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BIOMIMETIC STRUCTURE DESIGN OF DRAGONFLY
WING VENATION USING TOPOLOGY
OPTIMIZATION METHOD
JIYU SUN
*
and MINGZE LING
Key Laboratory of Bionic Engineering (Ministry of Education, China)
Jilin University, Changchun 130022, P. R. China
*
sjy@jlu.edu.cn
CHUNXIANG PAN
Department of Aircraft and Powertrains
Aviation University of Air Force, Changchun 130022, P. R. China
DONGHUI CHEN
†
and JIN TONG
†,‡
†
Key Laboratory of Bionic Engineering (Ministry of Education, China)
Jilin University, Changchun 130022, P. R. China
‡
Collaborative Innovation Center of Grain
Production Capacity Improvement in Heilongjiang Province
XIN LI
College of Materials Science and Engineering
Jilin University, Changchun 130022, P.R. China
Received 27 December 2013
Revised 16 April 2014
Accepted 22 April 2014
Published 18 June 2014
Scientists have carried out research for various biomimetic applications based on the dragonfly
wings because of the superbflying skills and lightsome posture.The wings of dragonflies are mainly
composed ofveins and membranes, which give rise to thespecial characteristics of their wingsthat
make dragonflies being supremely versatile, maneuverable fliers. Mimicking the dragonfly wing
motion is of great technological interest from application’s point of view. However, the major
challengeis the biomimetic fabrication to replicate the wingmotion due to the very complex nature
of the wingvenation of dragonfly wings. Inthis regard, the topology optimization method(TOM) is
usefulto simplify object’sstructure whileretaining its mechanical properties. In this paper,TOM is
employed to simplify and optimize the venation structure of dragonfly (Pantala flavescens Fab-
ricius) wing that is captured by a 3D scanner and numerical reconfiguration. Combined with the
material parameters obtained from nanoindentation testing, the quantitative models are estab-
lished based on a finite element (FE) analysis and discussed in static range. The quantitative
models are then compared with the square frame, staggered grid frame and hexagonal frame to
examine the potentials of the biomimetic structure design for the fabrication of greenhouse roof.
Keywords: Dragonfly wing; venation; topology optimization method; finite element method.
Journal of Mechanics in Medicine and Biology
Vol. 14, No. 4 (2014) 1450078 (17 pages)
°
cWorld Scientific Publishing Company
DOI: 10.1142/S021951941450078X
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1. Introduction
Dragonfly wings possess great stability and high load-bearing capacity during
flapping, gliding and hovering flight, despite the fact that the mass of the wings is
less than 2% of the total body mass of a dragonfly. Dragonfly achieves unique flight
abilities including hovering and flight abilities in multiple directions by passive
bending of the wing structure, because it cannot actively change the shape of its
wings.
1–7
Wings are subjected to aerodynamic and inertial forces during flapping
that induce deformation, bending and torsion. Venational patterns correspondingly
appear to reduce and control the extent of wing bending in both transverse and
longitudinal planes.
8
Further, strong structures stiffen the wing against aerody-
namic bending and torsional moment.
2
Dragonfly wings are composed of veins and thin two layers cuticular membrane.
The veins are hollow branching tubes that form the supporting framework, which
often have cross connections that form closed \cells"within the membrane. The
veins and membrane form a complex design within the wing that give rise to the
unique whole-wing characteristics, which result in supremely versatile and ma-
neuverable flight capabilities of dragonflies.
9
Venation serves to strengthen the
surfaces against deleterious deformations and to facilitate advantageous wing ge-
ometries and thickened veins that provide structural rigidity.
10
The cross sections of
the Costa at various points extend from root to nodus and the thickness of the Costa
decreases in the spanwise direction; while from nodus to stigma, the thickness
increases in the chordwise direction. This thickness variation is well adapted to the
forces acting at the location of the vein.
11
The venation pattern that may not affect
overall stiffness could influence how stiffness varies throughout the wing.
12
It was
reported that the microstructure of the vein is a complex sandwich structure which
consists of a chitin shell and protein/muscle with some fibrils.
13
Several attempts were made to quantify the dragonfly wing-remodeling process to
investigate and predict the structure and remodeling behavior of dragonfly wing that
were reported in the literature. The finite element method (FEM) was used to model
the wings of dragonflies.
