Proceedings of the International Association for Shell and Spatial Structures (IASS)
Symposium 2015, Amsterdam
17 - 20 August 2015, Amsterdam, The Netherlands
Modelling, Analysis and Construction of Bending
Active Tensile Membrane Hybrid Structures
Anders HOLDEN DELEURAN1, Michel SCHMECK2, Gregory QUINN2,
Christoph GENGNAGEL2, Martin TAMKE1, Mette RAMSGAARD THOMSEN1
1Centre for Information Technology and Architecture (CITA),
Royal Danish Academy of Fine Arts, School of Architecture
Philip de Langes Allé 10, 1435 Copenhagen, Denmark
2Department for Structural Design and Technology (KET),
University of Arts Berlin
Hardenbergstrasse 33, 10623 Berlin, Germany
The project is the result of an interdisciplinary research collaboration between CITA, KET and
Fibrenamics exploring the design of integrated hybrid structures employing bending active elements
and tensile membranes with bespoke material properties and detailing. Hybrid structures are defined
here as combining two or more structural concepts and materials together to create a stronger whole.
The paper presents the methods used and developed for design, simulation, evaluation and production,
as well as the challenges and obstacles to overcome to build a complex hybrid tower structure in an
Keywords: hybrid structures, computational design modelling, form finding, bending active, bespoke
knit, finite element analysis
1. Introduction and Design Principle
The Tower is a hybrid structural system constructed from stacking overlapping glass fibre reinforced
plastic rods embedded in a bespoke knitted membrane made from high tenacity yarn. Knitting enables
the inclusion of detailing for joining and tensioning the system into the membrane itself. The tower is
a form active structural system exploring the potential of combining bending and tensile members for
architectural design. Compared to static and homogenous systems this involves an increased level of
complexity in terms of modelling, analysis, fabrication and construction. Our research aims to
examine how architects and engineers may collaboratively engage with this challenge. We approach
this under the working hypothesis that developing new computational design models for implementing
feedback between different scales of engagement can lead to better, more creative and resilient
building practices. The project explores how design intent and feedback can be passed between
different scales of engagement and modelling. Here the project defines three central design
challenges: At the macro scale of the structure the architectural typology of a hybrid tower presents
challenges outside of common applications of form finding, such as shells and membranes. At the
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam
meso scale of the elements the project explores the potential of bending active tensile membrane
structures as a strategy for increasing resilience through actively deforming structures. At the micro
scale of the material the project introduces bespoke knit as the tensile membrane. The project
investigates if this type of construction is sufficiently strong and if it is able to create a continuous
force flow between discrete elements in the structure, circumventing the obstructive effect of stiff
connections between active bending members . The membrane between the rods of each layer is
radially pulled to the tower central axis. This results in a spoke wheel effect which provides horizontal
stiffness and braces the rods which carry vertical loads. The rods interface the membrane in pockets
and tubes integrated in the knit. The tower is a soft structure - flexible and bendable - capable of
responding to impact and its changes in its environment. This inherent flexibility is considered as a
property of potential resilience. That is, the ability to recover from or adjust to change of external
stimuli. Focusing on the strain of live loads from wind, the soft structure stores energy when it is
deformed elastically and releases that energy upon recovery.
Figure 1: The Tower in the Courtyard of the Danish Design Museum. The interior of the Tower is
characterised by the tensioning system and the resulting cone-like membranes. Photo: Anders
2. Computational Design Modelling
2.1. Development Challenges
The project contributes to two modelling challenges: 1) interfacing multiple heterogeneous
computational design models in pipelines characterised by cyclic dataflow, 2) resolving design cases
which are inherently complex and require phenomena to be modelled as the product of local
interacting behaviours. The first challenge probes how we interface generative and analytical design
models in integrated modelling pipelines with the goal of improving the design space search
delineated by the models. The second challenge explores how to model the hybrid behaviour of
bending active tensile membrane structures and its practical implementation in an interactive form-
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam
finding model. In terms of developing a robust, fast and flexible design modelling pipeline several
inquiries were examined:
• How to form find hybrid bending active tensile membrane structures?
