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As opposed to conventional, static structures, transformable structures possess a transformational capacity enabling them to efficiently respond to altered boundary conditions, such as climatic conditions, different locations, varying functional requirements, or emergency situations. Generally, this capacity is provided through built-in mobility (structural mechanisms) or by means of assembly/disassembly of its constitutive members (kit-of-parts systems). The former group demonstrates kinematic properties that allow them to rapidly respond to changing needs by folding, expanding, or by any other form of deployment. Generally they come in the form of lightweight deployable structures that can easily transform between different configurations. This makes them fit for temporary, mobile applications or for adding adaptable sub-structures to buildings. In what follows, the research performed at the Vrije Universiteit Brussel by the Transform Research Group, the Lightweight Structures Lab, and the Mechanics of Materials and Constructions research group (MeMC), all collaborating on lightweight deployable structures, is presented. Through six case studies, diverse possibilities of deployable structures in architectural and structural engineering are explored. Key aspects concerning the design, analysis and construction of mobile, as well as adaptable constructions, are explained. Finally, conclusions are drawn on the intricate relationship between the geometric configuration, the kinematic behaviour and the structural response of lightweight deployable structures.
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Lightweight transformable structures:
materialising the synergy between
architectural and structural engineering
N. De Temmerman1, K. Roovers1, L. Alegria Mira1,
A. Vergauwen1, A. Koumar3, S. Brancart1, L. De Laet2
& M. Mollaert2
1Transform research team, Vrije Universiteit Brussel, Belgium
2Lightweight Structures Lab, Vrije Universiteit Brussel, Belgium
3Mechanics of Materials and Constructions, Vrije Universiteit Brussel,
Belgium
Abstract
As opposed to conventional, static structures, transformable structures possess a
transformational capacity enabling them to efficiently respond to altered
boundary conditions, such as climatic conditions, different locations, varying
functional requirements, or emergency situations. Generally, this capacity is
provided through built-in mobility (structural mechanisms) or by means of
assembly/disassembly of its constitutive members (kit-of-parts systems). The
former group demonstrates kinematic properties that allow them to rapidly
respond to changing needs by folding, expanding, or by any other form of
deployment. Generally they come in the form of lightweight deployable
structures that can easily transform between different configurations. This makes
them fit for temporary, mobile applications or for adding adaptable
sub-structures to buildings. In what follows, the research performed at the Vrije
Universiteit Brussel by the Transform Research Group, the Lightweight
Structures Lab, and the Mechanics of Materials and Constructions research
group (MeMC), all collaborating on lightweight deployable structures, is
presented. Through six case studies, diverse possibilities of deployable structures
in architectural and structural engineering are explored. Key aspects concerning
the design, analysis and construction of mobile, as well as adaptable
constructions, are explained. Finally, conclusions are drawn on the intricate
relationship between the geometric configuration, the kinematic behaviour and
Mobile and Rapidly Assembled Structures IV 1
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the structural response of lightweight deployable structures.
Keywords: lightweight deployable structures, mobile structures, parametric
design, adaptable sub-structures, emergency sheltering.
1 Introduction
Transformable structures can adapt their shape or function according to changing
circumstances, to meet rapidly evolving needs, induced by a society that
increasingly embraces the concept of sustainable design. This is further
supported by the understanding that structures are not designed in an end state,
but in a transition state, hence ‘transformable structures’. Based on how this
transformation is realised, two groups of structures can be distinguished.
Structures within a first group are designed as a demountable kit-of-parts system
(cfr. Meccano® construction toy) with dry, reversible connections, usually
intended for a gradual adaptation over time. The second group – which will be
the focus of this paper – entails structures incorporating a mechanism
(deployable/foldable), enabling them to rapidly transform between different
states (e.g. a compact and an expanded state). This primarily results in
lightweight deployable structures particularly fit for temporary or mobile
applications or for adding adaptable layers to buildings.
Lightweight deployable structures cover a common area of interest of the
Transform Research Group (TRANSFORM), the Lightweight Structures Lab
(LSL), and the Mechanics of Materials and Constructions (MeMC) research
group, all active within the Research Lab for Architectural Engineering (æ-lab)
of the Vrije Universiteit Brussel. TRANSFORM studies the effect of designing,
engineering and constructing in a transformable way, researching both
aforementioned groups of transformable structures. When it comes to the second
group, the vast experience of LSL on a wide range of innovative lightweight
structures (such as membrane structures, kinematic form-active structures or
pneumatic/Tensairity structures) has proven to be invaluable. MeMC has a vast
experience in structural analysis and the design of steel and aluminium structures
and has the necessary lab space and expertise to build full-scale prototypes and
to test them. Through our combined research activities on the design and analysis
of lightweight deployable structures and all appropriate subtopics related to the
engineering of such systems we aim to expand the existing knowledge, develop
new concepts and disseminate our findings.
