Optimum Design of UAV Wing Skin Structure with a High Aspect Ratio Using Variable Laminate Stiffness

Abstract

This paper quickly calculated the design variables to satisfy the strength and stability conditions, the dominant design verification conditions of the composite wing structure, through a genetic algorithm. It developed a variable stiffness stacking optimization process applicable to aircraft wing structure design. We proposed a laminate parameter-based optimization strategy that considers the stiffness characteristics of the two-dimensional elements used as design variables. Compared with the optimization results obtained using continuous stiffness optimization as an optimization process function of laminate sequences with genetic algorithms, we obtained a reasonable stiffness distribution while complying with critical guidelines related to individual composite layup designs. The results of the stiffness optimization design were implemented as a finite element model, and the results were verified through NASTRAN. We demonstrated the functionality of the stiffness optimization process by obtaining results satisfying the set response conditions, i.e., strength and stability, in many design areas of the wing.

Full text

Citation: Jang, J.-H.; Ahn, S.-H.
Optimum Design of UAV Wing Skin
Structure with a High Aspect Ratio
Using Variable Laminate Stiffness.
Appl. Sci. 2022,12, 9436. https://
doi.org/10.3390/app12199436
Academic Editor: Dario Richiedei
Received: 6 September 2022
Accepted: 16 September 2022
Published: 21 September 2022
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applied
sciences
Article
Optimum Design of UAV Wing Skin Structure with a High
Aspect Ratio Using Variable Laminate Stiffness
Jun-Hwan Jang 1and Sang-Ho Ahn 2, *
1Department of Mechanical Design, Yuhan University, Bucheon 13809, Korea
2Department of Mechanical & Automotive Engineering, Shinhan University, Uijeongbu 11644, Korea
*Correspondence: ahnsh@shinhan.ac.kr; Tel.: +82-10-6617-8514
Abstract:
This paper quickly calculated the design variables to satisfy the strength and stability
conditions, the dominant design verification conditions of the composite wing structure, through a
genetic algorithm. It developed a variable stiffness stacking optimization process applicable to aircraft
wing structure design. We proposed a laminate parameter-based optimization strategy that considers
the stiffness characteristics of the two-dimensional elements used as design variables. Compared
with the optimization results obtained using continuous stiffness optimization as an optimization
process function of laminate sequences with genetic algorithms, we obtained a reasonable stiffness
distribution while complying with critical guidelines related to individual composite layup designs.
The results of the stiffness optimization design were implemented as a finite element model, and
the results were verified through NASTRAN. We demonstrated the functionality of the stiffness
optimization process by obtaining results satisfying the set response conditions, i.e., strength and
stability, in many design areas of the wing.
Keywords:
slender wing; genetic algorithm; variable stiffness; composite structure; high aspect
ratio; optimization
1. Introduction
Worldwide, unmanned aerial vehicles are drawing significant attention in the mil-
itary/private sector to carry out reconnaissance, tracking, surveillance, communication
broadcasting, and attacks. Until now, missions have been achieved mainly by human-
crewed aircraft, but the same mission can be achieved, or more dangerous missions can be
performed through unmanned aerial vehicles. In addition, unmanned aerial vehicles have
the advantage of being more economical than human-crewed aircraft. In order to increase
economic efficiency and practicality in aircraft design, the mass of the aircraft plays a deci-
sive role. Composite materials are essential for mass reduction and have excellent material
properties. Composite material has excellent stiffness and a significantly lower density
than the weight generated compared to the metal material. In addition, the orthogonal
rigidity properties of a single composite layer may be selectively applied, and the rigidity
may be adjusted to react better to load transfer. As design, analysis, and manufacturing
technologies develop, the frequency of applying composite materials to structures that
deliver aircraft loads rapidly increases.
In a related study, Mamalis et al. [
1
] presented the energy absorption capacity of compos-
ite materials and studied more practical aspects of collision characteristics.
Koohi et al
. [
2
] de-
veloped a modified 1-D structural dynamics model for the aeroelasticity analysis of composite
wings subjected to large deformations and performed deformation behavior.
Vasiliev et al.
[
3
]
proposed an actual method for interpretation after combining anisotropic beams with com-
posite beams with controlled characteristics. Farsadi et al. [
4
] studied the effects of the fiber
and torsion angles of CAS lamination composition on nonlinear aeroelasticity margins
and marginal behavior. Jiang et al. [
5
] studied the aerodynamic properties of synthetic
Appl. Sci. 2022,12, 9436. https://doi.org/10.3390/app12199436 https://www.mdpi.com/journal/applsci

