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Tailoring Self-Formation fabrication and simulation of membrane-actuated stiffness gradient composites

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This paper presents a design to fabrication framework for the mold-less construction of double curved composite lattice surfaces based on inherent material behavior. Fiber reinforced composite strands are sewn onto a flat prestressed high-strain membrane with the tailored fiber placement technique. Through the prestress release the contracting membrane actuates active bending of the composite elements, thus the system self-forms into an anticipated double curved geometry. Its geometric outcome is tailored by the stiffness gradient of the composites. The material system is introduced by the authors with the term membrane-actuated stiffness gradient composites (MASGC). The primary focus of this research is to establish the rules of self-formation on the basis of the system's governing parameters. Therefore, the fundamentals of the generation of synclastic and anticlastic curvatures, as well as combinations of both, from flat fibrous grids are revealed. Simulations with nonlinear finite element methods are deployed for the MASGC's form finding. The resulting understanding leads to the definition of rules for a form approximation process, where the system's input parameters are determined so that the self-formation satisfies an initial design intention. This control enables the exploration of the MASGC's design space. Furthermore, the MASGC's scalability and structural performance is evaluated. The proposed system offers the advantage to build lightweight surfaces of tailored variable double curvatures through rapid digital fabrication and mold-less formation.
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Proceedings of the IASS Symposium 2018
Creativity in Structural Design
July 16-20, 2018, MIT, Boston, USA
Caitlin Mueller, Sigrid Adriaenssens (eds.)
Copyright © 2018 by Lotte ALDINGER, Georgia MARGARITI, Axel KÖRNER, Seiichi SUZUKI, Jan KNIPPERS
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
Tailoring Self-Formation
fabrication and simulation of membrane-actuated stiffness gradient composites
Lotte ALDINGERa*, Georgia MARGARITIa**, Axel KÖRNERa, Seiichi SUZUKIa, Jan KNIPPERSa
a Institute of Building Structures and Structural Design (itke), Faculty of Architecture and Urban Planning,
University of Stuttgart, Germany, Keplerstrasse 11, 70174 Stuttgart, Germany
* l.aldinger@itke.uni-stuttgart.de
** giamargariti@gmail.com
Abstract
This paper presents a design to fabrication framework for the mold-less construction of double curved
composite lattice surfaces based on inherent material behavior. Fiber reinforced composite strands are
sewn onto a flat prestressed high-strain membrane with the tailored fiber placement technique. Through
the prestress release the contracting membrane actuates active bending of the composite elements, thus
the system self-forms into an anticipated double curved geometry. Its geometric outcome is tailored by
the stiffness gradient of the composites. The material system is introduced by the authors with the term
membrane-actuated stiffness gradient composites (MASGC).
The primary focus of this research is to establish the rules of self-formation on the basis of the systems
governing parameters. Therefore, the fundamentals of the generation of synclastic and anticlastic
curvatures, as well as combinations of both, from flat fibrous grids are revealed. Simulations with
nonlinear finite element methods are deployed for the MASGCs form finding. The resulting
understanding leads to the definition of rules for a form approximation process, where the system’s input
parameters are determined so that the self-formation satisfies an initial design intention. This control
enables the exploration of the MASGC’s design space. Furthermore, the MASGC’s scalability and
structural performance is evaluated. The proposed system offers the advantage to build lightweight
surfaces of tailored variable double curvatures through rapid digital fabrication and mold-less formation.
Keywords: self-formation, bending-active, membrane composite structures, stiffness gradient, form-finding, finite element
analysis, digital fabrication, tailored fiber placement
1. Introduction
1.1. Contextualization
The demand for customized double curved surfaces is increasing in contemporary architectural design
and construction. These surfaces are of interest by virtue of their appealing form as well as their
advantageous structural performance among others. Fiber reinforced polymers (FRP) offer a high degree
of customization and the ability to construct lightweight structures. Thus composite panels find
application as façade elements with customized freeform shapes. However, their complex and costly
fabrication is a current issue throughout all design fields. Conventionally double curved composites are
manufactured through manual lamination onto CNC-milled expanded polystyrene molds. This entails a
vast amount of waste, technology and labor [1]. Consequently, this mold process is more suitable for
mass production, rather than for individualized designs as are common in the field of avant-garde
architecture. Alternatively, double curved geometries can be formed by initially planar grids undergoing
distortion or by tessellation into planar segments or into bending-active developable plates. However,
these solutions result in less smooth surfaces and necessitate erection and connection strategies [2],[3].