It is the synergy between the three groups that gives rise to our common
research activities, with a focus on lightweight deployable structures. This is
presented through a selection of six diverse case studies executed by our
researchers. These do not aim to cover the full spectrum of our research, but will
demonstrate the main research topics, together with a number of relevant
additional topics, including the design and analysis of the proposed systems, the
development of digital design tools, model making and sustainable design.
Finally, some conclusions are drawn on the current state-of-the-art of this
research. To start off, a general introduction is given on lightweight deployable
structures.
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2 Lightweight deployable structures
Designing transformable structures entails a design approach in which time is
explicitly included from the earliest stages of conception [1]. So, besides the
three-dimensional space – well-known to engineers – the fourth dimension
becomes a determining design parameter. The structure is transformable over
time and can itself be described as being relocatable, reusable, demountable; its
building components can be reconfigurable, removable, replaceable, etc.
Temporary structures that have this transformational capacity, and are
lightweight or easily removable, have a lower impact on the site. This makes
them ecologically favourable.
Figure 1: Classification of structural systems for deployable structures by their
morphological and kinematic characteristics [3].
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By introducing a mechanism, a structure is provided with one or more
kinematic degrees of freedom (D.O.F.) and thus the capacity to transform from
one state to another, i.e. from a compact configuration to an expanded
configuration [2]. Generally, the process can be reversed and repeated.
Figure 1 shows a classification by Hanaor of the most common structural
systems for deployable structures, based on their morphology and their kinematic
behaviour [3]. Both structural mechanisms and demountable structures appear in
the classification, as well as hybrid systems. Although some of these systems are
more at home in the category ‘kit-of-parts systems’, the majority uses some sort
of structural mechanism to provide the necessary transformation. The structural
systems pictured in the classification are used for mobile applications as well as
for larger, permanent structures such as retractable roofs [4]. These architectural
engineering applications are described in more detail in the following
paragraphs.
2.1 Mobile deployable structures
Generally, mobile deployable structures are capable of transforming from a
small, closed or stowed configuration to a much larger, open or deployed
configuration. In the fully deployed configuration they perform their
architectural function. The most widespread applications are temporary
lightweight structures such as emergency shelters for disaster relief, maintenance
facilities, exhibition and recreational structures. These are typically small to
medium scale applications whereby portability and ease and speed of erection
are of utmost importance.
A wide range of structural systems have been used for mobile deployable
structures such as scissor (or pantographic) structures [5] (see case studies 2, 3
and 5), deployable tensegrity [6], structural origami [7], foldable membrane
structures [8] and Tensairity (see case study 6).
2.2 Adaptable building layers
For large sports facilities, retractable canopies are used to protect the grandstands
from the sun, wind or rain. Sports arenas are static and permanent buildings, but
by adding a retractable sub-structure, they are provided with the ability to react
to changing circumstances, and to extend their use through all seasons (e.g. the
retractable roof for Centre Court in Wimbledon). Similarly, buildings with large
glazed surfaces (e.g. office towers) can greatly benefit from adaptable solar
shading that controls the solar gains and thus simultaneously increases indoor
comfort and decreases energy demand (see case study 4). The structural system
used for the transformable sub-structures in permanent buildings can sometimes
be quite different from the systems typically used for mobile applications. The
biggest difference lies in the fact that there is a permanent structure that can act
as a supporting and guiding structure for the transformable system.
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3 Case studies
The diversity of current research topics within æ-lab on transformable structures
based on mechanisms is demonstrated by the following selection of six case
studies concerning recently finished or ongoing research. The first case study is
about the development of a pedestrian bridge based on curved line folding, while
the next two case studies are about the general design and analysis of deployable
scissor structures and the power of digital design tools. The fourth case study
presents the high-tech application of adaptable solar shading and the fifth one the
low-tech application of transformable emergency sheltering and its socio-cultural
aspects. Finally, the concept of deployable Tensairity is explained and valorised
by building a full-scale prototype.