Appl. Sci. 2022,12, 9436 2 of 23
laminated trapezoidal panels considering the compressibility of supersonic airflow and
shock waves and developed an effective finite element method. Gu et al. [
6
] analyzed
the simplified finite element model of a composite wing box and the analysis method
for the dimensional determination of structural members. Lee et al. [
7
] studied methods
and procedures for the structural design of improved unmanned air vehicles to improve
long-term flight and applied them to the entire wings of composite materials for room
temperature curing. Kim et al. [
8
] performed a static aeroelasticity analysis capable of
calculating the air force for the deformed shape of a composite wing. Han et al. [
9
] per-
formed load analysis on the wings of the composite material SUNMIK aircraft under
development. Zhao et al. [
10
] proposed a two-stage optimization in which the system is
adjusted according to structural deformation for composite wings, and the layout meets
the constraints at the subsystem level. Mastroddi et al. [
11
] developed an MDO approach
based on integrated modeling to perform optimization using shape variables and standard
structure design variables. Haddapour et al. [
12
] optimized composite material wings
using a linear horizontal change in the fiber direction resulting from a variable strength
structure. Jing et al. [
13
] suggested high efficiency and the possibility of a large-scale
composite material structure design by improving the variables handled separately and the
constraints imposed in each step and expanding them from individual panels to the entire
structure. Chintapali et al. [
14
] optimized composite wings’ reinforced panel structure
design that met the constraints by using lamination thickness and various stringer spacing.
However, while optimizing, research was conducted for a more efficient approach due
to increased design time and cost due to computational complexity and many design
variables.
Wan et al
. [
15
] studied wing optimization using an electron/sensitivity-based
mixing algorithm to minimize the structural load of wings using blade lamination thick-
ness as a design variable.
Kameyama et al.
[
16
] studied the effect of laminated shape on
the vibration and dispersion characteristics of composite wings using genetic algorithms.
Seesta et al. [
17
] studied the effect of wing box design optimization problems on optimal
design using a guide-based design methodology and a genetic algorithm. Fan et al. [
18
]
optimized the stacking order of composite material structures using ply-drops based on
genetic algorithms to increase the efficiency between symmetrical and balanced structures
and lower the structure weight. Kim et al. [
19
] applied genetic algorithm techniques and
branching methods to minimize the wing deformation energy and improve the wing’s
structural safety under wind gusts. Kang et al. [
20
] conducted movement analysis of a
composite material structure, which gets compressive load and optimized design with
minimum load and breaking strength using a finite element program and parallelization
genetic algorithms. Yoon et al. [
21
] performed an optimization design between multiple
fields at the primary stage, applied genetic algorithms to optimization, and used gradient
methods to non-planar shapes to compare and analyze efficiency.
Lim et al.
[
22
] performed
optimization to find an accurate solution to the aircraft’s performance and structure and
designed using PBLI, a genetic algorithm. Cho et al. [
23
] investigated various stacked
structures that were insufficient in existing optimization techniques by applying genetic
algorithms to rigid and weight optimization designs. Kim et al. [
24
] demonstrated that
the improvement of genetic algorithms and the optimization of applying genetic algo-
rithms to aerodynamic forms of 2-D/3-D wings are similar to traditional design methods.
Mahfoud et al.
[
25
] presented a genetic algorithm for adjusting optimal PID parameters in
DTC to control DFIM using objective functions such as integral square error, integral time
absolute error (ITAE), and integral absolute error.
Sitek et al
. [
26
] proposed a formal model
of constraints and questions about extended vehicle routing problems for drones, including
a dynamic selection of drone take-off points, two-way delivery (delivery and pickup),
various types of delivery, delivery allocation to drones, drone allocation to vehicles, and
optimal drone number selection.
Junqueira et al
. [
27
] described a simulation optimization
methodology that combines simulation, genetic algorithms, and new solution representa-
tions to design an integrated plan for container relocation in a port yard and a storage plan
problem to unload ships through the port. Finally, Chen et al. [
28
] used genetic algorithms

