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Environmental Data-Driven Performance-Based
Topological Optimisation for Morphology
Evolution of Artificial Taihu Stone
Z. Feng1,P.Gu
2, M. Zheng1,XYan
3, and D. W. Bao4(B)
1Suzhou University of Science and Technology, Jiangsu 215000, China
2Architectural Association, London WC1B 3ES, UK
3Centre for Architecture Research and Design, University of Chinese Academy of Science,
Beijing 100190, China
4School of Architecture and Urban Design, Centre for Innovative Structures and Materials,
RMIT University, RMIT University, Melbourne 3000, Australia
nic.bao@rmit.edu.au
Abstract. Taihu stone is the most famous one among the top four stones in China.
It is formed by the water’s erosion in Taihu Lake for hundreds or even thousands
of years. It has become a common ornamental stone in classical Chinese gardens
because of its porous and intricate forms. At the same time, it has become a cultural
symbol through thousands of years of history in China; later, people researched
its spatial aesthetics; there are also some studies on its structural properties. For
example, it has been found that the opening of Taihu stone caves has a steady-state
effect which people develop its value in the theory of Poros City, Porosity in Archi-
tecture and some cultural symbols based on the original ornamental value of Taihu
stone. This paper introduces a hybrid generative design method that integrates the
Computational Fluid Dynamics (CFD) and Bi-directional Evolutionary Structural
Optimization (BESO) techniques. Computational Fluid Dynamics (CFD) simu-
lation enables architects and engineers to predict and optimise the performance
of buildings and environment in the early stage of the design and topology opti-
misation techniques BESO has been widely used in structural design to evolve
a structure from the full design domain towards an optimum by gradually remov-
ing inefficient material and adding materials simultaneously. This research aims
to design the artificial Taihu stone based on the environmental data-driven per-
formance feedback using the topological optimisation method. As traditional and
historical ornament craftwork in China, the new artificial Taihu stone stimulates
thinking about the new value and unique significance of the cultural symbol of
Taihustone in modern society. It proposes possibilities and reflections on exploring
the related fields of Porosity in Architecture and Poros City from the perspective
of structure.
Keywords: Bi-directional Evolutionary Structural Optimization (BESO) ·
Intricate Architectural Form ·Computational Fluid Dynamics (CFD) ·Poros
City ·Porosity
© The Author(s) 2022
P. F. Yuan et al. (Eds.): CDRF 2021, Proceedings of the 2021 DigitalFUTURES, pp. 117–128, 2022.
https://doi.org/10.1007/978-981-16-5983-6_11
118 Z. Feng et al.
1 Introduction
Taihu stone (Fig. 1)[3] is limestone and the water’s erosion in Taihu Lake for hundreds
or even thousands of years makes it porous and intricate. It has become a common orna-
mental stone in classical Chinese gardens and a symbol of Chinese culture for hundreds
of years [1]. This research posits an innovative design methodology, including compu-
tational fluid dynamics (CFD) and bi-directional evolutionary structural optimisation
(BESO), to design new artificial Taihu stones. The focus of this paper is the experi-
ment to design a new Taihu stone with different parameters. This research contributes
to Porosity Crafts and The Theory of Porous City [2], Porosity in Architecture from a
structural standpoint and cultural symbols of Taihu stone in society.
Fig. 1. Taihu stone painting
2 Design Methodology
2.1 Principle of Experiment
The experiment of “Taihu stone” reveals a cross-iteration process of CFD simulation
[4–6] and topology optimisation (BESO) [7,8]. The whole process consists of three
parts: a. Test of Taihu Lake’s original fluid condition; b. Pressure analysis of original
mesh by CFD simulation; c. Topology optimisation based on pressure analysis. The fluid
condition will change each time after the change by topology optimisation (Fig. 2); thus,
iteration happens from ato cagain (the flow chart is seen in Fig. 3).
Environmental Data-Driven Performance-Based Topological 119
Fig. 2. Boundary Conditions during the process of topological optimisation
Fig. 3. Flow chart of CFD simulation and topology optimisation
2.2 Environment Parameters of Experiments
Studies [9–11] indicate the average depth of Taihu Lake, which is a dead lake with no
current, is 1.8 m, and the flow direction and velocity are mainly related to the speed of
the prevailing wind over Taihu Lake. These studies have shown that, at the bottom of
Taihu Lake, where Taihu stone is, the direction of wind-induced current is over 90%
likely to be opposite to the wind above Taihu Lake, and the velocity of lower flow is
relatively slower than the wind above.
Therefore, the CFD simulation of water flow in this paper applies data of the perennial
water flow direction and velocity at the bottom of Taihu Lake, identified by Suzhou and
Shanghai’s prevailing wind direction and velocity (called SuHu area) in China.
Among the widely accepted views on the formation of the Chinese Taihu stone [1],
water acidity is important for the erosion of limestone such as Taihu stone. The part that
is corroded by acid is mainly dense calcium carbonate and easy to wash away by water
currents. Moreover, this part is a variable that is difficult to determine its proportion and
location in BESO. This paper calculates the part directly corroded by the acid in the
water and eliminated by the water flow as a random ratio parameter.
