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Form-Finding and Design Potentials of Bending-Active Plate Structures

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Form-Finding and Design Potentials of Bending-Active Plate Structures

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This work presented investigates the form-finding and design potentials of bending-active plate structures. Using two reference projects from the recent past, the authors present different design methodologies that either follow a geometry-based or integrated approach. A closer look at the newly accessible tools for digital form-finding and analysis reveals their increasing importance for the design process. In order to better demonstrate their potential, the authors present three case studies, which each separately enhances the integrated approach and in combination indicate the existence of a much larger design space of bending-active plate structures.
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Form-Finding and Design Potentials
of Bending-Active Plate Structures
Simon Schleicher, Andrew Rastetter,
Riccardo La Magna, Andreas Schönbrunner,
Nicola Haberbosch and Jan Knippers
Abstract
This work presented investigates the form-nding and design potentials of
bending-active plate structures. Using two reference projects from the
recent past, the authors present different design methodologies that either
follow a geometry-based or integrated approach. A closer look at the
newly accessible tools for digital form-nding and analysis reveals their
increasing importance for the design process. In order to better demon-
strate their potential, the authors present three case studies, which each
separately enhances the integrated approach and in combination indicate
the existence of a much larger design space of bending-active plate
structures.
Introduction
Bending-active plate structures use the elastic
deformation of planar, off-the-shelf building
materials to generate curved surface structures
(Knippers et al. 2011). While the traditional
maxim in engineering is to limit the amount of
bending in structures, this typology actually
harnesses bending for the creation of complex
and extremely lightweight designs. In the past,
thin plates have rarely been used as primary
structure in architecture because of their low
bending stiffness. Many sheet materials like
plywood, metals, plastics, and bre-reinforced
polymers, however, are not only exible but also
have high tensile strength. The two properties
together are a perfect match for bending-active
structures because they enable elements to
undergo large elastic deformations and to resist
high stresses before failure. This behaviour opens
up new possibilities for the design of bent static
and kinetic structures (Lienhard et al. 2014;
Schleicher et al. 2015). The most signicant
advantage of these systems is that they can be
constructed from simple planar parts, which can
be fabricated with inexpensive, conventional
atbed processes. Additionally, the assembly of
S. Schleicher (&)A. Rastetter
College of Environmental Design (CED),
University of California, Berkeley, USA
e-mail: simon-s@berkeley.edu
R. La Magna A. Schönbrunner N. Haberbosch
J. Knippers
Institute of Building Structures and Structural Design
(ITKE), University of Stuttgart, Stuttgart, Germany
©Springer International Publishing Switzerland 2015
M.R. Thomsen et al. (eds.), Modelling Behaviour, DOI 10.1007/978-3-319-24208-8_5
53
these structures does not require skilled labour or
auxiliary formwork. Despite these benets, the
design of bending-active plate structures is a
major challenge. This is because it is difcult to
assess their structural behaviour and to accurately
anticipate their deformed geometry. Therefore, it
is essential to develop new design approaches.
Design Approaches
to Bending-Active Plate Structures
A recent study identied three main strategies for
the design of bending-active structures. These are
behaviour-based approaches, geometry-based
approaches, or integrated approaches (Lienhard
et al. 2013). Bent huts and tents of vernacular
architecture, for example, fall into the rst cate-
gory. Here, bending is used rather intuitively
during the construction process. While this rst
approach relies heavily on experience, the other
two categories are more scientic and require
experimental and analytical form-nding tech-
niques. Their similarities and differences are
illustrated by the examples of Buckminster Ful-
lers plydomes and the 2010 ICD/ITKE Research
Pavilion (Figs. 1and 2).
