Content uploaded by Farzaneh Oghazian
Author content
All content in this area was uploaded by Farzaneh Oghazian on Sep 04, 2023
Content may be subject to copyright.
Proceedings of the IASS Annual Symposium 2023
Integration of Design and Fabrication
10 – 14 July 2023, Melbourne, Australia
Y.M. Xie, J. Burry, T.U. Lee and J. Ma (eds.)
Bio-based Composite Spatial Shell Structures
Mostafa AKBARI∗,a, Farzaneh OGHAZIAN∗,c, Ji Yoon BAEd, Felecia DAVISc, Laia
MOGAS-SOLDEVILAdMasoud AKBARZADEHa,b
aPolyhedral Structures Laboratory, Weitzman School of Design, University of Pennsylvania, Philadelphia, USA
Pennovation Center, 3401 Grays Ferry Ave. Philadelphia, PA, 19146
bGeneral Robotic, Automation, Sensing and Perception (GRASP) Lab, School of Engineering and Applied
Science, University of Pennsylvania, Philadelphia, USA
cComputational Textile Lab, College of Arts and Architecture, Penn State University, PA, 16801, USA
dDumoLab Research, Department of Architecture, Weitzman School of Design, University of Pennsylvania,
Philadelphia, PA, 19146, USA
∗M. Akbari and F. Oghazian contributed equally to this work.
Abstract
The authors of this research investigate the possibility of fabricating shell-based cellular structures using
knitting techniques. Shellular Funicular Structures are two-manifold single-layer structures that can be
designed in the context of graphic statics. These are efficient compression/tension-only structures that
have been designed for a certain boundary condition. Although the shellular funicular structures are ef-
ficient geometries in transferring the forces, the fabrication process is challenging due to the geometric
complexity of the structure. Since Shellular structures comprise a single surface, they are suitable candi-
dates to be fabricated using knitting technique, a method by which yarn is manipulated to create a textile
or fabric. Using knitting approach, one can fabricate shellular structures with minimum production waste
in which the knit can work as a formwork for actual structure or act as a composite structure combined
with bio-based resin. This research proposes a workflow to fabricate shellular structures using knitting
that can be scaled up for industrial purposes. In this process, the designed shellular structures are di-
vided into multiple sections that can be unrolled into planar geometries. These geometries are optimized
based on the elastic forces in the knitted network and knitted and sewn to make a topologically complex
geometry of the shellular systems. After assembling the knitted parts and applying external forces at
the boundaries, the final configuration of the structural form in tension is achieved. Then this form is
impregnated with custom bio-resin blends from chitosan, sodium alginate, and silk fibroin to stiffen the
soft knit structures into a compressed system. Although this method is an efficient fabrication technique
for constructing shellular structures, it needs to be translated into an optimized method of cutting, knit-
ting, and sewing with respect to the complexity of the shellular geometry. As a proof of concept of the
proposed workflow, a mesoscale shellular structure is fabricated.
Keywords: Biocomposite Structures, Shellular Funicular Structures, Knitting, Graphic statics.
1. Introduction
The following section is divided into three primary sections. The initial section introduces a collection
of spatial shell geometries known as shellular funicular structures, designed within the framework of
graphic statics. The subsequent section discusses knitting structures and the historical progression of
knitting techniques used in the development of shell structures. Lastly, the third section delves into
Copyright © 2023 by Mostafa AKBARI et al. Published in the Proceedings of the IASS Annual Symposium 2023
with permission.
Proceedings of the IASS Annual Symposium 2023
Integration of Design and Fabrication
Figure 1: Biomaterial-based Stiffening of the knitting samples,
composite structures of fabric or knitting, which are subsequently solidified using synthetic or biological
compunds.