120 Z. Feng et al.
2.3 Special Parameters Tested in the Experiments
2.3.1 Percentage of Low-Density Volume Compared with the Whole Volume
in Taihu Stone
It should be noted that each part of the stone’s density will also affect the experi-ment’s
influence in reality [1]. Thus, a new constant is set to reveal the phenome-non called
’percentage of low-density part’. As a result, a fixed constant percentage of mesh will
undoubtedly be eliminated in every turn of iteration, closer to the ac-tual result.
2.3.2 Percentage of Elimination Volume Compared with the Whole Volume
During the Process of Topological Optimisation
In nature, both stone and water changes should happen simultaneously, so the interval
time between each step of iteration should be extremely short, which is unrealistic in
software operation currently. Thus, we will try different volume reduction to reveal the
result of a certain interval before the next iteration in which fluid condition refresh. The
experiment catalogue will be analysed in the next chapter.
2.3.3 Minimum Radius of Influence Number (Rmin)
Rmin is a parameter during BESO [12] that will affect the outcome of the calculation.
Refer to new research of topology optimisation, and the result will be different from
different settings, including Rmin, which means there is over one solution.
2.4 Self-criticism of the Experiment Methodology
The whole simulation can be regarded as a certain ideal condition of the formation of
Taihu stone. The core factor should be noted that the principle of BESO is not entirely
in compliance with the reality of volume reduction of Taihu stone because the change
of stone in the river contains both structure optimisation and some erosion/corrosion
process.However, in a sense, the experiment here proposed should be more conducive
to structural stability.
3 Quantitative Definition of Physical Characteristics of Artificial
Taihu Stone with the Parametric Method
3.1 Criteria of Traditional Aesthetics of Chinese Taihu Stone
According to the literature [13,14] on the cultural connotation of the artistic symbol of
“Taihu stone”, the ancient Chinese created a set of theoretical principles and proposed
the standard of phase stone. The four elements of “Shou, Lou, Zhou, Tou” were used to
judge the value of Taihu stone.
“Shou” refers to the ingenious structure of Taihu stone, supporting the shape with
the least amount of material, which is similar to BESO’s effect [15–17]. As the number
of iterations increases, the volume decreases, but the structure will always be one of the
optimal solutions; “Lou” means that most of the holes in the Taihu stone are connected,
Environmental Data-Driven Performance-Based Topological 121
which is a flowing space. “Zhou” is a judgment of formal aesthetics, which mainly
refers to the undulating rhythm of the shape of Taihu stone - pattern in the strange and
the rhyme in the difference, which parameters cannot quantify. We adopted the design
of the initial prototype of Taihu Stone to reach this standard as much as possible and
expressed it in the form of a model in this research. The object of “Tou” evaluation is the
material characteristics of Taihu stone, which cannot be achieved by the CFD & BESO
method, nor is it the focus of this experiment, but the later construction materials can
reflect it.
In conclusion, two aesthetic factors of “Zhou” (i.e., “wrinkling textures and furrows”)
and “Tou” (i.e., “passing through or transparency”) need to be expressed by images, while
the remaining two spatial factors of “Shou” (i.e., “leanness or thickness”) and “Lou”
(i.e., “eyes or hollowness”) are expressed in a parametric way.
3.2 Parametric Definition of “Shou”
In this paper, the number of spatial nodes is used to test the complexity of the spatial
topology, which is “Shou”, higher values indicates that the spatial topology is more
complex and the ingenuity of the structure.
3.3 Parametric Definition of “Lou”
"Lou", explained by the original Reference, is the interconnection between the holes in
the Taihu stone. Combined with the actual survey of Taihu stone, we found that it is
unadvisable to use the connectivity rate of holes =n/N (N represents the total number
of holes, and n represents the number of interconnections) to prove “Lou” because the
actual Taihu stone is not that the more holes connected to the middle, the higher the value
“Lou” of the Taihu stone, which is also related to the size of the connecting space of the
Taihu stone. The extent of hollowness relates to not only the ratio of interconnections
but also the size of connected holes.
Referring to the cell division method in biology, the ratio of volume to surface area
is preferable to show the Taihu stone’s connectivity. For example, when an organism
grows, it is because its cells are dividing not getting bigger, it is challenging to keep
up with taking in the extra nutrients it needs and expelling more waste, which means
as the cell gets bigger, it has less surface area compared to its size—the surface area to
volume ratio of the cell decreases. Cell division solves the problem of increasing size
by reducing cytoplasm volume in the two daughter cells and dividing up the duplicated
DNA and organelles, thereby increasing the surface to volume ratio of the cells. In this
case, treating cells as a whole like original Taihu stone, then the division can be regarded
as the connectivity of holes in Taihu stone, which means more cell divisions lead to
higher connectivity rate of holes, mathematically, increasing surface to volume ratio
leads to higher connectivity rate of holes. From this analysis method, if the cell’s growth
rate is stable, the higher the difference between surface and volume, the higher the cell
division rate (indicates, the higher connectivity rate of holes in Taihu stone).
