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Bioinspired Generative Architectural Design Form-Finding and Advanced Robotic Fabrication Based on Structural Performance


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Due to the potential to generate forms with high efficiency and elegant geometry, topology optimization is widely used in architectural and structural designs. This paper presents a working flow of form-finding and robotic fabrication based BESO (Bi-directional Evolutionary Structure Optimization) optimization method. In case there are some other functional requirements or condition limitations, some useful modifications are also implemented in the process. With this kind of working flow, it is convenient to foreknow or control the structural optimization direction before the optimization process. Furthermore, some fabrication details of the optimized model will be discussed because there are also many notable technical points between computational optimization and robotic fabrication.
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Bioinspired Generative Architectural Design
Form-finding and Advanced Robotic
Fabrication Based on Structural Performance
Ding Wen BAOa,b,1, Xin YANa,c,1, Roland SNOOKSb (), Yi Min XIEa ()
a Centre for Innovative Structures and Materials, School of Engineering, RMIT
Melbourne, 3001, Australia
b School of Architecture and Urban Design, RMIT University,
Melbourne, 3001, Australia
c Centre of Architecture Research and Design, University of Chinese Academy of
Beijing, 100190, China
1 These authors contributed equally to this work.
Abstract. Due to the potential to generate forms with high efficiency and elegant
geometry, topology optimization is widely used in architectural and structural de-
signs. This paper presents a working flow of form-finding and robotic fabrication
based BESO (Bi-directional Evolutionary Structure Optimization) optimization
method. In case there are some other functional requirements or condition limita-
tions, some useful modifications are also implemented in the process. With this kind
of working flow, it is convenient to foreknow or control the structural optimization
direction before the optimization process. Furthermore, some fabrication details of
the optimized model will be discussed because there are also many notable technical
points between computational optimization and robotic fabrication.
Keywords: generative design, form-finding, BESO method, robotic fabrication,
topological optimization, 3d printing, pavilion
Article published in
Architectural Intelligence, pp 147 - 170, 2020, Springer
1 Introduction
Throughout the history of architecture, there is always a close relationship between
the development of traditional architectural forms and the evolution of structural
morphology. From Rome to Gothic, the popular architecture prototype changes
from barrel arch to pointed arch based on the technology of flying buttress. Simi-
larly, after the Renaissance, many physical analysis methods are developed to help
architects to achieve more complex architecture forms structurally, like graphic stat-
ics and inverse lifting models by Antonio Gaudi. Furthermore, after Modernism, the
new construction techniques with glass and steel make the international style pop-
ular over the world. Recently, with the fast development of computational tech-
niques, the topic of form-finding based on structural performance has gained new
momentum [1]. Not only researchers have focused their view on structural form-
finding methods, but also many architects are attracted because it can generate
forms with a characteristic of high structural efficiency and more elegant shape po-
Among the form-finding methods, the topology optimization method of ESO
(Evolutionary Structural Optimization), developed by YM Xie and GP Steven in
1993 [2] and its modified version, known as BESO (Bi-directional evolutionary
structural optimization), published in 2006 [3], are widely implemented in architec-
ture practices, such as Qatar National Convention Centre and Shanghai Himalayas
With the further development of Ameba, a new GH plugin based on BESO al-
gorithm by YM Xie and his team [4], more and more architects and designers will
have opportunities to use a new intelligent method to work with the computer inter-
actively, to create innovative, efficient and organic architectural forms and facilitate
the realization of mass customization in the construction industry through the intro-
duction of advanced 3D printing technologies, such as large robotic 3D printing and
some hybrid fabrication strategies developed by Roland Snook and his research
team in RMIT Architectural Robotic Lab. The concept of topological optimization
and the inspiration of Gaudi’s Sagrada Familia Basilica will be reflected through
the pavilion form-finding and its optimization. The new approach of generative ar-
chitectural design and fabrication will be introduced in this project, which explores
the architectural implications of topological optimization design through robotic 3D
2 Basic Theory of BESO Method
BESO algorithm aims to find the solution with the highest structural performance
under certain material limitations by removing or adding material elements step by
step. The basic problem can be described mathematically as follows:
xC ukuKUUX
)( min
subject to
in which C, U, K, and X are the objective function (compliance), displacement
vector, global stiffness matrix, the objective volume and the global design variable
vector, respectively. The terms , , and are the volume, design variable,
stiffness matrix and nodal displacement vector for i th element. Furthermore, there
are only two alternative values for in BESO, which are 1 for the solid element or
prescribed value  for the void element.
For stiffness optimization problem, the sensitivity for i th element, which is
the criterion for design variable , can be calculated as the gradient of compliance
with respect to the design variable [5],
1 n whe
And when the penalty coefficient p tends to infinity, the sensitivity number be-
comes the one in hard-kill BESO method [5], i.e.,
1 when 1
0 when 0
i ii i
px xx
= =
u ku
The above sensitivity is usually modified to solve the mesh-dependent problem
[6,7] using a filtering scheme with
rw =
in which  is the distance between the centre of the j th element and the i th ele-
ment and
, is the filter radius and the original sensitivity of the j th element.
