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Bending-Active Plates: Form-Finding and Form-Conversion


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With this paper, the authors aim to contribute to the discourse on bending-active structures by highlighting two different design methods, form-finding and form-conversion. The authors compare the two methods through close analysis of bending-active plate structures, discussing their advantages and disadvantages based on three built case studies. This paper introduces the core ideas behind bending-active structures, a rather new structural system that makes targeted use of large elastic deformations to generate and stabilise complex geometrical forms based on initially planar elements. Previous research has focused mainly on form-finding. As a bottom-up approach, it begins with flat plates and recreates the bending and coupling process digitally to gradually determine the final shape. Form-conversion, conversely, begins with a predefined shape that is then discretized by strategic surface tiling and informed mesh subdivision, and which in turn considers the geometrical and structural constraints given by the plates. The three built case studies exem- plify how these methods integrate into the design process. The first case study applies physical and digital form-finding techniques to build a chaise lounge. The latter two convert a desired shape into wide-spanning constructions that either weave multiple strips together or connect distant layers with each other, providing additional rigidity. The presented case studies successfully prove the effectiveness of form-finding and form-conversion methods and render a newly emerging design space for the planning, fabrication, and construction of bending-active structures.
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Bending-Acve Plates
1 Berkeley Weave installed at the
courtyard of UC Berkeley’s College
of Environmental Design (CED).
University of California, Berkeley
Department of Architecture
University of Stugart, Instute
of Building Structures and
Structural Design (ITKE)
Form-Finding and Form-Conversion
With this paper, the authors aim to contribute to the discourse on bending-acve structures by
highlighng two dierent design methods, form-nding and form-conversion. The authors compare
the two methods through close analysis of bending-acve plate structures, discussing their
advantages and disadvantages based on three built case studies. This paper introduces the core
ideas behind bending-acve structures, a rather new structural system that makes targeted use of
large elasc deformaons to generate and stabilize complex geometrical forms based on inially
planar elements. Previous research has focused mainly on form-nding. As a boom-up approach,
it begins with at plates and recreates the bending and coupling process digitally to gradually
determine the nal shape. Form-conversion, conversely, begins with a predened shape that is then
discrezed by strategic surface ling and informed mesh subdivision, and which in turn considers
the geometrical and structural constraints given by the plates. The three built case studies exem-
plify how these methods integrate into the design process. The rst case study applies physical and
digital form-nding techniques to build a chaise lounge. The laer two convert a desired shape into
wide-spanning construcons that either weave mulple strips together or connect distant layers
with each other, providing addional rigidity. The presented case studies successfully prove the
eecveness of form-nding and form-conversion methods and render a newly emerging design
space for the planning, fabricaon, and construcon of bending-acve structures.
In recent years, the architecture community has witnessed an
increased availability and constant improvement of computa-
onal tools that enable not only advanced geometrical modeling,
but also the integraon of real-me physics-based simulaons
into the design process in common CAD environments. Programs
like Kangaroo Physics or SOFiSTiK are used, for example, to
rapidly form-nd and interact with parcle systems or accurately
analyze structures on the bases of Finite Element Methods (Piker
2013; Lienhard et al. 2011). With the help of these programs,
one can describe and evaluate the mechanical behavior and
structural capacity of a model under simultaneous consideraon
of external forces and internal material stresses.
With the rise of these tools, architects and engineers are
becoming more and more interested in structural systems whose
forms and load states cannot easily be predicted, but instead
result from a delicate balance between geometry, interacng
forces, and material properes. It is here, in parcular, where
physics-based simulaons that provide real-me feedback can
demonstrate their strength. Bending-acve structures illustrate
these interrelaonships and as such are chosen in this paper as a
detailed example (Figure 1).
This newly established structural system is characterized by the
use of large elasc deformaons of inially planar building mate-
rials to generate geometrically complex construcons (Knippers
et al. 2011). While the tradional maxim in engineering is to
limit the amount of bending in structures, this typology actually
harnesses bending for the creaon of complex and extremely
lightweight designs. The underlying idea of exploing a struc-
ture’s exibility in a controlled way is rather simple and extremely
versale. It can be used, for example, as a form-giving and
self-stabilizing strategy in stac structures or as compliant mech-
anism in kinec structures (Lienhard 2014, Schleicher 2015).
Bending-acve structures can be generally divided into two
main categories, which relate to the geometrical dimensions of
their fundamental components. One-dimensional (1D) systems
can be built, for instance, by bending slender rods, while
two-dimensional (2D) systems use thin plates as basic building
blocks. While extensive knowledge and experience exists for 1D
systems, with elasc gridshells as most prominent applicaon,
plate-dominant structures have not received much aenon
yet and are considered more dicult to design. One reason is
certainly that plates have a limited formability, since they bend
mainly along the axis of weakest inera and thus cannot easily be
forced into complicated geometries. However, what makes this
subset of bending-acve structures parcularly interesng from
a mathemacal point of view is the fact that plates have a clear
scale separaon. They are typically very large in one dimension
and progressively smaller in the other two. Their length is spec-
ied in meters, their width in cenmeters, and their height only
in millimeters. Having hierarchical geometrical features facilitates
the further design process of bending-acve plate structures and
makes it easier to assess the structural behavior and accurately
ancipate their deformed geometry with digital simulaons.
