PrintNervi – Design and Construction of a Ribbed Floor System in the Digital Era

Abstract

Ribbed floor systems, which include ribbed slabs and columns, are used extensively to enhance thestructural performance of buildings. With the emerging topology optimization and advancedmanufacturing techniques, the material usage and construction process of the ribbed floor systems canbe improved significantly to achieve higher efficiency and sustainability. This paper presents a digitaldesign and construction process for ribbed floor systems that combines a modified topologyoptimization method for ribbed slab design with a hybrid digital fabrication process for large-scaleconcrete casting. This new approach is tested through digital design and physical realization of a large-scale ribbed floor unit as proof of concept. The topologically optimized result and the constructed unitare compared with a famous historical floor system designed by Pier Luigi Nervi. The paper shows thatthe proposed design method, based on the bi-directional evolutionary structural optimization framework,can generate a slab design with a continuous rib layout and with higher structural stiffness. The paperalso demonstrates that 3D printing of formworks for casting ribbed slabs and complex-shaped columnsis feasible and sustainable. The new process presented in this paper can be used to design and constructa wide range of structures while minimizing material usage and labor cost.

Full text

JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: J. IASS
Copyright © 2022 by Jiaming Ma, Mohamed Gomaa, Ding Wen Bao, Anooshe Rezaee Javan and Yi Min Xie
Published by the International Association for Shell and Spatial Structures (IASS) with permission. 1
Article published in
Journal of the International Association for Shell and Spatial Structures, Vol. 63 (2022) pp. 241–251
https://doi.org/10.20898/j.iass.2022.017
PRINTNERVI – DESIGN AND CONSTRUCTION OF A RIBBED
FLOOR SYSTEM IN THE DIGITAL ERA
Jiaming MA1, Mohamed GOMAA2, Ding Wen BAO3, Anooshe REZAEE JAVAN4, Yi Min XIE5
1Postdoctoral Researcher, Centre for Innovative Structures and Materials, School of Engineering, RMIT University,
Melbourne, 3001, Australia. Email: jiaming.ma2@rmit.edu.au
2Postdoctoral Researcher, Centre for Innovative Structures and Materials, School of Engineering, RMIT University,
Melbourne, 3001, Australia. Email: mohamed.gomaa@rmit.edu.au
3Lecturer, School of Architecture and Urban Design, RMIT University, Melbourne 3001, Australia. Email:
nic.bao@rmit.edu.au
4Postdoctoral Researcher, Centre for Innovative Structures and Materials, School of Engineering, RMIT University,
Melbourne, 3001, Australia. Email: anooshe.rezaeejavan@rmit.edu.au
5Distinguished Professor, Centre for Innovative Structures and Materials, School of Engineering, RMIT University,
Melbourne, 3001, Australia. Email: mike.xie@rmit.edu.au
Editor’s Note:
The first author of this paper is one of the four winners of the 2022 Hangai Prize, awarded for outstanding
papers that are submitted for presentation and publication at the annual IASS Symposium by younger members of
the Association (under 30 years old). It is published here with permission of the editors of the proceedings of the IASS
Symposium 2022 “Innovation, Sustainability and Legacy”, that was held in September 2022 in Beijing, China.
DOI:
Digital Object Identifier to be provided by Editor when assigned upon publication
ABSTRACT
Ribbed floor systems, which include ribbed slabs and columns, are used extensively to enhance the structural
performance of buildings. With the emerging topology optimization and advanced manufacturing techniques, the
material usage and construction process of the ribbed floor systems can be improved significantly to achieve
higher efficiency and sustainability. This paper presents a digital design and construction process for ribbed floor
systems that combines a modified topology optimization method for ribbed slab design with a hybrid digital
fabrication process for large-scale concrete casting. This new approach is tested through digital design and
physical realization of a large-scale ribbed floor unit as proof of concept. The topologically optimized result and
the constructed unit are compared with a famous historical floor system designed by Pier Luigi Nervi. The paper
shows that the proposed design method, based on the bi-directional evolutionary structural optimization
framework, can generate a slab design with a continuous rib layout and with higher structural stiffness. The paper
also demonstrates that 3D printing of formworks for casting ribbed slabs and complex-shaped columns is feasible
and sustainable. The new process presented in this paper can be used to design and construct a wide range of
structures while minimizing material usage and labor cost.
Keywords: floor system, topology optimization, robotic fabrication, Pier Luigi Nervi
1. INTRODUCTION
With the increasing concerns about climate change,
reducing carbon emissions has drawn extensive
attention in the building industry [1, 2]. Buildings
can generate more than 40% of the global carbon
emissions [3], where slab structures alone can
occupy up to 85% of the total weight of a building
[4]. Innovating new design and construction
processes for floor systems can improve the
digitization and sustainability of the building