To achieve a convergent solution, another historical average,
, indifferent itera-
tions are introduced [8], i.e.,
In BESO method, the element sensitivities are ranked in each iteration to determine
a threshold with a target volume of next iteration, (), which is defined based on
the current volume (−1) and the evolutionary ratio δ.
The threshold can be used to evaluate if the element shall be changed in such a way
that if one solid element’s sensitivity is lower than the threshold, its design variable
will be the switch from 1 to , and the design variable of a void element will be
changed from  to 1 as well if its sensitivity is higher than the threshold.
3 Form-finding based on BESO
In this work, a pavilion structure is introduced to make a discussion about the BESO
form-finding details for architecture. There are mainly three steps in the form-find-
ing process:
1. Model definition
2. BESO topology optimized iterations
3. Post-modification
To generate an optimized model with not only high structural performance but
also some other characteristics to meet other functional requirements or aesthetic
preferences, there are many detail modifications which we should pay much atten-
tion to during the process.
3.1 Model Definition
BESO method is an FEA (Finite Element Analysis) based iterative process. The
BESO sensitive number, which is the criterion to add or remove the elements, is
also calculated with the data of FEA result. Therefore, defining an appropriate FEA
model is a fundamental work for BESO algorithm.
3.1.1 Initial Geometry
Before generating the FEA mesh, the initial geometry should be made as accurately
as possible if there is a rough objective form. Theoretically, BESO object is to find
the best answer within a solution domain about the material distribution, and we can
shrink the initial material distribution possibilities by modifying the initial geometry
to fit the objective form. In this pavilion design, with the inspiration of Gaudi’s
Sagrada Familia Basilica, the concept of this pavilion is to generate a tree-like struc-
ture form (Fig. 3.1).
Fig. 3.1 Natural tree branch (left), columns in Sagrada Familia Basilica (middle)
and one structure in this pavilion (right)
If the initial geometry were designed as a solid block (Fig. 3.2-a), BESO algo-
rithm would generate the form with the highest structural stiffness in Fig. 3.2-b,
which is far from the design concept. Therefore, to produce the branch-like supports
and leave enough space for visitors to go through, the initial geometry should be
modified with some cavities and thin columns (Fig. 3.3).
(a) Initial geometry (b) BESO optimized model
Fig. 3.2 The initial geometry without modification and its BESO result
(a) Initial geometry (b) BESO optimized model
Fig. 3.3 The modified initial geometry and its BESO result
3.1.2 Mesh Discretization
Another way to manually predesign the BESO result is to modify the calculation
mesh. In BESO method for continuum structures, the main element types of FEA
calculation mesh are solid for block structures or shell for surface structures, respec-
tively. For this pavilion design, considering symmetric geometry and boundary con-
ditions of the structure, only a quarter is generated with solid elements in the mesh
discretization process.
In BESO method, the structure evolves based on the element addition or deletion
so that the element size can influence the structure details on some level with a
proper BESO filter radius. In other words, the smaller the element size and the filter
radius are, the more details can be generated using BESO.
Furthermore, some mesh modification can also help us to control the final model.
For example, a space near the symmetric plane is imposed to interrupt some certain
force paths (Fig. 3.5) in case the unsafe horizontal beam (Fig. 3.4) occurs.
(a) Initial design mesh (b) BESO optimized model
Fig. 3.4 Initial mesh and BESO result without modification
(a) Initial design mesh (b) BESO optimized model
Fig. 3.5 Initial mesh and BESO result with modification
3.1.3 Material Property
The material property setting is another important aspect of FEA modelling. Differ-
ent material properties can also influence the BESO result indirectly. In the finite
element analysis, the material is assumed to be homogenous. For the homogenous,
isotropic, and linearly elastic materials, there are two main parameters, Young’s
modulus and Poisson's ratio. For the model with only one material, the BESO results
will change if they are assigned with different Poisson's ratios (Fig. 3.6) or Young’s
moduli (Fig. 3.7), and Poisson’s ratio has a closer correlation with BESO result than
Young’s modulus.
Fig. 3.6 BESO result with different Poisson’s ratios
(0.15 for the left, 0.30 for the middle and 0.45 for the right)
Fig. 3.7 BESO result with different Young’s moduli
(0.01GPa for the left, 1GPa for the middle and 100GPa for the right)
However, for the model with multi-materials, different relative material Young’s
modulus can be designed purposely to generate different forms. For example, Fig.
3.8 shows a control experiment about façade topology optimization. The initial de-
sign domain is divided into two parts, the non-design domain and the design do-
main. One bottom corner is fixed in all three displacement directions, and the non-
design domain is assigned with uniform pressure. The optimized structures vary
significantly with the different materials assigned to the non-design domain. Spe-
cifically, the following figures show the different results with different Young’s
modulus value of the non-design domain, and it can be concluded that with a de-
crease of non-design domain’s Young’s modulus, there will be an increase in the
area of the branch structure’s top to hold the soft materials.
