Investigation of highly flexible, deployable structures:
review, identification, control, application
by
Noémi Friedman
Summary of the thesis
to be presented to ENS de Cachan (France) and BME (Hungary) in
fulfillment of the thesis requirement for the degree of Doctor of Philosophy
in Civil Engineering
Responsible: Prof. György Farkas, Prof. Adnan Ibrahgimbegovic
Budapest, 2011
©Noémi Friedman 2011
Investigation of highly flexible, deployable structures:
review, identification, control, application
PhD thesis
Noemi Friedman
INDEX
1. Introduction, aim of scope ......................................... 3 3. Architectural background ........................................... 5 4. Analysis of a simplified planar model ......................... 7 5. Analysis of packing antiprismatic deployable lattice
structures ..................................................................... 10 5HDOL]DWLRQȸH[SHULPHQWVE\SK\VLFDOPRGHOVLGHDVIRU
control and applications ............................................... 15 6. Further research perspectives .................................. 16 Acknowledgement ........................................................ 16 References .................................................................... 17 List of publications ....................................................... 18 2
Investigation of highly flexible, deployable structures:
review, identification, control, application
1.
PhD thesis
Noemi Friedman
INTRODUCTION, AIM OF SCOPE
Observing nature, several transformable structures can be found, like the extensible
worm, deployable leaves and wing of insects (Vincent, 2001), expanding virus capsid (Kovács
et al., 2004), not to mention the movable structure of our own, human body. For centuries
several small scale man-constructed deployable structures have been constructed too, such as
umbrellas, chairs, fans etc. For the last four-five decades advanced man-made structures have
appeared mainly for spatial engineering applications (booms, solar arrays, antennas, reflectors ,
ex. (Gantes, 2001; Pellegrino, 2001; Wada et al, 1988)), as the volume and the weight of a
structure to be transported to space is crucial. On earth, for architecture it had been mainly used
until nowadays for only very small scale tents, yurts and shelters. Confirming to the novel
conceptions of the 21th century and due to available numerical and robotics technologies
advanced transformable structures are already applied in civil engineering and architecture too.
Structures used for off-shore industry and light deployable structures used for modern
architecture can be mentioned among these.
These structures are designed to undergo very large displacements and remain fully
operational (Ibrahimbegovic, 2003). Often the structures of that kind can integrate a multibody
system (e.g. Ibrahimbegovic and Taylor, 2003 or Ibrahimbegovic and Schiehlen, 2001) which
facilitates a construction phase before being integrated in a structural assembly (e.g. Gant,
1996). Modeling of the component of 3D frame-type flexible structures of this kind is
nowadays under control thanks to the geometrically exact beam model (Ibrahimbegovic and
Taylor, 2002; Ibrahimbegovic and Mamouri, 2000) capable of representing large displacement
and rotations, and solving the pertinent instability problems (Ibrahimbegovic and Al Mikdad,
2000).
:LWKWKHKHOSRIWKHVHWRROVWKHGHSOR\DEOHDQWLSULVPDWLFVWUXFWXUHSURSRVHGE\+HJHGĦV
(+HJHGĦV ) will be analyzed, which was chosen because of the lack of profound
knowledge about its mechanical behavior and the absence from transformable system practice.
Concerning mechanical behavior of space truss systems generated from the edges of a
regular antiprism the results are rather fascinating. Tarnai had shown that a space truss
generated from even sided regular antiprism is a finite mechanism while the ones from odd
sided antiprisms are stable forms (Tarnai, 2001). Nevertheless by building stable truss units
(formed from odd sided antiprisms) on top of each other, forming a cylindrical truss, small
displacements of boundary joints at the bottom grow exponentially along the height +HJHGĦV
1986). Consequently it is rather to be avoided to apply such regular antiprismatic trusses for
conventional engineering applications without any additional stiffening. Nonetheless this
geometry can serve for the construction of a very interesting pop-up mast.