Vol. 63 (2022) No. 4 December n. 214
2
industry. Throughout his distinguished career, the
famous engineer Pier Luigi Nervi (1891–1979) had
significantly explored the design and construction of
free-form ribbed slabs and columns for floor systems
[5]. Nervi’s unique method presents both adequate
structural performance and efficient material usage,
and it has become known globally as the “Nervi
System”. The slab ribs in Nervi’s method are
designed along isostatic lines of principal bending
moments and constructed using ferrocement and
prefabricated concrete elements [6, 7]. This method
has produced some of the most famous ribbed floor
systems in the world over the last century, including
the Gatti Wool Factory, and the Palace of Labor
Figure 1: Ribbed floor systems by Nervi: (a) Gatti Wool Factory, (b) Palace of Labor. Modified from [5]
(see Figure 1). With the recent advances in
computer-aided design, engineering analysis, and
digital manufacturing, the full potential of Nervi’s
system can be explored, extended, and enhanced.
In addition to a variety of digital design tools for
form finding [8–13], topology optimization has been
developing rapidly over the past decades. It adopts
an iterative process via engineering analyses and
material updates to achieve an optimum material
distribution within a specific design domain [14].
Among the plentiful methods of topology
optimization, four methods have been widely
investigated: the solid isotropic material with
penalization (SIMP) method [15], the evolutionary
structural optimization (ESO) method [16], the bi-
directional evolutionary structural optimization
(BESO) method [17], and the level-set method [18].
In topology optimization, extended functions and
constraints are progressively introduced to overcome
challenges in various science and engineering fields,
such as biological morphogenesis [19–21], advanced
manufacturing [22–24], and architectural design
[25–28]. For example, the construction field exhibits
several outstanding structures and buildings that
have been designed using the extended methods of
BESO [29].
The applications of advanced manufacturing and
robotic fabrication in construction have evolved
dramatically, especially in large-scale manufacturing
[30–32]. Cementitious 3D construction printing has
been investigated extensively to create sophisticated
concrete structures without formworks [33], but the
mechanical properties of 3D-printed concrete
structures tend to be lower than their cast concrete
counterparts [34]. Fabric formwork, using textile
sheets, has been proposed for casting complex
concrete surfaces; however, it is less durable and
reusable than solid formworks [35]. Robotic 3D
printing of polymers can produce accurate, free-
form, large-scale structures and formworks [36].
Using robotic 3D printing to print flat surfaces is
considerably more time consuming than subtractive
manufacturing methods, such as computer
numerically controlled (CNC) machining and laser
cutting [37]. Therefore, adopting a hybrid
manufacturing mode that combines robotic 3D
printing and CNC machining promises a faster
prototyping process for low-cost, reusable, and
recyclable formworks for concrete casting.
This research project, named PrintNervi, aims to
revisit Nervi’s distinguished system through
leveraging the latest structural design and
construction techniques. This project proposes an
evolution of Nervi’s original designs, where
topology optimization and digitally fabricated

JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: J. IASS
3
formworks are used to improve the design and
construction processes of his ribbed floor systems.
The achieved improvements will be evaluated by
investigating three aspects:
a) the structural performance of the ribbed slab
b) the improvement of the formwork fabrication
c) the sustainability of the formwork.
This paper consists of six sections. Section 2
introduces the topology optimization method for
ribbed slab design enhancement, and section 3
presents a case study of the design optimization
using the ribbed slab design from the Gatti Wool
Factory. Section 4 demonstrates the digital
fabrication process of the new formwork and the
construction process of a large-scale, ribbed floor
unit. Section 5 discusses and compares the new
design and construction result with Nervi’s work.
Finally, section 6 summarizes the advantages of the
proposed methods for creating ribbed floor systems.
2. A TOPOLOGY OPTIMIZATION METHOD
FOR RIBBED SLABS
A modified topology optimization method with a
constraint mapping and structural complexity control
(SCC) approach is developed to optimize the
stiffness of ribbed slabs. The slab model of the Gatti
Wool Factory is selected for algorithm
demonstration.
The design space

of a slab model can be
discretized into n elements. Each element i is
assigned a design variable
i

for material updates. In
the BESO framework, the design variable
i

can be
a bilateral value of one or
min

, which is close to
zero. The SIMP framework relaxes the
i

between
the two values. Here, we adopt the BESO framework
to demonstrate the algorithm. The stiffness
maximization problem can be treated as minimizing
the external work of a model and can be formulated
as
 
