Integrative Numerical Techniques for Fibre Reinforced Polymers - Forming Process and Analysis of Differentiated Anisotropy

Abstract

In the current paper, the authors developed two different numerical methods for fibre reinforced polymers. The first method deals with the simulation of an innovative manufacturing process based on filament winding for glass and carbon fibre reinforced polymers. The second developed numerical method aims at modelling a high level of material complexity and allowing reciprocal confrontation with a geometric differentiated global structure. The developed numerical techniques served as a basis for the design and implementation of a Pavilion built on the campus of the University of Stuttgart in 2012 and could thus be tested and proved.

Full text

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Integrative Numerical Techniques for Fibre Reinforced Polymers - Forming Process and
Analysis of Differentiated Anisotropy
Frédéric Waimer
1
, Riccardo La Magna
2
, Jan Knippers
3
1
Research and Teaching Associate, Ph.D.c., Institute of Building Structures and Structural Design (ITKE), University of Stuttgart, Stuttgart,
Germany, f.waimer@itke.uni-stuttgart.de
2
Research and Teaching Associate, Ph.D.c., Institute of Building Structures and Structural Design (ITKE), University of Stuttgart, Stuttgart,
Germany, r.lamagna@itke.uni-stuttgart.de
3
Professor, Institute of Building Structures and Structural Design (ITKE), University of Stuttgart, Stuttgart, Partner at Knippers Helbig, Stuttgart,
Germany, j.knippers@itke.uni-stuttgart.de
Summary: In the current paper, the authors developed two different numerical methods for fibre reinforced polymers. The first method deals with the
simulation of an innovative manufacturing process based on filament winding for glass and carbon fibre reinforced polymers. The second developed
numerical method aims at modelling a high level of material complexity and allowing reciprocal confrontation with a geometric differentiated global
structure. The developed numerical techniques served as a basis for the design and implementation of a Pavilion built on the campus of the University
of Stuttgart in 2012 and could thus be tested and proved.
Keywords: numerical techniques, simulation, fibre reinforced polymers, optimization, manufacturing process
1. INTRODUCTION
The interest in free-form surface generation in architecture and industrial
design is ever more increasing. For complex shaped structures, fibre-
based materials are often an obliged choice as they offer numerous
advantages compared to traditional building materials and techniques.
The wide variety of manufacturing methods allows the production of
complex shape components with low effort, but they must be selected
accordingly to the application they are meant for. The type of production
method strongly affects the radius of the achievable fibre placement,
along with the fibre volume content for a unidirectional layer and its
resulting stiffness. Unlike isotropic materials, the structural
characteristics of composites can be strongly influenced by the fibre
morphology. The design and simulation of fibre-based materials is very
challenging, since besides the material properties of the individual
components also the fibre orientation of each layer plays a decisive role
for the structural stiffness distribution within the system. Current
developments in the analysis and manufacturing simulation processes
are far advanced in the field of aerospace technology and automotive
engineering. Nevertheless, such simulation and analysis processes in
most cases are non-transferable or unsuitable for architecture and
structural engineering purposes. To fully exploit the potential of the
material in the construction industry, research must be focused on the
development of appropriate methods and techniques rather than
attempting to transfer known strategies from other engineering
disciplines. Novel approaches are currently being investigated to
generate highly efficient structures which take full advantage of the
material’s properties. It is therefore necessary to develop custom
manufacturing processes for the building industry and simulation tools
for structural engineers. The application possibilities in architecture and
civil engineering are very large and the potential for new structural
approaches have not been exhausted yet.
2. COUPLED GEOMETRY AND ANALYSIS
A range of different integrated design tools and workflow
methodologies have been developed in recent years. One common
procedure is certainly the coupling of parametric geometry models and
structural analysis. In the first instance it offers the designer the
opportunity to evaluate the structural behaviour and performance at an
early design stage [1]. Subsequently however, more precise engineering
models and detailed analysis are needed to draw a statement about the
ultimate limit state and the serviceability of the structure [2]. Contrary to
this established procedure the authors pursue a different aim, namely the
development of project-specific tools and solutions with a high degree of
accuracy right from the start.