A basis for an intelligent method to shape complex geometries is through a system inherent material
behavior. Research has been conducted by [4],[5] on material behavior based design, where solely
Proceedings of the IASS Symposium 2018
Creativity in Structural Design
2
through the interaction of contracting actuators and bending elements, forms are generated in one-step
without molds. Yet, their behavior is not investigated to a degree where an anticipated geometry with
controlled Gaussian curvature can be formed. Moreover, this would demand freedom and control in the
stiffness layout. Digital fabrication with the tailored fiber placement technology (TFP), originating from
the aerospace industry, enables a precise and automated fiber reinforced composite application onto a
substrate membrane. Conventionally their fiber layouts are informed for an optimized structural
performance, while their geometry is formed through molding [6].
1.2. Aim of the research
This research aims to combine the presented advantages in a material system introduced by the authors
with the term membrane-actuated stiffness gradient composites (MASGC). The proposed system offers
the construction of lightweight, composite surfaces of tailored variable double curvatures through rapid
digital fabrication and mold-less self-formation, relying solely on the systems inherent material
behavior. Thus, it offers a high degree of customization and in return minimizes material use, labor and
waste. Fiber reinforced composite strands are sewn onto a flat prestressed high-strain membrane with
the tailored fiber placement technique. Through the prestress release the contracting membrane actuates
active bending of the composite elements, thus the system self-forms into an anticipated double curved
geometry (Figure 1). Its geometric outcome is tailored by the stiffness distribution and fiber layout.
Through extensive form-finding with nonlinear finite element methods, self-formation rules are derived
that enable form approximation. A process where the input parameters of the system are determined so
that the self-formation satisfies an initial design intention. The research on the MASGC is concluded in
a design to fabrication framework.
Figure 1: Concept of tailoring self-formation of the membrane-actuated stiffness gradient composites
2. Methodology
2.1. Material System
The material system of the MASGC is comprised of materials, forces and fiber layout. For the materials,
glass and carbon fiber reinforced polymers (GFRP and CFRP) are explored for the bending elements
and a high-strain membrane is investigated as the actuator. The FRPs are highly suitable as bending-
active elements because of their low stiffness-to-strength ratio and their high strength-to-weight ratio
[7]. Moreover, as the composite stiffness increases throughout the curing process, the amount of self-
formation can be tailored. Releasing the prestress at a half-cured state facilitates the self-formation. The
system then reaches its full stiffness in the final state. Likewise, the formability of the uncured fibers
allows for an informed fiber placement in curved layouts with the TFP. The actuation requires high-
strain membranes as they store elastic energy during their prestress and distort during self-formation.
Thus, the chosen membrane for the prototyping scale is elastic tulle containing 90% elastane. Onto this
membrane the fibers are sewn with eccentricity creating an irregular grid that is informed by the
anticipated double curved geometry. The impact of all the parameters of the material system on its self-
formation are presented in section 4.
2.2. Form Finding
Given the material behavior based system and the large elastic deformations occurring during the self-
formation of the MASGC, form-finding with nonlinear finite element analysis is required to simulate its
final geometric outcome (Figure 2). The finite element software Sofistik allows the analysis in theory
third order with incremental prestress load steps as a custom routine. This builds upon advancements for
textile hybrids implemented by Lienhard [8] where the elements are form found separately. However, it
required further development, since for the MASGC the simultaneous stimulation of the bending
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Creativity in Structural Design
3
elements with the membrane is indispensable. Hence, the input of the realistic material properties and
cross-sectional dimensions is essential to predict the geometric outcome and to evaluate the stress state.
For their calibration and validation, material tests and physical form finding tests were conducted.
Figure 2: Form finding with finite element methods with theory third order analysis in Sofistik
3. Fundamentals of Self-Formation
3.1. Equilibrium of Form and Forces
The self-formation of the MASGC is determined by the interactions of the membrane prestress and the
active bending of the fiber composites. Once the prestress is released, the membrane minimizes its initial
surface area and initiates the self-forming process. The axial force combined with the eccentricity of the
composites causes major bending in the elements. Simultaneously, the lateral force causes bending in
the minor axis of the elements (Figure 2). The combination of both, major and minor bending, leads to
the self-formation from a two-dimensional to a three-dimensional shape: the eccentricity through major
bending moments drives the deformation out-of-plane, however, the minor bending of the elements
allows for the generation of double curvature.