1.1. Shellular Funicular Structures
Shell structures are thin, curved plate structures that transfer forces through compression, tension, and
shear stresses that act within the surface plane. These structures have numerous applications in science,
design, and construction [1–3]. As a category of cellular structures, shell cellular (shellular) structures
consist of continuous, smooth-curved shells. The geometry of these structures involves a surface with
minimal material, known as a minimal surface [4]. The geometry of these surfaces, found in nature such
as soap films, has inspired architects and engineers to design lightweight structures [5]. At each point
on the minimal surface geometry, the mean curvature (H=k1×k2) is zero, and the Gaussian curvature
(G=k1×k2<0, considering k1and k2as the principal curvatures of the surface) is negative [6]. Due
to their high surface-to-volume ratio and unique morphology, shells with these surfaces’ geometry ex-
hibit superior mechanical performance compared to other cellular structures, such as strut-based cellular
structures [7–9].
Utilizing graphic statics as a method for structural design, designers can create structures using recipro-
cal diagrams while controlling the flow of force within the structure and the external loading scenario
[10–14]. Polyhedral graphic statics (PGS), an extension of two-dimensional graphic statics (2DGS), en-
ables the user to design axially-loaded structures in 3D, in which no bending occurs [15–17]. The form
and force diagrams provide a clear relation between the geometry and the equilibrium of a 3-dimensional
node (Figure 2a). In this technique, the form diagram (denoted by Γ) represents the reaction forces
combined with the geometry of the structure while each force diagram (denoted by Γ†) explains the equi-
librium of forces. Each strut member eiin the form diagram is perpendicular to its corresponding face fi†
in the force diagram. In this technique, each vertexvi†, edge ei†, face fi†, and cell ci†in the force diagram
corresponds to a cell ci, face fi, edge ei, and vertex viin the form diagram [15]. In this technique, the
magnitude of the force in each strut member is proportional to the area of the corresponding face in the
force diagram. By applying different subdivisions to a force diagram, various cellular strut-based struc-
tures in equilibrium can be designed (Figure 2a-d). Adding thickness to each edge of the form diagram
proportional to the area of its corresponding face results in a strut-based cellular funicular structure.
The process of increasing the number of subdivisions in the force diagram leads to a form diagram with
2
Proceedings of the IASS Annual Symposium 2023
Integration of Design and Fabrication
Figure 2: Iterative subdivision of a tetrahedron as a force diagram approximates a discrete surface with
anticlastic curvature (a-d) as the form diagram. Using this subdivision between specific labyrinth graphs,
one can design a shellular funicular structure (e) and use the labyrinths as control handles to manipulate
the structure (f).
smaller edges and distributed forces in the members (Figure 2a-d). This procedure can eventually result
in edges with near-zero length, approximating a surface as a form diagram. Polyhedral Graphic Statics
(PGS) employs specific subdivision techniques to approximate surfaces with anticlastic or synclastic
curvatures as form diagrams [9]. Figure 2a depicts a tetrahedron as a force diagram corresponding to
a node in equilibrium with two upward and two downward forces as a form diagram (a node with an
anticlastic curvature). This tetrahedron is produced by connecting the endpoints of the two skew lines li†
and l′
i
†. Dividing these lines into equal segments and establishing a tetrahedron between every two skew
segments from each line subdivides the force diagram into multiple tetrahedrons, resulting in a discrete
anticlastic surface as a form diagram (Figure 2a-d) [9,18]. This subdivision method is referred to as
the anticlastic subdivision. These lines (li†and l′
i
†) serve as subdivision axes in the force diagram and
curvature axes in the form diagram (Figure 2d). These lines constitute two connectivity graphs known as
labyrinths, which connect two segregated regions divided by the anticlastic surface in between [19]. By
employing the anticlastic subdivision technique, one can design an anticlastic polyhedral surface, called
a Shellular Funicular Structure (SFS) [20]. The labyrinths serve as subdivision axes in the form diagram
and control handles in the force diagram, simplifying the design process and manipulation of the SFSs
form-finding technique [18].
1.2. Knitted Structures
Historically, textiles have been a primary material used to develop fully tensioned structural systems.
Knitted textiles, one of the many types of textiles, are created by producing loops with a continuous
yarn and pulling that yarn through previously formed loops to create new ones. The resulting loops, or
stitches, can be manipulated to form different stitch structures depending on the movement of the yarn.