3.1 Case study 1: pedestrian bridge over the Zwalm River
For an architectural or structural engineer there is something truly mesmerising
about the transformation from a flat piece of material with hardly any stiffness to
a three-dimensional folded shape that can bear loads an act as a fully fledged and
functional structure. This is exactly what N. De Temmerman (VUB), together
with architect G. Pauwels (Dial-architects) accomplished with the design of a
pedestrian- and bicycle bridge over the river Zwalm in Munkzwalm in Belgium.
The idea has its roots in a principle called ‘curved line folding’, which means
that a flat sheet of paper or another thin material is folded along curved fold
lines, as opposed to ‘rigid origami’ where only straight lines are used. Folding
along straight lines leads to a kinematic mechanism, whereas curved fold lines
force the controlled introduction of ‘active bending’. This principle gives rise to
interesting three-dimensional shapes with a surprisingly large stiffness.
The overall geometry of the bridge is derived from folding a flat piece of
paper along two parabolically curved fold lines, thereby obtaining a convex
bridge deck flanked by two concave side plates. The actual bridge is built from
10 mm thick corten plate steel (weathering steel) and can best be described as an
open caisson construction, braced and stiffened by ribs on the inside. With a span
of 10 m, an approximate width of 1.5 m and a total mass of 5000 kg this is truly
a lightweight structure. What sets this design apart is the simple yet elegant
design based on an abstract scientific principle and that all components have
been cut from the same plate steel, assembled and welded, with no other
elements added. Backed up by a vast amount of know-how and worldwide
expertise, Victor Buyck Steel Construction (W. Hoeckman, G. Hoste, K. Van
Hecke) acted as the contractor for the manufacturing of the bridge, resulting in a
fine example of the synergy between architectural and structural engineering.
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Figure 2: Scale model in cardboard demonstrating ‘curved line folding’
principle.
Figure 3: Designers G. Pauwels and N. De Temmerman standing on the
lightweight curved bridge deck in corten steel (yet to become
weathered).
Figure 4: The inside of the braced caisson construction (left) and a view of the
slender fish belly bridge deck (right).
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3.2 Case study 2: a generic design approach for angulated scissor structures
Scissor structures are a type of deployable structure consisting of hinged bars.
Because they display a large deployment range, a reliable deployment and are fit
for a broad range of applications, they form a particularly interesting sub-group
[2]. A scissor unit is formed by interconnecting two bars by a revolute joint at
the intermediate hinge point, which allows a relative rotation of the bars about an
axis perpendicular to their common plane. The total structure is obtained by
linking several of these units together at their end points using hinged
connections. One can distinguish three basic types of scissor units depending on
the proportions and shape of the bars: translational, polar and angulated scissor
units.
In order to expand the geometrical possibilities offered by scissor structures
and to propose innovative models, the angulated scissor unit was studied. This
unit is characterised by having two identical kinked bars. Hoberman, who
proposed the unit in 1990 [9], already demonstrated its capacity to generate more
exotic shapes with his transformable hypar and helicoid [10]. TRANSFORM
aims at exploring the full potential of the angulated scissor unit by developing a
theory which unravels how to create an angulated scissor structure based on any
arbitrary continuous surface. This opened the doors to a whole range of new
geometries. The design method is based on two general steps:
(i) firstly, the base surface is translated into a quadrilateral mesh suitable
as a base mesh for a scissor structure by discretising a network of
principal curvature lines on the surface, and
(ii) secondly, the resulting mesh (i.e. principal mesh) is populated with
angulated scissor units according to a number of predefined
geometrical relationships which will assure a functioning mechanism.
A detailed explanation of this design method and some examples can be
found in [11]. The theoretically endless new possibilities do however have a
practical limitation, namely the ability to find a suitable network of principal
curvature lines on the surface. A principal curvature line network is unique for
any surface (except for a sphere and a plane) and might display large
irregularities [12], which in turn can lead to ill-performing scissor structures.
However several surfaces and surface families have already proven to be very
suitable for application of these methods, such as the surfaces of revolution and
the moulding surfaces [11].
The generic nature of the proposed design approach does not only make it
applicable to a large number of surfaces and surface families, but also clears the
path for its integration in a parametric design environment. Digital design tools
are very useful to gain insight in the complex nature of these structures. They
provide the means to quickly generate a large variety of line models of the
scissor structures according to a number of user-defined parameters – giving
direct visual feedback on the influence of each parameter – and to
instantaneously simulate the corresponding deployment mechanism. Therefore
they can significantly speed up the conceptual stages of the design process.