Appl. Sci. 2022,12, 9436 3 of 23
and discrete particle cluster optimization algorithms to manage the complexity of the
problem, calculate feasible and quasi-optimal trajectories for mobile sensors, and determine
the demand for movement between nodes. Cheng et al. [
29
] described parametric mod-
eling and design sensitivity analyses performed on hat stiffener elements for single- and
multiple-hat-stiffened panels using parametrically defined scripting finite element analysis
(FEA) models and an idealized analytical solution. Schlothauer et al. [
30
] optimized a UAV
wing structure that carries more than 100 times its weight and was developed and tested to
validate the design approach and demonstrate load carrying ability and manufacturing
quality.
Sohst et al.
[
31
] conducted non-linear aeroelastic analyses using multi-fidelity tools
to assess whether geometric non-linearities affected the optimized designs. The wing
structure of the reconnaissance UAV is a thin and long shape, as it increases the duration
of flying time. To maximize the efficiency of mission performance, the duration of flight
in the mission area should be much longer than that of manned aircraft. Reducing drag
and improving productivity should also be considered a shape suitable for surveillance
reconnaissance and long-term flight. However, all shapes must be applied, and the fabri-
cation process of the structure requires considerable manufacturing know-how, and it is
difficult to ensure the reliability of the structure. In addition, interference between the outer
skin and the inner structure should be overcome, and a detailed optimal stacking design is
required for each wing part.
This paper uses genetic algorithms to consider the characteristics of thin and high
aspect ratio wing structures and to achieve mass optimization. It provides a framework
for a method for finding optimal stiffness or laminate sequence distribution. Through
genetic algorithms, design variables are calculated to quickly satisfy the dominant design
conditions of composite wing structures and strength and stability conditions through
variable lamination. The stiffness change should be performed directly when changing
the fiber angle or thickness within the part. In addition, it intends to develop a numerical
analysis that can be concerned with responses to static strength and stability in the design
of the UAV wings and is an optimization framework of variable stiffness. Finally, the
stiffness optimization design results obtained through genetic algorithms are implemented
as finite element models, and the results of finite element analysis are verified to satisfy the
design constraints using NASTRAN, a commercial structural analysis program.
2. Theory for UAV’s Wing Structure Optimization
2.1. Principle of Genetic Algorithm
Genetic algorithms apply the laws of the natural world in which individuals with
solid viability evolve into superior offspring by adapting to the natural world based on
genetics and the principle of biological evolution. Conventional optimization methods use
derivatives and methods of sequentially searching for objective functions in limited space
and constraints or selecting a starting point to start the search. Therefore, although it was
effective in a narrow area, there is a limit to exerting outstanding performance in a wide
area. The genetic algorithm can solve the optimization problem because it does not use the
objective function’s differential concept and performs probability and directional searches.
As shown in Figure 1, the genetic algorithm has a population composed of an array
of binary numbers and performs optimization through the evolution process of selection,
crossover, and mutation in the order of biological evolution. As the object evolves into the
next generation, it transmits highly compatible genetic characteristics to the next generation.
Crossover is the exchange of information by exchanging some of the information from the
selected chromosomes with each other. Through this process, chromosomes are allowed to
come close to the objective function by stochastic selection. In addition, a rapid convergence
speed can reduce the time of analysis. Finally, mutations are the process of obtaining
information that cannot be obtained through selection and crossover, which improves
the convergence of high conformity. This is because the mutation process at random
probabilities performs typical exploratory effects. Moreover, intersecting and mutant

Appl. Sci. 2022,12, 9436 4 of 23
operators increase the group’s diversity to satisfy the optimization objective function,
resulting in classic optimization and differentiation.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 4 of 23
obtaining information that cannot be obtained through selection and crossover, which im-
proves the convergence of high conformity. This is because the mutation process at ran-
dom probabilities performs typical exploratory effects. Moreover, intersecting and mutant
operators increase the group’s diversity to satisfy the optimization objective function, re-
sulting in classic optimization and differentiation.
Figure 1. General operation of the genetic algorithm.
2.2. Operator of Genetic Algorithm
The general genetic algorithm contains three operators: selection, crossover, and mu-
tation. The selection operator selects chromosomes from the object group for reproduc-
tion, as shown in Figure 2. The chromosomes selected are based on their suitability, and
higher suitability results in a large group of fit individuals, and a lower fit gives them a
long evolutionary time. Furthermore, the selection aims to reproduce objects close to the
fitted values, so the fitted values should be selected following the change and balance.
Finally, the crossover operator produces two offspring by exchanging some of the before
and after arrays of random locations in the selected chromosome.
Figure 1. General operation of the genetic algorithm.
2.2. Operator of Genetic Algorithm
The general genetic algorithm contains three operators: selection, crossover, and muta-
tion. The selection operator selects chromosomes from the object group for reproduction,
as shown in Figure 2. The chromosomes selected are based on their suitability, and higher
suitability results in a large group of fit individuals, and a lower fit gives them a long
evolutionary time. Furthermore, the selection aims to reproduce objects close to the fitted
values, so the fitted values should be selected following the change and balance. Finally,
the crossover operator produces two offspring by exchanging some of the before and after
arrays of random locations in the selected chromosome.
2.3. Optimization Procedure Using a Genetic Algorithm
2.3.1. Stacking Sequence for the Composite Structure
To better understand the concept of describing the stacking sequence using the stacking
sequence table, the concept of guide-based mixing should first be described. In variable
stiffness designs, there is generally an appropriate number of panels constituting a certain
rigidity and stacking order accordingly. The process of dropping or adding layers between
adjacent panels is called mixing and is described in Figure 3. In the case of internal and
external mixing, ply drops are allowed in sequential order from outside to inside or vice
versa. Another type of mixing can be found in Figure 3b. Panels I to II are composed of
generalized mixing of all plies from thin to thick layers continuously, and panels II to III
are composed of thick lamination and simple mixing. Two mixing types can be combined
with a guided approach. In this paper, we show the stacking of a single fly, which may
contain at least the thickest panel, according to consideration, and the mixing of Figure 3a
can be effectively explained using guidance. Following the instructions of each panel, the
stacking order is described by defining the fiber angle in the guide, with information about
the number of ply drops per panel.