Fig. 1. First architecture built entirely by a robotic winding technique
During the early design stages of the "ICD / ITKE RP12" research
prototype [Fig.1] a strong interaction between form, material and
manufacturing process was observed. Following this statement, the
desire was to combine the reciprocity of geometry, material anisotropy
and manufacturing process within a digital model in order to generate
the best possible solution. Such global integrative approaches of
different process phases are not common in construction [3], although in
fields like aerospace, the idea and the desire to view different processes
holistically or rather in a multidisciplinary relationship is well
established [4]. To enable this kind of workflow strategies, custom
simulation packages must be developed depending on the type of
project. In order to provide such an integrated and holistic model for the
ICD/ITKE RP12, the authors developed and programmed a new
framework for an accurate and adaptive simulation. The aim was to
combine different complex processes and relationship interfaces for the
different aspects involved in the project. Specifically, the analysis
system of the prototype includes a structural simulation of the geometry
and its anisotropic materiality, along with the definition of the fibres
orientation for the manufacturing process [Fig.2]. This allows the
engineer to examine different parameters and concurrently to consider
the influence these have on the manufacturing process, the bearing
capacity and the architectural design. The digital model makes it
possible to look at the system in its entirety but it requires a profound
knowledge about manufacturing processes, material behaviour and
modelling of fibre reinforced polymers.

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Fig. 2. Correlation of different simulations by geometric data
3. SIMULATION OF CORELESS WINDING PROCESS
3.1. Description of the novel manufacturing technique
In recent years, filament winding has appeared to be a very economic
fabrication method [5]. Particularly in the case of elements with low
repetitions, very cost-effective results can be achieved. Furthermore,
large components can be manufactured and high fibre volume contents
can be produced, providing high stiffness and strength. Typical filament
winding techniques involve the production of a positive mould onto
which the fibres are later laid upon [6]. The mould ensures that the fibres
are kept in place and do not assume inconsistent configurations while
the polymer matrix is still in the process of drying out. Due to geometric
constraints, the production of custom components is mainly limited to
synclastic surfaces such as pipes, vessels or aircraft fuselages, besides
requiring extra amount of work in the preparation of the mould, often a
milled foam core, with the obvious waste of material that this entails.
Automated tape and fibre placement methods leverage some of these
constraints, allowing the production of surfaces of negative Gaussian
curvature (anticlastic). By utilising a composite lay-up end-effector
normally installed on a robotic arm, the tape is laid over the surface of
the mould in direct contact. Whilst offering greater design freedom, tape
laying methods still suffer from the cumbersome necessity of producing
a positive core, which also heavily limits the size of the feasible
components due to obvious logistic issues. To overcome these major
drawbacks, a coreless winding process was developed for the production
of a large scale prototype meant to test the potential and advantages of
this innovative approach. This approach represents a novelty in the
production of double-curved surfaces by winding. So far, the only
method not requiring a winding core solely allows the manufacturing of
pipes [7].
Fig. 3. The construction setup
The main feature consisted in the replacement of the positive,
continuous mould with a discrete linear steel frame to hold the fibres in
place during the laying process. The frame serves as temporary
scaffolding onto which the resin soaked fibres are then tensioned,
building step by step a shell structure consisting of individual fibre
layers which achieve structural stiffness and bending resistance after the
matrix (epoxy) has dried out and the tempering process taken place. To
avoid gliding of the placed fibres onto the steel bars, custom milled
wooden elements with teeth profiles were attached to the frame, thus
ensuring a stable and suitable set of anchor points for the fibres. The
complete setup was mounted on an external turntable which provided an
extra axis of rotation for a 6-axis industrial robot, equipped with a
specifically designed end-effector, which accurately wrapped the resin-
saturated carbon and glass fibres together [Fig.3].