Self-strutted Geodesic Plydomes
As part of his research on geodesic dome struc-
tures, Buckminster Fuller (18951983) experi-
mented with various structural systems and
materials. His motivation was to nd an optimum
balance between a structures stability, weight,
and cost (Marks et al. 1973). While the majority
of his larger dome structures are triangulated
lattice shells that use steel struts as structural
framework and solid panels or textiles as clad-
ding, some of his smaller projects investigated
different structural typologies that further
increased the efciency of the systems. Of par-
ticular interest are the geodesic plydomes that he
developed from the fties on. Here, the key idea
was to construct a dome-shaped enclosure
through repetitive tiling of rectangular plywood
sheets. Plywood sheets were used because they
are mass-produced, easily obtainable, relatively
inexpensive, and can be stacked compactly for
shipment. Fuller used a geometry-based
approach to t the at sheets to the doubly
curved surface of a sphere. This approach is
described in Fullers 1959 patent for the system
(Richard 1959). He rst approximates the target
geometry of a sphere with a regular polyhedron
(Fig. 3a).
Next, he arranges individual plates along the
edges of the polyhedron (Fig. 3b). Adjacent
Fig. 1 Two-frequency geodesic plydome in Des Moines,
Iowa, 1957. The hemisphere spans 7.3 m and is made out
of marine plywood sheets with a thickness of 6.4 mm.
(Marks 1973, p. 210)
Fig. 2 ICD/ITKE research pavilion 2010 spans 10 m and
consists of 80 birch plywood strips with a thickness of
6.4 mm
54 S. Schleicher et al.
plates are partially overlapped, pulled together,
and fastened to one another with pre-drilled
holes. This generates the double curvature of the
global geometry even though the individual
plates only experience single curvature at any
given location (Fig. 3c). The greatest challenge
in implementing Fullers system is determining
the amount of overlap between adjacent sheets
and the location of the attachments points. Both
are dictated by the deformed geometry of the
plates and may also vary according to the sheets
position in the overall pattern. Without the digital
tools that we have today, Fuller was forced to
compute this information mathematically. Over
time he calibrated these numerical results to the
actual behaviour of the system.
ICD/ITKE Research Pavilion 2010
A good example of a more advanced approach
to bending-active plate structures is the
ICD/ITKE Research Pavilion 2010 (Fig. 2). This
pavilion, which follows an integrated approach,
was designed and built by students and teachers
at the University of Stuttgart, as a collaborative
effort between the Institute of Computational
Design (ICD) and the Institute of Building
Structures and Structural Design (ITKE) (Lien-
hard et al. 2011; Fleischmann et al. 2012). The
project achieves a more complex curved geom-
etry by alternating segmentally bent plywood
strips that are linked together. The team began
the design process by considering the limiting
material characteristics of the plywood strips.
The rst step was to calibrate nite-element
simulations with physical experiments. This
ensured that the digital form-nding techniques
provided an accurate description of the actual
material behaviour while at the same time
offering full control over the geometry. Of par-
ticular importance was the ratio between the
pitch and span of a bent strip (Fig. 4a).
This ratio describes the maximum achievable
deection under a given safety factor. Once
established, the ratio informed a parametric model
that was used to design the global geometry of the
pavilion (Fig. 4b). This model determined the
dimensions and connection logic for each
strip. The last step was to translate the geometry
from the parametric model to a more advanced
nite element analysis, which re-created the
bending process under consideration of relevant
material properties for birch plywood (Fig. 4c).
This last step was of key importance because
it provided precise information about the pavi-
lions deformations and structural performance
under different loading scenarios as well as
essential data for the subsequent fabrication and
assembly.
Fig. 3 Geometry-based approach of a plydome approximates a sphere with a polyhedron (a). Based on the
polyhedrons edges multiple sheets get to arrange spatially (b) and then bent and fastened together (c)
Form-Finding and Design Potentials 55
Form-Finding and Analysis
of Bending-Active Plate Structures
The biggest challenge regarding bending-active
plate structures is the difculty of predicting their
deformed geometry and structural performance.
As demonstrated by previous projects, options
for their form-nding and analysis include
physical modelling, mathematical calculations,
and advanced digital simulations. These digital
simulation tools, however, have only been
available for a few years to a broader public.