1
f
1
min
1
m
in : ( )
2
s.t. : ( )
ˆ
: =
0 : 1, 1, 2,
,
n
i i
i
n
i
i
i
C
v
v
v
or
i n
 


 


 


 


T
U K U
K U F
ρ
(1)
where compliance
C
is the work of external force,
U
is the global displacement vector,
K
is the global
stiffness matrix,
F
is the force vector,
i
v
is the
elemental volume, and
f
ˆ
v
is the target volume
fraction of rib material. The elemental sensitivity can
be yielded as
 


1
0
0
1
C11
2
p
i i i i
i
E
pE

  


 
   
 
 
u k u
(2)
where
1
E
and
0
E
represent Young’s moduli of rib and
void materials, p is a penalization number,
i
u
is the
elemental displacement vector, and
0
k
is the
elemental stiffness matrix with rib material.
Sensitivity filtering and history average techniques
can be applied to improve the numerical stability of
the optimization process. Based on the BESO
framework, a constraint mapping and an SCC
approach are introduced to ensure the uniform
thickness of rib structures and sustain their
continuity.
2.1. Constraint mapping
A planar design vector
{ | 1,2,3,..., }
j
x j n t
 
xis
defined within the rib design domain
d

to constrain
elements on the same in-plane position to have the
same design variables:
( 1, 2,3,..., | 1,2,3,..., )
l
j j r
x n t
j l t

   (3)
where
t
and
r
t
are the number of layers in

and
d

, as illustrated in Figure 2(b).
The elemental sensitivities in
d

are averaged
according to Equation 4 to update the planar design
vector
x
in topology optimization.
1
/
rl
j j r
l
t
t
 

 (4)
2.2. Continuity and complexity control of ribs
In addition to controlling the number of ribs and
cavities in the slab, a newly developed SCC method
[38] is integrated with the constraint mapping within
the BESO framework to sustain the continuity of the
ribs. The fundamental idea of SCC is to maintain the
invariance of a structural topology. Thus, the number
of connected components (e.g., beams and bars),
tunnels, and cavities in the structure can be
maintained for the remaining optimization
processes. By identifying the simple points within
x
, boundary elements can be selected to participate in
the design variable updates in each iteration. A
structural skeleton can also be obtained to control the
minimum size of the ribs.

Vol. 63 (2022) No. 4 December n. 214
4
The procedures for every iteration are as follows:
1) Perform the finite element analysis based on
the current design
ρ
.
2) Calculate the objective function C, the
elemental sensitivities
α
, and the constraint
functions.
3) Calculate the averaged sensitivities
α
with
constraint mapping.
4) Obtain structural skeleton and boundary
elements within
x
.
5) Update
x
according to
α
using BESO with
SCC.
6) Update
ρ
according to Equation 3.
Figure 2: The slab model used in the finite element analysis: (a) initial discretized design space, (b) number of layers in

and
d

as well as sensitivity labeling
3. CASE STUDY OF SLAB DESIGN
OPTIMIZATION
A case study was selected to illustrate the potential
of the design optimization algorithm presented in
section 2. The ribbed slab design from Nervi’s Gatti
Wool Factory was chosen to undergo the
optimization process and evaluate the prospective
design improvement (see Figure 3). A quarter of the
Nervi slab unit is created to mimic the slab’s original
geometry and boundary conditions. Uniformly
distributed loads are applied on the top surface of the
quarter unit. Symmetry conditions are applied to the
four boundaries of the quarter model to generate a
repetitive pattern for the floor system. The bottom-
left corner of the model is constrained with full fixity
where the column is located to support the floor slab.
The slab model is discretized into 10,000 elements in
each layer for finite element analysis using Abaqus
(Version 6.20) and topology optimization. Three
layers of elements are assigned to the flat slab at the
top non-design domain
n

and five layers of
elements are assigned to the design domain
d

for
ribs to ensure the accuracy of the bending analyses.
The target volume of the ribs in
d

is set as 28%, per
the original ribbed floor design of the Gatti Wool
Factory. Figure 4(a) shows the design of a unit of the
Gatti Wool Factory, while Figures 4(b) and (c) show
the optimized results using the proposed method as a
single unit and as a continuous floor system,
respectively. The optimized design achieved a
26.3% increase in stiffness compared with Nervi’s
original design.

JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: J. IASS
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Figure 3: Slab model for topology optimization: (a) slab units, (b) loading and symmetrical (Symm) boundary conditions on
a quarter of a slab unit
Figure 4: (a) Ribbed slab design of Nervi’s Gatti Wool Factory (C = 4.42 N

mm), (b) optimized ribbed slab design
(C = 3.5 N

mm), (c) slab pattern from the optimized result
4. DIGITAL FABRICATION AND
CONSTRUCTION PROCESS
The second objective of the PrintNervi project is to
utilize digitally fabricated formworks for concrete
casting of the modular ribbed floor units. The new
formwork system aims to provide high geometrical
complexity and accuracy using less labor and a
shorter fabrication time while also being reusable
and recyclable. This is expected to be achieved by
utilizing a hybrid fabrication method that combines
both robotic 3D printing and CNC machining. A
small-scale prototype (1:5) of the formwork was
initially fabricated and tested as a proof of concept;
it was then developed and fabricated into a full-scale
element. Since the form of the columns in the Gatti
Wool Factory is considered relatively plain in terms
of complexity, the more complex column design
from Nervi’s Palace of Labor project in Turin is
adopted to present more challenges for the new
formwork system.
4.1. Small-scale prototype
Small-scale prototyping in construction is an
important step in optimizing the cost of developing
and producing the actual construction. Examining
the process challenges and limitations on a small
scale can increase efficiency and reduce the risk of
failures in the large-scale production phase. For this
purpose, a small-scale formwork was fabricated
from 3D-printed polylactic acid and laser-cut acrylic
sheets. These materials and digital fabrication
methods imitate the full-scale formwork fabricated
from 3D-printed polymers and CNC-machined
plywood sheets. Further details on this will be
presented in section 4.2.

Vol. 63 (2022) No. 4 December n. 214
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Figure 5: Small-scale prototype: (a) 3D-printed slab
formwork, (b) 3D-printed column formwork, (c) assembled
small-scale ribbed floor unit
Nervi’s original slab design exhibits more-intricate
rib formation than the new optimized design
described in section 3, making the casting process
more challenging. Thus, Nervi’s original design is
adopted for the small-scale prototyping to examine
and demonstrate the capability of the new formwork
system. Figure 5 shows the small-scale formwork
and the resulting slab and column from casting. The
3D-printed formworks (see Figures 5(a) and (b)) are
designed for rib casting, while the laser-cut acrylic
formworks are used to cap the cavities between the
ribs and support the upper slab section. Industrial
grease is chosen as a release agent as it proved to
have better performance than oil in preliminary tests.
The resultant mortar ribs from casting present a
satisfying surface finish without breakage. The
column can be cast in one piece using the 3D-printed
formwork. The main challenge identified from the
small-scale formwork is the demolding of the 3D-
printed rib formwork of the slab. Hence, the bottom
panels of the large-scale slab formwork are improved
to be separated from and interlocked with the side
panels of ribs and manufactured using CNC
machining.
The small-scale prototyping stage generally presents
satisfactory results and provides promising evidence
to warrant proceeding with the full-scale
construction phase.
4.2. Large-scale construction
4.2.1. Formwork fabrication and assembly
The formwork fabrication process is twofold: the
column formwork and slab formwork. First, the size
of the original elements is adjusted to fit in the
selected construction site. The column, which is
adopted from Nervi’s original design, is scaled down
to 2,500 mm

476 mm

476 mm, while the slab is
scaled down to 2,000 mm

2,000 mm

130 mm.
The digital design and positioning of the formworks
are demonstrated in Figure 6.
The whole column formwork in Figure 6(b) is 3D
printed using a KUKA robot with a polyethylene
terephthalate glycol (PETG) pellet extruder. Each
extruded line has a height of 3 mm and a width of
7 mm after curing. A zigzag-shaped infill was
implemented in the formwork design to enhance the
rigidity, making the total thickness of the formwork
shell 25 mm. The bounding dimensions of the
column formwork are 320 mm