• Which constraint solvers meet our requirements and how do we implement them?
• How do we establish a flexible logic for generating the tower topology?
• How do we define meaningful modes of analysing form found geometry?
• How do we develop relevant and bespoke descriptions for fabrication?
2.2. Form Finding Hybrid Bending Active Tensile Membrane Structures
During the form finding of membranes, the membrane is set to a fraction of its real stiffness in order
to facilitate large deformations. The resultant shape represents the pure flow of forces. In a hybrid
system a different type of element is added. Unlike the membrane, the rods maintain their bending
stiffness during form finding. The higher the curvature and the diameter of the rods, the higher the
stresses in the material. The material of the rods needs to have a high strength and a low Young’s
modulus to be able to perform accordingly. It is important to create a curvature high enough to tension
the membrane without risking breaking the rod under excessive bending. Under influence of external
loading, deflections are quite big and can exceed the bearing capacity of the structure’s elements. That
is why structural analysis is essential to guarantee the performance of the tower. In case of exceeding
the bearing capacity, the design of the structure has to be revised.
The FE environment (Sofistik) is suited to the real-time form finding of complex structural systems
with large deformations; however it does provide a precise mathematical definition of the global
stiffness matrix. Large deformations must be simulated using an incremental process. To bend beam-
like elements into shape, the elastic cable approach, developed by Julian Lienhard , was used.
Single element elastic cables are connected to the initially un-deformed rod then a pre-tension force is
applied to the cable causing it to shorten in length and subsequently pull the cable ends towards one
another. After the rod is pulled to its defined curvature, the membrane is then fixed to the deformed
rod, and the system is released. The rod then tries to straighten again, subsequently tensioning the
membrane while the membrane restrains the rod and both find their equilibrium. With a complex
system like the tower, this method quickly hits its limits. Therefore, a two-stage process was used. In a
first step form-finding is carried out in the Grasshopper environment using a tool based on a mass
spring system (MSS). The high stability and speed of the process allows an experimental approach
which gives almost real-time feedback. The disadvantage is that the axial and bending stiffness
definitions in Kangaroo are dependent on assorted mathematical approximations whose numerical
precision is still undergoing validation. After completing form finding, the geometry can be baked and
exported to the FE-environment (Sofistik). Here the lines and surfaces are converted into structural
beam and membrane elements and materials, cross-sections and support conditions are defined. In a
second step the stresses from the FE simulation are superimposed with stresses from the form-finding.
The stress within the bent rod depends on the curvature, the diameter and the Young’s modulus of the
used material and is expressed by the following simple equation. Adding the resultant stress gives a
good impression of the overall stress level including bending and external impact
Proceedings of the International Association for Shell and Spatial Structures (IASS) Symposium 2015, Amsterdam
Figure 2: The elastic cable approach for bending beam elements generating highly accurate residual
2.3. Modelling Precedence and Implementation
The Tower extends research by CITA/KET exploring computational modelling of actively deforming
structures (Deleuran et al. , Quinn et al. , Alpermann & Gengnagel  and is related to work
on hybrid structures by Ahlquist & Menges , Lienhard  and Mele et al. . We built upon
this by similarly implementing a particle based constraint solver operating on discrete piecewise linear
geometries for modelling the behaviour of bending members and tensile membranes in one unified
and interactive system. This is integrated within a larger modelling pipeline in the Grasshopper
environment of the Rhino 3D CAD package. There are several solvers available for Grasshopper
including Kangaroo  and ShapeOp . These model bending behaviour accurately but require
uniform discretisation. This adversely affects the freedom with which to construct the input geometry
and has the consequence that one must dimension the members relative to each other prior to form
finding. We were fortunate to get involved in the early stage testing of Kangaroo2 (codenamed Joey).
