ArticlePDF Available

Abstract and Figures

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.
Content may be subject to copyright.
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
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:
2Postdoctoral Researcher, Centre for Innovative Structures and Materials, School of Engineering, RMIT University,
Melbourne, 3001, Australia. Email:
3Lecturer, School of Architecture and Urban Design, RMIT University, Melbourne 3001, Australia. Email:
4Postdoctoral Researcher, Centre for Innovative Structures and Materials, School of Engineering, RMIT University,
Melbourne, 3001, Australia. Email:
5Distinguished Professor, Centre for Innovative Structures and Materials, School of Engineering, RMIT University,
Melbourne, 3001, Australia. Email:
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.
Digital Object Identifier to be provided by Editor when assigned upon publication
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
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
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
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.
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
The design space
of a slab model can be
discretized into n elements. Each element i is
assigned a design variable
for material updates. In
the BESO framework, the design variable
can be
a bilateral value of one or
, which is close to
zero. The SIMP framework relaxes the
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
in : ( )
s.t. : ( )
: =
0 : 1, 1, 2,
i i
i n
where compliance
is the work of external force,
is the global displacement vector,
is the global
stiffness matrix,
is the force vector,
is the
elemental volume, and
is the target volume
fraction of rib material. The elemental sensitivity can
be yielded as
i i i i
u k u
represent Young’s moduli of rib and
void materials, p is a penalization number,
is the
elemental displacement vector, and
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
2.1. Constraint mapping
A planar design vector
{ | 1,2,3,..., }
x j n t
defined within the rib design domain
to constrain
elements on the same in-plane position to have the
same design variables:
( 1, 2,3,..., | 1,2,3,..., )
j j r
x n t
j l t
are the number of layers in
, as illustrated in Figure 2(b).
The elemental sensitivities in
are averaged
according to Equation 4 to update the planar design
in topology optimization.
j j r
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
, 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
The procedures for every iteration are as follows:
1) Perform the finite element analysis based on
the current design
2) Calculate the objective function C, the
elemental sensitivities
, and the constraint
3) Calculate the averaged sensitivities
constraint mapping.
4) Obtain structural skeleton and boundary
elements within
5) Update
according to
using BESO with
6) Update
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
as well as sensitivity labeling
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
and five layers of
elements are assigned to the design domain
ribs to ensure the accuracy of the bending analyses.
The target volume of the ribs in
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.
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
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
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
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.
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
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.
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)
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
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.
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.
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.
The results and the basic code of this work are
available from the corresponding author upon
reasonable request.
[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,
[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.
[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,
[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] H. Nooshin, R. Kamyab, and O. A. Samavati,
“Exploring scallop forms,” International
Journal of Space Structures, vol. 32, pp. 84–
111, July 2017. (DOI:
[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:
[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,
[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:
[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-
[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:
[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:
[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:
[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
[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-
[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:
[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:
[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:
[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:
[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:
[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:
[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:
[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-
[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:
ResearchGate has not been able to resolve any citations for this publication.
Full-text available
Shape and topology optimization techniques aim to maximize structural performance through material redistribution. Effectively controlling structural complexity during the form-finding process remains a challenging issue. Structural complexity is usually characterized by the number of connected components (e.g., beams and bars), tunnels, and cavities in the structure. Existing structural complexity control approaches often prescribe the number of existing cavities. However, for three-dimensional problems, it is highly desirable to control the number of tunnels during the optimization process. Inspired by the topology-preserving feature of a thinning algorithm, this paper presents a direct approach to controlling the topology of continuum structures under the framework of the bi-directional evolutionary structural optimization (BESO) method. The new approach can explicitly control the number of tunnels and cavities for both two- and three-dimensional problems. In addition to the structural topology, the minimum length scale of structural components can be easily controlled. Numerical results demonstrate that, for a given set of loading and boundary conditions, the proposed methodology may produce multiple high-performance designs with distinct topologies. The techniques developed from this study will be useful for practical applications in architecture and engineering, where the structural complexity usually needs to be controlled to balance the aesthetic, functional, economical, and other considerations.