Prominent examples for bending-acve plate structures are
Buckminster Fuller’s plydomes and the ICD/ITKE Research
Pavilion 2010 (Figures 2 and 3). While the rst example follows a
raonal approach in which the shape of a sphere is approximated
with a regular ling of idencal plates (Fuller 1959), the second
example takes advantage of computaonal mass customizaon
and joins 500 individual parts together (Fleischmann et al. 2012).
A previous study idened three main design strategies for
bending-acve structures: a behavior-based, geometry-based,
and integrave approach (Lienhard et al. 2013). According to
this study, the rst category refers to the tradional approach
by skilled crasmen who bend building materials intuively
on the construcon site. The other two categories describe a
more scienc approach, in which hands-on experiments and
analycal tests were conducted beforehand and informed the
further design and construcon process. While the geome-
try-based approach relates to the idea of forcing an object to
match a specic target geometry without further consideraon
of material properes, the integrave approach takes exactly
these liming factors into account when exploring a reachable
design space. In order to best contribute to the above-men-
oned classicaon of bending-acve structures, it is the aim
of this paper to further elaborate emerging design trends in the
integrave approach by having a closer look at the techniques of
form-nding and form-conversion.
2 3
2 Buckminster Fuller’s geodesic plydome in Des Moines, Iowa, 1957. The hemi-
sphere spans 7.3 m and is made out of marine plywood sheets with a thickness
of 6.4 mm.
3 ICD/ITKE Research Pavilion 2010 by the University of Stugart spans 10 m and
consists of 80 birch plywood strips with a thickness of 6.4 mm.
The term form-nding is best known for its role in the design
of membranes and shell structures and refers to the concept
of using physical models and numerical simulaons to nd
an opmal geometry of a structure in stac equilibrium with
a design loading (Adriaenssens et al. 2014). From the 1950s
onwards, architects and engineers focused on form-nding stra-
tegies that both incorporated materials and forces while enabling
a systemac exploraon of lightweight construcons. They
became an essenal part in the work of people like Buckminster
Fuller, Félix Candela, Heinz Isler, and Frei Oo (Chilton 2000;
Oo 2005). While these early pioneers implemented form-
nding strategies to design shells and membranes determined by
the shape of hanging chains and cloth, these techniques can also
be applied for bending structures.
In the context of bending-acve plate structures and digital
simulaon, form-nding is oen used for a boom-up design
approach. It starts with planar sheets or strips to create the
bending and coupling process in the nal shape (Lienhard,
Schleicher, and Knipper 2011; Fleischmann et al. 2012). By using
spring-based simulaons in Kangaroo Physics or nite element
methods in SOFiSTiK, one can not only determine the resulng
geometry of the deformed structure but also visualize the evolu-
on of stresses within the material while the system is deforming
(Figure 4) (Schleicher et al. 2015). Based on this informaon,
one can cauously bend a component, for instance by following
an ultra-elasc cable approach unl a permissible stress state
is reached (Lienhard et al. 2014). The nal shape and caused
stresses are oen unknown at the beginning, especially when
mulple parts are bent and fastened together, which is a consid-
erable drawback. A designer with a certain aim in mind would
therefore have to conduct mulple simulaons with gradually
changing parameters to move closer to the design objecve.
In comparison to the previous method, form-conversion pursues
a dierent approach when integrang geometrical and material
consideraons into the design of bending-acve plate struc-
tures. Here, the process begins with a predened target surface
or mesh, which is then discrezed and further subdivided into
smaller bent les based on the exibility of the used plates. The
main restricon in this regard is the knowledge concerning the
plates’ material formability. Here, it is parcularly important to
know that for strips and plate-like elements, the basic shapes
that can be achieved by pure bending without stretching are
conical and cylindrical surfaces. These shapes are also referred to
as single-curved or developable surfaces. Aempng to bend a
sheet of material in two direcons simultaneously either results
in irreversible, plasc deformaons or ulmate material failure.
Thus, to expand the range of achievable shapes, it is necessary to
develop other methods for the inducon of Gaussian curvature
into the system.
To overcome the limitaons related to Gaussian curvature,
muldireconal bending can be induced by strategically removing
material and freeing the plates from the sening constraint of
their surroundings. This principle is illustrated in Figure 5 and
a similar approach was presented by Xing et al. (2011). Here, a
connuous rectangular plate is reduced to two orthogonal strips.