14
This method can be used not only to predict effects of
particular veins and their geometry, but also to explore biomechanical consequences
of venational designs.
10
Wootton et al.
15
summarized works on the structural
modeling of insect wings and showed how such research has progressed from simple
conceptual models of wing structure to analytical methods and numerical approa-
ches. Some other researchers have also modeled the wings using FEM.
16–19
The FE
models are more complete and accurate than previously reported models since they
accurately represent the topology of the vein network, as well as the shape and
dimensions of the veins and membrane cells.
20
However, a major limitation of these
works is the lack of detailed information about the structure and mechanical prop-
erties of the veins and membranes along the entire wing structure that is required for
the development of an FE model.
4
Moreover, the complex venation of dragonfly
wings poses additional challenges to the effective biomimetic design.
J. Sun et al.
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Structural optimization is an effective tool that is commonly used for the
design of stiff structures, and more recently for the synthesis of compliant
mechanisms.
5
It is classified into size, shape and topology optimization.
21
To-
pology optimization is a mathematical approach that optimizes material layout of
thestructuresothatoneormoregivencriteria (objective function) are minimized
or maximized, which replaces time consuming and costly design iterations and
hence reduces design development time and overall cost while improving design
performance.
5
The mechanisms and methods have been summarized in several
excellent reviews,
22–27
we will not review the extensive literature here. Using
topology optimization, engineers can find the best concept design that meets the
design requirements. A few approaches have been proposed to solve various
continuum structural optimization problems, such as, the homogenization design
method (HDM), the solid isotropic microstructures with penalization (SIMP)
method, the evolutionary structural optimization (ESO) method and the level
set method (LSM). The HDM introduced by BendsøeandKikuchi
28
to determine
the optimal material distribution in a design domain has been applied to many
elastic structure cases.
29
Its disadvantage is that the evaluation of microstructure
and its orientations is often cumbersome.
30
ESO is based on the simple concept of
slowly removing inefficient material from a structure so that the residual shape
evolves toward the optimum.
31
Nevertheless, ESO has some drawbacks and
weaknesses, such as rejection criteria, the final solution can result in jagged
edges, post-processing must be carried out to smooth the boundary, the presence
of checkerboard patterns which compared with other methods has less computing
efficient.
32
The LSM is a numerical technique for tracking interfaces and shapes,
and it performs numerical computations involving curves and surfaces on a fixed
Cartesian grid, its disadvantage include that need to do reinitialization for the
level set functions in some cases and computationally expansive.
33
The SIMP is
originally introduced by Bendsøe,
34
which has been recognized as a computa-
tionally efficient tool for structural topology optimization problems.
35
The pop-
ular SIMP method, for instance, models the search space as discrete functions on
the discredited design domain, where the layout is sought. In a sense, the value of
this function at each point represents a \pixel"of the design blueprint as shown in
Eq. (1).
36
This has been shown to confirm to microstructure of the materials.
In addition, the topology optimization is important to consider the evolution and
function of various branched structures, e.g., dragonfly wing venation, lotus leaves
venation and axis system of plants that are fascinating to scientists and engineers
alike for developing new routes of biomimetic design and fabrication of unique
structures for new engineering applications.
6,7,10,37
For example, mimicking the
microvascular venation of natural leaf in various synthetic substrates paved the way
for the fabrication of nature-inspired microfluidic network for perfusable tissue
constructs.
38
Similarly, new insights into leaf venation and biomimetic microvas-
cular networks could also open new avenues for autonomic healing, active cooling,
novel microfluidic devices and tissue engineering.
39–41
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For biomimetic wings, the venation was designed primarily for light weight
reason,
42–45
such as level vertical veins, parallel bias vein or radial venation. The
venation has an important structural role to play. Apart from its biological function
of delivering hemolymph to insect wing tissue, the size and shape of each vein, as
well as the topology of the vein framework influence the structural stiffness and
inertia of the wing.
5
McLendon
1
investigated the different frames with the total
magnitude of deflection of each element and showed that the square frame structure
is slightly stiffer than the modeled hexagonal structure.
