist's sensory architecture (Ahlquist, 2015(Ahlquist, , 2016. These structures are, however, with some exceptions, mainly based on the principle of tensile textiles, in which the material is stretched until the structure is virtually stiff. ...
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... The general goal of bending-active structures, as defined by Knippers et al. (2012) is to use large elastic deformations of initially straight or planar building elements for the construction of complex curved geometries and load-bearing systems. Recent work by research teams around the world has shown various successful applications for this concept using bending-active structures for lightweight architectural installations, temporary pavilions, kinetic structures, and compliant mechanisms (Lienhard et al. 2013;Ahlquist and Menges 2013;Schleicher 2015;La Magna 2017;La Magna et al. 2018). However, there are some challenges associated with this construction process. ...
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Gaining rigidity and strength from malleable and flexible parts is the key challenge in the emerging field of bending-active structures. The goal of this construction approach is to use the large elastic deformations of planar elements for the building of complex curved structures. Aiming to contribute to this research and to make new discoveries, the authors of this paper will look at nature for inspiration and explore how structures in the plant kingdom successfully combine high flexibility with high resilience. The focus of this study are the structural principles found in fibrous cactus skeletons. Not only do the cactus skeletons show impressive structural behavior, but also their optimized form, fiber orientation, and material distribution can inspire the further development of bending-active structures. Learning from these models, the authors will present key cactus-inspired design principles and test their practical feasibility in a prototypical installation made from millimeter-thin strips of carbon fiber reinforced polymers (CFRP). Similar to the biological role model, this 6-meter-tall lamellar structure takes advantage of clever cross-bracing strategies that significantly increase stability and improve resilience. The authors explain in more detail the underlying design and construction methods and discuss the possible impact this research may have on the further development of bending-active structures.
... Developed for the 2018 Venice Biennale, it represents a CNC knitted membrane architecture based on a system of arches pulled into tension by a cable-net system. Being a site-specific installation, it required the bespoke variation of each membrane through functional material grading [12]. In order to increase the structural performance of the arches, the knit variation took place through the methodical evaluation of fibre length and its deduced extendability to increase the depth of tensioned cones. ...
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This paper examines the use of machine learning in creating digitally integrated design-to-fabrication workflows. As computational design allows for new methods of material specification and fabrication, it enables direct functional grading of material at high detail thereby tuning the design performance in response to performance criteria. However, the generation of fabrication data is often cumbersome and relies on in-depth knowledge of the fabrication processes. Parametric models that set up for automatic detailing of incremental changes, unfortunately, do not accommodate the larger topological changes to the material set up. The paper presents the speculative case study KnitVault . Based on earlier research projects Isoropia and Ombre , the study examines the use of machine learning to train models for fabrication data generation in response to desired performance criteria. KnitVault demonstrates and validates methods for shortcutting parametric interfacing and explores how the trained model can be employed in design cases that exceed the topology of the training examples.
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Bending-active structures are able to efficiently produce complex curved shapes from flat panels. The desired deformation of the panels derives from the proper selection of their elastic properties. Optimized panels, called FlexMaps, are designed such that, once they are bent and assembled, the resulting static equilibrium configuration matches a desired input 3D shape. The FlexMaps elastic properties are controlled by locally varying spiraling geometric mesostructures, which are optimized in size and shape to match specific bending requests, namely the global curvature of the target shape. The design pipeline starts from a quad mesh representing the input 3D shape, which defines the edge size and the total amount of spirals: every quad will embed one spiral. Then, an optimization algorithm tunes the geometry of the spirals by using a simplified pre-computed rod model. This rod model is derived from a non-linear regression algorithm which approximates the non-linear behavior of solid FEM spiral models subject to hundreds of load combinations. This innovative pipeline has been applied to the project of a lightweight plywood pavilion named FlexMaps Pavilion, which is a single-layer piecewise twisted arch that fits a bounding box of 3.90x3.96x3.25 meters. This case study serves to test the applicability of this methodology at the architectural scale. The structure is validated via FE analyses and the fabrication of the full scale prototype.
This paper shows a computational approach for knitting net shape preforms with bespoke 3D shapes and patterns. The approach takes partial knitting as the major shaping technique and as the fabrication constraints to generate multicolored pixel-based knitting maps based on given 3D meshes. The generation process includes five steps: 1 generation of wales, 2 generation of courses, 3 generation of 2D knitting maps, 4 stitch placement optimizations, and 5 pattern variations. At final stage, users can get a knittable 3D mesh with each face representing each stitch, as well as a 2D pixel-based knitting map. The knittable 3D mesh allows designers to further design pattern variations; the 2D knitting map can be directly used for generating knitting information in knitting software or easily followed by users.