The first challenge already is to fully master the construction phases of a flexible,
deployable structure which takes any structure component from initial unstressed state to a
`deformed` yet equilibrated state. Naturally the popping up of the structure necessitates a
thorough dynamical analysis and vibration control. However the packing of the structure ͸
even by smoothly controlling boundary displacements ͸ may also cause inertial effects that
cannot be ignored due to intermediate snapping of the structure. However within the refines of
the thesis the scope was only to investigate the packing behavior of the structure without taking
into account these inertial effects in the simulations.
3
Investigation of highly flexible, deployable structures:
review, identification, control, application
PhD thesis
Noemi Friedman
The thesis was organized in four larger blocks.
In the first block an extensive but not exhaustive review on different transformable
V\VWHPVʊUHWUDFWDEOHURRIVGHSloyable and retractable pantographic lattice systems, tensegrity
VWUXFWXUHV VRIW PHPEUDQHVWUXFWXUHVDQGSQHXPDWLFV\VWHPVʊXVHG LQDUFKLWHFWXUHDQGFLYLO
engineering will be given. Though the main research topic of the authors within the theme of
transformable structures is just a small slice, this study was carried out to explore earlier and
current researches and technologies to demonstrate the wide range of available systems, their
historical background and their potentials in the future.
The second block introduces the problem of investigating packing behavior of the
antiprismatic deployable structure through a simplified 2D structure possessing similar packing
properties. The equilibrium paths of packing and the concerning difficulties (bifurcation of the
path, snap-back phenomenon, singular configurations etc) as well as the packing sequences
will be revealed through analytical and numerical research.
The third block deals with the same problem but already for the targeted 3D problem.
The same analysis presented for 2D structures is carried out for two different type of
antiprismatic systems. In this chapter approximations for main mechanical characteristics were
also provided from the analytical investigation that can serve as a tool for preliminary design
and verification of the numerical results.
Finally in the fourth block a try is given to provide ideas for application of antiprismatic
structures by compounding the ideas and characteristics of the available systems reviewed. The
small physical models built for experimenting was also presented in this block. In this chapter
different applications and control systems were sketched without aiming to give detailed
solutions.
4
Investigation of highly flexible, deployable structures:
review, identification, control, application
3.
PhD thesis
Noemi Friedman
ARCHITECTURAL BACKGROUND
After shortly summarizing the historical background an overview on transformable
structures used in civil engineering and architecture have been presented. The feature of
transformability in case of architectural use can arouse from two different motivations. The
first motivation is to create a fast and/or safe construction method and in some cases it can be
also the need for a quick demounting process and the possibility of reusability. The second
motivation is to adapt the structure to external excitations like functionality requirement or
weather conditions.
A common example is the off-shore industrial installations where transformability is
needed coming from functionality requirements. Less familiar structures are the ones where
transformability is coming from energy-saving consideration or the aim can also be to
ameliorate occupant comfort, raise the attraction of the building.
The former motivation resulted in exotic inventions of some pantographic systems, like
the collapsible movable theatre of Pinero, the quickly retractable swimming pool cover of
Escrig, even the pop-up dome of Zeigler and its further developments. The minimal material
use Tensegrity systems also offer the possibility of foldability. Ongoing research works try to
find a greater variety of possible architectural applications. Some soft membrane systems like
cable-stiffened textile structures and pneumatic structure can be quickly installed too. F. Otto
remarkable systematic study on foldable membrane structures with the recent available
material and calculation technologies led to a wide variety of
architectural membrane designs even used for big span
permanent structures. Pneumatic systems can also serve as a
supplementary system for the erection of 3D structures making
the installation easier, faster and safer. The “pantadome”
structural system invented by Momoru Kawaguchi, and some
earlier and novel pneumatic formwork methods for constructing
monolithic and precasted concrete domes can be mentioned
among these systems.
Though these structures mentioned above still attract
the military and provisory events in first place a trend can be
observed to apply them for permanent buildings where
translucent or extremely light construction is needed.
With membrane structures that can move while in
use can be designed too. The goal to design dynamic
structures
that
are
able
to
change
morphological/mechanical/physical
properties
and
behavior as a response to external excitations and
requirements was first addressed in the 1960s and 1970s.