Biomimetic design of such structural frames is of immense importance as it could
be leveraged to construct greenhouse roofs. A greenhouse roof consists of different
types of covering materials, such as a glass or plastic roof along with usually glass or
plastic walls. They have some important characteristic in common. These include
high strength that guarantees the safety and stability, optically transparent or semi-
transparent and light-permeable material that allows the plants inside the green-
house to receive the light and heat they need to grow. The structure designs of
greenhouse roof have become an interesting topic of research and development of
greenhouse. In this regard, dragonfly wings offer much potential as structural frames,
and as a result, the morphology will be effective to drag reduction.
46
Replicating such
unique structural frames by biomimetic structural design could be leveraged to
fabricate robust greenhouse roofs that are light weight with outstanding mechanical
properties that remain stable in extreme conditions of heavy rain and high wind.
Here, we present the biomimetic films design used for greenhouse roof inspired by
dragonfly wing venation. We have used the SIMP method to acquire the simplified
wings model that meets the feasible fabrication requirements of a strong aerody-
namic film. The biomimetic structures, such as the square frame, staggered grid
frame, hexogen frame and the simplified topology optimization structures are
established film models. We have compared different models and discussed their
advantages and disadvantages of the biomimetic structure design for the fabrication
of greenhouse roof.
2. Methods and Materials
2.1. Dragonfly wing specimens
The specimens of the dragonfly, Pantala flavescens Fabricius, were collected in the
suburbs of the city of Changchun as shown in Fig. 1(a). There are several different
kinds of patterns present in the dragonfly wing vein framework.
2–4
The leading edge
consists primarily of rectangular frames whereas the trailing surface is largely
formed of hexagons and some other polygons with more than four sides as shown in
Fig. 1(b).
2
A network of fine veins forms a group of small cells in the middle of the
wing (Fig. 1(b)).
3
For the 3D scanning test, the dragonfly wing specimens were
anesthetized within 12 h, rinsed with distilled water and finally dried at room
temperature. Dragonfly wings have a highly reflective waxy surface layer. This
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implies that direct laser scanning would lead to incomplete data. Hence, to decrease
the effect of the reflectivity of the surface along with color and curvature char-
acteristics on the capture of the point group data, the imaging agent (DPT-5) was
applied to the surface shading of the dragonfly wings (Fig. 1(c)). Because the
dragonfly wings are composed of free-form surfaces, the application of DPT was as
thin as possible to ensure uniform coating and reduce any effect on test results. After
spraying, the dragonfly wing specimens were allowed to air-dry, and then 3D
scanning test was performed.
2.2. 3D scanner and reconfiguration
The digital measurements of the dragonfly wings were carried out with a 3D laser
scanner after the wings were treated with the dye check agent. Using the reverse
engineering software IMAGEWARE, the scanning data point groups of the drag-
onfly wings were processed, where error points were deleted, the scanning data were
smoothed with a Gaussian filter and the data were reduced with the chordal devi-
ation method. Based on the shape features of the dragonfly wings, the boundary
curves were picked up by circle-select points from the scanning data point groups.
(a) (b)
(c) (d)
Fig. 1. (a) Photographs of a dragonfly wing, which consists mainly of the tubular veins and membranes
(the region surrounded by veins). (b) A network of fine veins forming a group of small cells in the middle
of the wing.
3
There are several different patterns present in the wing vein framework. The leading edge
consists primarily of rectangular frames whereas the trailing surface is largely formed of hexagons and
some other polygons with more than four sides. (c) Imaging agent (DPT-5) was applied to the surface
shading of the dragonfly wings. (d) The FE model of dragonfly hindwing.
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The 3D models of the dragonfly wings were reconstructed with the boundary curves
and the scanning data point groups. The models were then introduced into Auto-
CAD software. With reference to Fig. 1(a), structural model of dragonfly hind wing
were constructed as shown in Fig. 1(d). The model consisted of the wing framework
without membranes. The membranes were subsequently filled in with ANSYS
software to complete the full dragonfly wing model.
In most of the previous studies, the mechanical properties of insect wings were
assumed as uniform values. Sun et al.
4
used nanoindenter to measure the material
properties of dragonfly wing veins and used in FE model, which demonstrated the
material properties induced effects on whole-wing mechanical properties. Therefore,
in this work, two models were established, in which uniform value was used for
model I and the model II was defined as reported previously.