3.2. Generation of Double Curvature
This research aims to develop self-forming lattice surfaces with positive and negative Gaussian
curvature from a flat fabrication setup. However, the generation of double curved surfaces from a
developable flat surface requires distortion: For the formation of synclastic dome-like surfaces, their
perimeter must contract, for anticlastic hypar-like surfaces, their perimeter must extend (Figure 3). The
high-strain membrane is extensible and distortable; however, the composite elements are inextensible.
Thus, they should not be oriented along the perimeter, but rather in a grid-like layout that allows
distortion along the perimeter. This distortion of the composite grid with bending-stiff connections is
achieved through the minor bending of the elements. To facilitate distortion, the cells of the grid are
diamond-shaped with non-rectangular angles, realized through curved application of the fibers. The
diamonds contract between their obtuse angles and extend between their acute angles. Therefore,
depending on the targeted geometry, synclastic or anticlastic, the cells must be oriented according to the
required contraction or extension, respectively.
Figure 3: Impact of cell angles and eccentricity on the generation of double curvature from a flat grid
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4. Rules of Self-Formation
The primary focus of this research is to reveal the rules that govern the self-formation of the MASGC.
Therefore, an extensive parametric investigation of the systems parameters, the materials, forces and
fiber layout, was conducted. All of the latter must be calibrated carefully and all must be in unison since
the self-formation is highly sensitive to deviations. When the rules are not applied in accordance with
each other, their forming effects contradict or compete. Thus, self-formation cannot take place or results
in highly unpredictable outcomes. The understanding of the parameters and their interactions enables
the establishment of self-formation rules (Figure 4), which lay the basis for controlled tailoring of the
MASGCs in order to design with its material system.
Figure 4: Rules of Self-Formation for all the parameters of the system illustrated with examples of MASGCs
I. Eccentricity: The fibers are sewn with eccentricity onto the upside or downside of the membrane. The
side of eccentricity affects the direction of the major bending. For positive Gaussian curvature, all fibers
must be applied on the same side, and for negative Gaussian curvature, the two crossing directions of
the fibrous grid must be placed on opposite sides.
II. Density: The degree of double curvature is inversely proportional to the fiber density because the
minor bending impact in short segments results in low distortion. Furthermore, density variations in the
two different directions can be utilized to tailor the deformation caused by major bending.
III. Angle and Curvature: For synclastic or anticlastic curvatures the diamond-shaped cells should be
oriented along the perimeter with their obtuse or their acute angle, respectively, according to their
contraction direction (cf. section 3.2). These variations of angles are generated through the application
of the fibers in curved lines, possible through the freedom of fiber placement with the TFP.
IV. Directions and Cell Shape: If contraction or extension is blocked either by hindering cell distortion
through triangular cell shapes or by orientating composites along the perimeter, double curvature cannot
be formed. This rule can be utilized to design within one design developable and double curved areas.
V. Supports: The supports should be positioned so that the moving directions during self-formation are
freed. However, through intentional blocking a variety of geometric outcomes can be achieved.
VI. Membrane Prestress: Through the intensity of the membrane prestress, the amount of deformation
can be tailored in a controlled manner as their relation behaves linear. Furthermore, variations of uni- to
biaxial prestress allow for design variations.
VII. Membrane Stiffness: The higher the strain and lower the stiffness of the membrane, the more it has
the ability to contract or extend and to distort. This is crucial for the generation of Gaussian curvature.
Contrary, a low-strain membrane hinders the generation of double curvature.
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VIII. Composite Stiffness: The intensity of deformation depends on the stiffness and is thus affected by
the choice of fibers, e.g. GFRP or the significantly stiffer CFRP. Moreover, the deformation can be
tailored depending on the moment of prestress release: The semi-cured state was proven successful as
earlier curing states lead to uncontrolled buckling of the composite fibers.
IX. Composite Cross-Section: The cross-sectional ratio can be controlled with the TFP. A vertically
oriented cross section results in a lower moment of inertia in the minor direction and allows for higher
minor bending moments which facilitate distortion and thus Gaussian curvature. Furthermore, the self-
formation is highly sensitive to the sectional area: smaller leads to instability and larger resists bending.