They can be subdivided into two categories:
The rst method relates to real-time
physics-based simulations. These are used
extensively in the computer graphic community
and are now also available for common CAD
environments. The Rhinoceros®plugin Kanga-
roo Physics is a good example of this type of
software. For the simulation of the bending
behaviour of shells, it employs a discrete shell
exural energy model as described in Grinspun
(2008) and Piker (2013). Mesh deformations are
computed employing a dynamic relaxation
scheme, requiring the introduction of lumped
mass values and damping coefcients in the
computational model. During the simulation
process, the system converges to an equilibrium
position that represents the nal bent geometry.
Although the denition of such additional
parameters (mass, damping coefcients) is often
arbitrary and not physically motivated, the
strength of this computational scheme relies on
the calculation speed and easiness of setup. This
makes it ideally suited for iterative studies in
early design stages or design explorations for
structures with many elements.
The second method relies on nite element
simulation (FEM). While this technique was
originally used mainly for post-design analysis,
non-linear FEM routines have advanced so much
over the last few years that it has become prac-
tical to integrate them early in the design process
(Lienhard et al. 2011). Programs like SOFiS-
TiK®, for example, allow a designer to calculate
the deformations and stresses of structures under
large deformations and to predict complex equi-
librium states. In doing so, the software simulates
the bending of a structure by considering both
external forces and internal material stresses.
Considering both simultaneously is particularly
important because the geometry of a deformed
structure depends signicantly on the balance of
forces that are exerted on it. Unlike real-time
physics simulations, FEM can be also used to
visualize the evolution of stresses within the
material during the form-nding process. FEM
simulations offer the most complete and correct
mechanical description of the behaviour of shell
elements, representing an invaluable tool for the
correct evaluation of the mechanical behaviour
and structural capacity of bendingactive
structures. On the other hand, the completeness
Fig. 4 ICD/ITKE research pavilion 2010 illustrates an integrated approach to the design of bending-active plate
structures
56 S. Schleicher et al.
of the mechanical model does not come for free,
as it is computationally more intensive and can
be rather slow for large models.
Contracting elastic cables provide a practical
method to induce bending in both of these digital
simulation techniques (Fig. 5). The cables are
shortened through a reduction in stiffness and a
simultaneously applied pre-stressing load (Lien-
hard et al. 2014). Each cable is attached to pairs
of nodes on one or multiple meshes. These nodes
are pulled together during the simulation pro-
cess, which produces a controlled deformation of
the attached meshes. This technique is very
versatile and easy to use because it does not
require the input of an explicit nodal displace-
ment path.
Case Studies that Render New
Potentials
The authors conducted a series of case studies to
enhance the previously described integrated
approach. These case studies separately explore
new design potentials but also build upon each
other to generate more complex bending-active
plate structures.
Case Study 1Effective Pinching
The rst example explores the benets and
opportunities of the single-curvature that typi-
cally results from bending thin plates. Unlike the
reference projects, which primarily use cylindri-
cal shapes, this case study explores the potential
of conical bending (Fig. 6). It conceptualizes a
triangular facade module out of initially at
panels and challenges the design process by
investigating shapes whose cutting patterns are
not predened from the start but needed to be
determined through a series of simulations.
In this example, internal openings are pinched
together to provoke global deformations in a
plate. Material is strategically removed from the
sheets centre and the internal edges are forced
together with contracting cables in Kangaroo
Physics (Fig. 7a). This leads to a conical
out-of-plane buckling that gives the plate a
unique developable form. Each plate is then
mirrored, merged, and trimmed with its coun-
terpart, which brings about rst changes to the
initial cutting pattern (Fig. 7b). The result is a
dual layer module with two plates that affect each
other in form and signicantly enhance the
structural rigidity of the system. Trimming the
Fig. 5 Form-nding with contracting elastic cables using Kangaroo Physics and SOFiSTiK
Form-Finding and Design Potentials 57
modules periphery with an extruded triangular
prole produces the second substantial modi-
cation to the initial pattern. This step is necessary
to guarantee that the module will t into a sym-
metric facade tessellation. What makes this
trimming action so special, however, is the fact
that it is conducted on a plate that is already
deformed, which results in a unique cutting pat-
tern. The surprising complexity of the nal pat-
tern becomes particularly apparent in the last step
of the form-nding process, where the layers of
the module are separated and attened by
applying a uniformly distributed load that presses
the mesh against a virtual oor (Fig. 7c).