Early transformable designs appeared in first place for
housing sport venues. With the currently growing media
5
Investigation of highly flexible, deployable structures:
review, identification, control, application
PhD thesis
Noemi Friedman
focus on sport events the demand for retractable structures seems to be steadily increasing.
Most of these designs use rigidly moving parts to retract the roof structure. In most of the cases
the slicing of an ideal structural shape results in gigantic structural height, and mechanical
instruments enabling retraction further increase the costs of these structures. With new
generation roofs like the retractable pantograph structure of Hoberman and Pellegrino and the
application of a retractable skin fixed to the permanent structure can rather count with
economical aspects. Several research topics focus on adapting tensegrity and pantographic
structures to adaptive architecture. Combining transformable structures with a highly
distributed control system which is already available in today’s technology an intelligent
responsive architecture is born. This possibility does not only prospect indoor environmental
quality enhancement and better occupant comfort but a better use of natural energy resources
and thus a rather sustainable design.
6
Investigation of highly flexible, deployable structures:
review, identification, control, application
4.
PhD thesis
Noemi Friedman
ANALYSIS OF A SIMPLIFIED PLANAR MODEL
To better understand the behavior of snap-through type antiprismatic lattice structures
first a simplified 2D model was identified and investigated manifesting similar properties to the
targeted 3D structure. The simplified model consists of elastic horizontal bars of initial length
lH0=2r0 and rigid bracing bars (shown on the right). The bracing is
only connected to the horizontal bars with joints allowing free
rotations. The bracings are not connected to each other at their
u
crossing point hence allowing free sliding on each other. The top
horizontal bar and every second horizontal bar are rigid. A vertical
packaging can be obtained by stretching the elastic horizontal bars.
The structure has non-symmetrical freedom of motions as
well which is to be avoided in the case of a simple deployable mast.
Furthermore the analysis will be restricted to only symmetrical
movements to the vertical symmetry axis of the structure. This is to
be mentioned that it is an important and large restriction. It involves
the restriction of global buckling of the structure which should be
also investigated in the future.
First the packing of the basic segment of the mast was
analyzed. Through the kinematical, equilibrium and constitutive
equations the force-displacement diagram was deduced associated
with the function:
The initial and the closed configurations both correspond to zero force. While the
former being a stable state the latter is an instable one. The given diagram exhibits an
instability phenomenon, which occurs at the critical height:
After clarifying the mechanical behavior, the packing of the multi-storey masts were analyzed.
Two different type of mast were defined. One is called ‘doubly stiffened’ which is constructed
by pilling the basic segment on top of each other and the other is called ‘not stiffened’ which is
corresponds to the same topology but all the horizontal stiff bars are replaced to elastic ones.
It was shown that the behavior of the ‘doubly-stiffened’ mast can be calculated
from the behavior of its basic segments. In case of perfectly identical physical and
geometrical parameters the mast can be packed with a uniform packing pattern that is the
segments can close simultaneously. Nevertheless this hypothesis is not realistic and
consequently the typical equilibrium path corresponds to a bifurcated one. A method to
construct the typical force-displacement diagram is provided with and without taking the
self-weight into account (see figure beneath for the construction of the latter one).
7
Investigation of highly flexible, deployable structures:
review, identification, control, application
PhD thesis
Noemi Friedman
From the construction method of the force-displacement diagram the critical segment
number was deduced:
If the number of analyzed segments was more than
violent intermediate snapping is
sure to take place during deployment if no segment closes simultaneously.
The post-packed phenomenon was defined and presented (see next figure) which may
withhold the structure from complete packing and consequently it is to be avoided. Packing
sequences and equilibrium paths have been presented for both the restricted and the nonrestricted case. The restricted simulation means restraining the model from disengaging from
the completely closed configuration during packing that is with restricted simulation the
structure is kept from the post-packed phenomenon.
Numerical simulations of the basic segment and the two types of multi-storey structures
were carried out. Incremental displacement control analysis was used with the software FEAP
with non-linear truss elements with logarithmic stretch model. Different control possibilities
have been presented for the investigation of packing behavior.