Once again, the strips are bent using the ultra-elasc cable
approach of Lienhard et al. (2014). The bending sness of the
plate, depending proporonally on its width, results in a radical
increase of sness in the connecng area between the strips.
Schleicher, La Magna
4 The form-nding approach
starts from a at sheet and uses
contracng elasc cables elements
to generate the nal bent shape.
Simulaons in Kangaroo Physics
allow for quick and interac-
ve models while the soware
SOFiSTiK enables precise shape
and stress analysis based on Finite
Element Methods. (Schleicher et al.
As a result, the connecng area remains almost planar and the
perpendicular bending axis remains unaected by the induced
curvature. In this way, it becomes possible to bend the strips
around mulple axes, spanning dierent direcons but sll main-
taining the material connuity of a single element. The center
image of the cross-like strips in Figure 5 depicts the resulng von
Mises stresses and clearly displays an area of unstressed material
at the intersecon between the two strips, which supports the
previous arguments. A local stress concentraon appears at the
juncon of the strips due to the sharp connecng angle as well
as the inevitable geometric sening in that area.
The result of muldireconal bending can be compared with an
analysis of Gaussian curvature on the right. From the plot, it is
clear that the discrete Gaussian curvature of the deformed mesh
is zero everywhere apart from a small, localized area at the inter-
secon of the two branches. This conrms the assumpon that,
for inextensible materials, most developable surfaces (or slight
deviaon thereof) are achievable. Based on this approach, other
arbitrary freeform surfaces can be converted, following the logic
of strategic material removing and dened zones of local bending
and planarity, as demonstrated in the lower images of Figure 5.
To further illustrate the design potenals of a form-nding and
form-conversion approach, the following secon will have a
closer look at three built case studies. While the rst case study
takes advantage of a boom-up, form-nding technique to
design a load-bearing chaise lounge, the laer two demonstrate
the form-conversion of pre-dened shapes into wide-spanning
construcons that gain rigidity by either weaving mulple strips
together or connecng distant layers with each other.
The rst case study represents the previously menoned form-
nding process and demonstrates its design possibilies in the
context of a furniture-scale object. The goal of this bending-ac-
ve plate structure is to meet the highest structural demands yet
only use a minimum amount of material. The applicaon chosen
to address this challenge in built form was a chaise lounge for
one person.
In this project, bending is primarily induced by strategically
removing material from the center of a thin sheet and then
pinching its naked edges together and fastening the deformed
shape with rivets. This technique has mulple benets: gener-
ang intricate forms out of a single planar surface and achieving
three-dimensional shapes that perform structurally in the bent
state. The general design of the chaise lounge followed a gradual
form-nding approach that comprised a series of physical models
and digital simulaons. In a rst step, the geometry of dierent
reference chairs and the relaonship with the human body was
studied and a group of target angles were idened that allow
for a comfortable seang posion (Figure 6). Based on this
informaon, quick sketch models were built out of paper to gain
a beer understanding of the interdependencies between the
cung paern and the angles of the deformed structure aer
the pinching.
The second step was to turn these cung paerns into digital
models. This was done in Grasshopper and the pinching simu-
lated in Kangaroo Physics. At this point, the main advantage of
using this type of spring-based simulaon was the possibility for
real-me feedback and user-interacvity to further modify the
cung paern and improve the design (Figure 7). Furthermore,
5 The form-conversion approach
is informed by the mechanical
characteriscs of a bent material
and applies these principles to
the subdivision process of a
given target geometry. The upper
row shows the muldireconal
bending of a cross-like strip based
on contracng elasc cables.
The center image indicates the
distribuon of von Mises stress.
The image on the right shows the
Gaussian curvature. The boom
row uses these liming factors
for a form-conversion of a target
mesh into an assembly of bent
6 Dierent reference chairs were analyzed for their seang posion and the angles
therein were recreated by pinching at sheets into a deformed shape.
7 Digital simulaons in Kangaroo Physics were used to quickly test dierent
cung paerns and form-nd the desired geometrical form.
8 Structural validaon of the form-found shape based on FEM simulaons and a
thorough analysis of the appearing minimal bending radii.
9 A series of paper and plasc sketch models were used to gradually approach the
nal shape and ascertain the required cung paern.
10 Full-scale prototype of the bending chaise lounge is built out of 1.6 mm thin
HDPE plasc and is able to carry the weight of a person.
11 Berkeley Weave installaon spans over 4 m and is built out of 480 individual
plywood strips with a thickness of only 3 mm.
tracking the curvature of the mesh and idenfying minimal
bending radii allowed us to draw rst conclusions if this form
could be built out of a specic target material.