320 mm at the top
and 500 mm

500 mm at the bottom. The formwork
is divided into four sections, two vertically and two
horizontally, facilitating the assembly and
demolding processes and providing easier access for
concrete vibration.
The side panels of ribs in the slab formwork are also
3D printed using the same setting as the column
formwork. However, since these panels are not
required to withstand high pressure, the overall
thickness of the shell was reduced to 14 mm to
shorten the manufacturing time and save printing
material. The flat areas of the slab formwork are
manufactured from plywood using CNC machining,
which provides rapid cutting and engraving.
Plywood is selected as it provides a balance between
strength, cost, and sustainability. Figure 7 shows the
fabrication of the large-scale formworks.
The column formworks are assembled using bolts
horizontally and turnbuckles vertically. Gaskets are
placed between the contact surfaces to prevent the
leakage of concrete. The 3D-printed side panels of
the slab formwork are bound using clips and
interlocked with the plywood panels, as shown in
Figure 8(a). A two-layer reinforcement is bent and
connected according to the shape of the ribbed slab,
as in Figure 8(b). Four 12 mm rebars are also
prefabricated for the column formwork. They are
fixed within the formworks as reinforcement to
provide extra tensile strength for the concrete.

JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: J. IASS
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Figure 6: Digital model of large-scale formworks: (a) slab formwork, (b) column formwork
Figure 7: Large-scale formwork fabrication: (a) CNC machining, (b) robotic 3D printing

Vol. 63 (2022) No. 4 December n. 214
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Figure 8: Assembled large-scale formwork: (a) unfinished slab formwork with side panels for casting ribs, (b)
reinforcement of slab formwork, (c) column formwork with reinforcement
4.2.2. Casting and demolding
After the formworks and reinforcements are settled,
the concrete is poured, vibrated, and leveled. After
two weeks, the column formworks can be easily
demolded from top to bottom. The slab is lifted and
mounted temporarily on a short, 1,000 mm-high
column to facilitate the demolding process from the
bottom. The interlocking mechanism implemented
between the plywood panels and the 3D-printed side
panels of the slab formwork improved the demolding
process considerably. After demolding, the slab is
lifted to the full-size column to complete the
assembly process. Figure 9(a) presents the intricate
surface of the cast column, which exhibits the
excellent capability of 3D-printed formworks on
casting free-form concrete surfaces. Figure 9(b)
shows the assembled floor unit. The used formworks
can be collected, reassembled, and reused to cast
identical slabs and columns.

JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: J. IASS
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Figure 9: (a) Surface of the cast column, (b) final assembled ribbed floor unit (slab dimensions: 2.2 m×2.2 m, column
height: 2.5 m)
5. DISCUSSION
The new digital tools for design and construction
have revealed new potential for Nervi’s renowned
ribbed floor systems. Compared with Nervi’s
original design of the Gatti Wool Factory, the
proposed topology optimization method in this study
shows a considerable improvement of 26.3% in the
structural stiffness of the ribbed slab. However,
Nervi’s designs also considered several other
engineering and aesthetic factors; therefore, the
presented comparison between the original and the
optimized design is limited to structural stiffness.
Despite the shortage of computational tools for
engineering analysis in the last century, Nervi’s
design and construction concepts were
groundbreaking and are still considered pioneering,
even by today’s standards.
The ferrocement proposed by Nervi was deemed
feasible to produce free-form ribbed floor systems in
his time. However, the demand for labor-intensive
works and the ever-increasing cost of labor have
limited the large-scale application of the Nervi
System. The developed hybrid method to digitally