8
Investigation of highly flexible, deployable structures:
review, identification, control, application
PhD thesis
Noemi Friedman
For ‘doubly stiffened’ masts the uniform and the
successive control was offered by guiding the boundary nodes of
paired
nodes
each segment. The typical path can be traced by introducing
for
physical imperfections and controlling only the displacement of
contact
the top nodes. In case of the latter restraining the structure from
forces
‘post-packed phenomenon’ is necessary. This was simulated
with a penalty method by pairing the end nodes of the rigid
bars one under the other (figure on the right). The induced
contact force is disproportional to the distance in between the
paired nodes and keeps the segments from disengaging from the
closed configuration. The intensity of the contact force depends
on the manually given penalty parameter which should be
carefully chosen. If no snap-back phenomenon occurs during packing capturing the restraint is
not difficult (force-displacement diagram from the simulation in the beneath figure). However
at the snap-back large value of penalty parameter is needed in order to restrain the ‘post-packed
phenomenon’ which may turn the tangent stiffness matrix bad conditioned.
The basic segment of a ‘not stiffened’ mast is half of the one of the ‘doubly stiffened’
one. For ‘not stiffened’ masts the same type of controls were applied with some deviations. For
uniform and successive packing control all the nodes were guided, however it was shown that
this procedure is not practical in case of successive control. Instead only the displacement of
every second node was controlled which neither proved to be very efficient because of possible
‘post-packed phenomenon’.
With the numerical simulations carried out it was found that the ‘non-stiffened’
masts can only be completely packed in case of even number of segments. This hypothesis
was confirmed with analytical explanation.
9
Investigation of highly flexible, deployable structures:
review, identification, control, application
PhD thesis
Noemi Friedman
5. ANALYSIS OF PACKING ANTIPRISMATIC
DEPLOYABLE LATTICE STRUCTURES
An antiprism is a polyhedron composed of
two parallel, identical polygons connected by
triangles. Antiprisms are similar to prisms except
the two polygons are twisted relative to each other
and thus the lateral faces are not quadrilaterals but
triangles (see Figures to the left). A regular
antiprism is formed with a 180/n degree of twisting angle between the two
n-sided polygons.
7KH GHSOR\DEOH F\OLQGULFDO FROXPQ RIIHUHG E\ +HJHGĦV shown on the right, consists of rigid panels (octagonal panels in the figure)
and rigid and elastic bars (drawn with continuous and dashed lines
respectively). The mast is packaged with pushing the top polygonal panel
in the vertical direction. With a uniform cyclic symmetric folding the elastic bars are stretching
out and the parallel polygonal panels are pushed together. The structure cannot be controlled
E\ DQ RQO\ D[LDO IRUFH +HJHGĦV nonetheless with a careful symmetry control the
structure can be packed to a theoretically planar truss. In this packaged configuration the
structure is in equilibrium without any external forces. This state of self-stress is not a stable
position, consequently with a small perturbation the structure can snap back to the initial,
deployed, strain-free configuration.
First analytical investigations were
carried out to describe the mechanical
behavior of one segment of the pop-up
column. The results can serve for
better understanding the basic
characteristic of such structures, for a
tool to check numerical results before
analyzing more complex structural
solutions and for a method of
preliminary design of optional
architectural
solutions
(mast,
framework, bridge, etc.).
The basic unit can be packaged by
pushing down the top facet of the
structure until the bottom facet. This
can be achieved by extending the
middle polygon to the radius (see
Figure to the right):
that is the polygonal bars have to stretch to
times their initial length, where
10
is:
Investigation of highly flexible, deployable structures:
review, identification, control, application
PhD thesis
Noemi Friedman
This stretching depends only on the initial height/radius ratio and on the number of the vertex
of the polygon (
), but not on the dimension of the structure.
The equilibrium path (see figure beneath) was diagrammed in case of cyclic symmetrical
folding assuming linear elastic behavior of polygonal bars end rigid bracings. The function of
the equilibrium path is:
Where ‘n’ is the number of vertex of the polygon.