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Figure 2. Selection, crossover, and mutation.
2.3. Optimization Procedure Using a Genetic Algorithm
2.3.1. Stacking Sequence for the Composite Structure
To better understand the concept of describing the stacking sequence using the stack-
ing sequence table, the concept of guide-based mixing should first be described. In varia-
ble stiffness designs, there is generally an appropriate number of panels constituting a
certain rigidity and stacking order accordingly. The process of dropping or adding layers
between adjacent panels is called mixing and is described in Figure 3. In the case of inter-
nal and external mixing, ply drops are allowed in sequential order from outside to inside
or vice versa. Another type of mixing can be found in Figure 3b. Panels I to II are com-
posed of generalized mixing of all plies from thin to thick layers continuously, and panels
II to III are composed of thick lamination and simple mixing. Two mixing types can be
combined with a guided approach. In this paper, we show the stacking of a single fly,
which may contain at least the thickest panel, according to consideration, and the mixing
of Figure 3a can be effectively explained using guidance. Following the instructions of
each panel, the stacking order is described by defining the fiber angle in the guide, with
information about the number of ply drops per panel.
Figure 2. Selection, crossover, and mutation.

Appl. Sci. 2022,12, 9436 6 of 23
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Figure 3. Schematic overview of a GA stacking sequence optimization in combination with approx-
imations.
The general genetic algorithm contains three operators: selection, crossover, and mu-
tation. The selection operator selects chromosomes from the object group for reproduc-
tion, as shown in Figure 4c. The chromosomes selected are based on their suitability, and
higher suitability results in a large group of fit individuals, and a lower fit gives them a
long evolutionary time. The selection aims to reproduce objects close to the fitted values,
so the fitted values should be selected following change and balance. The crossover oper-
ator produces two offspring by exchanging some of the before and after arrays of random
locations in the selected chromosome. For the optimization of composite material struc-
tures, the genetic algorithm was implemented by FORTRAN, and the developed optimi-
zation code allowed the user to set design variables, limiting functions, and initial values
and consisted of three main components. First, data files that set inputs, such as design
variables, limiting functions, repeatability, initial values to perform optimization, and de-
sign opti-mization tools developed to solve various optimization problems, are available
for linear and nonlinear optimization problems, regardless of the constraints or not. Sec-
ond, factors within the range of design variables are randomly selected, and the upper
factors that best match the objective function are selected and converged through
Figure 3.
Schematic overview of a GA stacking sequence optimization in combination with approximations.
The general genetic algorithm contains three operators: selection, crossover, and muta-
tion. The selection operator selects chromosomes from the object group for reproduction,
as shown in Figure 4c. The chromosomes selected are based on their suitability, and higher
suitability results in a large group of fit individuals, and a lower fit gives them a long evolu-
tionary time. The selection aims to reproduce objects close to the fitted values, so the fitted
values should be selected following change and balance. The crossover operator produces
two offspring by exchanging some of the before and after arrays of random locations in the
selected chromosome. For the optimization of composite material structures, the genetic
algorithm was implemented by FORTRAN, and the developed optimization code allowed
the user to set design variables, limiting functions, and initial values and consisted of three
main components. First, data files that set inputs, such as design variables, limiting func-
tions, repeatability, initial values to perform optimization, and design opti-mization tools