5. Rules of Self-Formation for Form Approximation of Variable Double Curvature
The rules for the self-formation of purely synclastic or anticlastic surfaces are defined, leading to the
question how MASGCs with both Gaussian curvatures transitioning within one surface, entitled variable
curvature, can be self-formed. Since it was found, that the boundaries of the synclastic and anticlastic
samples are compatible in shape, fiber layout as well as in curvature, their layouts can be aggregated
into one, resulting in the self-formation of one variable curved MASGC (Figure 5). Further layout
aggregations in both directions prove that the distortion of the layouts stand in coherence with each other
if their behavior is respected, enabling the definition of self-formation rules for variable double
curvature: First, geometric rules must be derived on how synclastic low and high points and anticlastic
saddles transition. Between two high or two low points there must be a saddle with opposite curvature
in the connecting direction, while a low point and high point can transition directly with a 45° rotated
fiber layout. Second, the angles of the fiber layouts must be set according to the required distortions,
resulting in oscillating curves. Last, the eccentricity must be oriented according to the synclastic high
point and low point in both fiber directions on top or downside, respectively, and for the saddles in
connection direction opposite to the high points eccentricity and same for the transversal one. This leads
to fiber discontinuity which does not cause problems with the suggested fabrication strategy.
Furthermore, more irregular variable designs can be approximated by the modification of the sub-layouts
using scaling or distorting. This principle is translated into a computational process of form
approximation as described in section 7.1.
Figure 5: Rules of self-formation for form approximation of variable double curvature and their derivation
6. Evaluation of the MASGC
6.1. Design Space of the MASGC
The control of the self-formation process enables the exploration of the MASGC’s design space that
comprises synclastic and anticlastic curvatures, as well as combinations of both within one design.
Through the internal shortcut of forces, the edges can be freed, which is an essential feature for the
MASGCs design space. Tailoring the parameters of the MASGC enables the design of mold-free
formed double curved composite surfaces with manifold variations and articulations (Figure 6).
However, the minimum bending radius limits the curvature. Thus, kinks and folds would only be
possible through fiber discontinuity, or cross sectional reduction. This has not yet been investigated.
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Figure 6: Design space of the MASGC, with synclastic, anticlastic and variable curvatures and generic variations
6.2. Scalability of Self-Formation
Given the material behavior based nature of this system, an essential aspect of this research is the
evaluation of the MASGCs limitations of the scalability of self-formation. The manipulation of the input
parameters of fiber density and cross-sectional area are investigated in an attempt to achieve the same
targeted shape up to a size of 10m. The appropriate approach is a reciprocally decreasing density and a
quadratically increasing cross-sectional area. This entails constant mass per area which facilitates
deformation. The relatively low resulting density allows for distortion, thus for double curvature.
Simultaneously, the cross-sectional height prevents instabilities while still allowing active bending. The
required prestress to actuate the MASGC has a constant increase (Figure 7). It can be concluded that the
MASGC self-forms into a double curved geometry up to a scale of 10m. However, there is no membrane
proposed that offers the mechanical properties required.
Figure 7: Scalability of the Self-Formation of the MASGC, with suitable prestress, cross-section and density
6.3. Structural Performance of the MASGC post Self-Formation
After the MASGC has self-formed, the structural performance is investigated. The deformations and
buckling load factors (BLF) are investigated for the fully cured FRPs with the residual stresses from the
formation process, as well as self-weight and external applied loading. As expected, for the same sample
CFRP results in significantly lower deformations and higher BLF compared to the GFRP. Further
improvement could be obtained, if post self-formation, the membrane would have higher stiffness. The
structural performance is relatively low and reinforcement strategies would be required for its suitability
as a load bearing structure. However, in its current state of development it could be applied as a non-
loadbearing element, i.e. interior applications or façade cladding.
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7. Design to Fabrication Framework
Figure 8: Design to fabrication framework, e.g. for MAGC with irregular variable double curvature
7.1. Computational Workflow Form Approximation
The research concludes in a design to fabrication framework for the MASGC (Figure 8). The curvature
of an intended design surface is analyzed to determine the synclastic or anticlastic areas. Starting from
the generic fiber layout for variable curvature and manipulating the parameters based on the self-
formation rules, the fiber layout of the flat configuration is obtained. Then, the stresses and the
geometrical outcome of the form finding are evaluated and compared to the intended geometry. Multiple
iterations of calibration of the input parameters are required until they are handed over to the fabrication.