It is presented that equilibrium path manifests an instable phenomenon that results in a
snapping of the structure after passing the critical force. This critical force is reached at the
height:
And at the value:
where
The intensity of the critical force depends only on the number of vertex of the polygons, on the
initial height/radius ratio (
) and on the axial stiffness of the elastic bars ( ) but not on the
dimension of the structure.
11
Investigation of highly flexible, deployable structures:
review, identification, control, application
PhD thesis
Noemi Friedman
For the summarized results approximations were offered as a tool for a fast control of
numerical results and for preliminary design of architectural applications. These
equations for estimating the equilibrium path are:
where constants a,b,d,e depend only on the number of vertex of the polygons and are given in
the thesis dissertation in Table 4.2 and 4.3. The error of each estimation depends on the actual
value of
and on . The higher the number of vertex is the smaller the error of the
approximation gets. The smaller the value
is the smaller the error is.
The critical segment number defined for planar structures and its approximation was given for
antiprismatic structures as well:
The force-displacement diagram is highly asymmetrical. The increment of the
ratio and the increment of the number of vertex of the polygon leads to a more emphasized
asymmetry of the diagram. The more emphasized the asymmetry of the displacement diagram
gets the larger the critical segment number is.
The force-displacement diagram of the multi-storey structure can be constructed from
the one of the basic unit with the methodology described for planar structures. The typical
diagram of a pentagonal six-storey mast was constructed (figure beneath). An example of the
typical packing sequence is shown in the figure in the bottom of this page.
12
Investigation of highly flexible, deployable structures:
review, identification, control, application
PhD thesis
Noemi Friedman
To simulate the packing of the multi-storey structures
numerical models were built. The simulation was verified by the
comparism of the results with the analytical ones. For the constitutive
model logarithmic stretch was used.
The simulation of the multi-storey structures was carried out
with different controls. After giving examples for the uniform (see
next Figure) and successive control of the ‘doubly stiffened mast’ it
was shown that by controlling only the displacement of the top nodes
the problem of ‘post-packed phenomenon’ occurs. Two different
motions were identified under this definition. One is of the same kind
that was described for planar structures, that is the segment turns to
and upside down position when further pushing its top nodes from
completely closed configuration (figure to the right). The second
phenomenon is the flipping-up of the bracings (see figure beneath)
The problem of the
phenomenon was resolved by
defining
contact
elements
between the rigid polygons
similarly to the methodology used
for planar models. This was
effectuated by additional nodes
placed in the center of the rigid
polygons that were linked with a
master&slave method to the
vertex of the associated polygons.
This restricted simulation was
performed with controlling the
order of the segment-closing by
perturbing the axial stiffness of the
elastic bars.
For the packing analysis of ‘not stiffened’ masts only uniform control was analyzed. Through
the analysis it was shown that if the antiprismatic spatial structure has even sided
segments the packing takes effect in two phases; in the first phase every polygon expands,
in the second phase every first polygon compresses and every second polygon expands.
The transition state is where the bracings turn to an upright position. For masts
consisting of odd number of segments it was shown that contrary to the planar structure
complete packing might be possible if specific geometry is defined. The structure is
packable in case of geometry defined by:
13
Investigation of highly flexible, deployable structures:
review, identification, control, application
PhD thesis
Noemi Friedman
This condition can be demonstrated by a mast
consisting of three segments. The completely
packed position is shown on the figure to the
right. The closed configuration of the top and
bottom segment is predefined and the structure
is only packable if the length of the bracings
connecting the top and bottom segments
equals:
In contrary to the even sided structures the ‘not stiffened’ antiprismatic masts of odd number
of segments are packed by only expanding their polygons.
14
Investigation of highly flexible, deployable structures:
review, identification, control, application
PhD thesis
Noemi Friedman
5. 5($/,=$7,21ȸ(;3(5,0ENTS BY PHYSICAL
MODELS, IDEAS FOR CONTROL AND APPLICATIONS
For the verification of the results some physical models were
built (figure on the left). Unfortunately the symmetrical
control of ’not stiffened’ antiprismatic masts could not be
solved by the simple models. Symmetric conditions however
could be easier to control if more sophisticated joints could be
applied with limited rotations . In accordance with the built
physical models it was concluded that at the stage of the
research the initial assumptions of restraining the structure
from non-symmetrical motions is rather unrealistic.