Fig. 3.8 Initial FEA model settings
(a) 100GPa (b) 10GPa (c) 1GPa (d) 0.1GPa (e) 0.01GPa
Fig. 3.9 BESO result with different Young’s moduli of non-design domains
3.1.4 Load Case and Boundary Condition
Different from the above geometry part, load case and boundary condition are the
force defining part in FEA process, which can make significant influences on BESO
results. Load Case
Load case and boundary condition are two aspects in FEA to define the force field
where the model is located. Also, some impressive points can be concluded to de-
scribe the relationship between BESO results and the force field.
In architecture design, concentrate load and distributed load are two load types
which are usually used to define load cases. For concentrate load, especially pointed
load, materials always tend to concentrate around the local area where the concen-
trated load acts and form a local structure in the load direction to support that load.
While the distributed load, especially pressure, usually acts on a surface which is
treated as a non-design domain in BESO and supported by some branches in the
final BESO results.
Fig. 3.10 Initial model with pointed load and its BESO result
Fig. 3.11 Initial model with pointed load and its BESO result Boundary Condition
It is well-known that one point has six degrees of freedom in 3D space, including
three displacements and three rotations. Boundary conditions describe which direc-
tions are fixed in the model boundaries. The boundary condition should be made
based on the physical conditions around the model. However, when designing a
form, the BESO results can be different with various boundary conditions.
For example, BESO algorithm may generate some structures in certain directions
to resist the displacements or rotations of the boundary if there is not any constraint
in that direction. In the pavilion design, if the bottom corners are only fixed in z
directions, the ring beam at the bottom will be generated to resist the horizontal
displacements of the bottom. However, if the bottom points are pinned in three dis-
placement directions, the ring beam will be unnecessary and avoided by BESO.
Fig. 3.12 BESO results with different boundary conditions
3.2 BESO topology optimized iterations
Besides the above details in FEA model definitions, BESO algorithm also provides
users with some algorithm constraints and parameters to modify the designs. In the
past ten years, the topic of modifying the topology optimization method to solve
some specific problems, such as generating symmetric or periodic structures, print-
ing concrete and reserving functional parts, has attracted many attentions. In the
process of this pavilion form-finding, the modifications about the non-design do-
main and symmetric constraint have been introduced. And adjustments of BESO
parameters, such as filter radius (FR), evolution ratio (ER) and volume fraction (VF)
are also considered.
3.2.1 BESO Parameters
BESO main parameters are evolution ratio (ER), filter radius (FR) and volume frac-
tion (VF), describing the number of variable elements, the sample range of averag-
ing sensitivity number and the volume of the final model, respectively. Evolution Ratio (ER)
With different ER values, the topology optimization process will be completed in a
different time, and the results can also be different significantly. It is because, with
a large evolution ratio, the number of variable elements in each iteration will in-
crease too much to get the global optimized structure. In traditional topology opti-
mization theory, to achieve getting effective structures, ER value is suggested
smaller than 5% and as small as possible. However, for designers, the global opti-
mized structure is not necessary sometimes and changing ER value comes to be a
simple way to generate diversity local optimized results with similar structural per-
formances, although a little lower than the global best one.
Fig. 3.13 The BESO results with different ER values
(from left to right 4% 2% 1%)
Table 3.1 Iterations and compliances of BESO processes with different ER values
ER = 4%
ER = 2%
ER = 1%
0.603 Filter Radius (FR)
Filter radius (FR) is vital in predesigning the BESO result. In topology optimization
theory, the filter radius is introduced to solve the checkboard problem. However,
from the appearance of the final results, the filter radius can be used to predesign
the minimum size of whole structure details. As what the following figures show,
the BESO results of the same model can be different with different filter radiuses.
Fig. 3.14 The BESO results with different FR values
(from left to right 16mm, 24mm, 32mm and 40mm)
Table 3.2 Iterations and compliances of BESO processes with different FR values
0.797 Volume Fraction (VF)
Volume fraction (VF) is the parameter to define the remaining part’s number, and
it is comprehensible that volume fraction has an obvious influence on BESO results.
However, there are also two points should be treated carefully. The first one is that
for some model, VF value cannot be too small in case the whole structure collapses
due to lack of materials. The other one is that the shell element model is easier to
get transparent holes than solid element model with the same VF value, while solid
element model can represent which parts should be thicker than other parts.
Fig. 3.15 The BESO result of the top surface with solid elements
Fig. 3.16 The BESO result of the top surface with shell elements
3.2.2 Algorithm Constraint
The three above parameters are the normal parameters in traditional BESO algo-
rithm, and there are also many types of research about the algorithm modifications
in topology optimization. For the pavilion design in this paper, two main algorithm
constraint parts are as follows. Non-design Domain
For some functional requirements, there are always some local parts which should
be reserved during the topology optimization process. Therefore, BESO method
permits the users to set the non-design domain in the initial model, which will take
part in the FEA calculation but will be reserved in the following optimization
iterations. To generate the tree-like structures in the pavilion, the initial domains are
set as Fig.3.17.