7.2. Fabrication Workflow Tailored Fiber Placement
In the fabrication sequence, first, the high-strain membrane is prestressed onto a frame. Second, the
layout of glass and/or carbon fibers is sewn onto the membrane with the TFP technique. The used TFP
machine comprises four stationary sewing heads and a mobile, computer-numerical-controlled frame
with two degrees of freedom. Dimensions of the machines working space are shown in Figure 9. The
TFP machine works with the same principle as a conventional sewing machine, attaching the fibers with
a polyester yarn through a zigzag stitch. The stitching speed of 5m/min makes the fabrication a fast and
automated process. Third, after the application is completed, the fibers are impregnated with epoxy resin
and let to semi-cure. Experiments showed that the appropriate moment of the prestress release ranges
from 22 to 26 hours. Finally, the self-formation takes place until equilibrium is reached. Then the
composites cure to reach their full stiffness.
Figure 9: Fabrication of the MASGC through CFRP application with the tailored fiber placement technique.
Total workspace of the TFP machine 2.75m by 1m with workspace of 4 individual sewing heads 1.25m by 1m.
As a proof of concept of the design to fabrication framework of the MASGC, prototypes with synclastic,
anticlastic and variable curvature were materialized (Figure 10). These samples have a size of 1.2m. The
comparison with the form-finding simulation through visual overlay was proven successful within small
tolerances, however, a more detailed survey has not yet been carried out.
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Figure 10: MASGC prototypes with synclastic, anticlastic (with GFRP), and variable curvatures (with CFRP)
8. Conclusion
With the proposed concept of tailoring self-formation with the MASGC, composite surfaces with a wide
range of designs exhibiting positive, negative and variable Gaussian curvatures can be formed solely
through the material behavior of the system. The design to fabrication framework enables the fabrication
of customized surfaces with high geometric control in a digital fabrication and mold-less, one-step
formation process.
This control is achieved through the establishment of the self-formation rules. It is demonstrated that all
the parameters of the system, in particular the membrane stiffness, eccentricity and cross-sectional ratio,
determine the self-formation into double curved surfaces. However, the most crucial aspect for
controlling double curvature in the MASGC is the insight on the impact of the cells angles and their
distortion. This can be considered a vital contribution to the general discourse on the control of double
curvature. Furthermore, the critical dilemma of bending active structures, of too stiff for formation and
too weak for structural performance can be overcome, through the deployment of the stiffness change
over curing time of the composites.
Acknowledgements
The research was realized as a master thesis in the framework of the Integrative Technologies and
Architectural Design Research M.Sc. program (ITECH) at the University of Stuttgart, led by the Institute
of Building Structures and Structural Design (itke) and the Institute of Computational Design and
Construction (ICD). The fabrication was conducted with the facilities and support of the Institute of
Aircraft Design (IFB).
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Fiber Reinforced Polymers (FRPs) are increasingly popular building materials, mainly because of their high strength to weight ratio. Despite these beneficial properties, these composites are often fabricated in standardized mass production. This research aims to eliminate costly molds in order to simplify the fabrication and allow for a higher degree of customization. Complex three-dimensional shapes were instead achieved by a flat reinforcement, which was resin infused and curved folded into a spatial object before hardening. Structural stability was gained through geometries with closed cross-sections. To enable this, the resource-saving additive fabrication technique of tailored fiber placement (TFP) was chosen. This method allowed for precise fibers' deposition, making a programmed anisotropic behavior of the material possible. Principles regarding the fiber placement were transferred from a biological role-model. Five functional stools were produced as demonstrators to prove the functionality and advantages of the explained system. Partially bio-based materials were applied to fabricate the stool models of natural fiber-reinforced polymer composites (NFRP). A parametric design tool for the global design and fiber layout generation was developed. As a result, varieties of customized components can be produced without increasing the design and manufacturing effort.