The structure of a knitted fabric is determined by the shaping of stitches, the manipulation of yarns,
and the type of knitting machine used to create it. Knitted textiles have unique properties that make
them suitable for developing complex and 3D shapes due to their multi-directional, heterogeneous and
anisotropic characteristic [21]. Knitted textiles have been used in developing tension structures [22–25],
3
Proceedings of the IASS Annual Symposium 2023
Integration of Design and Fabrication
Figure 3: Designing a low-resolution (a) and high-resolution (b) of the force and form diagram of a
shellular structure.
as well as in connection with concrete as a formwork system [26–28].
1.3. Biocomposite Structures
Materials such as silk, shell, chitin, cellulose, or bone present internal hierarchical configurations that
confer stiffness, flexibility, and buckling resistance unmatched by man-made materials [29,30]. Recent
research in chemical and biomedical engineering has derived new synthesis methods to extract these
materials from the natural structures they produce such as insect cocoons or shrimp shells [31,32], and
reverse-engineer them as water-based raw biopolymers to make new structures such as drug delivery
micro-devices, tissue scaffolds, resolvable electronics, small object casts, and natural adhesives [33,34]
that are not only biocompatible to the human body but also able to be naturally decomposed. As in nature
some of these materials perform as bio-resins binding together minerals and proteins into organism struc-
tures, we explore here if they could substitute toxic man-made synthetic resin compounds that are widely
used as stiffeners of woven fiber structures (i.e epoxy, vinylester, or polyester resins used on carbon fiber,
fiberglass, and aramid fiber). In this work, the authors used simple polysaccharides and proteins extracted
from shrimp shells, algae cell walls, and silk cocoons, because of their biodegradability, strength, and
flexibility properties, their compatibility with natural fibers of wool, cotton, and linen that compose our
knits, and their proven ability to be precisely distributed in large additive manufacturing platforms as
developed in the authors’ previous work [35,36].
1.4. Problem Statement and Objectives
Shellular funicular structures are highly efficient structures designed for a specific boundary condition.
However, their fabrication process can be challenging due to their geometric complexity. Shellular struc-
tures, consisting of a single surface, are suitable for fabrication using the knitting technique, a process
used to manipulate yarn to create fabric. Knitting can minimize production waste while serving as a
formwork or composite structure, when combined with bio-based resin. This study proposes a workflow
to fabricate shellular structures using knitting and scale them up for industrial purposes. The process in-
volves dividing the designed shellular structures into sections that can be unrolled into planar geometries.
These geometries are optimized based on the elastic forces in the knitted network and stitched together
to form a topologically complex shellular system. After assembling the knitted parts, external forces are
applied to achieve the final configuration of the structural form in tension. The form is then impregnated
4
Proceedings of the IASS Annual Symposium 2023
Integration of Design and Fabrication
Figure 4: Unrolling the low-resolution shellular structure (a), and holding it using a jig (b). Turning the
screws in the jig controls the height of the knit structure, assuring that the structure is in tension (c).
with custom bio-resin blends made from chitosan, sodium alginate, and silk fibroin to stiffen the soft
knit structures into a compressed system. Although this method is efficient, an optimized method for
cutting, knitting, and sewing must be developed to match the complexity of the shellular geometry. To
demonstrate the proposed workflow’s viability, a mesoscale shellular structure has been fabricated as a
proof of concept.
2. Methodology
In this section, first, the process of designing a shallular structure for specific boundary conditions has
been explained. In the next sections, this structure will be knitted and impregnated using bio-based
materials. In the next section the knitting process will be explained through three different trials. In the
last section, the biomaterial-based stiffening through different impregnation technique will be explained.
2.1. Shellular Structural Design
In order to develop a form for the structure in tension, shellular method in the context of graphic stat-
ics have been used [20,37]. A rectangular prism (h:25 cm, w,l:20 cm) has been considered. Figure
3a displays the force diagram (left) corresponding to a structure comprising 30 edges, 7 faces, and 24
reaction forces. It is worth mentioning that the labyrinths graphs have been marked with black and red
in the force diagram. Faces in the form diagram corresponding to these graphs have been removed in
order to result in a 2-manifold structure [9]. To generate the form diagram, after designing the labyrinth
graphs, a tetrahedron has been constructed for each pair of labyrinths (red and black labyrinths that are
in a skew position together). This force diagram results in a low-resolution shellular funicular structure.