Case Study 2Mutual Reinforcement
The second case study aims to push the research
one step further and focuses not only on an
individual model but also on the complexity of
the global system. It explores the question of
Fig. 6 Triangular facade tessellation with a module that is based on pinching and cross-connecting two thin sheets
Fig. 7 Pinching a plate in the centre causes a conical deformation (a). Two plates can be merged with each other and
trimmed (b) in order to derive with a special informed cutting pattern (c)
58 S. Schleicher et al.
how at plates can be bent into a doubly curved,
multi-layered structure that is extremely light-
weight and has a high load-bearing capacity.
Similar to a piece of corrugated cardboard,
this project uses the technique of pleating to
cross-connect multiple thin sheets in order to
form an assembly that is more rigid than the sum
of its individual layers. What is most special
about this project, however, is that it transfers the
idea to a doubly curved global geometry (Fig. 8).
This is not an easy task because a continuous at
plate can only be bent into single but not into
double curvature. In order to achieve the global
double curvature, the individual plates are per-
forated with holes and slits. These perforations
divide the plates into individual zones that can be
bent differentially. The role of the perforations,
therefore, is to liberate individual plate segments
from the necessity to take on double curvature.
Instead, the Y-shaped subunits are only single
curved and can conform to different synclastic
and anticlastic target geometries. Multiple sur-
faces are stacked, offset, and then connected to
one another in order to lock the shape of the
global geometry and to provide a load path
through the structure. In this way, every hole in
the rst layer gets lled and structurally sup-
ported by the second layer. This process is
repeated by adding a third layer and more layers
can be added to increase the stiffness of the
structure.
A series of physical and digital studies were
used to design and test the structural system.
Material tests were synchronized with FEM sim-
ulations in order to determine the limit of feasible
deformation, which is dictated by the local stress
concentrations in the material (Fig. 9a). An addi-
tional factor that had to be considered was the
amplication effect that results from the interac-
tion between the interconnected layers. This
interaction was used to determine the degree of
variation between adjacent perforation patterns
(Fig. 9b). Once a feasible deformation for a given
sheet material was found, it was possible to
develop an abstracted parametric model that pre-
served the internal relationships of the system and
limited the design space to achievable solutions
(Fig. 9c). This approach required less computing
power than a comprehensive FEM analysis and
allowed for the efcient tessellation of various
doubly curved surfaces.
Case Study 3Functionalized
Instability
The third case study builds on the insights of the
previous two examples and explores bending
Fig. 8 Mock-up of a 2 ×1 m plate structure uses the coupling of three PET-G layers of 1 mm thickness to obtain a
freeform geometry with a high load-bearing capacity
Form-Finding and Design Potentials 59
both as a form-giving strategy and also as prac-
tical means to quickly assemble a larger structure
out of multiple smaller subunits. It uses a
snap-through instability mechanism to connect
the components of the system.
Like the previous examples, this project
restricts itself to elements that are constructed
from at sheet material. In this case, the structure
is assembled from variations of only four basic
shapes. These include two annular components
and two longer undulating strips (Fig. 10). The
components vary in size and edge conditions,
and are tted with mortise and tenon joints to
connect adjacent pieces together. The annular
components get pulled together at their ends to
create conical frustums. These truncated cones t
precisely to the undulating strips and act as
spacers between two layers in the system. Once
all parts are loosely assembled, they are fastened
together by pressing on the cones and deliber-
ately causing them to buckle until they snap
through to a new equilibrium position. This
process is used to clamp adjacent parts and it is
repeated three times to fully lock all of the
structural components together. The result is a
double-layered sandwich structure that is geo-
metrically versatile and can be applied to both
synclastic and anticlastic shapes (Fig. 11).