The following third step provided much more accurate results
regarding the materializaon of the chaise lounge. Here,
SOFiSTiK was used to generate nite element models with
dened material characteriscs (Figure 8). All surfaces were given
the material properes of high-density polyethylene (HDPE) with
a Young’s modulus of 1200 N/mm2 and a thickness of 1.6 mm
or 3.2 mm for a single or double layer. The model was then
deformed using the ultra-elasc cable approach. Consulng this
slightly more me-consuming method at this stage of the design
process had mulple benets. It allowed us to calculate the
exact geometry of the highly deformed structure and assess the
stresses within. Thus, this simulaon is a much more complete
descripon of the mechanical behavior and structural capacity
of the bending-acve system. Furthermore, the feedback on
the structure’s complex equilibrium state also allowed localizing
potenally dangerous stress concentraons. And last but not
least, having done the simulaon in typical engineering soware
also made it possible to further analyze the chair’s structural
performance once the weight of a human body was added.
As a proof of concept, the chaise lounge was built both as a
series of small-scale models as well as a full-scale chaise lounge
with the dimensions of 2.44 m x 1.22 m x 1.6 mm (Figures
9–10). The construcon material was HDPE, the paerns for
the dierent sheets were cut on a Zünd blade cuer, and the
pieces were connected together with steel rivets. Riveng, and in
parcular blind riveng, was used in this project both to perma-
nently pinch each surface as well as to connect mulple plates
with each other. Since rivets can only transmit tension and shear
forces, their exact posion needed to be determined carefully. In
this regard, the iterave from-nding over mulple simulaons
Schleicher, La Magna
played an important role. It provided crucial informaon about
the precise geometry of the deformed plates as well as the exact
posion of the rivet holes, which was needed to guarantee the
alignment of all layers. As far as the actual assembly of the chaise
lounge is concerned, the bending of the plasc was rather easy
and could be done manually. In fact, it was surprising how rigid
the structure became once all pieces were fastened together
and the stored elasc energy began to pre-stress the structure.
The nal chaise lounge was capable of carrying the weight of a
person, of course under some deecons but within permied
tolerances (Figure 10).
In contrast to the previous example, which uses only a small
number of parts, designing bending-acve plate structures out
of mulple components is very challenging and thus requires a
dierent approach. For this reason, the second case study applies
a dierent method and aims to demonstrate the design poten-
al of form-conversion (Figure 11). It invesgates an integrave
approach that considers not only bending but also torsion of
slender strips. The saddle-shaped design of the Berkeley Weave
is based on a modied Enneper surface (Figure 12a). This par-
cular form was chosen because it has a challenging anclasc
geometry with locally high curvature. The subsequent conversion
process into a bending-acve plate structure followed several
steps. The rst was to approximate and discreze the surface
with a quad mesh (Figure 12b). A curvature analysis of the
resulng mesh reveals that its individual quads are not planar but
spaally curved (Figure 12c). The planarity of the quads, however,
will be an important precondion in the later assembly process.
In a second step, the mesh was transformed into a four-layered
weave paern with composed strips that feature pre-drilled
holes. Here, each quad was turned into a crossing of two strips
in one direcon with two other strips at a 90-degree angle. The
resulng interwoven mesh was then opmized for planarizaon.
However, only the regions where strips overlapped were made
planar, while the quads between the intersecons remained
curved (Figure 12d). A second curvature analysis illustrates the
procedure well and shows zero curvature at the intersecons of
the strips (blue areas) while the connecng arms are both bent
and twisted (Figure 12e). Specic rounes in the form-conver-
sion process guaranteed that the bent zones stayed within the
permissible bending radii. In the last step, this converted shape
was used to generate a fabricaon model that featured all the
connecon details and strip subdivisions (Figure 12f).
A closer look at the most extremely curved region illustrates the
complexity related to this last step (Figure 13). To allow for a
proper connecon, bolts were only placed in the planar regions
between intersecng strips. Since the strips are composed out of
smaller segments, it was also important to control their posion
in the four-layered weave and the sequence of layers. A paern
was created which guaranteed that strip segments only ended in
layer two and three and are clamped by connuous strips in layer
one and four. A posive side eect of this weaving strategy is
that the gaps between segments are never visible and the strips
appear to be made out of one piece. The drawback, however, is
that each segment has a unique length and requires individual
posions for the screw holes (Figure 14).
To demonstrate proof of concept for this design approach, this
case study was built in the dimensions of 4 m x 3.5 m x 1.8 m
(Figure 11). The structure is assembled out of 480 geometri-
cally dierent plywood strips that were fastened together with
400 bolts. The material used is 3.0 mm thick birch plywood
with a Young’s modulus of EmII = 16471 N/mm2 and Em
1029 N/mm2. Dimensions and material specicaons were
employed for a nite element analysis using the soware
SOFiSTiK. Under consideraon of self-weight and stored elasc
energy, the minimal bending radii are no smaller than 0.25 m
10 11
and the resulng stress peaks are sll below 60% of permissible
material ulizaon.