The shellular structure with the higher resolution has a smoother surface along with a higher number of
faces. In order to increase the smoothness of the structure, each labyrinth edge is subdivided into smaller
segments, and a tetrahedron has been constructed between smaller edges in the force diagram (Figure
3b). In fact, each tetrahedron in Figure 3a is subdivided into 25 tetrahedrons in order to result in the force
diagram in Figure 3b. This force diagram corresponds to a smooth form diagram, representing a shellular
funicular structure.
5
Proceedings of the IASS Annual Symposium 2023
Integration of Design and Fabrication
In order to construct the geometry out of knitting, one needs to unroll the shellular structure to the
XY plane. Due to the ease of unrolling the first form diagram prior to smoothing, the authors made the de-
cision to unroll the form diagram consisting of seven faces. In this process, faces fi,1,fi,2,fi,3,fi,4,fi,5,fi,6
(Figure 3a), have been rotated along one of their edges in order to unroll the whole structure (Figure 4a).
Using an elastic material for constructing this structure and tensioning it would result in a smooth struc-
ture, approximating the form diagram in Figure 3b. To apply tension to the structure, a jig comprising
two flat panels and 6 screws have been constructed (Figure 4a). The screws will give the user the possi-
bility to control the height of the structure, assuring that the whole knitting structure is in tension (Figure
4b).
Figure 5: Trial 1, The geometry of a shellular funicular structure (a), the knitting fabrication of a shell
(b,c), and the tensioned model of it (d).
2.2. Knitting Technology
The knitting process design for the shellular knit structure involves a series of trials aimed at achieving a
seamless surface. The initial trial involved making a planar surface with holes, with the goal of making
the entire surface seamless. However, the first attempt did not result in a shellular structure. For the
second trial, a rough representation of the overall form was used, which was then unrolled as a seamless
flat shape. The stitches were then generated over this flat shape and knitted. The knitted unrolled seamless
flat shape was then sewn together to give an overall shape to the knitted textile. The rough 3D knitted
structure was then tensioned to obtain a smooth tensioned structure. However, the model did not precisely
replicate the digital model. Therefore, in the next step, efforts were made to increase the accuracy of the
initial shape that should be knitted to achieve the final shape. At this stage, the focus was on only a
portion of the overall form.
2.2.1. Trial 1
In the initial attempt, the focus was on creating a planar surface with holes (Figure 5). The aim of this
trial was to knit the exterior skin first, and then add the interior planar surfaces. However, in this method,
the exterior and interior surfaces were not connected and required more sewing to achieve the desired 3D
shellular shape. This approach proved to be less efficient and required more effort and time to achieve
the desired result. Therefore, further trials were conducted to explore alternative methods to create the
6
Proceedings of the IASS Annual Symposium 2023
Integration of Design and Fabrication
Figure 6: Trial 2, distribution of stitches (a), Sequence of knitting (b), knitted form pattern (c), the knitted
structure in tension (d).
Figure 7: Trial 3, Sequence of knitting (a), Knitting fabrication (b), and Knitted piece for the main
alternative (c).
shellular structure more efficiently and with fewer seams.
2.2.2. Trial 2
In the second trial, the authors aimed to improve the seamless feature of the shellular knit structure.