4
The 3D model was analyzed using two different material properties for com-
parison. For model I, two values of the Young’s modulus, E, of veins and mem-
branes were taken as 6.10 GPa (the maximum value of Efor the entire wing)
14
and
1.5 GPa,
47
respectively. For model II, the veins and membranes of the model were
defined as an isotropic material with the Young’s modulus measured by Sun et al.
4
In the horizontal direction, the Young’s modulus values for the wing were set for
three groups: the Costa vein, the postal vein and the others’ that were set as Rudius.
In the vertical direction, the Young’s modulus values for the wing were set for five
groups. The values of the average parts of the five nanoindentation testing points for
their respective centers are the same as their center nanoindentation testing points
(Fig. 2).
2.3. The topology optimization method
Topology optimization problems are usually constructed as the minimum compli-
ance (or minimum strain energy, maximum stiffness) within a specified design re-
gion under the constraints of the given volume of material (or the structural
weight). In the given initial design domain of structure, loads and boundary con-
ditions, the continuum structural topology design can be described using the fol-
lowing constrained optimization problem. Structural design domain is divided into
Nunits by FEM using the interpolation model by the adoption of SIMP methods,
where the elastic modulus of each unit represents the relative density of the expo-
nential function for the cell material, which is described as follows:
min : CðXÞ¼UTKU ¼X
N
e¼1
ðxeÞPuT
ek0ue;ð1Þ
s:t::VðXÞ
V0
f;
KU ¼F;
0<xmin xexmax 1;
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where, Xis design variable (that is unit materials relative density vector), CðXÞis
structural compliance; xeis unit design variables (e¼1;2;...;N,Nis the number
of design variable); Fis load matrix; Uis displacement matrix; Kis global stiffness
matrix; ueis unit displacement matrix; k0is unit stiffness matrix; VðXÞis struc-
tural effective volume; fis volume coefficient; xmax and xmin are upper and lower
limits of unit design variable, respectively and Pis penalty factor (in general
P3). The penalty approach just outlined maintains the existence of solutions for
the problem of minimum compliance and the maximization of the fundamental
frequency.
20
It is used to acquire the simplified wings model that meets the feasible
fabrication requirements of a strong aerodynamic film.
3. Results and Discussions
The pipe20 and shell43 program (special shell model topology optimization in
ANSYS) was used with the following data: diameter of vein 1 mm, thickness of
(a) (b)
(c)
Fig. 2. (Color online) In model II, the various group were defined different modulus according to the
nanoindentation results which is shown in different color groups.
4
C is costa vein, R is rudius vein and P is
postal vein.
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membrane 0.1 mm, tensile loading 1:75 103N (static loading with animal’s own
weight with reference to wing area), for chitin (isotropic) and Poisson’s ratio, 0.25,
respectively, as reported by Kesel et al.
14
The uniform loading was set as
4:5105MPa, which was similar to the basic wind pressure of the Changchun
region in the People’s Republic of China. Since the optimized structure acquired
from dragonfly wings was used in the design of roof greenhouse (which mainly bears
tensile force and wind pressure), the left side of the model was fixed, and a tensile
distributed load was applied on the right side for the analysis.
3.1. The models of rectangular frames and hexagon frames
In dragonfly wings, there are staggered grid structures in leading edge, square
structures in main longitudinal veins, and hexagon structures in the middle, where
structures are larger near the leading edge and smaller near the trailing edge as
shown in Fig. 1(b). Extracting those structures, the square, staggered grid and
hexagon frames were designed and analyzed. The models of square frame and
hexagonal frame are shown in Fig. 3. The size is according to those structures of
dragonfly hind wing. The elastic modulus was set as 6.1 GPa. The differences in the
mechanical properties between these frame shapes were examined using FEM.
The FEM analysis results show that under tensile loading, the deformation of the
model of hexagon structure frame is the largest in those models (the maximum
displacement is 12.12 mm, as shown in Table 1), while the minimum displacement,
strain and stress values occur in the square frame model. It coincides with the
reference that demonstrates that the four-side frameworks are stiffer, and the square
frame structure is less stiff than the hexagonal structure.
2
Under uniform loading,
the hexagon frame appears with better wind resistant properties.