Appl. Sci. 2022,12, 9436 7 of 23
developed to solve various optimization problems, are available for linear and nonlinear
optimization problems, regardless of the constraints or not. Second, factors within the
range of design variables are randomly selected, and the upper factors that best match the
objective function are selected and converged through generation. Because we randomly
screen the stacking angles, we can find the overall minimum of the optimization problem.
Lamination thickness optimization is performed to obtain a minimized mass satisfying
global and regional limiting conditions. The convergence speed is also fast and performs
similarly to the most preferred optimization algorithm. The genetic algorithm program
code was implemented using FORTRAN, and an optimization analysis was performed.
In genetic algorithms, mass is defined for minimization, and applying the same load case
and stiffness optimization code applies the same constraints for deformation and buckling.
Figures 3and 4show the overall optimization process. First, primary stiffness conditions
should be met using genetic algorithms. The optimized framework then maximizes the
stiffness function by changing the stacking angle. The factors within the scope of the design
variables were selected at random, and the top factors that best matched the objective
function were selected and converged over the generation. The random selection of stack-
ing angles allowed us to find the overall minimum of optimization problems. Finally,
stacked thickness optimization was carried out to obtain a minimized mass that satisfies
the limiting condition. Figure 4shows the variable group exchange location criteria, and
the ply is replaced based on the front of the chromosomes of the two stacks, the primary
operator intersecting the two stacking chromosomes in the variable group, and the partial
exchange of the stacking layers between the crossover points. Then, the crossover is ex-
changed exclusively within the variable group. Moreover, providing an opportunity to
escape from optimal with mutant operators reverses a portion of the chromosome with
tiny probabilities.
2.3.2. Stacking Initialization and Replication
Genetic algorithms were sequentially performed to perform optimization, as shown in
Figure 5. Initialization in composite material lamination begins by generating a minimum
number of laminations. Then, any executable ply angle at which any position in the stack
from the adjacent ply matches the design conditions can be selected. The angles were
randomly selected and added to the stacking sequence. The same ply was added to the
corresponding symmetric position in the next step, creating a different column in the
stacking sequence. Crossover of the stacking sequence consists of choosing the same stack,
and the stacking sequence selects the same number from two types and exchanges this
subtype. A stack order mutation was randomly selected from a group of angles allowed
at that location to form a
±θ
change within the stack order, and crossover in the stack
was randomly selected and exchanged between two identical stack groups in two shapes.
The mutation was replaced by a randomly generated number between the minimum and
maximum stack numbers. The selection of genotypes for replication begins with dividing
populations into feasible and non-realizable designs. Genotype selection for reproduction
after recombining was classified into a single population, including non-executable designs.
Two of the genotypes were randomly selected and placed in a new group. There are three
categories of deployed groups: viable genotypes, one possible genotype, and one not
possible genotype. It was performed as necessary for total population generation, with
many cross-operations generated by randomly selecting two contributing factors from
newly placed groups. Eventually, a mutation according to the specified percentage was
performed to complete the creation of a new entity.

Appl. Sci. 2022,12, 9436 8 of 23
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generation. Because we randomly screen the stacking angles, we can find the overall min-
imum of the optimization problem. Lamination thickness optimization is performed to
obtain a minimized mass satisfying global and regional limiting conditions. The conver-
gence speed is also fast and performs similarly to the most preferred optimization algo-
rithm. The genetic algorithm program code was implemented using FORTRAN, and an
optimization analysis was performed. In genetic algorithms, mass is defined for minimi-
zation, and applying the same load case and stiffness optimization code applies the same
constraints for deformation and buckling. Figures 3 and 4 show the overall optimization
process. First, primary stiffness conditions should be met using genetic algorithms. The
optimized framework then maximizes the stiffness function by changing the stacking an-
gle. The factors within the scope of the design variables were selected at random, and the
top factors that best matched the objective function were selected and converged over the
generation. The random selection of stacking angles allowed us to find the overall mini-
mum of optimization problems. Finally, stacked thickness optimization was carried out
to obtain a minimized mass that satisfies the limiting condition. Figure 4 shows the vari-
able group exchange location criteria, and the ply is replaced based on the front of the
chromosomes of the two stacks, the primary operator intersecting the two stacking chro-
mosomes in the variable group, and the partial exchange of the stacking layers between
the crossover points. Then, the crossover is exchanged exclusively within the variable
group. Moreover, providing an opportunity to escape from optimal with mutant opera-
tors reverses a portion of the chromosome with tiny probabilities.
Figure 4. Progress of genetic algorithm of binary code according to composite material stacking and
angle (chromosome, cross-over, mutation).
Figure 4.
Progress of genetic algorithm of binary code according to composite material stacking and
angle (chromosome, cross-over, mutation).