To achieve this, the whole structure (Figure 5left) was unrolled and a single connection between the
hexagons in the middle of the structure was ensured. The process involved creating a seamless flat shape
7
Proceedings of the IASS Annual Symposium 2023
Integration of Design and Fabrication
and generating the stitches over this flat shape. The objective was to create pieces with the knitting direc-
tion pointing towards the center of the hexagon. This was considered crucial as the direction of knitting
plays a significant role in determining the behavior and performance of the textile. It was important to
achieve a consistent behavior throughout the entire structure. Therefore, special attention was given to
the direction of knitting during the fabrication process to ensure a more uniform and reliable behavior of
the knitted textile. In addition, by ensuring a consistent knitting direction, the overall aesthetics of the
structure were also improved, resulting in a more visually appealing end product. Figure 6show the pro-
cess of the knitting and after knitting the whole structure, in which the legs were sewn to the hexagon to
obtain a rough 3D shape. This figure includes the unrolled diagram, distribution of the stitches, sequence
of the knitting of different parts of the model, and the knit model in tension. By following this sequence,
the authors were able to create a knitted shape that was more closely aligned with the digital model.
2.2.3. Trial 3
In order to achieve a higher degree of accuracy, the structure that is explained in section 2.1 is knitted.
This structure is a portion of the structure displayed in Figure 5left, which is magnified in order to result
in a more accurate model. The boundary shapes of this piece were then generated using a more precise
digital model, and the stitches were generated accordingly. This approach aimed to improve the accuracy
and consistency of the knitted structure, resulting in a more reliable and efficient end product.
2.3. Biomaterial-based Stiffening
Biomaterials used as bio-resins here are chitosan from shrimp shells, sodium alginate from algae cell
walls, and Fibroin protein from silk cocoons. Silk Fibroin solution was produced by Canon Virginia
Inc. Chitosan (medium molecular weight at 85% deacetylation) was purchased from TidalVision Inc.
Acetic acid, glycerol, and sodium alginate were purchased from Sigma-Aldrich (USA). Fibroin aqueous
solutions at 7%w/vcombined with sodium alginate at 4.5%w/vas well as Chitosan at 4%w/vin 3%w/v
acetic acid in gel solution are both blends used as homogeneous stiffeners throughout all knit samples
(Figure 9). A blend of silk Fibroin at 7%w/vcombined with sodium alginate at 4.5%w/v, natural col-
oring, and glycerol is used to additively manufacture targeted stiffening. To impregnate these blends
onto knitted forms, casting and printing methods are used. Casting is based on spatula distribution of
pre-measured biomaterial quantities according to surface area and knit thickness. Printing is performed
with our exiting custom platform [35,38]: a 3-axis computer numerically controlled (CNC) system
with a 1x1m print bed that positions a pneumatic extrusion system in space. Toolpaths are designed
in Rhinoceros3D® computer-aided design software and machine instructions are translated into custom
Gcode via C# scripts. Positioning instructions are interpreted and sent via Serial Port JSON Server to the
3-axis CNC system. Extrusion machine instructions are sent via Serial Port to a dispense valve controller
and precision valve using a 1.5mm inner diameter nozzle at 10PSI and receiving materials from 100PSI
pressured reservoirs.
3. Results
The authors commenced their study by conducting experiments on stiffened knitted pieces composed of
linen, wool, or cotton, as illustrated in Figure 8. Each of these materials was knitted in sparse and dense
versions. The linen pieces were impregnated with Chitosan or Chitosan + Fibroin (Figure 8S.01 - S.03).
The wool pieces were impregnated with Fibroin + Alginate or Chitosan + Fibroin (Figure 8S.04 - S.06).
Lastly, the cotton pieces were impregnated with chitosan (Figure 8S.07 - S.08). All specimens were
subjected to loading after impregnation, and their loading capacity is presented in Figure 8. Based on the
8
Proceedings of the IASS Annual Symposium 2023
Integration of Design and Fabrication
Figure 8: Biomaterial-based Stiffening of the knitting samples, in these experiments, only half of the knit
is impregnated in order to compare the stiffness of the rigid part with the part that is draped.
9
Proceedings of the IASS Annual Symposium 2023
Integration of Design and Fabrication
Figure 9: Biomaterial-based homogeneous stiffening of a knit structure: applying tension to the sample
on the jig (a), impregnating the sample (b), and final structure after drying (c).