... Exploiting economic benefits of sheet materials, numerous researchers investigate how to decompose a free-form surface to planar components on architecture scale (Pottmann, 2013). Meanwhile, various advanced approaches have been proposed to transform sheet material to double-curved surface, and pilot prototypes have been produced on laboratory scales, such as paper origami (Tachi, 2013), reconfigurable prestressed composite (Aldinger, Margariti and Suzuki, 2018) or deployable auxetic shells (Konakovic-lukovic, Konakovic and Pauly, 2018). These approaches make materials reconfigurable, yet leave them vulnerable to bending stresses. ...
... During the ambient changes, the layered materials expand unevenly, cause curvatures on the composites. Meanwhile, some other researchers deposit stiff components on pre-tensioned membranes (Guseinov, Miguel and Bickel, 2017;Aldinger, Margariti and Suzuki, 2018). Once the pre-tensioning is removed, the contracting membranes actuate the composites to the curved configurations. ...
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Advances in architectural geometry make free-form architecture explicitly definable and economically manufacturable. Enhancing the efficiency of fabrication, this research investigates strategies of translating free-form synclastic surfaces to flat pre-programmed reconfigurable mechanisms. The presented bi-stable mechanisms are produced by creating voids on flat materials. In such mechanisms, the generated blocks are outlined by the voids that are connected by the hinges. The position and the orientation of the hinges allow the blocks to rotate around each other, and then reconfigure from flat to synclastic. During the reconfiguration process, the blocks are temporarily deformed. As the elasticity brings the blocks back to the original dimensions, the materials reach the second stable states. Distribution of hinges on the flattened surface needs to be designed according to certain geometric constraints. This paper demonstrates the workflow of identifying the positions of the hinges. The developed methods are validated through prototypes such as a spherical surface and a free-form synclastic surface.
... Geometric self-shaping mechanisms in planar lattices have been demonstrated on smaller scales [5,6]. At a similar scale, prestressed reinforced elastic membranes have been used for deployable elements that spring from flat to curved when released [7]. These systems are scalable but require control of high stresses at deployment. ...
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Double curvature enables elegant and material-efficient shell structures, but their construction typically relies on heavy machining, manual labor, and the additional use of material wasted as one-off formwork. Using a material’s intrinsic properties for self-shaping is an energy and resource-efficient solution to this problem. This research presents a fabrication approach for self-shaping double-curved shell structures combining the hygroscopic shape-changing and scalability of wood actuators with the tunability of 3D-printed metamaterial patterning. Using hybrid robotic fabrication, components are additively manufactured flat and self-shape to a pre-programmed configuration through drying. A computational design workflow including a lattice and shell-based finite element model was developed for the design of the metamaterial pattern, actuator layout, and shape prediction. The workflow was tested through physical prototypes at centimeter and meter scales. The results show an architectural scale proof of concept for self-shaping double-curved shell structures as a resource-efficient physical form generation method.
... Other examples look at analogue processes by applying slightly different digital fabrication techniques, such as tailored fiber placement rather than 3D printing (Aldinger et al., 2018).The majority of case studies exploring self-shaping textiles focus on the process of simulating or fabricating target threedimensional geometries. This approach resembles a common trend in the architectural practice where the form comes first and materials need to follow. ...
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Despite the cutting edge developments in science and technology, architecture to a large extent still tends to favor form over matter by forcing materials into predefined, often superficial geometries, with functional aspects relegated to materials or energy demanding mechanized systems. Biomaterials research has instead shown a variety of physical architectures in which form and matter are intimately related (Fratzl, Weinkamer, 2007). We take inspiration from the morphogenetic processes taking place in plants' leaves (Sharon et al., 2007), where intricate three-dimensional surfaces originate from in-plane growth distributions, and propose the use of 3D printing on pre-stretched textiles (Tibbits, 2017) as an alternative, material-based, form-finding technique. We 3D print open fiber bundles, analyze the resulting wrinkling phenomenon and use it as a design strategy for creating three-dimensional textile surfaces. As additive manufacturing becomes more and more affordable, materials more intelligent and robust, the proposed form-finding technique has a lot of potential for designing efficient textile structures with optimized structural performance and minimal usage of material. Keywords: self-shaping textiles, material form-finding, wrinkling, surface instabilities, bio-inspired design, leaf morphogenesis
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The formulation of tasks applies to the transfer of information, analysis, and conclusions on the achievements of architecture based on new solutions in terms of aesthetic, economic, and practical aspects. The investigation process is dedicated to searching for an optimal freeform canopies’ geometry of temporary pavilions, in which parametric tools were used. The research aimed to study different spatial construction variants based on four connected double-curved surfaces, considering minimising the total weight while maintaining the strength of the structure. The results present new possibilities to create more efficient and sustainable canopies. The key findings show which geometric variables greatly influence the final performance of the shape of the area of double-curved geometry and its need to be explored for a better understanding of this type of structure. The results show the benefits of implementing structural optimisation at the early design stage, linking to aesthetically attractive and structural logic design.