Vol. 63 (2022) No. 4 December n. 214
10
fabricate formworks in this study benefits from the
advanced automation and manufacturing methods,
which are reflected in the accuracy, design freedom,
time efficiency, and reduction of human interaction.
CNC machining can rapidly produce plywood
formworks with reasonable complexity for low
costs, which is perfectly efficient for the flat parts of
the formworks. Meanwhile, robotic 3D printing can
produce the free-form elements of the formworks,
offering reasonable rigidity and minimizing material
consumption. The fabrication of the formworks takes
less than 90 hours in total and is completed digitally
by machines. Furthermore, this study has shown that
3D-printed PETG formworks are strong enough for
large-scale concrete casting. It is also worth
mentioning that the hybrid fabricated formwork
system is reusable, and both the plywood and PETG
materials are recyclable.
6. CONCLUSION
This paper presents a digital workflow for designing
and constructing innovative ribbed floor systems
inspired by Pier Luigi Nervi. A modified topology
optimization method is developed for enhancing the
structural stiffness of ribbed floors. The optimized
ribbed slab exhibits higher stiffness than Nervi’s
original slab design for the Gatti Wool Factory. In
addition, using a hybrid digital approach to mold
fabrication proves to be highly sustainable and
efficient for concrete casting applications.
Combining 3D-printing technologies with CNC
machining provides a rapid fabrication process for
free-form geometries with minimal material usage
and adequate rigidity. Both the formworks from
PETG and plywood materials are reusable and
recyclable. The large-scale floor unit constructed in
this study reflects the aforementioned advantages.
Overall, the proposed design and construction
methods offer a contemporary evolution of Nervi’s
pioneering techniques for designing and constructing
ribbed floor systems. The new workflow promises
higher efficiency and sustainability for creating
ribbed floor systems in modern architectural and
engineering applications.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the financial
support provided by the Australian Research Council
(FL190100014). The authors also thank Yunzhen
He, Hesameddin Mohamed, Anbang Chen, Ting-Uei
Lee and all workers and volunteers who participated
in the slab and column construction. Figure 1 is
reproduced from Aesthetics and Technology in
Building: The Twenty-First-Century Edition.
Copyright 2018 by the Board of Trustees of the
University of Illinois. Used with permission of the
University of Illinois Press.
DATA AVAILABILITY
The results and the basic code of this work are
available from the corresponding author upon
reasonable request.
REFERENCES
[1] M. De Vita, P. Beccarelli, E. Laurini, and P.
De Berardinis, “Performance analyses of
temporary membrane structures: energy
saving and CO2 reduction through dynamic
simulations of textile envelopes,”
Sustainability, vol. 10, Article 2548, July
2018. (DOI:10.3390/su10072548)
[2] S. Colabella, B. D’Amico, E. Hoxha, and C.
Fivet, “Structural design with reclaimed
materials: an elastic gridshell out of skis,” in
Interfaces: Architecture.Engineering.Science:
Proceedings of the IASS Annual Symposium
2017, Hamburg, Germany, September 25–28,
2017, A. Bögle and M. Grohmann Eds. IASS,
2017.
[3] M. Robati, D. Daly, and G. Kokogiannakis,
“A method of uncertainty analysis for whole-
life embodied carbon emissions (CO2-e) of
building materials of a net-zero energy
building in Australia,” Journal of Cleaner
Production, vol. 225, pp. 541–553, July 2019.
(DOI: 10.1016/j.jclepro.2019.03.339)
[4] C. Georgopoulos and A. Minson, Sustainable
Concrete Solutions. Chichester: John Wiley &
Sons, 2014.
[5] P. L. Nervi, Aesthetics and Technology in
Building: The Twenty-First-Century Edition.
Urbana: University of Illinois Press, 2018.
[6] A. B. Halpern, D. P. Billington, and S.
Adriaenssens, “The ribbed floor slab systems
of Pier Luigi Nervi,” Journal of the
International Association for Shell and
Spatial Structures, vol. 54, pp. 127–136, Sept.