Full-text available
Purpose: Irregularly shaped architectural designs with surfaces curved in multiple directions, known as free-form designs, have gained significant public interest in recent decades. However, it is challenging to convert complex designs into real structures. This paper aims to realize free-form construction by developing a novel workflow in which additively manufactured thermoplastic polyurethane (TPU) molds are used. Design/methodology/approach: The workflow is developed through mechanical tests on additively manufactured TPU specimens, determination of TPU mold design criteria and exploration of mold preparation methods. Two concrete elements with free-form geometries are fabricated using the proposed workflow. Findings: TPU is a thermoplastic elastomer that is strong and inexpensive, making it an ideal mold material for casting complex concrete structures. An innovative workflow is developed in which TPU molds are used, appropriate release agents are selected for different concrete casting conditions and a mold subdivision method is proposed to facilitate the demolding process. Furthermore, the integrity of TPU molds can be maintained by following the proposed workflow, enabling repetitive use of molds. The fabrication of the two free-form structures shows that complex concrete members with high dimensional accuracy and excellent surface quality can be manufactured using the proposed method. Originality/value: To the best of the authors’ knowledge, this is the first systematic study on using additively manufactured TPU molds for concrete casting of complex structures. The new techniques developed in this research can be applied to large-scale architectural, engineering and construction projects.
Full-text available
Failures induced by either instability (elastic buckling) or green strength (plastic collapse) mechanisms have been commonly encountered in 3D concrete printed (3DCP) structures. In this work, a numerical model of the 3D concrete printing process is implemented to simulate these two failure mechanisms. Early-age mechanical properties of two printable mixes are used as input data for the simulation. The finite element (FE) modelling is then validated by comparison with 3DCP experiments of a hollow cylinder. The numerical analysis program can accurately predict the deformation and its failure modes during the 3D concrete printing process. Besides, the FE model is also used for validating a printed free thin wall. Further, sensitivity and parametric analyses are investigated to unveil the influence of printing process parameters, i.e., printing speed, extrusion width, and different mesh sizes on buildability.
Full-text available
Natural phenomena have been explored as a source of architectural and structural design inspiration with different approaches undertaken within architecture and engineering. The research proposes a connection between two dichotomous principles: architectural complexity and structural efficiency through a hybrid of natural phenomena, topology optimisation and generative design. Both Bi-directional Evolutionary Structural Optimisation (BESO) and multi-agent algorithms are emerging technologies developed into new approaches that transform architectural and structural design, respectively, from the logic of topology optimisation and swarm intelligence. This research aims to explore a structural behaviour feedback loop in designing intricate functional forms through encoding BESO logical structure rules into the multi-agent algorithm. This research intends to study and evaluate the application of topology optimisation and multi-agent system in form-finding and later robotic fabrication through a series of prototypes. It reveals a supposition that the structural behaviour-based design method matches the beauty and function of natural appearance and structure. Thus, a new exploration of architectural design and fabrication strategy is introduced, which benefits the collaboration among architects, engineers and manufacturers. There is the potential to seek the ornamental complexities in architectural forms and the most efficient use of material based on structural performance in the process of generating complex geometry of the building and its various elements.
Full-text available
Concrete is a principal construction material in building industry. Formwork plays an important role in assisting geometry realisation and strength development of concrete elements. It is also one of the major costs in the construction of concrete structures. The use of formwork has a long history, and various formwork systems have been used in different projects. In the design and selection of formwork system, the requirements, such as safety, cost, structural geometry, construction time and surface quality need to be taken into account. This paper presents a comprehensive review of various formwork systems in concrete construction, including their raw materials, flexibility, fabrication methods, applications in concrete structures and environmental impacts. The advantages and current limitations of different formwork systems are compared and discussed, and finally recommendations are given.
Full-text available
Recent years have witnessed a rapid adoption of digital manufacturing techniques in the architecture and construction industry, with a strong focus on additive manufacturing and 3D concrete printing. The increasing awareness of the undesirable environmental implications of cement-based products has led to reapproaching earth materials within a digitally based construction process. The attempts to digitise earth construction started in 2011; however, the past three years have seen a surge in the number of research projects that explore the potentials of digital earth construction. This paper collected, reviewed and analysed the state-of-the-art research on digital earth construction since 2011, then focused on highlighting the potential of, as well as the challenges associated with the process of adopting this new construction method on an industrial scale. The insights from this study will bridge the gaps in knowledge among disparate research threads and collectively provide critical information for an enhanced utilisation of digital techniques in earth construction in the future.