Fig. 9 Considering local stress concentrations in the individual unit as well as in the interacting layers, allowed to
simplify the system to a parametric model with which to easily populate given freeform surfaces
Fig. 10 The entire structure consists of four basic shapes that are clamped together by a local snap-through instability
mechanism
60 S. Schleicher et al.
An important step in this project was to translate
this construction method into a computational
process that allows for morphological differentia-
tion. In order to do so, an integrated approach was
developed to incorporate both geometric and
material constraints. FEM analyses were con-
ducted at two different scales. At the level of the
subunit, FEM simulations were used to determine
suitable material characteristics and restricting
geometric dimensions to ensure that the truncated
cones can be snapped by hand. At the global level,
FEM simulations were used to optimize the
thickness of the sandwich structure depending on
the stress distribution in the target surface (Fig. 12).
Areas with larger bending moments have more
distance between the two layers, while areas with
higher shear forces have smaller cones and thus
feature greater material density. This structural
information was used to inform the packing pattern
that was applied to the target surface. There is a
direct relationship between cone radius, assembly
thickness, and material density, which all act
together on the nal composition of the structure.
Finally, the detailing and layout of the individual
parts was automated in order to facilitate an easy
translation to new global geometries. Each indi-
vidual component is automatically unrolled and
detailed with the mortise and tenon joints that are
used to connect the parts together. As a proof of
concept, a large-scale model was constructed using
atbed fabrication technologies and light PET-G
plates of 0.5 and 0.75 mm thicknesses (Fig. 13).
Fig. 11 This construction methodology can be applied to the design of synclastic and anticlastic surfaces
Fig. 12 Analysing the structural performance of a target
surface informs the composition of the structure, which
then gets optimized by either increasing the static height
of the sandwich or the material density in the zones where
it is needed the most
Form-Finding and Design Potentials 61
Conclusion
The evolution of bending-active plate structures
and the associated form-nding and analysis
techniques demonstrate the signicant advance-
ments that have occurred since Buckminster
Fullersrst plydomes. The increasing avail-
ability of computing power and advancement of
simulation tools have made it much easier to
understand the complex interdependencies of
bending-active structural systems as well as to
master them for new designs. The integration of
both geometric and material constraints from the
start of the design process is a powerful approach
that renders great potential for many applica-
tions. The case studies that are described in this
paper indicate that the possible design space for
bending-active plate structures is rich and offers a
plethora of beautiful, efcient, and lightweight
designs.
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Form-Finding and Design Potentials 63
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Bio-inspired architectural designs are often superior for their aesthetics and structural performance. Mimicking forms and loading states of a biological structure is complex as it requires a delicate balance among geometry, material properties, and interacting forces. The goal of this work is to design a biomimetic, ultra-lightweight, bending-active structure utilizing an informed integral design approach, and thereby constructing a self-supporting cellular pavilion. A bioinspired pavilion has been designed and constructed based on the natural cellular organization observed in Radiolaria, a deep-sea microorganism. The cellularity was mimicked via Voronoi tessellation in the structure of the pavilion, whose structural performance was evaluated using finite element analysis. Accordingly, funicular structure design strategies were studied with a focus on cellular distributions and concentration responding to areas with high structural stress. The computer aided custom designed pavilion was constructed with engineered, in-house fabricated fiberglass composite materials. The bending-active lightweight structure was also validated through material performance inquiry, a partial full-scale cellular assembly, and the full-size pavilion construction. This work contributes to the design approach comprising a bending-active form-finding schematic strategy to construct the elastic bending-active structure physically and simulate computationally within the context of nature inspired innovative lightweight structure design.
... A good example for the new possibilities emerging from a physics-informed digital design process is the research done on bending-active structures. This type of structural system uses large-scale deformations as a form-giving and self-stabilising strategy (Knippers et al. 2011, Lienhard et al. 2013, Schleicher et al. 2015. Typically, bending-active structures can be divided into two main categories, which relate to the geometrical dimensions of their constituent elements. ...
... The presented novel construction method allows for the construction of simple shell structures, such as halls for events, storage, vehicles or planes, noise prevention tunnels for traffic, as well as aesthetical shell constructions, such as freeform surfaces from single curved panels [24][25][26] with little material expenditure. There are advantages which can be expressed as follows: ...