Without the constraints of a prefabricated positive mould, this
manufacturing process specifically enables the production of anticlastic
double curved surfaces as long as the different fibre layers are allowed
to undergo relatively large elastic deformations, therefore assuming
geometric configurations other than that of a ruled surface. This is
achieved by tensioning transverse layers of fibres which would naturally
lie on a deeper geometrical plane compared to the previous ones,
resulting in a global displacement of the system which gradually tends to
a continuous saddle shape as the number of rovings increases. Having
replaced the continuous full core with a series of voids and discrete
anchoring points, the fibres are allowed to freely deform and assume
their natural funicular shape under the load introduced by the
overlapping fibres. Furthermore, by differentiating the pre-stressing
force within the single fibres it is also possible to control and steer the
global shape assumed by the surface, as the deformation within the
surface itself can vary locally from point to point. To successfully
implement the described manufacturing technique, it was necessary to
simulate the entire fabrication event to detect possible faults in the
global design and in particular major losses of fibre pre-stress during the
wrapping process.
3.2. Geometrical Influences
To accurately predict the final geometric configuration of the prototype,
it was necessary to simulate the entire wrapping process to assess in
advance the correct position of the fibres. As the resin soaked fibres do
not possess any bending resistance whilst the epoxy is still in the process
of drying out, successive layers wrapped on the previous ones have the
effect of further deforming the system. This implies that the overall
design of the shell cannot be entirely dictated and decided beforehand,
but it is rather the result of a form-finding process which has to take into
account the physical and mechanical behaviour of the different layers
which simultaneously react to the external load of the wrapped fibre at
each step. The number of degrees of freedom involved in the simulation
varies quadratically at each step, as the contact points between the fibres
double each time a new roving is introduced in the system. Given the
complexity of the simulation model and the increasing number of
variables involved at each step, it is not possible to predict in advance
the outcome, hence the iterative form-finding process adopted for the
simulation. The deformations involved in the process, being of
consistent magnitude (meaning that the deformation components of
higher order may not be neglected), along with the contact problem
between the fibres, result in a highly complex simulation scenario that
has to be solved adopting ad hoc computational strategies to handle all
the aspects involved in the calculation. The main reason which requires
the simulation of the fabrication process is to check the pre-stress values
of the fibre bundles [8]. As it has later been assessed through the
simulation and also observed on the final prototype, the stress
distribution greatly varies amongst the fibres. This is due to the
particular geometric configuration, as specific areas tend to be
overstressed as they absorb most of the load introduced by the later
wrapped fibres. Conversely, given the constant change of shape during
the wrapping process, other fibres run into the risk of totally losing their
pre-stress as a result of the support surface which has further relaxed
within a number of wrapping cycles, leading to bundles of fibres lying
loosely on the surface. To avoid this dual problem of overstressing and
loosening of the fibres, optimal pre-stress values have to be chosen in
order to avoid or at least minimise this effect. Especially the loosening
of the fibres during curing time represents a major setback in fibre
composite products, as the distinct layers do not offer a homogeneous
contact surface anymore, giving rise to relative deformations between
the layers which, not being coupled together, act independently and lose
completely their mechanical characteristic and strength of a compact
bond, potentially leading to serious delamination problems during the
lifetime of the element.

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In the context of the project, besides checking the local stress values the
simulation of the forming process was needed to evaluate the shape of
the prototype before production start. At an early stage, the Finite
Element analysis of the whole structure was performed on a simplified
digital model of the single layers which made up the entire prototype.