Nonetheless the packing of non-stiffened multi-storey
antiprismatic masts are rather fascinating to analyze. Though
result of the experiments with ‘not stiffened’ structures
resulted negatively, it is to be mentioned that trying to build
the ‘not stiffened’ model led to the discovery of a new type of
deployable structure (upper structure in the figure to the left).
Concluding the experiments ideas for application and control
were only investigated for ‘doubly stiffened’ structures.
As a possible application a pedestrian pop-out
bridge application is proposed (figure to the right). The
elastic stretchable bars could be of rubberlike material
while the rigid bars of a more general stiff, light-weight
material. In the deployed configuration the elastic bars
should resist to compression forces too. For that the elastic
material could be thread into a tubular stiff bar, which is
loose and can move freely along the elastic bars in the
packaged configuration. In the deployed configuration the
corresponding joints tighten the stiff bar which has to click into its proper place to be
integrated into the structure to ensure the necessary rigidity of the opened bridge. The
efficiency of the structure can be raised by keeping it pretensioned in the deployed
configuration. The self-stress state can be applied by the elastic bars being still stretched in the
opened configuration and by additional longitudinal cables that could be of good help also for
the packing control.
The geometry of the antiprismatic masts is attractive even without making them a popup structure. If for example instead of the elastic bar a cable is led through the polygon’s edges
this cable can already effectively stiffen the structure by prestressing it and at the same time it
can serve for deploying the mast. This tensile elements could be either separate ones for each
polygon or similarly to the deployable mast designed by Pellegrino a single cable could be led
through the structure that can control the deployment (Figure 5.7).
If the restriction of symmetrical behavior is relieved the interesting asymmetrical structural
forms can be used for adaptive architectural designs, for structures that could change
morphological properties due to different external excitations.
15
Investigation of highly flexible, deployable structures:
review, identification, control, application
PhD thesis
Noemi Friedman
6. FURTHER RESEARCH PERSPECTIVES
In level of the mechanical analysis there are still open questions regarding the ‘not
stiffened’ antiprismatic masts. For example the packing pattern of multi-storey masts can seem
to be absolutely stochastic but regularities regarding the order of segment closing can be
observed. There are different controls that have not been tried yet to simulate the packing of
these structures.
The most important defect of the thesis is the dynamical analysis of the packing (where
snap-through effect occur) and of the pop-up behavior as well as the concerning vibration
control. This investigation is intended to carry out in the near future.
Regarding the application part only sketches were made, and general ideas were
targeted but it is worth to explore the possibilities of architectural applications and to better
expertise in the possible controlling options, structural details.
ACKNOWLEDGEMENT
This work is connected to the scientific program of the ‘Development of qualityoriented and harmonized R+D+I strategy and functional model at BME’ project. This project is
supported by the New Hungary Development Plan (Project ID: TÁMOP-4.2.1/B-09/1/KMR2010-0002).