Full-text available
Purpose Furniture plays a significant role in daily life. Advanced computational and manufacturing technologies provide new opportunities to create novel, high-performance and customized furniture. This paper aims to enhance furniture design and production by developing a new workflow in which computer graphics, topology optimization and advanced manufacturing are integrated to achieve innovative outcomes. Design/methodology/approach Workflow development is conducted by exploring state-of-the-art computational and manufacturing technologies to improve furniture design and production. Structural design and fabrication using the workflow are implemented. Findings An efficient transdisciplinary workflow is developed, in which computer graphics, topology optimization and advanced manufacturing are combined. The workflow consists of the initial design, the optimization of the initial design, the postprocessing of the optimized results and the manufacturing and surface treatment of the physical prototypes. Novel chairs and tables, including flat pack designs, are produced using this workflow. The design and fabrication processes are simple, efficient and low-cost. Both additive manufacturing and subtractive manufacturing are used. Practical implications The research outcomes are directly applicable to the creation of novel furniture, as well as many other structures and devices. Originality/value A new workflow is developed by taking advantage of the latest topology optimization methods and advanced manufacturing techniques for furniture design and fabrication. Several pieces of innovative furniture are designed and fabricated as examples of the presented workflow.
Conference Paper
Full-text available
This study addresses the relationship between the geometry and structural performance of branching columns using an example case based on a square grid shell supported by four branching columns. The branching columns are configured with three levels of members, bifurcating into four members as each member branches upwards. A range of solutions is parametrically generated using the concepts of formex algebra and its associated software system, Formian 2.0. The form exploration uses the GA-based method, ParaGen which incorporates both quantitative structural performance and qualitative architectural considerations in the exploration process. Certain design constraints, as well as multiple objectives, are established including minimizing structural weight and deflection, and increasing vibration stiffness, in addition to the designer’s satisfaction with the visual appearance of the columns. Within the iterative process of form generation, the structural performance of the branching columns under a combination of self-weight and snow load is evaluated using the Finite Element Analysis (FEA) software, STAAD.Pro. The branching members are sized based on the AISC LRFD steel code. ParaGen creates a database of suitable solutions, which can be explored by filtering and sorting based on a variety of performance parameters. Different techniques are demonstrated in the exploration of good solutions including scatter point graphs, Pareto front analysis, and images of the design alternatives.
Full-text available
The unique, hierarchical patterns of leaf veins have attracted extensive attention in recent years. However, it remains unclear how biological and mechanical factors influence the topology of leaf veins. In this paper, we investigate the optimization mechanisms of leaf veins through a combination of experimental measurements and numerical simulations. The topological details of three types of representative plant leaves are measured. The experimental results show that the vein patterns are insensitive to leaf shapes and curvature. The numbers of secondary veins are independent of the length of the main vein, and the total length of veins increases linearly with the leaf perimeter. By integrating biomechanical mechanisms into the topology optimization process, a transdisciplinary computational method is developed to optimize leaf structures. The numerical results show that improving the efficiency of nutrient transport plays a critical role in the morphogenesis of leaf veins. Contrary to the popular belief in the literature, this study shows that the structural performance is not a key factor in determining the venation patterns. The findings provide a deep understanding of the optimization mechanism of leaf veins, which is useful for the design of high-performance shell structures.
Full-text available
Interlayer bond strength is one of the key aspects of 3D concrete printing. It is a well-established fact that, similar to other 3D printing process material designs, process parameters and printing environment can significantly affect the bond strength between layers of 3D printed concrete. The first section of this review paper highlights the importance of bond strength, which can affect the mechanical and durability properties of 3D printed structures. The next section summarizes all the testing and bond strength measurement methods adopted in the literature, including mechanical and microstructure characterization. Finally, the last two sections focus on the influence of critical parameters on bond strength and different strategies employed in the literature for improving the strength via strengthening mechanical interlocking in the layers and tailoring surface as well as interface reactions. This concise review work will provide a holistic perspective on the current state of the art of interlayer bond strength in 3D concrete printing process