The underlying digital model resulted from the translation of the
physical scale prototypes developed during the design phase into 3d-
models, which later served as basis for the development of the Finite
Element analysis of the layers’ differentiated anisotropy. To confirm the
results acquired from the analysis of the structure, it was absolutely
necessary in the first place to validate the geometric model used for the
calculation. Comparing the Finite Element model with the output model
obtained from the forming process simulation, resulted in a maximum
deviance of 12,5cm which was considered acceptable and within the
tolerance boundaries for the purposes of the project. The simulation was
finally conducted to correct the laying paths followed by the robotic
arm. In filament winding it is known that two major problems may arise
in relationship to the followed path, namely uplifting and lateral sliding
of the fibres with respect to the underlying surface. Whilst uplifting does
not represent an issue for the developed coreless winding technique (no
underlying positive mould onto which the fibres lie upon), lateral sliding
may still be present and lead to potential damage of the rovings or
significant losses of pre-stress. To avoid possible sliding effects, the
fibres should lie within a given boundary defined by the geodesic line
running between two support points on the reference surface and an
offset dependent on the friction value between the fibres. As the path
followed by the fibre-laying robotic arm also defines the path taken by
the roving, to minimise the side effects of lateral sliding the proposed
path is later updated following the newly achieved results. This process
required the definition of a preliminary wrapping path along which the
intersection points between the fibres are geometrically resolved,
updating the mechanical model with the newly defined nodes and
elements, solving the system and correcting the path with the found
results.
3.3. Simulation Process and Finite Element Model
The whole analysis process relies on two main interfaces, namely the
geometric interface and the analysis (Finite Element based) interface. To
speed up the process and make the exchange of data viable between the
two programs, the workflow was fully customised and automated to
allow the automatic generation and analysis of the whole simulation
process. In a looping procedure, the 3d-modeling software (Rhino3d)
first reconstructs the displaced geometric model which is retrieved
directly from the results database of the Finite Element program
(SOFiSTiK), along with important mechanical information as stress
values, nodal forces, support reactions etc. The model is then updated
with the new information deriving from the actual wrapping step, i.e.
nodes and cable elements which define the new roving. Following, the
generation of the code automatically takes place from the updated
geometric setup, and once completed fires an event to the Finite Element
program which performs the new calculation and finally saves the
results into its native database. The whole simulation process is then
looped until the last roving has been set into the model.
Fig. 4. Mechanical model of the coupling between fibres; relative
displacement after the calculation process
Fig. 5. Full scale test windings without resin
The analysis model is based on cable net mechanics. At each step, the
intersection nodes between the existing cable elements in the model and
the new cable are found geometrically. This process takes place within
the 3d-modeling software, where the displaced geometry of the cable net
is first imported and rebuilt as a network of polylines. To find the points
which make up the new cable element the approximated robot tool path
is needed, as the nodes are found by intersecting the plane defined by the
two support points and the average point of the robotic arm’s spatial
trace with the cable net already present. The intersection points define
the structural nodes of the next fibre which is later added to the global
Finite Element model. Besides defining the new cable element to be
added to the system, the newly defined nodes need to be inserted in the
definition of the previous cables. In order to successfully update the
model, all mechanical information has to be acquired from the results
database and processed to accommodate the new nodes which further
subdivide the cable elements. As the number of nodes grows
quadratically as previously mentioned, to reduce the complexity of the
system and the overall computational time required, nodes too close to
each other (the threshold value being defined in advance) are merged
together, thus keeping the model size more compact and minimising the
processing time. Although this process has displayed the production of
geometrical artifacts in areas of the model densely cluttered, the
mechanical results have been proven to be consistent and the overall
required computational time sensibly reduced. As in most cases the fibre
does not lie on the geodesic line of the surface, considerable lateral
sliding effects may occur during the wrapping process. In order to take
into account such sliding effects due to lateral forces which appear if the
fibre does not lie on the geodesic line of the surface, the coupling
between the structural nodes is modelled through spring elements with
infinite axial stiffness and a threshold lateral stiffness which derives
from the friction value between soaked fibres previously tested in the
laboratory. With a reduced lateral stiffness, the spring is allowed to
stretch perpendicularly to the axis of the cable, resulting in a sliding
effect on the underlying cable [Fig. 4]. The stretching effect stops as
soon as the residual lateral force on the node balances the threshold
stiffness of the spring. As springs tend to be computationally intensive
elements, the coupling is provided only for the last roving to be
simulated in order to find the correct nodal position. Due to the missing
bending stiffness of the structure during the wrapping process, the
considerable displacements of the fibres have to be taken into account
by resorting to a non-linear calculation which considers the internal
stress state in the displaced reference configuration. After the calculation
is run, the position of the displaced nodes are updated once again in the
3d-model by merging the two nodes and deleting the spring connection,
providing a coupled connection between the two cable elements. Finally,
the process is looped in the exposed order until the last cable element
has been imported and the system calculated, leading to the end
geometric configuration with the corresponding stress map [Fig. 6].