Fig. 3.17 The initial domain's settings of the pavilion Symmetric Constraint
Because of the symmetric characteristic, this pavilion needs to be kept symmetrical
during the iterations. However, numerical calculation errors or odd void element
numbers may cause asymmetries to the whole model. In BESO, there is also a con-
straint function to keep the model symmetrical all the time.
Fig. 3.18 The BESO result without symmetric constraint
Fig. 3.19 The BESO result with symmetric constraint
3.3 Post-modification
It is easy to see that the rough mesh model optimized by BESO method cannot
satisfy the atheistic and fabrication requirements for architecture. As a result, the
optimized mesh model should be modified carefully after the optimization for the
following fabricating works.
3.3.1 Mesh Smooth
For finite element analysis, the calculation mesh is composed of some fundamental
elements, such as triangles or quadrangles for shell and cubes or tetrahedrons for
solid. As a result, the BESO model is always a mesh with a coarse, irregular surface.
Fortunately, the GH plugin, Ameba, has a really strong mesh optimization functions
to deal with that problem. With the help of Ameba mesh tools, it is easy to get a
smooth mesh model for the following fabrication works [9].
Fig. 3.20 The smooth mesh workflow in Ameba
Fig. 3.21 The pavilion generation process
3.3.2 Over-hanging
In this pavilion work, large 3D printing techniques are implemented. The current
technique has some printing limitation by the issue of large overhang angles without
any supporting material, so the model should be modified to avoid large draft angles
in the model. The maximal overhang angles are 32 degrees.
3.3.3 Fine-tuning based on the feedback of FEA analysis
Once the form of pavilion is finalised, it has been imported into Abaqus for finite
element analysis to get the more accurate structural performance feedback which
helps to re-test and fine-tune the form to fix some structural defects and ensure the
pavilion has a better structural performance based on keeping the basic generated
geometry (Fig. 3.22).
(a) Displacement (b) Mies Stress (c) Strain Energy Density
Fig. 3.22 FEA analysis
4 Advanced Robotics Fabrication
Fig. 4.1 The digital model of the innovative pavilion for fabrication
The digital pavilion structure (Fig. 4.1 left) is finalized based on generative method
topological optimization. To fabricate it, it has been further designed for fabrication
and construction that includes main three parts: top transparent 12mm thickness
acrylic panel, 3d printing main structural bodies and timber base (Fig 4.1 right).
4.1 Application of KUKA Robotics
Fig. 4.2 RMIT Architectural Robotic Lab
The Architectural Robotic Lab (Fig.4.2) sits within the RMIT University School of
Architecture, and Urban Design directed by Associate Professor Roland Snooks
leads the school’s development of architectural robotic research and advises on the
development of its infrastructure. The lab consists of nine industrial robots ranging
in scales from a large Kuka KR 150 mounted on a five-meter track, down to small
UR10 robots. Currently, the main robotic research is primarily focused on large 3D
printing of polymers. Roland Snooks and his team have developed a series of inno-
vative 3D printing technologies to build up several pilot project and large-scale pro-
totypes, such as Monash SensiLab (2017) and NGV Floe pavilion (2018) [10].
4.1.1 Advantages of Robotic 3D printing
Fig. 4.3 The eight pieces of components of the pavilion structure
The innovative technology that combines KUKA KR 150 6 axis robot with a 3D
polymer printing extruder is applied on printing large scale prefabricated building
components. The folding, corrugated, translucent printed polymer components can
refract intricate patterns of light and create varying transparencies. The X-Form 1.0
pavilion was printed in 8 pieces with non-screw joint connections (Fig.4.3). This
updated “start-stop” 3D polymer printing approach is a development from previous
one-curve continuous printing path. It achieves the aim of printing fractal-like
geometries. The total printing time is 64 hours, including four upper part tree col-
umns and four lower part base columns (Fig. 4.4).
4.2 Modified Printing Path Code for fractal-like geometries
Fig. 4.4 The digital model of fractal-like structure & grasshopper simulation
4.2.1 Start-Stop script development
Fig. 4.5 The updated start-stop script based on grasshopper KUKA PRC
Due to the tree branches system of the pavilion columns, the new start-stop script
can achieve the aim of printing fractal-like forms. The script is originally written in
C# code by Roland Snooks’s research team (Fig.4.5).
4.2.2 Import the printing file into KUKA machine & run printing
Firstly, the geometry needs to be imported into rhino/grasshopper. Later, the code
convert geometry into the mesh, slice it in the Z direction and generates the printing
file “prc_kuka.src” based on the printing parameters (speed, layer height, tempera-
ture. etc.). Import the generated .src file into KUKA and run the machine. (Fig 4.6)
Fig. 4.6 The process of robotic large 3D printing using updated code
4.3 Printing Parameters
Fig. 4.7 Testing results of polymer materials with various parameters
Materials behaviour in the printing process is an important factor that impacts the
quality of the printing result. Due to some uncontrollable factors, it is hard to avoid
uncertainty, such as the interior humidity, temperature, old/new plastic. However,
it can decrease the risk of uncertainty through repeated experiments and data record.