The third case study showcases another take on form-conversion
for bending-acve plate structures that consists of many compo-
nents. This project is a mul-layered arch that spans over 5.2
m and has a height of 3.5 m. It was built to prove the technical
feasibility of using bending-acve plates for larger load-bearing
structures. In comparison to the previous case study, this project
implements a dierent ling paern and explores the possibility
of signicantly increasing a shape’s rigidity by cross-connecng
distant layers with each other. To fully exploit the large deforma-
ons that plywood allows for, the thickness of the sheets had
to be reduced to the minimum, leading once again to the radical
choice of employing 3.0 mm birch plywood. Since the resulng
sheets are very exible, addional sness needed to be gained
by giving the global shell a peculiar geometry, which seamlessly
transions from an area of posive curvature (sphere-like) to one
of negave curvature (saddle-like) (Figure 15a). This pronounced
double-curvature provides addional sness and helps avoid
undesirable deformaon of the structure. Despite the consid-
erable strength achieved by the shape alone, the choice of
using extremely thin sheets of plywood at that scale asked for
addional reinforcement to provide further load resistance.
These needs were met by a double-layered structure with two
cross-connected shells.
As in the previous example, the rst step of the process was to
convert the base geometry into a mesh paern (Figure 15b).
In the next step, a preliminary analysis of the structure was
conducted and informed the oseng of the mesh to create
a second layer. As the distance between the two layers varies
to reect the bending moment calculated from the preliminary
analysis, the oset of the surfaces changes along the span of
the arch (Figure 15c). The oset reects the stress state in the
individual layers, and the distance between them increases in the
crical areas to increment the global resistance of the system.
The following form-conversion process was once again driven
by material constraints and previously determined permissible
stress limits with respect to bending and torsion. The resulng
ling logic that was used for both layers aected the size of
the members and guaranteed that each component could be
bent into the specic shape required to construct the whole
surface. More precisely, this is achieved by strategically placing
voids into target posions of the master geometry, ensuring that
the bending process can take place without prejudice for the
individual components (Figure 15d). Although inially at, each
element undergoes mul-direconal bending and gets locked
into posion once it is fastened to its neighbors. The exible 3.0
12 Form-conversion process and analysis of the Berkeley Weave.
13 Analysis of Gaussian curvature in the area with the highest deformaon.
14 Schemac drawing of the technical details in the four-layered weave.
Schleicher, La Magna
mm plywood elements achieve consistent sness when joint
together, as the pavilion, although a discrete version of the inial
shape, sll retains substanal shell sness. This was validated in
another nite element analysis that considered both self-weight
as well as undesirable loading scenarios (Figure 15e).
Finally, aer fabricaon, the structure was assembled on site.
The built structure employs 196 elements unique in shape and
geometry (Figure 16). 76 square wood proles of 4 cm x 4 cm
were used to connect the two plywood skins (Figure 17). Due
to the varying distance between the layers, the connectors had
a total amount of 156 exclusive compound miters. The whole
structure weighs only 160 kg, a characterisc that also highlights
the eciency of the system and its potenal for lightweight
construcon. The smooth curvature transion and the overall
complexity of the shape clearly emphasize the potenal of the
construcon logic. Furthermore, the implemented form-con-
version process can be applied to any kind of double-curved
freeform surface, not only the one built at UC Berkeley’s campus
(Figure 18).
In summary, it can be concluded that the three case studies
clearly illustrate the feasibility of form-nding and form-conver-
sion techniques for the design of bending-acve plate structures.
All three examples showcase an integrave approach that is
directly informed by the mechanical properes of the thin plasc
and plywood sheets, which were employed in the dierent proj-
ects. Their overall geometry is therefore the result of an accurate
negoaon between the mechanical limits of the materials and
15 The form-conversion process of
Bend9 pavilion started from a base
geometry (A) and approximated
this shape with a mesh (B). Based
on a rst structural analysis, the
mesh was oset and turned into
a double layer. This structure was
then converted into an assembly of
bent plates (D). Aer another nite
element analysis (E), a fabricaon
model was generated (F).
16 Detail of the assembled structure
shows the layering of dierent
components and the strategically
placed voids to prevent conicts
between the bent parts.
17 Custom wood proles were used
to cross-connect the two layers
together and thus increase the
structural capacity of the pavilion
their deformaon capabilies. The very nature of all three case
studies required a ght integraon of design, simulaon, and
assessment of fabricaon and assembly constraints.
Due to its small number of parts, the bending chaise lounge
was a good case study to demonstrate the potenal of design
processes based on iterave form-nding. Depending on the
simulaon soware used, this method can be very quick and
interacve or parcularly accurate and reliable regarding its
results. This precision, however, comes at the expense of simula-
on speed. Therefore, form-nding meets its natural boundaries
when the number of parts exceeds a certain limit.
The second and third case studies aimed to tackle this challenge
by presenng form-conversion as an alternave design approach
for bending-acve plate structures that consist of many parts.