Figure 10: Biomaterial-based targeted stiffening; by impregnating the whole structure with a homoge-
neous Chitosan base layer (a), then printing a Fibroin-based stiffening toolpath on top (b), resulting in a
fully impregnated piece with expected differential behavior (c).
experimental results, the primary knitted structure shown in Figure 7was homogeneously stiffened by
impregnating sparse wool knit with a blend of Chitosan + Fibroin (silk fibroin at 7%w/vcombined with
chitosan at 4%w/v) in the subsequent stage, and the model was held under tension in the jig. After one
day, the dried model was loaded, and its structural capacity was evaluated. In the final stage, targeted
heterogeneous stiffening was performed the same knitted model in Figure 7, a base impregnation of
Chitosan (at 4%w/v) was followed by an additively manufactured layer of Fibroin + Alginate blend
(using, in this case, silk fibroin at 7%w/vcombined with sodium alginate at 4.5%w/v, natural coloring,
and glycerol to optimize the blend for our printing technology). Given that the smooth version of the
model in Figure 3a is depicted in Figure 3b, the pattern of the smooth model has been applied and
projected onto the model prior to smoothing. In fact the pattern that is printed on the model displays the
force flow of the smooth version of the model. This pattern would increase the material in places that we
need, improving the structural capacity of the system. Figure 11 displays the process of global stiffening
(with a clear Chitosan gel) and locally targeted stiffening of this specimen (with black silk fibroin blend).
10
Proceedings of the IASS Annual Symposium 2023
Integration of Design and Fabrication
In this process, a 3-axis computer numerically controlled (CNC) system with a 1x1m print bed has been
used to print the pattern on top of the knitted piece. Final experimental results display that both global
and local impregnation of the knitted structures results in a stiff structure with specific structural capacity.
It is noteworthy that the structure depicted in Figures 7requires an identical boundary condition to the
one it has been designed for, to attain adequate structural capacity. Consequently, several tension ties are
necessary at the top and bottom of the structure to reinforce it.
Figure 11: Biomaterial-based targeted stiffening.
4. Conclusion and Future Work
This research investigated the possibility of fabricating shell-based cellular structures using knitting tech-
niques. The research proposed a workflow to fabricate shellular structures using knitting that can be
scaled up for industrial purposes. In this process, the designed shellular structures are divided into mul-
tiple sections that can be unrolled into planar geometries. These geometries are optimized based on the
elastic forces in the knitted network and knitted and sewn to make a topologically complex geometry of
the shellular systems. After assembling the knitted parts and applying external forces at the boundaries,
the final configuration of the structural form in tension is achieved. Then this form is impregnated with
custom bio-resin blends from chitosan, sodium alginate, and silk fibroin to stiffen the soft-knit structures
into a compressed system. In forthcoming research, it is crucial to concentrate on numerically assessing
the structural efficacy of each structural specimen and contrasting it with experimental testing. Further-
more, it is imperative to concentrate on structures with greater dimensions, whose structural efficacy
must be examined under actual loads.
Acknowledgement
This research was partially funded by University Research Foundation (URF) to Dr. Laia Mogas-
Soldevila. This research was also funded by the National Science Foundation CAREER Award (NSF
CAREER-1944691 CMMI) and the National Science Foundation Future Eco Manufacturing Research
Grant (NSF, FMRG-CMMI 2037097) to Dr. Masoud Akbarzadeh.
11
Proceedings of the IASS Annual Symposium 2023
Integration of Design and Fabrication
References
[1] T. Teng, M. Jia, and J. E. Sabin, “The designing of epithelial cell inspired-brick inmasonry shell
system,” 2020.
[2] T. Teng and J. Sabin, “The design and 4d printing of epithelial cell-inspired programmable surface
geometry,” 2021.
[3] S. Adriaenssens, P. Block, D. Veenendaal, and C. Williams, Shell structures for architecture: form
finding and optimization. Routledge, 2014.
[4] W. Meeks III and J. P´
erez, “The classical theory of minimal surfaces,” Bulletin of the American
Mathematical Society, vol. 48, no. 3, pp. 325–407, 2011.