The main factors include printing speed, layer height, bead size, extrude tempera-
ture and purging step. From table (Fig.4.7), stability of printing will be significantly
influenced by printing speed once it is more than 200 mm/s; the Z height impacts
the stability and speed of printing, and bead size will cause the thickness of extru-
sion; one of the most influent parameters is extruded temperature, it significantly
affects the transparency of printing result. Thus, the most successful result is with
the 60 mm/s, 2.8mm Z-height, 4.2 bead size and 210 degrees extrude temperature
[10]. The purging step is important that can clean the nozzle and ensure the fused
polymer extruded from nozzle equally and smoothly. (Fig. 4.8)
Fig. 4.8 Printing examples with various qualities (from left to right: bad to good)
4.4 Joint Design & Assembly Methodologies
Fig. 4.9 Plug-in joint design for connecting lower part and upper part structures
There are two types of joints design applied to this pavilion. One is the plug-in joint
design without any screws. The plug-in joint provides convenience for connecting
the lower and upper part of structures through printing an internal offset layer and
inserting the lower part tubes into the upper part tubes. (Fig. 4.9). The other joint
design is applied to the connection between the top panel and structure branches.
Instead of screws, nails and glues, the white reusable cable ties are used to tie up
through the reserved holes on 3d printing structures, and laser-cut acrylic top panel
(Fig. 4.10).
Fig. 4.10 white cable plastic ties are applied on connecting top panel and structure
Due to the efficient fabrication process by large-scale robotic 3D printing in the lab,
the construction process only took one hour to assemble the whole pavilion by five
students supervised by authors. Five students elevated the upper parts of structures
up to 1 meter, then authors moved the lower part columns to the corresponding
location, and let lower columns are plugged into the columns of the upper part (Fig.
Fig. 4.11 on site assembly process
5 Conclusion and Future works
Fig. 5.1 The final built pavilion (2m x 2m x 2.5m)
The paper explores the integration of emerging technologies in both digital design
and advanced manufacturing, respectively topological optimization-based genera-
tive architectural forming finding and advanced robotic large 3D printing fabrica-
tion. In this work, a pavilion is introduced to demonstrate the combination of new
design & construction techniques and explain the design & construction process
(Fig. 5.1).
Pavilion X-Form 1.0 is an experimental prototype which tested how important role
the optimized structure play in architectural form-finding (Fig 5.2). The Bi-direc-
tional Evolutionary Structural Optimization (BESO) method provides not only an
efficient structure but also elegant architectural form. The integrated technologies
have the potential to serve the building industry due to its capability of producing
large-scale free form architectural components with high structural performance
and efficient materials.
In a further study, major barriers to the implementation of these technologies in the
building industry will be resolved to apply this new technology widely to the mass
customized design and manufacturing in the building industry. Also, the further re-
search project X-Form 2.0 will be investigated and focus on more complex topo-
logical optimization form-finding, curved top panel, and more advanced 3D printing
Fig. 5.2 The X-Form 1.0 pavilion in the Digital FUTURES 2019 exhibition
(From left to right: Feng ‘Philip’ Yuan, Wen Jun Zhi, Dingwen ‘Nic’ Bao, Mark
Burry, Yi Min ‘Mike’ Xie, Xin Yan, Tong Yu Sun)
The authors would like to thank several colleagues whose support helped fulfil the
research project described in this paper:
Professor Feng PhilipYuan (Archi Union, Fab Union, DigitalFU-
TURES, Tongji University)
Professor Yi Min MikeXie (Centre for Innovative Structures & Materi-
als, RMIT University)
Associate Professor Roland Snooks (School of Architecture and Urban
Design, RMIT University)
Dr Jiawei Yao, Dr Xiang Wang, Miss Reina Zhewen Chen (Tongji Uni-
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... Both ESO and BESO algorithms are based on finite element analysis (FEA) for topology optimisation of continuum structures. BESO algorithm aims to find the solution with the highest structural performance under certain material limitations by removing or adding material elements step by step (Bao et al., 2020). The ESO method also inspires the Extended ESO method, widely used in architecture design projects, such as the Akutagawa River Side Project in Japan by Ohmori and Qatar National Convention Centre by Arata Isozaki, to generate an optimised model with not only high structural performance but also some different characteristics to meet more functional requirements or aesthetic preferences. ...
... OptiGAN demonstrates the ability of a novel approach and its application in architectural and structural form-finding. It is the extension of the SwarmBESO (multiagent-based topology optimisation) method proposed by Bao & Yan in 2020 to improve the diversity of the topological optimisation generative method. It has the potential to significantly help architects and engineers save material and produce more efficient structural layouts and building envelopes. ...