The paper presents the design to construction process of an ultra-lightweight hybrid temporary structure consisting of a combination of bending-active glass fiber-reinforced polymers arches, a restraining system made of stainless steel cables, and a translucent membrane envelope. After a brief introduction to the basic design concepts and versatility of the modular system to create different shapes, the paper focuses on the fast-track erection procedure that enables to build the pavilion in a very short time. A multi-disciplinary team had collaborated at the design development of the temporary pavilion, built with the aim of deepening a wide range of aspects that are peculiar to temporary architecture. The aim of the second design-to-construction loop, following the first loop which resulted in the construction of the first full-scale prototype, is two-fold: firstly to optimize the innovative mix of lightweight structural components with the aim of reducing the total weight of the building (and thus facilitate transport and installation), and secondly to test the technical details designed to favor reversibility and to ensure the re-usability of the structure for multiple cycles of use. The paper concludes by showing the results achieved and the lesson learned from the first construction of the temporary pavilion in occasion of a one-week event and anticipating the further studies regarding the interface between structure and membrane envelope, also in relation to the building expected life-span and requirements.
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In this paper, we are presenting a design to fabrication system, which allows to produce efficiently and highly automated customised knitted textile elements for architectural application on industrial computer-controlled knitting machines (Computer Numerical Control (CNC) knitting machines). These textile elements can, in this way, be individual in both geometry, detailing and material behaviour. This work extends recent work on CNC knitted tensile members and presents a set of innovations in design and manufacturing, which together allow to build structural systems, in which highly individualised membrane members allow a structure to take on multiple structural states. Underlying these innovations is a shift from the focus on geometry and homogeneity in material and behaviour, expressed in current state-of-the-art membrane structures and materials. Instead our research lays the foundation for a new class of membrane materials with varying bespoke local material properties. In this paper we present the underlying digital tools and processes for design, analysis and manufacturing of these hyper specified textile membranes. We showcase and evaluate the potentials of Computational Knit for novel structural membrane systems through the large-scale installation Isoropia designed and built for the Danish Pavilion in the 2018 Venice Architectural Biennale.
This paper describes the structural design, digital fabrication and construction of KnitCandela, a free-form, concrete waffle shell with KnitCrete, a falsework-less formwork approach using a custom prefabricated knitted textile as multi-functional, structural shuttering layer and a form-found cable net as the main load-bearing formwork. The digitally designed and fabricated textile provided integrated features for inserting and guiding elements such as cables and inflatables that helped shape the sophisticated mould. With a total weight of only 55 kg, the 50 m² formwork was easy and compact to transport. On site, the formwork was tensioned into a timber and steel rig, the pockets were inflated, and then coated with a thin layer of custom-developed, fast-setting cement paste. This paste served as a first stiffening layer for the textile, minimising the formwork’s deformations during further concrete application. Fibre-reinforced concrete was manually applied onto the formwork to realise a 3 cm-thick shell with 4 cm-deep rib stiffeners. The novel approach, for the first time applied at architectural scale in this project, enables the building of bespoke, doubly-curved geometries in concrete, with a fast construction time and minimal waste, while also reducing the cost and labour of manufacturing complex parts.
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Emerging directly from a masterclass held by the authors at IASS 2017, this paper presents a quantitative and qualitative benchmark comparison between three distinct software environments, namely SOFiSTiK, Kangaroo and Kiwi3d, framed specifically within the context of designing and simulating bending-active structures. The three environments differ significantly not only in their numerical methods and implementation but also in their stages of software development, licensing structure and design intent and so their comparison represents a timely and valuable insight into the status quo for the design of bending-active hybrid structures.
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Hybrid, bending-active structures constitute a challenging task for structural design due to the high dependency between shape and forces. Isogeometric analysis suggests itself in this context because of several advantages. Model conversion with concomitant corruption of the simulation results can be overcome. All stages of the construction, which are necessary for the correct simulation of such structures, can be modeled and correctly linked. Moreover, the parameter space of the NURBS description provides a perfectly suited, additional design space for embedded entities, which can be defined independently of the parametrization. The contribution of this paper is a presentation of the basics for embedding within isogeometric analysis and reveals beneficial aspects of nested NURBS descriptions in the context of staged construction. A case study of a staged simulation is carried out and another one for the form-finding procedure of hybrid structures.