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Figure 5. Process of operating a genetic algorithm for a composite wing structure [32].
3. Design Setting of Optimum Design in UAV Main Wing Skin
For the battlefield to expand, reconnaissance UAVs also need to expand their mission
radius and structural design to increase the flying time of drones. The time to stay in the
mission area is much longer than crewed aircraft and can maximize the efficiency of the
flight. Figure 6 shows the shape of UAV with a large wing structure applied in this paper.
The application of a fixed, high aspect ratio of main-wing, considering the design weight
and drag-reduction effects, and suitable features for surveillance and long-term construc-
tion should also be considered to reduce drag and improve production. The wing struc-
ture was applied with integral composites and cold bonding, preventing interference
problems between the cladding and interior structures, and the optimum laminate design
for each part was applied.
Figure 5. Process of operating a genetic algorithm for a composite wing structure [32].
3. Design Setting of Optimum Design in UAV Main Wing Skin
For the battlefield to expand, reconnaissance UAVs also need to expand their mission
radius and structural design to increase the flying time of drones. The time to stay in
the mission area is much longer than crewed aircraft and can maximize the efficiency of
the flight. Figure 6shows the shape of UAV with a large wing structure applied in this
paper. The application of a fixed, high aspect ratio of main-wing, considering the design
weight and drag-reduction effects, and suitable features for surveillance and long-term
construction should also be considered to reduce drag and improve production. The wing
structure was applied with integral composites and cold bonding, preventing interference
problems between the cladding and interior structures, and the optimum laminate design
for each part was applied.

Appl. Sci. 2022,12, 9436 10 of 23
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Figure 6. Structure configuration and optimization area of UAV slender wing.
3.1. Idealization of UAV Wing Structure
The optimum design was carried out on reinforced composite laminates using ge-
netic algorithms. The optimum design aims to find the reinforcement’s size and location
to minimize weight, the skin and reinforcement stacks, and the number of stacks and
stacks of the stiffener with a quasi-isotropic layer in a skin of a constant size. The stiffener
performs the optimum design for the I-type case, and the stiffener and skin are laminated
to be shaped and then glued or co-shaped. Figures 6 and 7 show the overall shape, load,
and boundary conditions. To determine the buckling load, the location and size of the
reinforcement were arranged, as shown in Table 1, and the size of the stiffener was calcu-
lated for both the skin and reinforcement. Table 2 shows the properties and strength of
the material applied to the blade type structure and skin shape, which are optimized ob-
jects. The material's properties are the input value of the optimization analysis, and the
strength value is used as a reference value for comparing the optimal design results.
Table 1. Geometry information and blade-type stiffener shape dimensions.
Blade-Type Stiffener Shape Dimensions
length (Skin), L [mm]
250
width (Skin), W [mm]
160
location (Stiffener), s [mm]
30
width (Flange), F [mm]
24
width (Web), W [mm]
25
Laminate Stacking (Skin)
[04/-454/+454/904]s
Figure 6. Structure configuration and optimization area of UAV slender wing.
3.1. Idealization of UAV Wing Structure
The optimum design was carried out on reinforced composite laminates using genetic
algorithms. The optimum design aims to find the reinforcement’s size and location to
minimize weight, the skin and reinforcement stacks, and the number of stacks and stacks of
the stiffener with a quasi-isotropic layer in a skin of a constant size. The stiffener performs
the optimum design for the I-type case, and the stiffener and skin are laminated to be shaped
and then glued or co-shaped. Figures 6and 7show the overall shape, load, and boundary
conditions. To determine the buckling load, the location and size of the reinforcement were
arranged, as shown in Table 1, and the size of the stiffener was calculated for both the
skin and reinforcement. Table 2shows the properties and strength of the material applied
to the blade type structure and skin shape, which are optimized objects. The material’s
properties are the input value of the optimization analysis, and the strength value is used
as a reference value for comparing the optimal design results.

Appl. Sci. 2022,12, 9436 11 of 23
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Laminate Stacking (Stiffener)
[02/-452/+452/902]s
Weight [kg]
0.30
Table 2. Composite material properties, wing skin material.
E11 (GPa)
E22 (GPa)
G12 (GPa)
G13 (GPa)
G23 (GPa)
ν12
146.00
9.00
3.40
3.40
2.60
0.33
XTension (MPa)
XComp (MPa)
YTension (MPa)
YComp (MPa)
Shear (MPa)
t-ply
(mm)
2251.00
1078.00
44.00
200.00
69.00
0.19
Figure 7. The geometry of the blade stiffened the panel.
3.2. Factor and Design Variables for the Genetic Algorithm
The more constraints there are, the smaller the generation can find an optimization
value. In this paper, only the constraints for the first failure mode and the buckling failure
mode were used, and optimization was carried out based on the values used in the actual
work. Positive margin of safety (M.S.) values used in actual work are generally deter-
mined by the experience of development projects or engineers, and it is recommended to
set the minimum safety rate within the range of 0 < M.S. < 0.5. If the minimum safety rate
is 0.5 or more, it becomes too conservative, which does not mean much of the structural
optimization work. As shown in Equation (1), the Tsai-wu breakage theory used in the
initial breakage mode showed the interaction of flat stress on the right side, and the failure
index on the left side determines that breakage occurs if it is equal to or greater than 1. In
this paper, the convergence value was set to 0.8.
2 2 2
1 1 2 2 11 1 22 2 66 12 12 1 2
2 1 F F F F F F
      