Conference Paper
Full-text available
With the rapid development of computers and technology in the 20th century, the topological optimisation (TO) method has spread worldwide in various fields. This novel structural optimisation approach has been applied in many disciplines, including architectural form-finding. Especially Bi-directional Evolutionary Structural Optimisation (BESO), which was proposed in the 1990s, is widely used by thousands of engineers and architects worldwide to design innovative and iconic buildings. To integrate topological optimisation with artificial intelligence (AI) algorithms and to leverage its power to improve the diversity and efficiency of the BESO topological optimisation method, this research explores a non-iterative approach to accelerate the topology optimisation process of structures in architectural form-finding via conditional generative adversarial networks (GANs), which is named as OptiGAN. Trained with topological optimisation results generated through Ameba software, OptiGAN is able to predict a wide range of optimised architectural and structural designs under defined conditions.
... TO is a type of computational method that allows to obtain the optimal distribution of the material in a given design space for a specific set of constraints (e.g., loads, boundary conditions) [1,2]. TO has a wide range of applications in multiple disciplines such as automotive [3,4], aerospace [5,6], architecture [7,8], biomedical engineering [9,10] and engineering structures design [11][12][13][14]. The use of TO in the designing process enables a significant reduction in the mass of the designed product while maintaining the desired strength properties and stiffness. ...
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This article aims to review a redesign approach of a student racing car’s clutch lever component, which was topologically optimized and manufactured by Additive Manufacturing (AM). Finite Element Method (FEM) analysis was conducted before and after a Topology Optimization (TO) process in order to achieve equivalent stiffness and the desired safety factor for the optimized part. The redesigned clutch lever was manufactured by using AM–Selective Laser Melting (SLM) and printed from powdered aluminum alloy AlSi10Mg. The final evaluation of the study deals with the experimental test and comparison of the redesigned clutch lever with the existing part which was used in the previous racing car. Using TO as a main redesign tool and AM brought significant changes to the optimized part, especially the following: reduced mass of the component (10%), increased stiffness, kept safety factor above the 3.0 value and ensured the more aesthetic design and a good surface quality. Moreover, using TO and AM gave the opportunity to consolidate multi-part assembly into a single component manufactured by one manufacturing process that reduced the production time. The experimental results justified the simulation results and proved that even though the applied load was almost 1.5× higher than the assumed one, the maximum von Mises stress on the component was still below the yield limit of 220 MPa.
... The pavilion is named X-Form 1.0, which is exhibited at Digital Futures Exhibition in 2019. It is the first experimental prototype designed with the above framework (Bao et al., 2020). This architectural installation's height is 2.8m, and its floor space is about 4m 2 . ...
Since the 21st century, the rapid development of computer technology has brought new inspiration to the long-standing topic of the relationship between architecture, structure, and environment. Performance data have become the driving force for new design and fabrication methods. Nowadays, in the field of engineering, computer-aided design methodologies, such as finite element analysis and computational fluid dynamics and, have become essential in evaluating architectural and structural designs. However, these engineering analysis techniques have not become widespread for architectural design form-finding. On the other hand, with the development of digital architecture theory, form-finding technology based on biological patterns has gradually moved from avant-garde design to actual practice. As a result, bionic computational design techniques, such as swarm intelligence algorithm and multi-agent system, have become more popular; and architects can assign the behavioural logic in nature to architectural design form-finding so that biological, environmental response strategies can be reproduced in intelligent tectonics. However, this emergent design methodology is often difficult to obtain data feedback from the building itself and its performance, and hardly form the mainstream design strategy in architectural practice. In this context, applying the data of structural performance to multi-agents to realise the research of computational design driven by performance will help break through the above dilemma and provide new ideas to architects and engineers. Both bi-directional evolutionary structural optimisation (BESO) for topology optimisation method and multi-agent system from swarm intelligence algorithm are emergent technologies developed into new approaches that transform performance-based architectural & structural design. This thesis posits a performance-driven design methodology that establishes a complementary relationship between topological optimisation, behavioural multi-agent algorithms, architectural design, and robotic fabrication. Firstly, the thesis systematically explores and evaluates the application of topology optimisation and multi-agent algorithms in a form-finding design process and, later, robotic fabrication through literature review, case studies and a series of architectural scale prototypes. Through a combination of natural inspiration, topology optimisation, multi-agent systems and robotic fabrication, the thesis also establishes a new connection between two dichotomous principles: architectural complexity and structural performance. It demonstrates the process of testing two digital design methods and integrating these two algorithms to establish a real-time structural feedback loop in designing intricate forms. Finally, the thesis describes a hybrid of architectural and structural performance behaviours by integrating multi-agent generative design algorithms and the BESO method and the closeness of their interaction. This approach creates a negotiation between architectural design concerns and structural optimisation in a simultaneous generative approach. It is an essential shift from the normative sequential workflows that either inform generative approaches with structural analysis or operate sequentially to optimise the complex geometries already created within generative processes structurally. At the same time, the complexity and intricacy of the geometry generated through this process are demonstrated to be feasible to build through robotic fabrication with large-scale additive manufacturing. A series of installations have been completed to prototype and compare two individual approaches and an integrated method at a small scale, to understand the implications of long-span large spatial structures. Overall, this thesis has contributed to the research field of performance-driven digital design and fabrication. It offers a new approach that enables creating a complex, expressive architectural form that is highly efficient in material and structural performance. This approach also has the potential to create a closer collaboration between architect and structural engineer in the early stages of design and to avoid the structural rationalisation of unfeasible architectural forms in the architectural, engineering and construction industry The new method also seeks the ornamental complexities in architectural forms and most efficient use of material based on structural performance in the process of generating complex geometry of the building and its various elements, later for the market of mass customisation manufacturing.