Furthermore, the Berkeley Weave and the Bend9 pavilion
exemplify the capacity of bending-acve plate structures to be
employed as larger scale, space-framing architectural interven-
ons. For future research, the presented case studies and the
underlying design rounes of form-nding and form-conversion
will serve as rst prototypes for the exploraon of more complex
surface-like shell structures that derive their shape through
elasc bending.
The authors would like to thank the following student team for their
amazing work on the bending chaise lounge and their indirect contribu-
on to this paper: Cindy Hartono, Fei Du, Shima Sahebnassagh, Eleanna
Panagoulia as well as their addional supervisors Prof. Kyle Steinfeld, Prof.
Jonathan Bachrach, and Luis Jaggy. For the Berkeley Weave installaon, the
authors would parcularly like to thank Sean Ostro, Andrei Nejur, and Rex
Crabb for their support. Finally, the Bend9 pavilion would not have been
possible without the kind support of Autodesk’s Pier 9 and its enre sta.
Adriaenssens, Sigrid, Philippe Block, Diederick Veenendaal, and Chris
Williams, eds. 2014. Shell Structure for Architecture: Form Finding and
Opmizaon. London: Routledge.
18 View of the Bend9 structure assembled out of 3 mm thin birch plywood in the courtyard at UC Berkeley’s College of Environmental Design (CED).
Schleicher, La Magna
Chilton, John. 2000. The Engineer’s Contribuon to Contemporary
Architecture: Heinz Isler. London: Thomas Telford.
Fleischmann, Moritz, Jan Knippers, Julian Lienhard, Achim Menges,
and Simon Schleicher. 2012. “Material Behaviour: Embedding Physical
Properes in Computaonal Design Processes.Architectural Design 82
(2): 44–51.
Fuller, R. Buckminster, and Robert W. Marks. 1973. Dymaxion World of
Buckminster Fuller. New York: Anchor Books.
Fuller, R. Buckminster. 1959. Self-strued geodesic plydome. US Patent
2,905,113, led April 22, 1957, and issued September 22, 1959.
Knippers, Jan, Jan Cremers, Markus Gabler, and Julian Lienhard. 2011.
Construcon Manual for Polymers Membranes: Materials, Semi-Finished
Products, Form-Finding Design. Basel: Birkhauser Architecture.
Lienhard, Julian, Simon Schleicher, and Jan Knippers. 2011. “Bending-
Acve Structures—Research Pavilion ICD/ITKE.” In Proceedings of the
Internaonal Symposium of the IABSE-IASS Symposium. London, UK:
Lienhard, Julian, Holger Alpermann, Christoph Gengnagel, and Jan
Knippers. 2013. “Acve Bending, A Review on Structures Where Bending
Is Used as a Self-Formaon Process.Internaonal Journal of Space
Structures 28 (3–4): 187–196. doi:10.1260/0266-3511.28.3-4.187.
Lienhard, Julian, Riccardo La Magna, and Jan Knippers. 2014. “Form-
nding Bending-Acve Structures with Temporary Ultra-Elasc
Contracon Elements.” In Proceedings of 4th Internaonal Conference
on Mobile, Adaptable and Rapidly Assembled Structures, edited by N. De
Temmerman and C. A. Brebbia. Ostend, Belgium: MARAS. 107–116.
Lienhard, Julian. 2014. “Bending-Acve Structures: Form-Finding
Strategies Using Elasc Deformaon in Stac and Kinec Systems
and the Structural Potenals Therein.” PhD Dissertaon, University of
Oo, Frei. 2005. Frei Oo: Complete Works: Lightweight Construcon,
Natural Design, edited by Winfried Nerdinger. Basel: Birkhäuser.
Piker, Daniel. 2013. “Kangaroo: Form Finding With Computaonal
Physics.Architectural Design 83 (2): 136–137.
Schleicher, Simon. 2015. “Bio-Inspired Compliant Mechanisms for
Architectural Design: Transferring Bending and Folding Principles of Plant
Leaves to Flexible Kinec Structures.” PhD Dissertaon, University of
Schleicher, Simon, Andrew Rasteer, Riccardo La Magna, Andreas
Schönbrunner, Nicola Haberbosch, and Jan Knippers. 2015.
“Form-Finding and Design Potenals of Bending-Acve Plate Structures.
In Modelling Behaviour, edited by M. Ramsgaard Thomsen, M. Tamke, C.
Gengnagel, B. Faircloth, F. Scheurer. Berlin: Springer. 53–64.
Xing, Qing, Gabriel Esquivel, Ergun Akleman, Jianer Chen, and Jonathan
Gross. 2011. “Band Decomposion of 2-Manifold Meshes for Physical
Construcon of Large Structures.” In Posters of the 38th Internaonal
Conference and Exhibion on Computer Graphics and Interacve Techniques.
Vancouver, BC: SIGGRAPH.