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In 2016 and 2017 a master class was held at the Hafencity University Hamburg (HCU) which focused on collaborative design and engineering methods using textile hybrid structures as a case study. After an initial design competition where individual student groups explored design and modelling techniques, the winning design was chosen as a case study to build to scale. The challenge was then to set up a parametric work flow which allowed a large number of students, divided into expert groups, to work on one single design model. The expert groups covered the fields of design, form-finding, structural analysis, material testing, detailing, manufacturing and project management. A collaborative workflow template was set up, which equally addressed complex analysis as well as the need for continuous geometric adjustment to achieve a model which interactively functioned on design, structural and material level. The paper will discuss the workflow models, including the principles that allowed the iterative development of the initial and final form finding, detail design and fabrication planning, as well as material testing across different computational design platforms. It will also provide an overview of the development process through a design narrative. In order to critically discuss the key methods supporting communication between architects and engineers within computational design development and secure project specific design processes, a productive learning environment for all members involved was established. The built case study structure will be exhibited in the foyer of the HCU during the IASS conference.
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Isogeometric analysis provides the fundamental features for a fully CAD-integrated design process. Simple further processing of simulation results is enabled and therefore perfectly suited for the simulation of a building process. This is especially useful if slender (bending-active) structures with highly flexible components and large deformations are part of the simulation. Here, the consideration of construction stages plays a crucial role. This contribution presents essential aspects of an isogeometric building process, and reveals its benefits and challenges. Structural isogeometric analysis together with its basis functions (NURBS) is briefly introduced. The special issues of building processes are demonstrated. The essential feature of coupling within the construction is presented and further extended to an automatic connection between two points. In the end, several modelling aspects w.r.t. suitability of the NURBS patches provided by CAD for structural analysis are outlined.
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Non-standard discretization methods for finite element application allow to rethink common design strategies and planning processes, particularly in the context of lightweight design. Isogeometric Analysis (IGA) methods in particular unveil significant potentials regarding the computer-aided working background, as they enable to use one consistent mathematical model description (Non-Uniform Rational B-Splines, NURBS) throughout architectural and engineering design phases. In order to exploit the potentials derived, the authors developed an interface, which fully integrates isogeometric finite element analysis into standard CAD software environment and consequently unifies the individual features into a single design toolbox. After a brief introduction of the principles of IGA, this paper will present this newly developed design environment and highlight the potentials when applied for structural design via multiple case studies.
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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.
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This paper describes research for the development and implementation of a functionally and structurally intricate textile hybrid architecture, entitled M1, built in Monthoiron, France as a part of the La Tour de l’Architecte complex. The term textile hybrid stands for the mutual exchange of structural action between bending- and form-active systems based on textile material behaviour. The implementation of such a structural logic is critical to this particular project as its presence is minimally impactful to the site which houses a historically-protected and decrepit stone tower from the 1500’s. To explore the complexities for minimal site imposition, lightweight material deployment and spatial differentiation, a set of multi-scalar and multi-modal prototyping procedures are developed. In both physical and numerical simulation, data towards eventual full-scale implementation is cumulatively compiled and calibrated, interleaving aspects of topology, material specification, force distribution and geometry. This paper defines prototyping as the interplay between modes of design in physical form-finding, approximated simulation through spring-based methods, and finite element analysis to form, articulate and materialise the textile hybrid structure. A particular feature in the exchange between and within these modes of design is the consideration of geometric input as a critical variable in the form-finding of bending-active behaviour.
These lecture notes for a graduate course present an introduction to the mathematical theory of finite element methods for the numerical solution of partial differential equations. Covered are conforming and nonconforming (in particular, discontinuous Galerkin and mixed methods) for elliptic partial differential equations and Galerkin methods for parabolic equations.
Early difficulties with motor skills are a common indicator of autism. Overcoming these can improve both the health and the social opportunities of those affected. Sean Ahlquist, Leah Ketcheson and Costanza Colombi – respectively academic specialists in architecture, kinesiology and psychiatry – here describe their cross-departmental collaboration at the University of Michigan which aims to do just that, through specially designed interactive sensory environments.
We present a new method for implicit time integration of physical systems. Our approach builds a bridge between nodal Finite Element methods and Position Based Dynamics, leading to a simple, efficient, robust, yet accurate solver that supports many different types of constraints. We propose specially designed energy potentials that can be solved efficiently using an alternating optimization approach. Inspired by continuum mechanics, we derive a set of continuum-based potentials that can be efficiently incorporated within our solver. We demonstrate the generality and robustness of our approach in many different applications ranging from the simulation of solids, cloths, and shells, to example-based simulation. Comparisons to Newton-based and Position Based Dynamics solvers highlight the benefits of our formulation.