+ + + + + =
,
(1)
where
0.5
1 1 1 1 1 1 ( )
11 22
, , , ,
1 2 11 66 12
22
FF
FF
t c t c t c
X X Y Y X X S
F F F= − = − = = =
.
Figure 7. The geometry of the blade stiffened the panel.
Table 1. Geometry information and blade-type stiffener shape dimensions.
Blade-Type Stiffener Shape Dimensions
length (Skin), L [mm] 250
width (Skin), W [mm] 160
location (Stiffener), s [mm] 30
width (Flange), F [mm] 24
width (Web), W [mm] 25
Laminate Stacking (Skin) [04/-454/+454/904]s
Laminate Stacking (Stiffener) [02/-452/+452/902]s
Weight [kg] 0.30
Table 2. Composite material properties, wing skin material.
E11 (GPa) E22 (GPa) G12 (GPa) G13 (GPa) G23 (GPa) ν12
146.00 9.00 3.40 3.40 2.60 0.33
XTension (MPa) XComp (MPa) YTension (MPa) YComp (MPa) Shear (MPa) t-ply (mm)
2251.00 1078.00 44.00 200.00 69.00 0.19
3.2. Factor and Design Variables for the Genetic Algorithm
The more constraints there are, the smaller the generation can find an optimization
value. In this paper, only the constraints for the first failure mode and the buckling failure
mode were used, and optimization was carried out based on the values used in the actual
work. Positive margin of safety (M.S.) values used in actual work are generally determined
by the experience of development projects or engineers, and it is recommended to set the
minimum safety rate within the range of 0 < M.S. < 0.5. If the minimum safety rate is
0.5 or more, it becomes too conservative, which does not mean much of the structural
optimization work. As shown in Equation (1), the Tsai-wu breakage theory used in the
initial breakage mode showed the interaction of flat stress on the right side, and the failure

Appl. Sci. 2022,12, 9436 12 of 23
index on the left side determines that breakage occurs if it is equal to or greater than 1. In
this paper, the convergence value was set to 0.8.
F1σ1+F2σ2+F11σ12+F22 σ22+F66 τ
122+2F12σ1σ2=1, (1)
where F1=1
Xt−1
Xc,F2=1
Yt−1
Yc,F11 =1
XtXc,F66 =1
S2,F12 =(F11 F22)0.5
2.
In the buckling failure mode, the safety rate was calculated using the interaction
between the compression load and the shear load to verify the structural safety of the wing
skin. In this paper, the convergence value was set to 0.05. In Equation (2), N
x,cr
,N
xy,cr
of
the compression buckling critical load of the simple support structure is as follows:
Nx,cr = ( π
b)2"D11m2(b
a)
2
+2(D12 +2D66)n2+D22 (n4
m2)( a
b)2#, (2)
Nxy,cr = ( π
b)2(D11 ×D223)1/4 "8.125 +5.05(D12 +2D66 )
(D11 ×D22)0.5 #, (3)
Here, aand bare the shape dimensions, D
11
,D
12
,D
22
, and D
66
are the reduced stiffness
Dmatrix, and nand mare 1, 2, or 3.
The values of the factors used in this optimum design issue are shown in Table 3. The
main design variables for performing the optimization analysis of the reinforced composite
laminate are the number of laminations and the lamination angle. Only 0
◦
,
−
45
◦
, +45
◦
,
and 90
◦
were used for the stacking angles, and the values of the genetic algorithm factors
used in this optimization design problem are shown in Table 3. Because the proportion
of appropriate evolution depends on the goodness-of-fit variance within the population,
the size of the population was initially important, and 100 were selected as sufficient
to produce the optimal string. Interbreeding typically involves an exchange between
0.5 ≤p≤0.8 probabilities
, and within that range, the probability of interbreeding is 0.8,
and mutations are the only source of evolution, using the probability of a mutation of 0.5
so that the population is not fixed at a particular location. Generation refers to the process
of repetitive processes, such as selection, hybridization, and mutation, and generally, it is
common to repeat generations of 50 to 500 or more, and here, it is 300 generations. This
study was set based on general criteria because, when implementing genetic algorithms,
various parameters cannot be optimized at once, and there are many things to discuss with
various approaches and variables.
Table 3. Parameters of the genetic algorithm and laminating guidelines.
Parameter Value
Population size 100
Mutation probability 0.8
Crossover probability 0.5
Number of generations 300
Min number of plies 6
Max number of plies 40
Ply thickness 0.19 mm
Max. dropped plies 10
Contiguous plies 2
Fiber angles 45◦-steps
Max. disorientation between adjacent plies 90◦
The design guidelines for optimizing composite material stacking are as follows. The
maximum number of laminated plies was set at least 6 to 40 sheets, and each ply thickness
was 0.19 mm. A maximum of 10 drops between the lamination and lamination were
proposed, and a maximum of 2 consecutive laminations were proposed. The fiber angle