16
Investigation of highly flexible, deployable structures:
review, identification, control, application
PhD thesis
Noemi Friedman
REFERENCES
Gant C. (1996): Proceedings `Conceptual Design of Structures`, Stuttgart, pp. 222-229
Gantes C.J. (2001): Deployable Structures: Analysis and Design, WIT Press, Southampton,
Boston;
+HJHGĦV , Branching of Equilibrium Paths in a Deployable Column, International
Journal of Space Structures, Special Issue, vol 8, page 119-125
+HJHGĦV , Analysis of Lattice Single Layer Cylindrical Structures, Space Structures,
vol. 2, page 87-91
Ibrahimbegovic A., Taylor R. L. (2003): Nonlinear Dynamics of Flexible Multibody Systems,
Computers and Structures, 81, pp. 1113-1132
Ibrahimbegovic, A., Schiehlen W. (2001): Computational Techniques and Applications in
Nonlinear Dynamics of Structures and Multibody System, Proceedings EUROMECH-427,
Cachan, September 24-27
Ibrahimbegovic A., Taylor R.L. (2002): On the role of frame-invariance of structural
mechanics models at finite rotations, Computer Methods in Applied Mechanics and
Engineering, 191, pp. 5159-5176;
Ibrahimbegovic A., Mamouri S. (2000): On Rigid Components and Joint Constraints in
Nonlinear Dynamics of Flexible Multibody Systems Employing 3D Geometricallz Exact
Beam Model, Computer Methods in Applied Mechanics and Engineering
Ibrahimbegovic A., Al Mikdad (2000): Quadratically Convergent Direct Calculation of
Critical Points for 3D Structures Undergoing Finite Rotations, Computer Methods in
Applied Mechanics and Engineering
Kovács F., Tarnai T., Guest S.D, Fowler P.W., (2004): Double-link expandohedra: a
mechanical model for expansion of a virus, Proc. Roy. Soc. A, vol. 460, No 2051, pp. 31913202
Pellegrino S. (2001): Deployable Structures, Springer-Verlag Wien, New York
Tarnai T. (2001): Infinitesimal and Finite Mechanisms in S. Pellegrino Deployable Structures,
page 13-143, Springer Wien New York
Vincent J.F.V.(2001): Deployable structures in nature, S. Pellegrino: Deployable Structures,
Springer-Verlag Wien, New York, pp 37-51;
Wada B.K., Fanson J.L., Garba J.A., Chen G.S.(1988): Adaptive structures to meet future
requirements for large precision structures, Proceeding of the International Conference on
Spacecraft Structure and Mechanical Testing, Noordwijk, Netherlands, pp. 121-126;
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Investigation of highly flexible, deployable structures:
review, identification, control, application
PhD thesis
Noemi Friedman
LIST OF PUBLICATIONS
Book, chapter in book
Friedman, N. ʊ .LVV 5 0 ʊ 9|OJ\L , ʊ .OLQND . Vasbetonszkerkezetek Méretezése az
Eurocode 2 Alapján: Gyakorlati Útmutató, ed.LVV50ʊ )ULHGPDQ1$0DJ\DU0pUQ|NL
Kamara gondozásában, PI Innovációs Kft., Budapest, Hungary, 2010., 289 p. ISBN: 978 963 88427
49
,EUDKLPEHJRYLF $ ʊ .XFHURYD $ ʊ %UDQFKHULH ' ʊ +DXWHIHXLOOH 0 ʊ &ROOLDW - % ʊ
)ULHGPDQ 1 ʊ =ODWDU 0 Civil Engineering Structures: Multiscale Damage Representation,
Identification, Controlled Destruction and Quick Reconstruction, ed. ,EUDKLPEHJRYLF $ ʊ
Zlatar, M., Damage Assessment and Reconstruction after War or Natural Disaster, NATO Science
for Peace and Security Series, Springer, Dordrecht, Hollandia, 2009. pp. 3-28., ISBN:978-90-4812384-1
)ULHGPDQ1ʊ)DUNDV*\Összecsukható-kinyitható rúdszerkezetek mérnöki alkalmazása, A
%XGDSHVWL 0ĦV]DNL pV *D]GDViJWXGRPiQ\L (J\HWHP eStWĘPpUQ|NL .DU +LGDN pV 6]HUNH]HWHN
Tanszéke Tudományos Közleményei, ed 7DVVL * ʊ +HJHGĦV , ʊ .RYiFV 7 0ĦHJ\HWHPL
Kiadó, Budapest, 2004, pp. 49-56., ISSN 1586-7196
Article in journal
)ULHGPDQ 1 ʊ )DUNDV *\ Roof Structures in motion - on retractable and deployable roof
structures enabling quick construction or adaption to external excitations, Concrete Structures,
Vol. 12, ed.: Balázs, Gy. L., Hungarian Group of fib, Budapest, 21 pp. 41-50., 2011.