[5] B. Burkhardt, “Natural structures-the research of frei otto in natural sciences,” International journal
of space structures, vol. 31, no. 1, pp. 9–15, 2016.
[6] D. Hilbert and S. Cohn-Vossen, Geometry and the Imagination, vol. 87. American Mathematical
Soc., 2021.
[7] S. C. Han, J. W. Lee, and K. Kang, “A new type of low density material: Shellular,” Advanced
Materials, vol. 27, no. 37, pp. 5506–5511, 2015.
[8] S. C. Han, J. M. Choi, G. Liu, and K. Kang, “A microscopic shell structure with schwarz’s d-
surface,” Scientific reports, vol. 7, no. 1, pp. 1–8, 2017.
[9] M. AKBARI, M. AKBARZADEH, and M. BOLHASSANI, “From polyhedral to anticlastic funic-
ular spatial structures,” in Proceedings of IASS Symposium, 2019.
[10] J. C. Maxwell, “On Reciprocal Figures and Diagrams of Forces,” Philosophical Magazine Series 4,
vol. 27, no. 182, pp. 250–261, 1864.
[11] W. J. M. Rankine, “Principle of the Equilibrium of Polyhedral Frames,” Philosophical Magazine
Series 4, vol. 27, no. 180, p. 92, 1864.
[12] L. L. Beghini, J. Carrion, A. Beghini, A. Mazurek, and W. F. Baker, “Structural Optimization Using
Graphic Statics,” Structural and Multidisciplinary Optimization, vol. 49, no. 3, pp. 351–366, 2013.
[13] L. Cremona, Graphical Statics: Two Treatises on the Graphical Calculus and Reciprocal Figures
in Graphical Statics. Translated by Thomas Hudson Beare. Oxford: Clarendon Press, 1890.
[14] K. Culmann, Die Graphische Statik. Z¨
urich: Verlag Meyer und Zeller, 1864.
[15] M. Akbarzadeh, 3D Graphic Statics Using Reciprocal Polyhedral Diagrams. PhD thesis, ETH
Zurich, Zurich, Switzerland, 2016.
[16] Y. Lu, M. Cregan, P. Chhadeh, A. Seyedahmadian, M. Bolhassani, J. Schneider, J. Yost, and M. Ak-
barzadeh, “All glass, compression-dominant polyhedral bridge prototype: form-finding and fabri-
cation,” in Proceedings of IASS Symposium and Spatial Structures Conference 2020/21, Inspiring
the next generation, (Guildford, UK), August 23-27 2021.
[17] H. Chai and M. Akbarzadeh, “Web-based Interactive Polyhedral Graphics Statics Platform,” in
Proceedings of the IASS Annual Symposium 2020/21, (Surrey,UK), 2021.
12
Proceedings of the IASS Annual Symposium 2023
Integration of Design and Fabrication
[18] M. Akbari, A. Mirabolghasemi, H. Akbarzadeh, and M. Akbarzadeh, “Geometry-based structural
form-finding to design architected cellular solids,” in Symposium on Computational Fabrication,
pp. 1–11, 2020.
[19] W. Fischer and E. Koch, “Genera of minimal balance surfaces,” Acta Crystallographica Section A:
Foundations of Crystallography, vol. 45, no. 10, pp. 726–732, 1989.
[20] M. Akbari, A. Mirabolghasemi, M. Bolhassani, A. Akbarzadeh, and M. Akbarzadeh, “Strut-based
cellular to shellular funicular materials,” Advanced Functional Materials, p. 2109725, 2022.
[21] C. L. McKnelly, Knitting behavior: a material-centric design process. PhD thesis, Massachusetts
Institute of Technology, 2015.
[22] R. La Magna, V. Fragkia, R. No¨
el, Y. ˇ
Sinke, M. Tamke, P. L¨
angst, J. Lienhard, and M. Thomsen,
“Isoropia: an encompassing approach for the design, analysis and form-finding of bending-active
textile hybrids,” 07 2018.