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Shells are impressive structures due to the high load‐bearing capacity they exhibit when appropriately designed. Their construction, however, is usually associated with great efforts. In this paper, a novel approach for shell‐construction is presented that circumvents the necessity for doubly curved formwork. Instead, shells are erected from flat plates to which an eccentric force is applied causing them to bend into a desired curved shape. The form‐activating forces are induced by coupling a system of tendons to a thin—thus flexible—plate made from reinforced concrete. This approach may seem controversial as concrete exhibits a small ultimate strain and a brittle failure behavior. Therefore, it does not appear suited for the large deformations expected during the construction of actively bent structures. The investigations presented in this paper show the suitability of textile‐reinforced concrete for the fabrication of actively bent shells.
... The proposal builds upon previous research in the area of bending-active structures and pushes this concept one step further. The basic idea behind this design approach is to use large elastic deformations and the bending of initially straight or planar building elements for the construction of curved, load-bearing structures [23][24][25]. However, one of the major challenges for this construction technique is to predict and control the equilibrium shape of multiple bent and interconnected members and to feed this information back into the fabrication process. ...
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The increasing specialization in architecture has clearly left its marks not only on the general profession but also on architectural education. Many universities around the world react to this development by offering primarily conventional and overly discipline-specific courses that often lack bold new concepts. To remedy this situation, the authors propose an alternative teaching model called Studio One, which seeks to facilitate new dynamic links between architecture and other disciplines based on the interplay between fundamental research, design exploration, and practical application. The goal is to develop an interdisciplinary, collaborative design training that encompasses the best that nature has to teach us, realized through the technology that humans have achieved. At the core of this class is the study of biological structures and the development of bio-inspired construction principles for architectural design. Both aspects are rich sources of innovation and can play an important role in the training of future architects and engineers. This paper seeks to provide a coherent progress report. After a brief introduction to the general objectives of Studio One, the authors will specify the methods and 21st century skills that students learned during this class. Relying on four student capstone projects as examples, the paper will then go into more detail on how natural structures can inspire a new design process, in which students abstract basic biomimetic principles and transfer them into the construction of architectural prototypes and pavilions. Finally, the authors conclude by discussing the particular successes and challenges facing this teaching model and identify the key improvements that may give this program an even bigger impact in the future.
Chapter
This paper presents a novel building technique for the formwork of thin shell structures with 3d-printed bending-active mesh sheets. To enhance the structural stiffness of the flexible plastic materials, bending-active form is applied to utilize the geometry stiffening effect through the large deformation of bending. As it is the main problem to determine the final geometry of the bent surface, design methods with consideration of the numerical simulation is researched and both simulations via dynamic relaxation and finite element method are presented. Several demonstrator pavilions and the building process are shown to test the feasibilities of the presented building techniques in the real shell project. It is expected that this method could be applied into more thin shell projects to realize an efficient building technology with less exhaust of materials.
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Putting forward an innovative approach to solving current technological problems faced by human society, this book encompasses a holistic way of perceiving the potential of natural systems. Nature has developed several materials and processes which both maintain an optimal performance and are also totally biodegradable, properties which can be used in civil engineering. Delivering the latest research findings to building industry professionals and other practitioners, as well as containing information useful to the public, ‘Biotechnologies and Biomimetics for Civil Engineering’ serves as an important tool to tackle the challenges of a more sustainable construction industry and the future of buildings.