This research comprehensively selects the optimal solution of Taihu stone accord-
ing to respective weights of 50% and combined with the visual images from the two
parameters above.
122 Z. Feng et al.
Fig. 4. The profile results of 10 iterations of stones with different parameters of “Lou”
Environmental Data-Driven Performance-Based Topological 123
4 Screening and Evaluation of Artificial Taihu Stone Through
Experiment
4.1 The Degree of Complexity of the Spatial Topology
The experience uses the same piece of Taihu stone to experiment with controlling vari-
ables for the above-mentioned main parameters. (Estimate the theoretical range of the
parameter range before the experiment). For seven different data, 70 different results
are obtained after ten iterations of each, and their cross-sectional forms are recorded
as shown in Fig. 4. Furthermore, take the parameter of Volume Fraction (Vf) =80_
Random ratio (Rnd) =40%_ Minimum Radius of Influence Number (Rmin) =1×Size
to illustrate the iterative calculation process of the experiment (seen in Fig. 5).
Fig. 5. Iterative calculation process in CFD
In this paper, spatial nodes are the joints in the artificial Taihu stone skeleton to show
the degree of complexity in Taihu stone (Fig. 6).
To find the number of spatial nodes of each Taihu stone. Moreover, draw a line chart
(seen in Fig. 7).
124 Z. Feng et al.
Fig. 6. Spatial nodes in artificial Taihu stone
Fig. 7. Numbers of spatial nodes of each Taihu stone
According to the line chart:
1. Vf =80_Rnd =40%_Rmin =1×Size has the highest value of average spatial
nodes during ten times iterations, and Vf =90_Rnd =50%_Rmin =3×Size has
the least average number of spatial nodes during ten times iterations.
2. When the values of Rmin and Rnd are invariant, the higher the value of Vf, the more
complicated the final generated space, while the data of Vf =70 is unstable.
3. When the values of Rmin and Vf are invariant, the smaller the value of Rnd, the
more complicated the generated space.
4. When the values of Vf and Rnd are invariant, the space complexity: 2 ×size <3×
size <1×size. (size: element size)
4.2 The Degree of Connectivity Between the Holes
In this paper, the ratio of the difference between the standard value and the experiment
value to the standard value is used to express the degree of connectivity between holes.
Environmental Data-Driven Performance-Based Topological 125
Compare the area to volume ratio of the experiment with the area to volume ratio
when the Vf =90%, Vf =70%, Vf =80%, data shown in charts. To make the data
more intuitive, division level is used to show the connectivity between the holes (seen
in Fig. 8).
Fig. 8. Division level of a different situation
Fig. 9. A composite indicator of Taihu stone
To conclude the charts above (Fig. 9):
1. All data will first reach its peak in the iterative process, then decline till eventually
stabilised. Vf =80_Rnd =40%_Rmin =3×Size has the highest peak and the
highest average connectivity rate when stabilised.
2. Vf =70_Rnd =50%_Rmin =3×Size has the earliest peak, and the value of the
average connectivity rate when stabilised is the lowest.
3. Vf =80_Rnd =40%_Rmin =1×Size has a minimum value of peak.
126 Z. Feng et al.
4. When the values of Rnd and Rmin are invariant, the smaller the Vf, the earlier the
peak appears and the higher the peak value.
5. When the values of Vf and Rmin are invariant, though Rnd does not affect the time
when the peak appears, the smaller the value of Rnd, the higher the value of the peak.
6. When the Vf and Rnd values are invariant, the peak value shows the extent of
connectivity between holes in Taihu stone and the average value when stabilised: 2
×size <3×size <1×size.
5 The Value of Artificial Taihu Stone in Fields of Crafts and Porous
Space
5.1 Porosity Crafts
In this article, relative design is made by new material like stainless steel and inlaid drawn
steel wire or glass fibre, new technology like sound, light, electricity to extract the beauty
of shape from Taihu stone. Using parametric design methods through CFD&BESO, the
Taihu stone structure gets improved and can provide more possibilities (seen in Fig. 10).
The definition as a symbol of aesthetics was then researched in the following parts to
discuss how traditional crafts can have a new way of living with contemporary society.
Fig. 10. Parametric Taihu stone samples
5.2 Porosity Architecture
Porosity in Taihu stone, featured in porous shape and façade, can be used in modern archi-
tecture design [18]; the sample of porosity architecture. In Suzhou traditional gardens,
Taihu stone has an architectural contribution in light changes and circulation connection;
different interpretation methods can be absorbed and improved in architecture design.
a) Porosity City
In today’s city organisation, as the addition of single building units, Poros City
[2] tries to get a holistic result with uniform density. We try to conclude a series of
space prototype and typical ways of combination in Taihu stone. As Fig. 11 shows, the
comparison was made between diagrams of Poros City and diagrams of Poros structure
extracted by Taihu stone, and methodology differs in organisation methods.
Environmental Data-Driven Performance-Based Topological 127
(a) Diagrams of Poros City (b) Diagrams of Poros structure
Fig. 11. (a) Diagrams of Poros City (b) Diagrams of Poros structure
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