Figure 5 demonstrates the working of such a design tool based on the proposed
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design method. It was developed in Grasshopper [13], a generative modelling
plug-in for the computer-aided design package Rhinoceros
®
[14]. Aside from
generating a myriad of different models and an instant analysis of its kinematic
behaviour, the tool can be extended with other features benefiting the design
process, such as a structural FE analysis (see case study 3) or the automatic
generation of parts for a scale model (figure 6).
Figure 5: Main steps in a digital design tool for generating angulated scissor
structures based on surfaces of revolution: (i) the base surface is
designed; (ii) the base surface is discretised to obtain a principle mesh;
(iii) the principal mesh is populated with scissor units and the
deployment is simulated.
Figure 6: Physical scale model of an angulated scissor structure with
membrane [11].
3.3 Case study 3: design through parametric finite element modelling
Despite the advantages scissor structures can offer, not many have successfully
been realised. The design process is inherently complex: a scissor structure
requires a thorough understanding of the specific two-and three-dimensional
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configurations that will give rise to both a fully deployable morphology and
good structural properties. Due to this complex design process it is beneficial to
evaluate these structures at a pre-design stage according to their structural
performance.
By using a methodology of preliminary evaluation through parametric finite
element (FE) modelling, the scissor structures could be geometrically and
structurally optimised at an early stage (figure 7). This will enhance the overall
design process, facilitate further detailed analysis and improve the performance
of these structures, allowing the further development of various applications.
Karamba® – a commercially available parametric FE tool developed by
Preisinger [15] – is employed in TRANSFORM research on deployable scissor
structures. More specifically, Karamba® is an FE program embedded in the
parametric geometric modelling environment Grasshopper (GH) (figure 8), also
implemented in case study 1. With the use of these tools we can design and
analyse deployable scissor structures in a single software environment which
even more simplifies and speeds up the complex design process (figure 7).
An important aspect of Karamba® is its bi-directionality with respect to
calculation data: the model response attained through physical simulation can be
fed back into the geometric model. This allows setting up automated design
loops that rationalise designs by taking into account structural data. For example,
the geometrical height of a deployable scissor arch can be quickly determined to
minimize deflection. Alternatively, the deflection can be investigated for
different deployment stages of the arch. The absolute advantage is that
the interaction between the geometrical and structural model is very fast. The
designer can immediately understand the effects of geometrical parameters on
the structural performance.
An aspect of this digital tool that adds to its speed of calculation is the fact
that its capabilities are deliberately limited to those necessary in the early design
phase: instead of e.g. employing isoparametric finite beam elements, hermitian
elements are used. The latter are confined to linear elastic calculations of
elements with straight axes. Yet the calculation of the element stiffness matrix
can be done without the need for numeric integration and therefore very
efficiently with respect to computation time. The reader is referred to Preisinger
[15] for more information on Karamba®.
In this tool, scissor elements are modelled as one-dimensional beams
connected by zero-length springs (representing the revolute hinges), which is an
easy and effective method for a preliminary structural evaluation. The
translational stiffness of the springs is set in such a way that connecting nodes
share the same coordinates and only the springs’ rotational stiffness about the
axis perpendicular to the plane of the scissor unit is zero.
At an early design stage the focus is put on the structural performance of the
scissor beams in the overall structure. Thus, the structural influence of the hinges
can be ignored. This means that the non-zero stiffness values for the springs are
set to a high value (1011–1013 kN(m)/m), though limited to avoid a badly
conditioned stiffness-matrix which would lead to inaccurate numerical results in
the FE calculations.
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A preliminary investigation of this methodology has been conducted by the
authors, in which the structural influence of different scissor configurations was
determined [16].
Figure 7: This flowchart illustrates how a parametric evaluation methodology
for deployable scissor structures can benefit the overall design
process: design improvements are made at an early stage through
various iterations exclusively in the modelling environment of
Rhinoceros®.
3.4 Case study 4: deployable structures and adaptive building envelopes
The building envelope acts as the interface between inside and outside and
therefore has a significant influence on the indoor climate, comfort and energy
use of a building. As most of the constraints acting upon the building envelope
are time-dependent (weather conditions, the sun path, user preferences, noise,
wind), the building envelope is increasingly considered as a dynamic structure,
able to change its configuration, features or behaviour over time in response to
changing conditions. Such building envelopes are known as adaptive (or
responsive) building envelopes. In order to attain this kind of adaptability,
deployable structures can be used, providing change in the building envelope
through motion.
The folding process of deployable structures is particularly interesting for the
active control of solar radiation and daylight. Recently, architects and engineers
have been experimenting with the use of foldable structures as shading devices.