JOURNAL OF THE INTERNATIONAL ASSOCIATION FOR SHELL AND SPATIAL STRUCTURES: J. IASS
11
2013.
[7] R. Gargiani and A. Bologna, The Rhetoric of
Pier Luigi Nervi: Concrete and Ferrocement
Forms. Lausanne: EPFL Press, 2016.
[8] R. Motro, Tensegrity: Structural Systems for
the Future. London: Kogan Page Science,
2003.
[9] S. Gellin and R. M. O. Pauletti, “Necking
limits of conoid membrane structures with
variable stress ratio,” Engineering Structures,
vol. 50, pp. 90–95, May 2013. (DOI:
10.1016/j.engstruct.2012.09.023)
[10] H. Nooshin, R. Kamyab, and O. A. Samavati,
“Exploring scallop forms,” International
Journal of Space Structures, vol. 32, pp. 84–
111, July 2017. (DOI:
10.1177/0266351117717519)
[11] J. Cai and J. Feng, “Form-finding of tensegrity
structures using an optimization method,”
Engineering Structures, vol. 104, pp. 126–
132, Oct. 2015. (DOI:
10.1016/j.engstruct.2015.09.028)
[12] P. von Buelow, A. Khodadadi,
“Computational form exploration of
branching columns using concepts of formex
algebra and the ParaGen method,” in Inspiring
the Next Generation: Proceedings of the IASS
Annual Symposium 2020/21 and the 7th
International Conference on Spatial
Structures, Guilford, UK, August 23–27,
2021, S. A. Behnejad, G. A. R. Parke, and O.
A. Samavati Eds. IASS, 2021.
[13] T. Tachi, “Freeform rigid-foldable structure
using bidirectionally flat-foldable planar
quadrilateral mesh,” in Advances in
Architectural Geometry 2014, C. Ceccato, L.
Hesselgren, M. Pauly, H. Pottmann, and J.
Wallner Eds. Vienna: Springer, 2010, pp. 87–
102. (DOI: 10.1007/978-3-7091-0309-8_6)
[14] X. Huang and Y. M. Xie, Evolutionary
Topology Optimization of Continuum
Structures: Methods and Applications.
Chichester: Wiley, 2010.
[15] M. P. Bendsøe and O. Sigmund, Topology
Optimization: Theory, Methods, and
Applications. (2nd ed.). Berlin: Springer, 2004.
[16] Y. M. Xie and G. P. Steven, Evolutionary
Structural Optimization. London: Springer,
1997.
[17] L. Xia, Q. Xia, X. Huang, and Y. M. Xie, “Bi-
directional evolutionary structural
optimization on advanced structures and
materials: a comprehensive review,” Archives
of Computational Methods in Engineering,
vol. 25, pp. 437–478, Nov. 2018. (DOI:
10.1007/s11831-016-9203-2)
[18] M. Y. Wang, X. Wang and D. Guo, “A level
set method for structural topology
optimization,” Computer Methods in Applied
Mechanics and Engineering, vol. 192, pp.
227–246, Jan. 2003. (DOI: 10.1016/S0045-
7825(02)00559-5)
[19] J. Ma, Z.-L. Zhao, S. Lin, and Y. M. Xie,
“Topology of leaf veins: experimental
observation and computational
morphogenesis,” Journal of the Mechanical
Behavior of Biomedical Materials, vol. 123,
Article 104788, Nov. 2021. (DOI:
10.1016/j.jmbbm.2021.104788)
[20] Z.-L. Zhao, S. Zhou, X.-Q. Feng, and Y. M.
Xie, “On the internal architecture of emergent
plants,” Journal of the Mechanics and Physics
of Solids, vol. 119, pp. 224–239, Oct. 2018.
(DOI: 10.1016/j.jmps.2018.06.014)
[21] Z.-L. Zhao, S. Zhou, X.-Q. Feng, and Y. M.
Xie, “Morphological optimization of scorpion
telson,” Journal of the Mechanics and Physics
of Solids, vol. 135, Article 103773, Feb. 2020.
(DOI: 10.1016/j.jmps.2019.103773)
[22] Y. Xiong, S. Yao, Z.-L. Zhao, and Y. M. Xie,
“A new approach to eliminating enclosed
voids in topology optimization for additive
manufacturing,” Additive Manufacturing, vol.
32, Article 101006, Mar. 2020. (DOI:
10.1016/j.addma.2019.101006)
[23] M. Bi, P. Tran, and Y. M. Xie, “Topology
optimization of 3D continuum structures
under geometric self-supporting constraint,”
Additive Manufacturing, vol. 36, Article
101422, Sept. 2020. (DOI:
10.1016/j.addma.2020.101422)
[24] Z. Zhuang, Y. M. Xie, and S. Zhou, “A
reaction diffusion-based level set method
using body-fitted mesh for structural topology
optimization,” Computer Methods in Applied
Mechanics and Engineering, vol. 381, Article
113829, Aug. 2021. (DOI:

Vol. 63 (2022) No. 4 December n. 214
12
10.1016/j.cma.2021.113829)
[25] T. Zegard, C. Hartz, A. Mazurek, and W. F.
Baker, “Advancing building engineering
through structural and topology
optimization,” Structural and
Multidisciplinary Optimization, vol. 62, pp.
915–935, Feb. 2020. (DOI: 10.1007/s00158-
020-02506-6)
[26] D. W. Bao, X. Yan, and Y. M. Xie, “Encoding
topological optimisation logical structure
rules into multi-agent system for architectural
design and robotic fabrication,” International
Journal of Architectural Computing, vol. 20,
pp. 7–17, Mar. 2022. (DOI:
10.1177/14780771221082257)
[27] Y. He, K. Cai, Z.-L. Zhao, and Y. M. Xie,
“Stochastic approaches to generating diverse
and competitive structural designs in topology
optimization,” Finite Elements in Analysis
and Design, vol. 173, Article 103399, June
2020. (DOI: 10.1016/j.finel.2020.103399)
[28] Q. Cai, L. He, Y. M. Xie, R. Feng, and J. Ma,
“Simple and effective strategies to generate
diverse designs for truss structures,”
Structures, vol. 32, pp. 268–278, Aug. 2021.
(DOI: 10.1016/j.istruc.2021.03.010)
[29] N. Aage, O. Amir, A. Clausen, L. Hadar, D.
Maier, and A. Søndergaard, “Advanced
topology optimization methods for conceptual
architectural design,” in Advances in
Architectural Geometry 2014, P. Block, J.
Knippers, N. Mitra, and W. Wang Eds. Cham:
Springer, 2015, pp. 159–179. (DOI:
10.1007/978-3-319-11418-7_11)
[30] E. Elsacker, A. Søndergaard, A. Van Wylick,
E. Peeters, and L. De Laet, “Growing living
and multifunctional mycelium composites for
large-scale formwork applications using
robotic abrasive wire-cutting,” Construction
and Building Materials, vol. 283, Article
122732, Feb. 2021. (DOI:
10.1016/j.conbuildmat.2021.122732)
[31] M. Gomaa, W. Jabi, A. Veliz Reyes, and V.
Soebarto, “3D printing system for earth-based
construction: case study of cob,” Automation
in Construction, vol. 124, Article 103577,
Apr. 2021. (DOI:
10.1016/j.autcon.2021.103577)
[32] M. Gomaa, W. Jabi, V. Soebarto, and Y. M.
Xie, “Digital manufacturing for earth
construction: a critical review,” Journal of
Cleaner Production, vol. 338, Article 130630,
Mar. 2022. (DOI:
10.1016/j.jclepro.2022.130630)
[33] V. Nguyen-Van, H. Nguyen-Xuan, B. Panda,
and P. Tran, “3D concrete printing modelling
of thin-walled structures,” Structures, vol. 39,
pp. 496–511, May 2022. (DOI:
10.1016/j.istruc.2022.03.049)
[34] J. B. Adewumi, J. T. Kolawole, M. J. Miah, S.
C. Paul, and B. Panda, “A concise review on
interlayer bond strength in 3D concrete
printing,” Sustainability, vol. 13, Article 7137,
June 2021. (DOI: 10.3390/su13137137)
[35] W. Li, X. Lin, D. W. Bao, and Y. M. Xie, “A
review of formwork systems for modern
concrete construction,” Structures, vol. 38, pp.
52–63, Apr. 2022. (DOI:
10.1016/j.istruc.2022.01.089)
[36] T. Xu, W. Shen, X. Lin, and Y. M. Xie,
“Additively manufactured thermoplastic
polyurethane (TPU) mold for concrete casting
of complex structure,” Rapid Prototyping
Journal, vol. 28, pp. 1717–1730, Apr. 2022.
(DOI: 10.1108/RPJ-11-2021-0307)
[37] J. Ma, Z. Li, Z.-L. Zhao, and Y. M. Xie,
“Creating novel furniture through topology
optimization and advanced manufacturing,”
Rapid Prototyping Journal, vol. 27, pp. 1749–
1758, Oct. 2021. (DOI: 10.1108/RPJ-03-
2021-0047)
[38] Y. He, Z.-L. Zhao, K. Cai, J. Kirby, Y. Xiong,
and Y. M. Xie, “A thinning algorithm based
approach to controlling the structural
complexity in topology optimization,” Finite
Elements in Analysis and Design, vol. 207,
Article 103779, Sept. 2022. (DOI:
10.1016/j.finel.2022.103779)