It improves upon existing solvers on several levels instrumental to the project: 1) The API is designed
for being implemented through scripting, allowing us to develop a bespoke, minimal and optimised
pipeline. 2) Constraint weights can be set arbitrarily high and still remain stable, enabling the
simulation of stiff materials with fast convergence. 3) The bending constraint implements the
resolution independent Adriaenssens and Barnes model , enabling the modelling of non-uniformly
discretised bending members.
Figure 3: Early prototype demonstrating basic modelling, analysis and fabrication results
2.5. Computational Design and Form Finding Modelling
The computational design modelling pipeline is divided into five parts integrated in one multi-stage
Grasshopper definition. The central algorithms and functionality are implemented as GHPython
components which implement the RhinoCommon and JoeyPhysics libraries:
Figure 4: The computational design modelling pipeline on the Rhino/Grasshopper side.
2.5.1. Generate Tower Topology and Member Geometries
The design principle of stacking overlapping bending members around a central vertical axis is used
as the geometrical principle for generating tower topologies. The model input variables for this
process is a list of values which sets the number of sides, the side length and the number of floors. The
model outputs equilateral polylines representing the un-discretised bending members and membrane
cells. A list of membrane cells forms a membrane patch spiralling around the tower. These polylines
are further processed to generate the geometries which form the input for the form finding process.
This process has three models which generate the bending member polylines, the membrane patch
meshes and the tension member lines. The bending members are discretised and extended to overlap
with bending members from one floor to the next. A second layer of bending members is added to the
ground floor and the anchoring points of these layers are moved apart. The membrane cells are used to
generate and subdivide meshes representing the knit patches. The tension system is generated by
cross-referencing the centroids of the membrane cells with the membrane patch meshes.
2.5.2. Form Finding and Bending Member Dimensioning
The form finding and dimensioning process has three stages: generating, exercising, and refining
constraints. A bending member is represented by a spring constraint for each edge maintaining its
length, and, a bending constraint for each vertex along the polyline and its neighbours which tries to
keep the angle formed by the three points at 180 degrees. A membrane patch is represented by a
spring for each edge which minimises its length. Naked edges are given a weight multiplier, enabling
the effect of tension wires along the membrane perimeter. The internal tension system is represented
as springs. Constraints are fed to a component which allows the designer to interactively manipulate
constraint values and geometries. The component uses the Joey physical system to iteratively solve
the constraints in a feedback loop and converge to a state of equilibrium. The designer manipulates
two lists of constraint values, on a per floor basis, which dynamically dimension the bending member
lengths and the distances along the bending members where they intersect their neighbours. This
enables the designer to control the macro shape of the tower using exact member dimensioning. The
value lists are implemented as scripted “gene pools” which automatically adapt to changes in the
tower topology. The process outputs the form found geometries and solver statistics. The bending
member results were verified using 3D scanning of physical prototypes.
Figure 5: Three instances of tower topologies tagged by genotype. The local polyline members of the
system are highlighted in the fourth image, followed by the three structural member types and their
Figure 6: Five steps in the iterative and interactive form finding and dimensioning process.
2.5.3. Analysing Form Found Geometries
The pipeline has two analysis models which guide the designer towards design instances which may
perform better in relation to structural performance. A desired geometric property in membrane design
is high double curvature as this stabilises the membrane. This property is analysed by a component
which returns the local curvature of each vertex and visualises it in the viewport. For the bending
members a key geometric property with structural implications is the local bending radii. This value
can be mapped to the bending stress, utilisation and reserve of the member in isolation of other load
cases. The local radius is 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 which
also provide a visual representation of the bending orientation.
Figure 7: Comparative bending radii analysis of differently dimensioned towers. Note the relationship
between macro shape and bending radii.