A prime example is the “Dynamic Façade” project, better known as the Kiefer
Technic Showroom located in Austria (figure 9, left). The metal panels can fold
in various positions allowing occupants to adjust the light or temperature in a
room. In this way, the façade changes continuously, creating a dynamic sculpture
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[17]. Another example, the Abu Dhabi Investment Council (figure 9, right)
consists of foldable shading elements based on an origami pattern. The solar
shading elements can individually open and close in response to the movement
of the sun throughout the course of the day [18].
Figure 8: The scissor geometry is parametrically defined in Grasshopper (left)
and converted into a beam model and calculated with Karamba®
(right).
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Figure 9: The Kiefer Technic Showroom located in Austria [17] (left); Picture
showing the installation of the dynamic shading elements of the Abu
Dhabi Investment Council [18] (right).
Given these examples, there is a growing interest to study to what extent
origami-based structures are appropriate for the use in adaptive building
envelopes. Whereas the previous examples have proven the successful
application of rigid-foldable plate structures as dynamic solar shading devices,
the use of curved-line folding in this context remains unexplored. Moreover, by
investigating the use of curved-line folding for the design of dynamic solar
shading devices, new aesthetic opportunities for the design of building envelopes
can be provided. As an example figure 10 shows the conceptual design of a
façade with adaptive shading elements based on curved-line folding. Three
different phases of the folding process are illustrated.
Figure 10: Conceptual design of a façade with adaptive shading elements based
on curved-line folding.
The design and optimisation of a dynamic solar shading system is not an easy
task. The diagram in figure 11 demonstrates that a whole series of parameters is
involved in the design process: parameters defining the kinematic behaviour,
parameters in relation to the morphology of the building and parameters
influencing the energy flow through the façade. It is important to understand
the relationship between these parameters and to study their effect on the
performance of the shading devices, as explained in [19].
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Figure 11: The diagram shows the relationship between all parameters to
consider in the design of adaptive shading elements [19].
All things considered, it is clear that in order to improve the performance and
the practical application of adaptive building envelopes, the development of a
new generation of adequate transformable components is essential. Accordingly,
(our) research on origami-based structures will play an important role in this
process.
3.5 Case study 5: a design method for a deployable adaptable shelter based
on multi-criteria optimisation
Disasters such as floods, earthquakes, volcano eruptions, famine and wars have
occurred for ages and continue to do so. Knowing that a disaster occurs when a
vulnerable community is hit by a hazard, and that the most vulnerable
communities are struck the hardest, it can be stated that decreasing vulnerability
is the key to enhancing a community’s resilience. This resilience is best
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guaranteed by participatory and sustainable development processes involving the
local community and all of the opportunities it has to offer, guided by a
long-term vision. Rather than to impose a static short-term relief solution when a
disaster strikes, both relief and development have to be addressed simultaneously
in order to guarantee successful recovery using the socio-economic and cultural
assets at hand to their full potential.
Shelter and housing are of utmost importance, as they play a crucial role in
people’s lives and in society: the loss of a home does not only constitute a
physical deprivation, but can also cause a loss of individual and collective
identity, orientation, security, privacy, thereby undermining many aspects of
daily life, with a profound negative effect on the community. A home acts as a
hub for a household’s socio-cultural and economic interactions and thus can act
as a catalyst for development.
There should be a link between relief and future development perspectives for
those hit by disasters, if we want to offer a sustainable solution. Due to its
multi-facetted character, housing has the potential to support and facilitate
personal, social and economic recovery, i.e. to act as a catalyst for development.
But in order to do so, the shelter solutions should be able to adequately fulfil
their function in every stage of the relief and development process: from
emergency, to rehabilitation to reconstruction.
Therefore, shelters cannot be static, but need to be adaptable in order to be
able to evolve along with the changing context, hence act as transitional shelters.
If a transitional shelter is designed as a kit-of-parts system, it can be
disassembled into its constitutive components, which can then be rearranged and
reused in a different configuration. Moreover, because of the open nature of the
system, local materials and locally produced components can be introduced, thus
involving the community and its human and material resources into the process.
Transitional shelter intervention has a positive impact on communities and their
development: communities take ownership of the concept by adapting it to their
specific (socio-cultural) needs. This mutually interactive process for transitional
shelters, stemming from a long-term vision, aims at effectively realising
sustainable and participatory development.