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In this paper structures that actively use bending as a self-forming process are reviewed. By bringing together important material developments and various historical as well as recently built samples of such structures, the aim is to show coherences in their design approach, structural systems and behaviour. Different approaches to bending-active structures are defined and described. By making this work accessible and categorising it, this paper aims to contribute to an emerging development. A differentiation of such structures is suggested based on their design approaches. Three such approaches are differentiated: the behaviour based approach, the geometry based approach and current research that seeks to integrate the two. In this paper the nature of these approaches and some important project samples are discussed
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In architecture, kinetic structures enable buildings to react specifically to internal and external stimuli through spatial adjustments. These mechanical devices come in all shapes and sizes and are traditionally conceptualized as uniform and compatible modules. Typically, these systems gain their adjustability by connecting rigid elements with highly strained hinges. Though this construction principle may be generally beneficial, for architectural applications that increasingly demand custom-made solutions, it has some major drawbacks. Adaptation to irregular geometries, for example, can only be achieved with additional mechanical complexity, which makes these devices often very expensive, prone to failure, and maintenance-intensive. Searching for a promising alternative to the still persisting paradigm of rigid-body mechanics, the authors found inspiration in flexible and elastic plant movements. In this paper, they will showcase how today’s computational modeling and simulation techniques can help to reveal motion principles in plants and to integrate the underlying mechanisms in flexible kinetic structures. Three case studies will be presented key motion principles and discuss aspects concerning their scaling, distortion, and optimization. Finally, the acquired knowledge on bio-inspired kinetic structures will be applied to a representative application in architecture, in this case as flexible shading devices for double curved facades.
Thesis
This thesis aims to provide general insight into form-finding and structural analysis of bending-active structures. The work is based on a case study approach, in which findings from prototypes and commercial building structures become the basis for generalised theoretical investigations. Information is continuously fed back from these case study structures into theoretical research, which creates the basis for overall working methods. The behaviour of five investigated structures is found to be independent of clearly predictable load bearing categories. Their load bearing mechanisms are largely dependent on the boundless variety of topologies and geometrical expressions that may be generated. The work therefore understands active bending as an approach to generating new structural forms, in which common load bearing behaviour is found due to the structures inherently large elasticity and inner stress state. Based on engineering and historical background, methodological, mechanical and material fundamentals of active-bending are discussed in Chapter B and C. The case study structures introduced in Chapter D open a wide field of active-bending applications, in lightweight building structures. Whether the conclusions drawn from case studies, are generally viable for bending-active structures is then discussed in the core of the work presented in two chapters on Form-Finding (Chapter E) and Structural Behaviour (Chapter F). The chapter on form-finding introduces the working methods and modelling environments developed for the present work. The chapter on structural behaviour is concerned with the influence of residual bending stress on the stiffness, scaling and stability of bending-active structures. Based on these findings, generalised design rules for bendingactive structures are highlighted in a concluding chapter.
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A trained architect, who works with the Specialist Modelling Group (SMG) at Foster + Partners, Daniel Piker is also the developer of the Kangaroo plug-in for Rhinoceros® and Grasshopper®. He explains how Kangaroo has been devised to simulate aspects of the behaviour of real-world materials and objects in order to modify designs in response to engineering analyses, engendering an intuitive sense of the material world.
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Material behaviour computes form. In the physical world, material form is always inseparably connected to internal constraints and external forces; in the virtual space of digital design, though, form and force are usually treated as separate entities – divided into processes of geometric form generation and subsequent engineering simulation. Using the example of the interdisciplinary ICD/ITKE Research Pavilion, constructed at the University of Stuttgart in 2010, Moritz Fleischmann, Jan Knippers, Julian Lienhard, Achim Menges and Simon Schleicher explain how feedback between computational design, advanced simulation and robotic fabrication expands the design space towards previously unexplored architectural possibilities. Copyright © 2012 John Wiley & Sons, Ltd.
A discrete model of thin shells
  • E Grinspun
Grinspun E (2008) A discrete model of thin shells. Discrete Differ Geom 325-337. doi:10.1007/978-3-7643-8621-4_17
Atlas Kunststoffe+Membranen: Werkstoffe und Halbzeuge, Formfindung und Konstruktion
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Knippers J et al (2010) Atlas Kunststoffe+Membranen: Werkstoffe und Halbzeuge, Formfindung und Konstruktion. Institut für Internationale Architektur-Dokumentation, München
Bending-active structures-research Pavilion ICD/ITKE
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Lienhard J et al (2011) Bending-active structures-research Pavilion ICD/ITKE. In: Proceedings of the international symposium of the IABSE-IASS symposium