)ULHGPDQ 1 ʊ )DUNDV *\ ʊ ,EUDKLPEHJRYLF $ Deployable/retractable structures towards
sustainable development, Pollack Periodica, ed ,YiQ\L 0 ʊ ,YiQ\L $ $NDGpPLDL .LDGy
Budapest, 12 p. (befogadva, kiadás alatt)
)ULHGPDQ1ʊ)DUNDV*\ʊ,EUDKLPEHJRYLF$$]HVHUQ\ĘWĘOD]DGDSWtY-interaktív épületekig
ʊ 1\LWKDWy-csukható rúdszerkezetek az építészetben, 0DJ\DU eStWĘLSDU 9RO 1R ed.:
Antalffy, K., Budapest, pp. 67-73. 2011.
Article in proceeding
)ULHGPDQ1ʊ,EUDKLPEHJRYLF$ʊ)DUNDV*\ʊ'DYHQQH/Deployment analysis of an
antiprismatic snap-through type cylindrical space truss and proposal for a pop-up bridge
construction, Proceeding of the IASS-IACM 2012: Computational Mechanics for Spatial
Structures (befogadva, kiadás alatt)
)ULHGPDQ 1 ʊ ,EUDKLPEHJRYLF $ ʊ )DUNDV *\ ʊ 'DYHQQH / Quick Construction by
Deployable Structures: A study on Deployable Structures Enabling a Quick Constructional
Method, Proceeding of the NATO-ARW, 2008: Damage Assessment and Reconstruction After
Natural Disasters and Previous Military Activities, Sarajevo, Bosznia-Hercegovina, 2008.09.052008.09.09, Springer, Dordrecht, Hollandia, pp. 315-321. 2008.
)ULHGPDQ 1 ʊ )DUNDV *\ ÒMV]HUĦ N|QQ\ĦV]HUNH]HWHN .H]GHWL SUyEiONR]iVRN D]
összehajtogatható szerkezetek általános mérnöki alkalmazására, ÉPKO 2005: IX. Nemzetközi
eStWpVWXGRPiQ\L .RQIHUHQFLD (OĘDGiVDL, Csíksomlyó, Románia, 2005.06.03-2005.06.05., ed.:
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Investigation of highly flexible, deployable structures:
review, identification, control, application
PhD thesis
Noemi Friedman
.|OOĘ*(UGpO\L0DJ\DU0ĦV]DNLTudományos Társaság, Kolozsvár, Románia , pp. 48-54., 2005.,
ISBN: 973-7840-05-4
Friedman, N.: $IDPLQWPRGHUQpStWĘDQ\DJ)DV]HUNH]HWHVFVDUQRNRNpVWHUYH]pVLHOYHLN, ÉPKO
;,1HP]HWN|]LeStWpVWXGRPiQ\L.RQIHUHQFLD(OĘDGiVDL, Csíksomlyó, Románia, 2003.05.29HG.|OOĘ*(UGpO\L0DJ\DU0ĦV]DNL7XGRPiQ\RV7iUVDViJ.ROR]VYiU5RPiQLD
pp. 63-69., 2003., ISBN: 973-86097-3-9
Electronical publication
)ULHGPDQ1ʊ+XV]iU=Vʊ.LVV50ʊ.OLQND.ʊ.RYiFV7ʊ9|OJ\L,Példatár a
YDVEHWRQV]HUNH]HWHN , FtPĦ WDQWiUJ\KR], (electronic booklet), BME Hidak és Szerkezetek
Tanszék, 2007., 110 p., ISBN 978-963-420-903-4, source:
www.hsz.bme.hu/hsz/oktatas/feltoltesek/BMEEOHSAT18/vb1-gyakorlati_anyag.pdf
)ULHGPDQ 1 ʊ .LVV 5 0 Kéttámaszú gerenda vasalása, gyakorlati segédlet a tervezési
feladathoz, 26 p., 2009, source:
www.hsz.bme.hu/hsz/oktatas/feltoltesek/BMEEOHSAT18/vb-1_tervezesi_feladat.pdf
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