Under the influence of prof. T. Tysmans (MeMC) and prof. R. F. Coelho
(BATir, ULB, Belgium), this research is opting for a new design approach based
on multi-criteria optimisation to combine the solutions of both the emergency
phase (phase 1) and the development phase (phase 2) into one type of structure
(figure 12). The aim is to provide a design tool that can be used by NGO’s in
order to design optimal deployable adaptable scissor shelters for the emergency
phase. Furthermore, the elements of those shelters can be combined, after
dismantling, in such a way that they result in several housing solutions for the
development phase of the affected population. The design must take into account
(i) the durability of materials and components over the permanent building’s
lifetime (fifty years), (ii) the possibility to integrate local building materials both
for structural as for insulation purposes, and (iii) the significantly superior
structural capacities that are required of its elements in the permanent state
(larger spans, higher environmental loads, higher self-weight of building skin).
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Figure 12: Scheme illustrating the proposed concept for a transitional shelter: in
the first phase a scissor structure is used for a quick and easy
deployment (photo: Alegria Mira L., Thrall A., De Temmerman N.,
prototype built at the VUB in MeMC lab); in the second phase the
components are disassembled and reused for the housing of the local
population (photo: [20]).
3.6 Case study 6: a full-scale prototype of a deployable Tensairity beam
Inflatable structures have been used by engineers and architects for several
decades. These structures offer lightweight solutions and provide several unique
features, such as collapsibility, translucency and a minimal transport and storage
volume. In spite of these exceptional properties, one of the major drawbacks of
inflatable structures is their limited load bearing capacity. This is overcome by
combining the inflatable structure with cables and struts, which results in the
structural principle called Tensairity.
Tensairity is a synergetic combination of struts, cables and an inflated
membrane (by low pressurized air), as illustrated in figure 13. The tension and
compression elements are physically separated by the air inflated beam, which –
when inflated – pretensions the tension element and stabilizes the compression
element against buckling.
A Tensairity structure has most of the properties of a simple air-inflated
beam, but can bear several times more load [21]. This makes Tensairity
structures very suitable for temporary and mobile applications, where
lightweight solutions that can be compacted to a small volume are a requirement.
However, the standard Tensairity structure cannot be compacted without being
disassembled. By replacing the standard compression and tension element with a
mechanism, a deployable Tensairity structure is achieved that needs – besides
changing the internal pressure of the airbeam – no additional handlings to
compact or erect the structure.
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Figure 13: Basic cylindrical Tensairity beam [22].
This research is concerned with the development of a new type of deployable
Tensairity beam. An earlier concept of a deployable Tensairity structure was
developed in [23], and although it was promising, there were still issues to be
solved and optimised. Within this study, a new proposal is made for a deployable
Tensairity beam which is improved in terms of its structural and kinematic
behaviour (figure 14). The system’s load bearing capacities are ameliorated by
changing the longitudinal shape from cylindrical to spindle, by decreasing the
amount of hinges and segments and by positioning hinges on the compression
side towards the middle. By means of a redesign of the configuration of the
foldable truss, the kinematic behaviour is improved. The segments of upper and
lower strut do not have to ‘fold’ into each other anymore. In addition, less hinges
and less complicated joints are necessary. As a result, a more easily foldable
proposal for the deployable Tensairity structure was obtained.
Figure 14: The mechanism of the deployable Tensairity beam [22].
Finally, a full-scale prototype (5 m span) of the deployable Tensairity beam
has been designed and built, valorising the proposed concept (figure 15). Special
attention was directed towards the hinge design and the attachment and
positioning of the membrane to ensure an unimpeded deployment mechanism.
An experimental investigation has been performed towards the structural
behaviour of the full-scale prototype, which is presented in [22].
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Figure 15: Prototype of the deployable Tensairity beam during experimental
investigations [22].
With this research, the first step is taken towards a functional large-scale
deployable Tensairity beam. However, many aspects in this research, such as the
detailing and the gained insight, can also be applied to the development and
research of other structures, such as Tensairity arches, cushions and grids. The
application of the deployable technology on other scales or in other domains than
civil engineering will bring forward new questions and knowledge and is
certainly worth investigating.
4 Conclusion
This paper provided a selection of the research done on lightweight deployable
structures at the Vrije Universiteit Brussel by TRANSFORM, the Lightweight
Structures Lab, and the Mechanics of Materials and Constructions research
group (MeMC), all active within or collaborating with æ-lab (Research Lab for
Architectural Engineering). This selection serves as a demonstration of the
variety of the research being performed and the methods being used to achieve
our goals.