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Fig. 6. Stress map of coreless winding
4. ADAPTIVE SIMULATION OF HIGH DIFFERENTIATED
ANISOTROPY
The modelling and analysis of fibre-reinforced polymers strongly differs
from conventional materials such as timber, reinforced concrete or
membrane structures. Simplified approaches are often used in these
cases to describe the anisotropic behaviour of the materials and their
failure criteria. For the analysis of glass and carbon fibre reinforced
polymers in construction, engineers mainly resort to simplified
simulation models. The investigation of the Ultimate Limit State and the
Serviceability Limit State normally takes place on the component level.
This rough and inaccurate approach of analysis is often due to the lack
of basic knowledge on behalf of the structural engineer regarding the
material behaviour and the modelling on the macro and micro level. The
fact that the anisotropic material behaviour is not taken into account for
the material design obviously leads to oversized and inefficient
structural components. The Finite Element descriptions for the
simulation of fibre based materials according to the Classical Laminate
Theory (CLT) are currently considered the state of the art and are
already implemented in some FE programs [9][10]. The calculation of
the stiffness of each element does not constitute a problem but rather the
accurate modelling of complex fibre directions of the individual layers
of the laminate. The challenge lies in the correct alignment of the
varying fibre orientations of the individual layers and is primarily a
geometric problem to be solved.
Fig. 7. User Interface: Coupled geometrical and material analysis
4.1. Coupling of geometry and fabrication process to FE-
analysis
To take into account and analyse the interaction between geometry and
anisotropic materials, an interface between the parametric modeller
Grasshopper
®
and ANSYS was developed and programmed [13]. The
user interface thereby is present only within Rhino3d and Grasshopper
®
and was already used during the investigation of first working models
[Fig.7]. From the defined parametric geometry in A and the allocation of
the fibre lay-up and number of layers corresponding to the surface
section from the manufacturing process in B [Fig. 7], the direct
interaction between geometry and fibre direction in the individual layers
is considered. This means that by changing the geometry parameters and
according to the implementation of the winding logic, the fibres’
orientations of the individual layers change too and are consequently re-
orientated. The change in orientation of the individual fibres or layers
ultimately influences the material properties (rigidity and strength) at
each point of the surface. The assignment and the definition of the
material properties and thickness of the individual layers along with
supports and load actions also take place within the programmed
Grasshopper interface. The orientation and the generation of the
coordinate systems of the single layers and the following calculation of
the Finite Element stiffness by the CLT are processed directly in
ANSYS. In section 4.2, this implementation is explained in detail. After
the FE calculation, the forces in the element are back-calculated in batch
mode with the CLT into the individual layers, and following Puck’s
criterion, the material utilisation is calculated [4]. The distortion
condition, the material utilisation or the stress states can then be
displayed in C and D [Fig.7].
Fig. 8. Example of the element coordinate systems of a curved surface
4.2. Geometric adaptive element stiffness calculation
The interaction of the geometry and the manufacturing process with the
anisotropic materiality is generated by geometric parameters. The fibre
directions of the individual layers are defined by support curves on the
surfaces. For the export of the fibre configuration from Rhino3d in
ANSYS a simple geometry file is therefore sufficient. .For each area, the
number of layers must be defined, and to describe the fibre orientation,
the corresponding curve along with the appropriate material and
thickness which must be assigned for each layer. These parameters are
stored in a .txt-file and loaded again in ANSYS [13]. After ANSYS has
imported the geometry, the surfaces are meshed. As it can be seen in
[Fig. 8], for complex geometries the coordinate systems of single
elements are of limited use for the simulation of an anisotropic material
behaviour. This aspect differs from software to software. In ANSYS, the
orientations of the coordinate systems of the elements are defined by the
topology of the mesh, respectively by the first edge of the quad [10].