Figure 2: Marks, 1973
Figure 3: Schleicher, 2010
Figure 4: Schleicher et al. 2015
Figures 6–9: Hartono, Du, Sahebnassagh, Panagoulia, 2015
All other photography: Schleicher and La Magna, 2016
 is an Assistant Professor in the Department of
Architecture at the University of California, Berkeley. Simon holds a
doctoral degree from the University of Stugart and worked for the
Instute of Building Structures and Structural Design (ITKE). His trans-
disciplinary work draws from architecture, engineering, and biology. By
cross-disciplinary pooling of knowledge he aims to transfer bending
and folding mechanisms found in nature to lightweight and responsive
systems in architecture.
 is a structural engineer and PhD candidate at
the Instute of Building Structures and Structural Design (ITKE) at
the University of Stugart. In his research he focuses on simulaon
technology, innovave structural systems, and new materials for building
... Therefore, a healthy interdependent analogy between architectural (geometric) form and engineered structure is often observed in the bendingactive structures. Additionally, the integration between the form and the structure is frequently achieved and simulated via Computer-Aided Design (CAD) partnered with structural analysis [9], form-finding (i.e., equilibrium force of a form) design [10][11][12] and more. A geometry created by such processes may offer a superior balance between structural performance and aesthetics. ...
... Three design approaches such as material behaviorbased [13], geometry-based [15], and integral-based [1] are broadly considered when designing a bending-active structure. The advantages and deficiency of the bending-active structures were distinguished in the prior works by Lienhard [1], Riccardo [2], Schleichaer [11], and Sonntag [16]. The material behavior-based design approach relies upon material properties [17] to shape the structure and determine its performance. ...
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.
... The remaining challenge however lies in the development of structurally active covering and cladding systems. [13]. One reason is that plates have a limited formability since they deform mainly along the axis of weakest inertia and thus cannot be easily forced into more complex double curved geometries. ...
... Recent research and realized prototypes have been exploring the structural and form inducing potential of bending-active plate structures. The work by La Magna and Schleicher explores formfinding principles by placing voids in double curved surfaces to minimize double curvature in the elastically bent plates [13][14] (Figure 2 a and b). The possibility to assemble a larger structure from modular plate segments was realized with volumetric bent plate modules in the ICD/ITKE research pavilion 15/16 [15] (Figure 2 c). ...
Conference Paper
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Active-bending was established as a new Study Group within the IASS Working Group 15, "Structural Morphology Group" (SMG) in 2012 at the IASS conference in Seoul. Starting point was the publishing of a review paper [1] to establish common terminologies and references. In this paper many important historical examples of active-bending were gathered, dating back as far as early Mesopotamian dwellings up to the comparatively few contemporary examples of bending-active structures existing at that moment. Since the founding of the study group the community of researchers as well as practicing architects and engineers has rapidly grown and managed to establish the subject within multiple simulation software, many realized prototypes and some commercial building structures. The current paper highlights some recent developments in the field of active-bending. As part of an outlook, some future trends are discussed to critically highlight the potentials of using active-bending as a promising approach to novel hybrid building structures.
... This problem is particularly complicated since information about the precise geometry and acting forces is usually unknown at the beginning of the design process and would need to be determined through a series of form-finding, form-conversion, or other analyses steps. In previous work, the author has successfully shown that interactive simulations, for example in Kangaroo Physics, as well as more advanced Finite Element Methods (FEM) using SOFiSTiK, can be used to recreate the bending process digitally [8]. With the assistance of these design tools, it becomes possible to predict the deflections and combined equilibrium state of multiple cross-connected components, while at the same time considering material properties and calculating the stresses and forces in the structure. ...
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With this paper, the author aims to contribute to the exploration of bending-active structures by investigating the promising role that additive manufacturing technologies may play in the production of mass-customized joints and other practical connection elements. After a general introduction to the basic concept of bending-active structures, the author will discuss the particular opportunities and challenges related to the joinery for this structural system. Engineering nodes and connections for bent components can be a rather difficult task since the structure's exact geometry and loading condition is often unknown at the beginning of the design process and can only be ascertained through a series of form-finding and analysis steps. It is not unusual that this process results in the need for highly complex and difficult to produce connection details. 3D printing could be a potential remedy to this problem as it simplifies the fabrication of complex parts and renders the possibility to fine-tune joints to the structure's specific requirements. On the example of three early-stage design experiments, the author will share the gained experience and thereby conclude the paper by showcasing an integrated approach to the design and fabrication of bending-active structures that takes full advantage of 3D printed joinery.
... The most prominent example can be found in Buckminster-Fuller's 1957 Plydome (Fuller [3]) and more examples have been emerging recently. Plate-dominant bending-active structures have not yet received much attention and are generally considered difficult to design (Schleicher and La Magna [4]). One reason is that plates have a limited formability since they deform mainly along the axis of weakest inertia and thus cannot be easily forced into complex geometries. ...