3.2. The models of topology optimization structure frames
TheTOMsolvesthebasicengineeringproblem of distributing a limited amount
of material in a design space. The TOM is used in this paper for simple models I
and II, which incorporates all veins present in the wing. For easier fabrication
and higher stiffness, the topology optimization method (TOM) was used to the
minimum area of dragonfly wing while keeping its strength. The optimization
removing area from 20% to 40% was investigated in models I and II as shown in
Figs. 4(a) to 4(e),andFigs.5(a) to 5(e), respectively, compared with the original
network of the hind wing (Fig. 1(d)). The number of optimization steps selected
was 10.
It is observed on the hind wing of the coupling model I topology optimization
that the root of dragonfly wings was the main pressure bearing parts. Because its
material properties were set as uniform, it resulted in Costa and Rudius that
demonstrated similar carrying capacity, and no obvious trend was found in model I
under bearing pressure. For model II, the topology optimization results show that
Costa, Rudius, Media and Cubitus vein are mainly pressure bearing parts, which
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coincide with the observed micrograph results. This indicates that those veins are
relatively thick and play an important role in dragonfly flight because of its carrying
capacity and stability. Further, the stress is concentrated in the major veins, so the
wing membrane stress is smaller, which shows that the veins are the principle load-
bearing component. The stress exhibited in the finite element model of the dragonfly
wings is distributed radially along the longitudinal veins. So, we selected model II to
design biomimetic fabrication. It was found that for the optimization area of 25%
that the structure was continuous and the simplest, and was therefore chosen as
shown in Fig. 5(c). We note that the simpler frame can endure the same loading as
the complex one. Table 1shows the FEM analysis results of different topology
optimization structures of model II.
(a)
(b)
(c)
Fig. 3. The sketchs of (a) the square frame, (b) staggered grid frame and (c) hexagonal frame.
Biomimetic Structure Design of Dragonfly Wing Venation Using TOM
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Table 1. The FEM analysis results of the different frames, the different topology optimization structures (removing 60%, 70%, 75% and 80% of the original area)
in model II, the combination of different cells, respectively.
Different frames Removing percent of the original area The combination of different cells
Load
function
Square
frame
Staggered
grid frame
Hexagon
frame 60% 70% 75% 80% 1-cell 2-cells 4-cells 16-cells
Tensile
loading
Max displacement, mm 1.87 2.46 12.12 4.44 4.46 4.24 4.69 6.15 3.84 5.25 4.80
Max stress, MPa 8.97 9.60 41.77 1.79 1.78 1.81 1.83 3.31 1.88 1.64 0.92
Max strain 1:84 1031:97 1038:77 1033:87 1043:87 1043:94 1043:98 1040:72 1030:41 1030:36 1030:2103
Uniform
loading
Max displacement, mm 21.51 0.29 0.41 / / / /////
Max stress, MPa 3.15 11.51 0.08 / / / /////
Max strain 0:65 1032:36 1031:64 105////////
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In order to produce a stronger film, several cells were assembled together.
Figures 6(a) to 6(c) shows an example of an assembly of 2, 4 and 16 cells. Table 1
shows the FEM analysis results of the combination of different cells. Compared with
the models of square frame, staggered grid frame and hexagonal frame, the topology
optimization model’s deformation is the least one. Those over all values obtained
from the topology optimization model are much lower than that of square frame,
staggered grid frame and hexogen frame. When the assembly changes to a four-cell
combination, there exists a long slanting blank region in the middle as shown in
Fig. 6(b) which results in the large stress region. The same thing also occurs in a
16-cell assembly as shown in Fig. 6(c). The maximum stress and strain occurs for the
1-cell assembly, and the possible reason is the bilaterally asymmetrical structure
distribution that leads to poor tensile properties. The minimum stress and strain
(a) (b)
(c) (d)
(e)
Fig. 4. (Color online) The topology optimization results show that of removing 50%, 60%, 70%, 75%
and 80% of the original area of model I by using the SIMP method. The red color means the most
necessary part of the wing frame. Blue region means removing area.
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occurs in the 16-cells model. For the maximum displacement, the 2-cells model
exhibits the least deformation, because in the 4- and 16-cell model, there are regular
higher stress and strain regions which will easily lead to higher extension and in the
1-cell, little structure in the bottom region leads to high extension.