Within TRANSFORM, chaired by N. De Temmerman, the main focus lies on
the transformation of structures, in order to provide them with a transformational
capacity enabling them to adapt to changing circumstances. These changing
circumstances can range from a sudden need (emergency), to climate conditions
(sun, wind, rain, heat/cold), to altered functional requirements (transport,
expansion, reuse), or any other boundary condition requiring a physical
transformation. The transformation can take the form of deployment, in case of
structural mechanisms providing a system with kinematic behaviour, or it can
take the form of adding, reconfiguring, reusing components, as is the case with
demountable kit-of-parts systems. The key aspect in the latter group is that the
complete life cycle of the construction is taken into account, as an important step
towards sustainable design and development. Even though this paper focused on
the first system, both types of transformation are being researched in our group.
In some cases even a hybrid system, combining the two systems is possible (as
seen in case study 5 or in [24]).
The vast experience – spanning more than 25 years – of the Lightweight
Structures Lab chaired by M. Mollaert, in the search for maximum lightness
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combined with an optimal structural performance results in substantial added
value to the research of æ-lab. Through a wide range of research topics, the
group contributes to the further development of ‘tensile surface structures’,
‘kinetic structures’, ‘graphic statics and form finding’. This currently translates
in specific projects, investigating the design and implementation of pneumatic
components in structural systems (see case study 6), the comfort assessment of
spaces enclosed by translucent membranes, the design and calculation of new
typologies for fabric structures, emergency shelters and the development of
so-called ‘bending-active’ structures.
Added to that, the experience of MeMC is a huge asset in transferring an
abstract concept to a full-scale realisation. Their expertise in the structural
analysis of steel structures, their knowledge on materials for constructions, and
their vast experience in developing and testing prototypes of innovative
lightweight is of great value in the collaboration between ARCH (Architectural
Engineering) and MeMC. Based around the legacy of W. P. De Wilde, young
research leaders T. Tysmans and L. Pyl today continue the tradition of exploring
the synergy between architectural and structural engineering. In another paper by
Pyl et al., you can read about how this synergy came about, and what successful
collaborations it has yielded.
The possibilities of deployable structures are immense, but the challenges that
they impose remain great. We aim to face these challenges and provide
sustainable solutions for them. The capacities and behaviour of deployable
scissor structures are being investigated on a structural level ( Alegria Mira
[24]) as well as from a geometrical and kinematical point of view (Roovers
et al. [11]). They are being deployed in the field of emergency
sheltering and disaster relief, where it is researched how their components can
live on as structural elements to rebuild the local housing stock (A. Koumar).
Responsive building skins are being developed using foldable origami
structures, acting as the interface between inside and outside, therefore
enabling to regulate e.g. airflow, solar shading in the façade of a building
(Vergauwen et al. [19]). New concepts for foldable Tensairity are proposed,
leading to lightweight, yet very high performing structural elements that can
easily be transported and deployed (De Laet et al. [22]). In addition, exiting
new fields are being explored such as deployability in bending active
structures, thus expanding the boundaries of our research (S. Brancart).
The design and analysis of deployable structures is quite particular. The
kinematic aspect lies at the very core of the concept and completely determines
the process starting from the first stages of the design: one has to evaluate the
final expanded configuration, in which the structure executes its architectural
function; but the deployment phase, used to get to that point, is equally important
[25, 26].
The design process of deployable structures inherently displays a high degree
of complexity, found in the relationship between their geometry, their kinematic
behaviour and their structural performance, sometimes combined with other
design variables such as socio-cultural factors that need to be taken into account.
Therefore, software tools have become indispensable during the design of
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deployable structures. Starting from the first steps, these tools can assist and
speed up the design process and simultaneously provide insight to the designer.
An interactive design environment can be integrated with analysis components,
resulting in direct feedback on the design choices made. Despite this wide range
of possibilities, one cannot underestimate the importance of physical (scale)
models and prototypes, as they still have the potential of revealing overlooked
design flaws and verifying the digital models.
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p. 2287-2294 In general, a quadrilateral mesh surface does not enable a continuous rigid motion because an overconstrained system, in which the number of constraints around degree-4 vertices (three for each vertex) exceeds the number of variables (the number of hinges), is constructed. However, it is known that the developable double corrugation surface, called Miura-ori, produces a rigid deployment mechanism. The rigid-foldability of Miura-ori is due to the singularity in its pattern, where a single vertex is repeated. We generalize the geometric condition for enabling rigid motion in general quadrilateral mesh origami without the trivial repeating symmetry. To ensure the existence of a finite motion, we derive the identity of functions from the formula for degree-4 single-vertex origami. This yields a variety of unexplored generalized shapes of quadrilateral mesh origami that preserve finite rigid-foldability in addition to developability and flat-foldability.