Article
This work aims to provide an approach to the development of a new structural system, representing a new typology of bending-active hybrids, working with planar elements. This system can be applied as temporary or semi-permanent structures. It takes advantage of utilizing parametric design and prefabrication in order to optimize its structural and sustainable characteristics. СBA-CFS (complex bending-active continuous flexible sheet) structures are made with flexible materials and based on the interaction of bent and tensioned elements in balance, complementing one another. The main element of the structure is a bending-active surface, bent bidirectionally in a complex buckled geometry to realize double curvature. The orientation and size of the buckles take into consideration the specific rules of the form-finding and its stress distribution. The innovation behind the proposal lays in a new comprehension of the concept of a bending-active surface, avoiding tessellation or cuts. The bent shape is kept static through a set of membranes working in tension. The proposed pavilion project is made-up of a unique knitted architectural material, inspired by spacer fabrics. This specific material proposal strongly supports the concept of uniform non-tessellated bending-active sheet, adapted to a wide range of forms with a single homogeneous piece. A sample of the material is produced manually at a 1:1 scale and a model of pavilion at 1:5 scale. The work is supported by physical and digital models, using the finite element method of analysis and particle spring system for simulation and form-finding.
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Commonly referred to as bending-active, the term has come to describe a wide variety of systems that employ the large deformation of their constituent components as a primary shape-forming strategy. It is generally impossible to separate the structure from its geometry, and this is even more true for bending-active systems. Placed at the intersection between geometry, design and engineering, the principle objective of this thesis is to develop an understanding of the structural and architectural potential of bending-active systems beyond the established typologies which have been investigated so far. The main focus is set on systems that make use of surface-like elements as principle building blocks, as opposed to previous and existing projects that predominantly employed linear components such as rods and laths. This property places the analysed test cases and developed prototypes within a specific category of bending-active systems known as bending-active plate structures.
Conference Paper
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A textile hybrid system is based upon a structural logic that generates form in the relationship between an elastic textile surface and the bending resistance of fiber-reinforced composite material. Such structures are always discretized as the materials are born of highly specialized manufacturing processes: weaving or knitting for manufacturing textiles and pultrusion for the production of the particular fiber-reinforced composite elements typically utilized in textile hybrid structures. The research described in this paper embeds properties of both elastic textile and bending-resistant composites within a single material structure. This is accomplished through a composite forming process which utilizes pre-stressed textiles integrated with isolated regions of stiffened material. The design of material behavior is utilized in both the forming process and the implementation of the material system itself. By calibrating curing time and the influence of the pre-stressed textile, complex 3D forms are generated without the use of complex 3D formwork (preforms). The resulting material systems have an inherent textile hybrid nature while also, as composites, offer high degrees of flexure. A series of studies depict the potential in forming complex 3D surface structures, and utilizing the ductile nature as reconfigurable material systems. Previous research in textile hybrid systems utilizing CNC knitted textiles (left) and multi-scalar applications of GFRP rods and textiles (right)
Bending-active segmented shells
  • J Bruetting
  • A Koerner
  • D Sonntag
  • J Knippers
J. Bruetting, A. Koerner, D. Sonntag, and J. Knippers, "Bending-active segmented shells," in Proceedings of the IASS Annual Symposium 2017, HafenCity Universität, Hamburg, 2017.
Towards Active Fabrication
  • Y Berdos
  • C Cheng
Y. Berdos and C. Cheng, "Towards Active Fabrication." in Proceedings of the IASS Annual Symposium 2017, HafenCity Universität, Hamburg, 2017.
Construction manual for polymers and membranes: materials, semi-finished products, form finding design
  • J Knippers
  • J Cremers
  • M Gabler
  • J Lienhard
J. Knippers, J. Cremers, M. Gabler, and J. Lienhard, Construction manual for polymers and membranes: materials, semi-finished products, form finding design. Basel: Birkhäuser GmbH, 2011.