... Louth et al. [15], Jipa [16], and Bhooshan [17] modified SIMP methods with mesh modelling techniques to get organic and elegant forms for Concrete Slab and Volu Dining Pavilion. Yan et al. [18,19] and Bao et al. [20,21] have introduced the BESO method to achieve diverse building structures and fabrications. ...
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Topology optimization methods gain extensive attention from many engineering fields for their capacities of meeting the diverse requirements of structural performances and innovative appearances. While most classical topology optimization techniques focus on globally optimal form generation around the whole design domain, there are still many demands for controlling local material proportion. This paper introduces a multi-volume constraint approach and its parameter configuration schemes to help users artificially pre-design the topologically optimized structure with the Bi-directional Evolutionary Structural Optimization (BESO) method. The numerical examples in this paper demonstrate that the presented method can be successfully applied in the computational structural form-finding for several building designs in various projects, e.g., high-rise building façades, circular shell domes, and nest-type stadium structures. It can provide the designers with diverse finely controlled structural layouts based on prescribed local material volume fractions. The structural performances of the diverse designs are very close to that of the globally optimal design. This study aims to make a bridge linking the computational optimization method to the human-centric design requirements, and it 2 holds an enormous application potential in industrial or building designs.
... Pavilions are another structure type explored on the topic of TO (Table 2). Reference [15] introduce the process of designing and manufacturing a pavilion using robotic 3D printing. The pavilion consisted of 8 components that are connected through plug-in joints and a laser-cut top panel that is connected to the rest of the structure using screws and glue. ...
Conference Paper
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Topology optimization (TO) is a structural optimization method that seeks the optimal material distribution within a design domain. Topology optimization applications in the architectural field remain limited in comparison to other engineering disciplines. With the shift to more computational and digital design and the advances in manufacturing techniques, TO has been gaining an increased interest in recent architectural research. This research aims to investigate available research in the field that studies the topology optimization and fabrication process of various elements and structures. The different materials, programs, and fabrication methods are discussed.
... Similar elegant shapes to this optimized bridge have been found in many natural structures (e.g. trees) and man-made buildings like pavilions [59], indicating it has the maximum stiffness. Fig. 24(b)]. ...
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This work uses the zero-level contour of a parameterized level set function, a linear combination of cubic B-spline basis functions, to express the structural profile in structural topology optimization. Together with mean compliance, diffusion energy is minimized under a volume constraint to control the structural complexity. The design variables, namely the coefficients of cubic B-spline basis functions, are updated by solving the reaction–diffusion equation within a finite element analysis framework. The bisectional algorithm accurately calculates the Lagrangian multiplier of the volume constraint in each iteration. In addition to expressing the optimized structure smoothly, the proposed method is highly efficient. For instance, it only takes 20 iterations to solve the cantilever and MBB beams in 2D. For 3D optimization, we obtain several elegant bridge designs using nearly one million elements, demonstrating the great potential of the proposed method for practical applications.
... FDM is not only a hobbyist technology but it also has noteworthy applications in the industry. In the realm of architecture and construction, FDM can be used to create multifunctional architectural components such as façade panels, 1,2 bespoke floors, 3 molds for concrete casting, [4][5][6] full-scale pavilions, [7][8][9] or it can be integrated into multimaterial prints with enhanced properties. 10,11 While three-axis gantry system printers commonly enable FDM, lately, a lot of research explores the potential of using machines with five or more degrees of freedom by attaching the extruder or print base to a robotic arm. ...
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The introduction of robotic arms in additive manufacturing enables the scaling up of three-dimensional (3D) printing processes and the realization of nonplanar path geometries. As a result, novel design potential is unlocked by having control over the layered configuration of paths in the object, and 3D printing becomes viable for architectural applications. However, the various challenges associated with creating feasible nonplanar layered paths for the realization of large-scale objects are hindering their integration in the design process and broad use. This work presents methods that contribute to the flexible and intuitive design of nonplanar layered paths for robotic printing. We focus on the challenges related to the realization of single-shell bifurcating structures, with emphasis on the paths’ behavior on the bifurcating moments of the shapes. Our methods are based on the use of design techniques that originate from implicit shape representation and on the detection of critical points on the surface through the lens of distance functions. We present fabricated prototypes printed with nonplanar paths that showcase the possibilities of our methods.