Additionally, the 16-cell model was analyzed under uniform loading and similar
condition and parameter as that of the set described in Sec. 3.1. The maximum
displacement and stress were observed to be 0.13 mm and 3.21 MPa, respectively
and the maximum strain was 7:35 104. Although the maximum stress of the 16-
cell model was larger than those of square frame (3.15 MPa) and hexagon frame
(0.08 MPa), it was found that the maximum displacement and strain were much
smaller than those of square frame, staggered grid frame and hexagon frame. In
general, the wind resistant property of 16-cells model is found to be the strongest.
(a) (b)
(c) (d)
(e)
Fig. 5. (Color online) The topology optimization results show that of removing 50%, 60%, 70%, 75%
and 80% of the original area of model II by using the SIMP method. The red color means the most
necessary part of wing frame. Blue region means removing area.
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For comparing 16-cell model with the square frame, staggered grid frame and
hexagon frame models, all the length and width values of models were set to 48 mm
and 24 mm, respectively. It was found that the total volume of 16-cell model was the
least that indicates a saving of about 50% of the manufacturing material (Table 2).
Further, the minimum displacement was found in 16-cell model among all the four
models. This demonstrates that the 16-cell model has the best ability to resist
deformation besides being able to accommodate the least expensive material. The
maximum stress of 16-cell model was smaller than that of the square frame, but
larger than that of the staggered grid frame and hexagon frame. The possible reason
for the maximum stress of staggered grid frame and hexagon frame is due to the
appearance in membranes. This implies that the influence of the structure is greater
than the influence of the material properties. The conditions of strains are similar. In
general, the 16-cell model uses the least amount of material and also can simulta-
neously meet the maximum stiffness requirements.
Figure 7(a) illustrates the schematic diagram of a 16-cell structure for the roof of
greenhouse. In this regard, further research needs to be done on the film which is
modeled as an isotropic and non-linear material. We note that since it is a complex
biological material with an anisotropic nature, it ignores the corrugation effect on
Table 2. The comparison of the volumes of different models.
Membrane
volume (mm3Þ
Reinforcing rib
volume (mm3Þ
Total
volume (mm3Þ
16-cell model 141.13 305.63 446.76
Square frame 115.21 779.93 895.14
Staggered grid frame 98.72 895.35 994.07
Hexagon frame 135.79 803.45 939.24
(a) (b)
(c)
Fig. 6. (a) to (c) images show the 2-, 4-, and 16-cells combination types.
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the actual dragonfly wing and the veins flow of tissue fluid mechanics of dragonfly
flight performance. However, it is also to be mentioned that the basic understanding
gained from this research lays the foundation for further, more specific investiga-
tions to be made into the subject of dragonfly wings. Fabricating the biomimetic
structural film will be the next step in this research according to the corrugation
structure found in dragonfly wing (Fig. 7(b)).
4. Summary
Nature has provided millions of inspiration for the engineering application. Dra-
gonfly’s air flight attitude and wings architecture play a critical role to achieve its
flying ability. The dragonfly wing venation was investigated for designing biomi-
metic lightweight and stable greenhouse roof. And the square frame, the staggered
grid frame, the hexagonal frame and the topology optimization structures were
established. The TOM was used to extract vein structure and design biomimetic
films. It was found that for the optimization area of 25%, the structure was con-
tinuous and the simplest, and was therefore chosen for the study. Our FEM analysis
confirmed superior tensile mechanical properties of the films. In order to produce
stronger films, several cells were assembled and the FEM analysis results showed
(a)
(b)
Fig. 7. (a) The schematic diagram of biomimetic structural film used in roof of greenhouse; (b) the
further biomimetic roof with the corrugation structure found in dragonfly wing.
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that the deformation of the 2-cell model was smaller compared with the 1-cell, 4-cell
and 16-cell models. Our results on the biomimetic structure design that mimicks the
dragonfly wings shows promise to design and engineer advanced biomimetic films
for the efficient greenhouse roof. Further research could include fabricating and
optimizing biomimetic films and structure that would replicate the actual dragonfly
wing along with the veins flow of tissue fluid mechanics.
Acknowledgment
This work was supported by National Natural Science Foundation of China (No.
31172144 and No. 51101072), National Science & Technology Pillar Program of
China in the Twelfth Five-year Plan Period (No. 2014BAD06B03), by the Devel-
opment Program of Science and Technology of Jilin Province of China (No.
201303040NY), and by \Project 985"of Jilin University.
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