Figure 8: Developing a membrane in the XY-plane. The values indicate differences between the form
found and the in-plane meshes (MAD = Mesh Area Difference, TELD = Total Edge Length
2.5.4. Developing Membrane Patches in the Plane
Getting the membranes into the plane for fabrication is challenging as they are double curved and may
not be discretised into panels as with conventional membrane design. Instead we developed a
constraint-based approach implementing Joey. A form found membrane mesh is input to a process
which also inputs a planar topological identical mesh with equilateral edges. A constraint is generated
for each vertex of the planar mesh restraining it to the XY plane. Each edge of the planar mesh is
constrained to the length as its corresponding edge in the form found mesh. The constraints are solved,
outputting a planar mesh which is nearly metrically identically to the form found mesh based on area
difference and total edge length difference. The bounding box of the output mesh is minimised using
the Galapagos evolutionary solver to ensure that it will fit the knitting machine.
3. Structural and FE Modelling
3.1. Superpositioning stresses
The total stress in the system to be evaluated is the addition of the residual stresses from form-finding
[FF], plus the residual stresses from membrane pre-stress [P] and finally stresses from the static load
cases of dead load [DL] and wind [W]. As described in sections 2.2 and 2.4.3 the stresses from the
form finding [FF] have not been calculated in the global model but are taken from a bending radius
analysis. Therefore the results of the FE-model do not include residual stresses from the form finding.
Total Stress = [FF] + [P] + [DL] + [W]
The larger the diameter, the smaller the stress reserve for the bending radii in our structure. This
means that a delicate balance is needed to be found between section diameter and internal stress
3.2. Material Properties
For the FE model, the material properties for GFRP rods were taken from the datasheets given by the
manufacturer. As the properties of the knitted material were to be designed during the project,
properties of a standard PVC Type I membrane with a thickness of 0.8mm were taken as a point of
departure. Tests of the biaxial behaviour of the fabric knitted from a high strength polyester yarn at the
University Duisburg-Essen, Laboratory for Lightweight Structures showed however significant
differences between the designed knitted material and our first assumptions on which we build our
Young's Modulus [N/mm²]
PVC Type 1 Membrane
Once finally available, definitive test results of the knitted fabric indicated that its stiffness was
approximately 50 times lower than that of a standard PVC1 membrane. While a FE simulation with
these lower stiffness properties was attempted, it became quickly apparent that the global stiffness was
far too low and subsequently the simulation failed. While the yarn of the knit is sufficiently strong, the
difference in behaviour between knit and woven, laminated membrane can be explained through the
structure of the material: in a woven membrane: multiple parallel fibres are laid out rectilinearly in a
more or less straight fashion and curve only slightly around each other. Membrane material therefore
has almost no geometric stretch in the two fibre directions under tension. In knitted fabrics one
continuous yarn runs in sinusoidal loops. Under tension, theses sinusoidal yarns are pulled straight,
which leads to a large amount of stretch. Only after “locking” in this linear configuration the material
starts to bear loads in a linear-elastic manner.
3.3. Wind Loads and Bracing System
The distribution of wind loads on the tower is similar to those of a cylindrical body. In addition to a
compressive stress on the front part of the structure the dominant influences are lateral suction forces.
These suction forces pull apart the tower to the sides. The size of the recognized expense corresponds
to the values for temporary structures in accordance with DIN 4112. To increase the radial stiffness
and that way keeping the structure from global buckling, a spoke-wheel was added the structure. This
kind of restraining mechanism has been described by Alpermann and Gengnagel for arcs  or
membrane restrained columns and girders .A set of tension cables is connected to the centre points
of each storeys membrane surfaces. That way opposing suction forces can be short-circuited and the
deflection in ground-plot can be reduced dramatically.
Figure 9: Wind load distribution and bracing system.
3.4. Prototype Analysis
3.4.1. Prototype 01 – Frame Only
The first analysed model is a tower with 6 floors and 6 support feet. The following tables summarize
the results from the 14mm beam simulations. The maximum stress values, stress utilisation and
maximum displacement. The stresses given here do not include residual stresses from form finding
[FF]. Regarding the simulation, it is quite clear to see that the stiffer the model, the more likely to
converge the FE simulation is. This explains some of the earlier challenges with the simulations: we
are dealing with a very soft structure.