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Full-text available
By distinguishing bending-active structures based on the geometric dimension of their elements, 1-d and 2-d systems can be identified. Rods and gridshells typically belong to the first category, plates to the latter. Plate-based bending-active structures present limited formability compared to rods due to the higher out-of-plane rotational inertia of the plates’ cross-section. Nonetheless, by following simple generative rules it is possible to substantially expand the formal possibilities of bending-active plates. This approach was tested and employed for the construction of a series of full-scale prototypes in order to demonstrate the wide range of shapes that can be achieved in this way. The research conducted so far was primarily focused on the main geometric and mechanical aspects associated to the form-finding process. The current paper looks instead into the global structural behaviour of bending-active plate shells. The process of converting an arbitrary freeform surface into a buildable plate shell requires the introduction of voids in the surface to allow the bending process to take place. The effect of this operation on the global mechanical behaviour of the shell will be analysed and discussed. Considerations on the scalability and buckling of bending-active plate structures will be also presented to highlight the potential of this approach to be employed for larger structural systems.
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This work aims to create sustainable design solutions for the construction industry. It focuses on compliant, shape-adaptable structures, and in particular, in rapidly organized active-bending structures. The research presents the thinking process for the design of a novel geometrical system, as well as data related with its structural performance. Being inspired by self-actuating mechanisms in microscale, the discussed form-giving system comprises a multi-layered structural element, whose layers are free to slip and interlock at a specific configuration, through embedded shear blocks. When the layers interlock, the cross-section of the element is enhanced and consequently its stiffness increases instantly. Thus, a low-tech structural element with 2-stage stiffness is generated. When various elements are combined in a grid-shell configuration, the system can transform from flat to curved surfaces when forces are exerted. To document the structural performance of the system, physical and digital experiments have been conducted. In particular, numerical results from load-deflection and form-finding tests of physical prototypes of various scales are presented in this thesis. These results verify the initial assumption for a scalable active-bending system with controllable curvature-stiffness relation. Demonstrators, such as transformable roofs, façade panels and furniture have been constructed to showcase some possible applications. The computational design processes and the digital fabrication techniques that have been employed for the development of the aforementioned prototypes are vital parts of this work. The research work concludes with reflections on potential future research on the topic.
This paper explores the role of frameworks and conventions in design computation workflows for collaboration on the development of design, structure and detailed fabrication within a visual scripting environment. The frameworks were developed in the computational team Dsearch of the architectural practice White Arkitekter and the engineering practice of structure, and was used in the part-time 12-month design and build workshop Textile Hybrids at the HafenCity Universität Hamburg. During the workshop, the framework was further developed to facilitate iterative design/analysis studies between design models in a visual scripting environment and a FEM simulation environment through cloud-based data exchange protocols. The authors regard this continuous re-development of workflow frameworks during design development as emergent, and regard this as a valuable and potential mode of development also for architecture and engineering practice. This is shown in the individual practices of the authors, where additional layers have been added.
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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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his 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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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
Best known for his amazing free-form shell structures, Heinz Isler has inspired both architects and engineers with his dazzling creations. His work transcends the definition of mere structural engineering to the extent of becoming structural art. This book considers the unique work of this exceptional engineer. Isler’s primary medium of expression is the reinforced concrete shell. Rejecting the use of mathematical formulae, he approaches the challenges of each new structure by using physical modelling to determine the form and subsequently to investigate its stability. Harmonious, natural and inspiring structures are the result. Isler’s sensitivity for the natural world is expressed in the quiet beauty of the shell forms that he has designed, which merge more easily into the landscape than most modern buildings. He creates structures of high efficiency with the lowest possible environmental impact. The author takes a look at Isler’s major works, at the philosophy behind these works and at Isler’s methods. This fascinating look at the work of a pioneer in this field will prove exhilarating. Available at
Bringing together experts from research and practice, Shell Structures for Architecture: Form Finding and Optimization presents contemporary design methods for shell and gridshell structures, covering form-finding and structural optimization techniques. It introduces architecture and engineering practitioners and students to structural shells and provides computational techniques to develop complex curved structural surfaces, in the form of mathematics, computer algorithms, and design case studies.
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.
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.
Conference Paper
With the design and construction of more and more unusually shaped buildings, the computer graphics community has started to explore new methods to reduce the cost of the physical construction for large shapes. Most of currently suggested methods focus on reduction of the number of differently shaped components to reduce fabrication cost. In this work, we focus on physical construction using developable components such as thin metals or thick papers. In practice, for developable surfaces fabrication is economical even if each component is different. Such developable components can be manufactured fairly inexpensively by cutting large sheets of thin metals or thin paper using laser-cutters, which are now widely available.
Self-strutted geodesic plydome. US Patent 2,905
  • R Fuller
  • Buckminster
Fuller, R. Buckminster. 1959. Self-strutted geodesic plydome. US Patent 2,905,113, filed April 22, 1957, and issued September 22, 1959.