Thus the element coordinate systems must be re-orientated to be able to
map the fibre orientation. This happens as follows:
in a first step, auxiliary geometric coordinate systems on the curve are
generated, which define and also reflect the fibre orientation of the
individual layer. These auxiliary coordinate systems KS
Ln
are located on
the nodes of the adjacent finite elements [Fig.9]. The coordinate systems
define the orientation of a specific laminate layer of a subarea of the
entire structure. For each coordinate system of one element, the closest
coordinate system on the curve will be defined and rotated accordingly
in a second step. The newly defined and designated as KS
En
coordinate
systems are treated for the modelling as superior coordinate systems and

5
are used for the anisotropic stiffness of the element. The coordinate
systems KS
En
likewise mirror the fibre orientation as the coordinate
system KS
En1
of the top layer [Fig.10].
Fig. 9. Generation of KS
Ln
and KS
En
4.3. Simulation and optimization of the layered elements
The orientation of the individual elements is decisive for the subsequent
layout modelling of the individual layers of the laminate. For an element
which consists of 4 layers for example, a coordinate system for each
layer is generated. Thus for each additional layer of the laminate a
coordinate system is generated by the help of an additional curve as
described in the previous section. These coordinate systems
subsequently represent the fibre orientation of each layer [Fig.10]. For
each layer a curve on the surface is modelled in Rhino which reflects the
orientation of the fibres. The individual coordinate systems are used to
determine the exact fibre orientation at each point on the surface. To
determine the overall stiffness by the Classical Laminate Theory (CLT),
the rotation angles of the coordinate systems of the individual layers
must be stored in the element specification. Through the cross product
between the x
1
-vector of the KS
En
and the x
1
-vector of the KS
E1n
it is
possible to define the precise angular relationship. Now the angle of
rotation in the KS
En
coordinate system of the individual layers can be
stored in the layered Finite Element. Subsequently, the effective
stiffness of the element can be determined by the CLT and after the
definition of the boundary conditions, the structure can be solved.
Fig. 10. Generating the overall stiffness of the element
The accurate modelling of the orientations of each layer is of
fundamental importance for the subsequent determination of the
stiffness and of the assessment of the load bearing capacity. At each
point of the structure another layer configuration and a different fibre
orientation exists, and a detailed modelling is possible only by the
presented routines.
Fig. 11. Consideration of first-ply-failure
In addition to the fibre orientation, the individual layer thicknesses are
relevant parameters because on the one hand they influence the
distribution of loads in the laminate, and on the other the manufacturing
costs. The winding of one layer with a thickness of 0.2mm meant at the
ICD/ITKE RP12 a pure robot time of ca. 3 hours. By a gradient-based
optimization, the first set laminate thickness was reduced from 10.0mm
to a total thickness of 4.5mm [Fig.12]. This approximately corresponds
to 82.5 hours of winding time. The maximum deflection of 350mm and
a material utilization by the criteria of Tsai-Wu of 1.5 were set as
constraints. The utilization was consciously fixed higher than 1.0 due to
the more conservative failure criteria of Tsai-Wu compared to the one of
Puck. In addition, a non-linear material behaviour of the laminate was
considered, which allows a matrix cracking in single layers. This was
verified by the failure criterion of Puck after the optimization in detail.
Unlike other criteria, the criterion of Puck allows a clear distinction of
the five failure modes in the micro-level [11]. This makes it possible to
identify a matrix fraction or a first-ply-failure and also to assume load
redistribution from the cracked layers to the adjacent layers [Fig.11].
Thus the entire load capacity of the laminate can be increased many
times over. By using the load-bearing reserves, the degree of utilization
of the laminate could be kept below 1.0.