Thesis
Over the last decade there has been a worldwide increase in the use of retractable roofs for stadia. This increase has been based on the flexibility and better economic performance offered by venues featuring retractable roofs compared to those with traditional fixed roofs. With this increased interest an evolution in retractable roof systems has followed. This dissertation is concerned with the development of concepts for retractable roof systems. A review is carried out to establish the current state-of-the-art of retractable roof design. A second review of deployable structures is used to identify a suitable retractable structure for further development. The structure chosen is formed by a two-dimensional ring of pantographic bar elements interconnected through simple revolute hinges. A concept for retractable roofs is then proposed by covering the bar elements with rigid cover plates. To prevent the cover plates from inhibiting the motion of the structure a theorem governing the shape of these plate elements is developed through a geometrical study of the retractable mechanism. Applying the theorem it is found that retractable structures of any plan shape can be formed from plate elements only. To prove the concept a 1.3 meter diameter model is designed and built. To increase the structural efficiency of the proposed retractable roof concept it is investigated if the original plan shape can be adapted to a spherical surface. The investigation reveals that it is not possible to adapt the mechanism but the shape of the rigid cover plates can be adapted to a spherical surface. Three novel retractable mechanisms are then developed to allow opening and closing of a structure formed by such spherical plate elements. Two mechanisms are based on a spherical motion for the plate elements. It is shown that the spherical structure can be opened and closed by simply rotating the individual plates about fixed points. Hence a simple structure is proposed where each plate is rotated individually in a synchronous motion. To eliminate the need for mechanical synchronisation of the motion, a mechanism based on a reciprocal arrangement of the plates is developed. The plate elements are interconnected through sliding connections allowing them mutually to support each other, hence forming a self-supporting structure in which the motion of all plates is synchronised. To simplify the structure further, an investigation into whether the plate elements can be interconnected solely through simple revolute joints is carried out. This is not found to be possible for a spherical motion. However, a spatial mechanism is developed in which the plate elements are interconnected through bars and spherical joints. Geometrical optimisation of the motion path and connection points is used to eliminate the internal strains that occur in the initial design of this structure so a single degree-of-freedom mechanism is obtained. The research presented in this dissertation has hence led to the development of a series of novel concepts for retractable roof systems.
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Geometry lies at the core of the architectural design process. It is omnipresent, from the initial form-finding stages to the actual construction. Modern constructive geometry provides a variety of tools for the efficient design, analysis, and manufacture of complex shapes. This results in new challenges for architecture. However, the architectural application also poses new problems to geometry. Architectural geometry is therefore an entire research area, currently emerging at the border between applied geometry and architecture. This book has been written as a textbook for students of architecture or industrial design. It comprises material at all levels, from the basics of geometric modeling to the cutting edge of research.
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The paper is a critical review of different structural systems that have been proposed to date for the purpose of deployable space enclosure. The structural systems are classified by their morphological and kinematic characteristics, and comparatively evaluated in terms of their structural efficiency, technical complexity and deployment/stowage efficiencies. Although the main focus is on kinematically deployable structures, some retractable and dismountable configurations are also reviewed. The paper includes an extended list of references.
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Deployable-collapsable structures have many potential applications ranging from emergency shelters and facilities, through relocatable, semi-permanent structures, to space-station components. Their main advantages are the small volume they occupy during storage and transportation, and their fast and easy erection procedure. A new concept of self-stabilizing deployable structures featuring stable, stress-free states in both deployed and collapsed configuration shows even higher promise.During the deployment phase these structures exhibit a highly nonlinear behavior. A large displacements/small strains finite element formulation is used to trace the nonlinear load-displacement curve, and to obtain the maximum internal forces that occur in the members of the structure during deployment. The influence of various parameters that affect the behavior of the structures, such as geometric shape, dimensions of the members, cross-sectional properties and kinematic assumptions is being investigated.
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Kinematic analysis is conducted to derive the geometric constraints for the geometric design of foldable barrel vaults (FBV) composed of polar or angulated scissor units. Non-linear structural analysis is followed to determine the structural response of FBVs in the fully deployed configuration under static loading. Two load cases are considered: cross wind and longitudinal wind. The effect of varying member sizes, depth-to-span ratio and geometric imperfections is examined. (C) 2000 Elsevier Science Ltd. All rights reserved.