[23] M. R. Thomsen, M. Tamke, A. Karmon, J. Underwood, C. Gengnagel, N. Strangh¨
oner, and J. Uhle-
mann, “Knit as bespoke material practice for architecture,” in Acadia 2016, pp. 280–289, ACADIA,
2016.
[24] J. E. Sabin, “mythread pavilion: generative fabrication in knitting processes,” in ACADIA, vol. 13,
pp. 347–354, 2013.
[25] J. E. Sabin, J. Hilla, D. Pranger, C. Binkley, and J. Bilotti, “Embedded architecture: Ada, driven by
humans, powered by ai,” Fabricate 2020, pp. 246–255, 2020.
[26] A. Pal, W. L. Chan, Y. Y. Tan, P. Z. Chia, and K. J. Tracy, “Knit concrete formwork,” in Proceedings
of the 25th CAADRIA Conference, vol. 1, pp. 213–22, 2020.
[27] M. Popescu, L. Reiter, A. Liew, T. Van Mele, R. J. Flatt, and P. Block, “Building in concrete
with an ultra-lightweight knitted stay-in-place formwork: prototype of a concrete shell bridge,” in
Structures, vol. 14, pp. 322–332, Elsevier, 2018.
[28] M. Popescu, M. Rippmann, A. Liew, L. Reiter, R. J. Flatt, T. Van Mele, and P. Block, “Structural
design, digital fabrication and construction of the cable-net and knitted formwork of the knitcandela
concrete shell,” in Structures, vol. 31, pp. 1287–1299, Elsevier, 2021.
[29] J. Vincent, Structural biomaterials. Princeton University Press, 2012.
[30] M. A. Meyers, J. Mckittrick, and P.-Y. Chen, “Structural Biological Materials: Critical Mechanics-
Materials Connections,” Science, vol. 335, pp. 199–204, jan 2012.
[31] J. G. Fernandez and D. E. Ingber, “Bioinspired chitinous material solutions for environmental sus-
tainability and medicine,” Advanced Functional Materials, vol. 23, no. 36, pp. 4454–4466, 2013.
[32] F. G. Omenetto and D. L. Kaplan, “New opportunities for an ancient material.,” Science (New York,
N.Y.), vol. 329, no. 5991, pp. 528–531, 2010.
[33] G. Guidetti, L. D’Amone, T. Kim, G. Matzeu, L. Mogas-Soldevila, B. Napier, N. Ostrovsky-Snider,
J. Roshko, E. Ruggeri, and F. G. Omenetto, “Silk materials at the convergence of science, sustain-
ability, healthcare, and technology,” Applied Physics Reviews, vol. 9, p. 011302, mar 2022.
13
Proceedings of the IASS Annual Symposium 2023
Integration of Design and Fabrication
[34] J. G. Fernandez and D. E. Ingber, “Manufacturing of large-scale functional objects using biodegrad-
able chitosan bioplastic,” Macromolecular Materials and Engineering, vol. 299, no. 8, 2014.
[35] L. Mogas-Soldevila, G. Matzeu, M. L. Presti, and F. Omenetto, “Additively manufactured leather-
like silk protein materials,” Materials Design, vol. 203, p. 109631, 2021.
[36] L. Mogas-Soldevila, J. Duro-Royo, and N. Oxman, “Water-Based Robotic Fabrication: Large-Scale
Additive Manufacturing of Functionally Graded Hydrogel Composites via Multichamber Extru-
sion,” 3D Printing and Additive Manufacturing, vol. 1, pp. 141–151, sep 2014.
[37] M. Akbari and M. Akbarzadeh, “Continuous approximation of shellular funicular structures,” in
Proceedings of IASS 2022 symposium affiliated with APCS 2022 conference, (Beijing, China),
September 19-22 2022.
[38] G. Ho, V. Kubuˇ
sov´
a, C. Irabien, V. Li, A. Weinstein, S. Chawla, D. Yeung, A. Mershin, K. Zolo-
tovsky, and L. Mogas-Soldevila, “Multiscale design of cell-free biologically active architectural
structures,” Frontiers in Bioengineering and Biotechnology, vol. 11, 2023.
14