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Topology optimization is a structural optimization method that mainly works on distributing the material within a design domain based on specific design objectives and parameters. Topology optimization results are often comparable to nature-inspired forms. Hence, this research explores tree-like structures, a key category of nature-inspired forms, through the lens of topology optimization. Nine design domains that differ in their number of columns and branching are used to explore these factors’ effect on resulting forms. These nine domains are topology optimized using Grasshopper and its tOpos plugin. Results are then compared based on visual and structural aspects. The study concludes by discussing the potential of using topology optimization as a method for designing tree-like structures and confirming that increasing the number of columns combined with some sort of branching within the structure does improve the final results.
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The additive manufacturing process is gaining momentum in the construction industry with the rapid progression of large-scale 3D printed technologies. An established method of increasing the structural performance of concrete is by wrapping it with Fibre Reinforced Polymer (FRP). This paper proposes a novel additive process to fabricate a FRP formwork by dynamic layer winding of the FRP fabric with epoxy resin paired with an industrial scale robotic arm. A range of prototypes were fabricated to explore and study the fabrication parameters. Based on the systemic exploration, the limitations, the scope, and the feasibility of the proposed additive manufacturing method is studied for large scale customisable structural formworks.
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Structural form-finding using computational simulations is helpful for architects during the conceptual design stage. However, due to the complexity and slow-speed, conventional form-finding tools are difficult to use for architectural design. This paper presents a new Rhinoceros plug-in named Ameba, which is a topology optimization tool based on the BESO method and FEniCS open-source computing platform. Firstly, 2D or 3D elasticity problem variational formulation is given in this paper according to the FEniCS format. The code for solving the variational formulation is provided in the context of automated modelling using FEniCS. The computational framework of Ameba is then described and its general operational process is shown. The capability of Ameba is demonstrated by solving a variety of architectural form-finding examples. The computational time of models with different element numbers is compared. The examples show that Ameba is highly efficient and easy-to-use. Finally, two future extensions of the Ameba framework that are particularly useful for architectural form-finding are outlined.
Conference Paper
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This research explores innovations in structural design and construction through the generative design technique BESO (Bi-directional Evolutionary Structural Optimization)[1]and the application of robotic fabrication to produce efficient and elegant spatial structures. The innovative pavilion discussed in this paper demonstrates a design and fabrication process and thecollaborationbetween architecture and engineering research groups through a series of small-scale test models and a full-scale model of topologically optimized spatial structures. The focus of this work is the use of a modified BESO technique to optimize the structure which features branches of various sizes, inspired by Gaudi’s Sagrada Familia Bacilica, and the introduction of large-scalerobotic 3D printing developed at RMIT University.The advantages of the new design and construction process are efficient material usage and elegant structural forms.
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IntroductionProblem Statement and Material Interpolation SchemeSensitivity Analysis and Sensitivity NumberExamplesConclusion Appendix 4.1References
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In this paper we seek to summarize the current knowledge about numerical instabilities such as checkerboards, mesh-dependence and local minima occurring in applications of the topology optimization method. The checkerboard problem refers to the formation of regions of alternating solid and void elements ordered in a checkerboard-like fashion. The mesh-dependence problem refers to obtaining qualitatively different solutions for different mesh-sizes or discretizations. Local minima refers to the problem of obtaining different solutions to the same discretized problem when choosing different algorithmic parameters. We review the current knowledge on why and when these problems appear, and we list the methods with which they can be avoided and discuss their advantages and disadvantages.
IntroductionProblem Statement and Sensitivity NumberFilter Scheme and Improved Sensitivity NumberElement Removal/Addition and Convergence CriterionBasic BESO ProcedureExamples of BESO Starting from Initial Full DesignExamples of BESO Starting from Initial Guess DesignExample of a 3D StructureMesh-independence StudiesConclusion References
In this paper, a new algorithm for bi-directional evolutionary structural optimization (BESO) is proposed. In the new BESO method, the adding and removing of material is controlled by a single parameter, i.e. the removal ratio of volume (or weight). The convergence of the iteration is determined by a performance index of the structure. It is found that the new BESO algorithm has many advantages over existing ESO and BESO methods in terms of efficiency and robustness. Several 2D and 3D examples of stiffness optimization problems are presented and discussed.
A simple evolutionary procedure is proposed for shape and layout optimization of structures. During the evolution process low stressed material is progressively eliminated from the structure. Various examples are presented to illustrate the optimum structural shapes and layouts achieved by such a procedure.
Evolutionary Structural Optimization (ESO) and its later version bi-directional ESO (BESO) have gained widespread popularity among researchers in structural optimization and practitioners in engineering and architecture. However, there have also been many critical comments on various aspects of ESO/BESO. To address those criticisms, we have carried out extensive work to improve the original ESO/BESO algorithms in recent years. This paper summarizes latest developments in BESO for stiffness optimization problems and compares BESO with other well-established optimization methods. Through a series of numerical examples, this paper provides answers to those critical comments and shows the validity and effectiveness of the evolutionary structural optimization method. KeywordsEvolutionary Structural Optimization (ESO)-Bi-directional ESO (BESO)-Local optimum-Optimal design-Displacement constraint