Figure 10: Stresses, utilisation and displacement of the basic model
3.4.2. Prototype 02 – adding the Membrane
After various iterations the tower was increased to 8 leg/8 storey subdivision. The ground floor
contains 4 openings while every second side is closed with membrane for structural reasons. The
convergence of the system was quite good and the simulation produced sensible structural output. The
stress analysis of the tower follows a two-step process
1. Bending radii for each storey are taken from the particle-spring based form-found model and
the initial stress level from bending the rods into shape is calculated.
2. Stresses of the FE-simulation are analysed and added to the stress level of the form-finding
Figure 11: Stresses of chosen design
The above mentioned results from the bi-axial testing from the Essener Labor für leichte
Flächentragwerke came only in during the actual production of the knit. With the new, 50-times lower
Young’s modulus a converging calculation could not be achieved.
3.5 Conclusion after FE-Analysis
Crucial to the stability of the chosen structure under wind load is a stabilisation of the curved
compression elements via the fabric. For this, a certain stiffness of the fabric is required. The knitted
membrane was so soft, that precisely this effect could not be sufficiently established. With the given
material properties, the FE simulation could only resist 20% of the actual load level. While the FE
model is a precise in the simulation of the rods and membrane, its representation of the joints was also
subject to imprecisions. In the final prototype the rods are only connected to one another by shared
pockets in the fabric, whereas in the FE model, the rods are rigidly fixed together at the intersecting
node. The effects of friction within the textile tubes and pockets were not simulated. Extensive testing
would be required to establish a precise representation of node behaviour in FE.
Figure 12: Different intersections in different environments.
4. Discussion and further work
The tower was built in Copenhagen and under first impressions performed quite well under external
loads. The overall stiffness seemed to be higher than the simulation suggested. This is due to
composite effects from friction, additional zip ties and geometrical stabilisation which were not fully
accounted for in the models. Furthermore, overstressing of the GFRP rods does not result in their
sudden failure but instead in subtle and non-catastrophic breaking of individual edge fibres.
The modelling pipeline performed very satisfactorily for generating and iterating design instances.
While the bending radii analysis was instrumental to this, an increased integration of material
properties in the form finding is desirable. This might include torsion and load cases as well as
providing more modes for visualising analysis results. The current form finding does not model
realistic properties of the membrane and the resulting interaction and deformation of the adjacent
bending members is not taken into account. This interaction turned out to be crucial in the physical
construction. A higher degree of integration between design modelling and structural analysis FEA
modelling would also be desirable. First steps have been taken to further explore this.
The project demonstrates, that a complex hybrid structure of bending active rods and membrane
systems can be form found and analysed using an interconnected particle spring and FE simulation.
As particle spring does not simulate external and internal forces a subsequent iteration with FE allows
to specify material and dimensions. The combination of the flexible particle-spring and the precise
FE-world can lead to satisfactory design outputs as well as solid analysis. A higher degree of
integration of the FE-analysis will reduce the feedback time and increase the degree of informational
feedback to the design process. Related work  shows further potential in this combination of tools,
as the integration of anisotropic behaviour in both tools would create a design environment, which
allows for the design of interacting material and structural behaviour all between macro and meso
scale. However current FE tools are not able to precisely simulate the highly nonlinear material
behaviour of the knitted fabric. The FE- model is very sensitive on changes of stiffness and force
parameters and can hence not follow the fast design iterations, which are enabled by the particle
The project is funded by The Danish Council for Independent Research (DFF). Membranes were
developed by Fibrenamics, Universidade do Minho, Guimarães, Portugal. Further development and
fabrication took place with AFF a. ferreira & filhos, sa, Caldas de Vizela, Portugal. Mechanical testing
of the knit was conducted by University Duisburg-Essen, Laboratory for Lightweight Structures. The
Tower was exhibited at Designmuseum Danmark. We wish to thank: Daniel Piker for involving us in
testing Joey/Kangaroo2. Ida Katrine Friis Tinning, Dongil Kim, Henrik Leander Evers, Esben Clausen
Nørgaard and the students of CITAstudio for their tireless support.
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