Fig. 12. Material optimisation
5. RESULTS
The mixed laminate consists of epoxy resin and 70% glass fibres and
30% carbon fibres. A total length of 47km glass and 15km carbon
rovings were spun. To define the external and internal wind pressure
coefficients the DIN EN 1991-1-4:2005 was used. The characteristics of
strength and stiffness of the glass fibre laminate and carbon fibre
laminate were determined according to DIN EN ISO 527-4. For each
laminate three specimens were taken directly from the manufacturing
process [tab.1]. By the safety factor on the material side, the fluctuations
of the production quality were covered. The assessment took place in
accordance to the design concept of the BÜV-Guideline [14].

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Table 1: material characteristics from the manufacturing process
E-Modulus Strength
GFRP 19514 N/mm² 348 N/mm²
CFRP 105584 N/mm² 576 N/mm²
6. CONCLUSION
To fully exploit the advantages of fibre reinforced polymers and to make
them usable in the construction industry, new approaches and ways of
thinking are needed. This is the case for the development of appropriate
production methods and the development of custom simulation and
analysis tools. The two novel developed numerical techniques served as
basis for the design and could be tested and proved by the realisation of
a full scale prototype. The semi-transparent skin of the Pavilion reveals
the system’s structural logic through the spatial arrangement of the
carbon and glass fibres. Despite its considerable span of 8m by a
thickness of 4.6mm [Fig.12] and its remarkable size, the Pavilion has a
weight of less than 320kg [Fig.13].
7. REFERENCES
[1] Van de Weerd, B., Rolvink, A., Coenders, J.,
StructuralComponents- A Software System for Conceptual
Structural Design. In: IASS-APCS 2012 Proceedings, Seoul
(2012)
[2] Fahlbusch, M., Hoffmann, A., Bollinger, K., Grohmann, M.,
Skylink at the Frankfurt Airport. In: IASS-APCS 2012
Proceedings, Seoul (2012)
[3] Knippers, J., From Model Thinking to Process Design,
Architectural Design 83.2 (2013): 74-81.
[4] Sobieszczanski-Sobieski, Jaroslaw, and Raphael T. Haftka.,
Multidisciplinary aerospace design optimization: survey of recent
developments. Structural optimization 14.1 (1997): 1-23.
[5] Bader, Michael G., Selection of composite materials and
manufacturing routes for cost-effective performance. Composites
Part A: Applied science and manufacturing, 913-934 (2002).
[6] Knippers, J., Cremers, J., Gabler, M., & Lienhard, J., Construction
Manual for Polymers+ Membranes, Birkhäuser (2010).
[7] Für gewöhnlich das Außergewöhnliche, Innovation Report,
February, CFK-Valley Stade (2011).
[8] Romagna, J. H., Neue Strategien in der Faserwickeltechnik. Diss.
Eidgenossische Technische Hochschule Zurich, (1997).
[9] Kunststoffe eV, A. I. V., Handbuch Faserverbundkunststoffe,
Vieweg & Teubner, Wiesbaden (2010).
[10] ANSYS® Academic Research, Release 14.0, Help System, Coupled
Field Analysis Guide, ANSYS, Inc.
[11] Puck, A., Festigkeitsanalyse von Faser-Matrix-Laminaten:
Modelle für die Praxis, Carl Hanser (1996).
[12] Schürmann, H., Konstruieren mit Faser-Kunststoff-Verbunden,
Springer (2007).
[13] Waimer, F, La Magna, R, Reichert, S, Schwinn, T, Menges, A,
Knippers, J., Integrated design methods for the simulation of fibre-
based structures, in: Proceedings of the Design Modelling
Symposium Berlin, 2013: p. forthcoming publication, Springer
(2013).
[14] BÜV-Empfehlung- Tragende Kunststoffbauteile im Bauwesen
[TKB] - Entwurf, Bemessung und Konstruktion - Stand 08 / 2010
Fig. 13. A: The glass fibres of the closed surfaces spread the light emitted by the spots (Halbe).
B: The top view shows the areal glass fibre roof and the carbon pressure ring (Halbe).