Appl. Sci. 2022,12, 9436 13 of 23
consisted of an interval of 45
◦
, the outer ply was
±
45
◦
, and the maximum angle between
adjacent stacks was 90◦.
3.3. Convergence of Crossover Operator
Setting different conditions at intersections in hybridization operators impacts con-
straints’ convergence because they can produce more diverse objects. To confirm that
convergence was improved over the initial hybridization operators according to the modi-
fied conditions of the cross operators, we compared the cross operators with the results
of Picek et al. [
33
], comparing them under various conditions. Although the optimization
program to which the genetic algorithm used in this paper was different, f(x) =
−
418.9829
was applied when the minimum value x= 420.968 was used in the range of [
−
500, 500]
using the functional expression (4) of the same conditions used in Picek et al. [33].
f(x) =
D
∑
i=1
−xi×sin(q|xi|), (4)
By applying the same conditions, the results in Figure 8show that the conver-
gence of the hybridization operator in a form similar to those of Picek’s results was con-
firmed. After resetting the conditions, the convergence was better than that of the initial
hybridization operator.
Figure 8. Comparison of fitness values for crossover [33].
3.4. Idealization of UAV Wing Structure Objective
The goal of the optimum design applied was to find the design point minimizing the
structural load by setting the buckling load as the design variable. First, the limitation
condition on load was not applied to the design point in which the buckling load was lower
than the design buckling point and increased the buckling load. Moreover, if the buckling
load was higher than the designed buckling load, the load should be minimized to make no
difference in weight but designed to increase the buckling load. The objective function was
defined so that the overall directionality was dominated by the weight factor, but about
10% of the total directionality impacted the buckling load.

Appl. Sci. 2022,12, 9436 14 of 23
4. Optimum Design of UAV Wing Skin
Optimum Design Results by Genetic Algorithm
The initial stacking angle and the number of stacks applied to the idealized UAV wing
cover were arbitrary, and the stacking angles were 0
◦
,
−
45
◦
, +45
◦
, and 90
◦
. The stacking
angle was [0
4
/
−
45
4
/+45
4
/90
4
]s, and the thickness was measured to be 6.08 mm, and the
weight was 0.30 kg. The design framework implements the stacking angle and number,
designs variables defined on the composite wing’s outer shell, and performs calculations
with genetic algorithms. The framework through the genetic algorithm was illustrated by
calculating a combination of optimized lamination angles while converging constraints
over 300 generations. The results in Figure 9were obtained. The number of stacks applied
to the initial wing outer skin was 32 sheets, consisting of [0
4
/
−
45
4
/+45
4
/90
4
]s at a rate of
25% of the laminating angle, and the ratio of the initial laminating number was 36%,
−
45
◦
was 27%, and 90◦was 18%, [06/−454/+453/903]s.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 14 of 23
with genetic algorithms. The framework through the genetic algorithm was illustrated by
calculating a combination of optimized lamination angles while converging constraints
over 300 generations. The results in Figure 9 were obtained. The number of stacks applied
to the initial wing outer skin was 32 sheets, consisting of [04/−454/+454/904]s at a rate of 25%
of the laminating angle, and the ratio of the initial laminating number was 36%, −45° was
27%, and 90° was 18%, [06/−454/+453/903]s.
Figure 9. Optimization results by lamination and weight variation.
Secondary optimization proceeded with optimization of the stacked number and the
stacking angle as a result of primary optimization, the stacking angle was rearranged from
32 to 22 sheets, and the stacking angle was rearranged to [+45/−45/−45/−45/0/0/0/0/0]s, re-
ducing the thickness and weight to 0.24 kg. From the initial shape to the secondary opti-
mization, the number of stacked layers and the stacking angle were optimized, and the
weight was reduced to about 20%.
Moreover, Figure 10 shows the mass optimization response according to generation
and can be divided into two areas based on 30,000 evolutions. From 1 to 30,000 evolutions,
the number of stacks changed significantly to find the optimal thickness, resulting in a
width of significant changes in thickness and weight, while finding the optimal
Figure 9. Optimization results by lamination and weight variation.

Appl. Sci. 2022,12, 9436 15 of 23
Secondary optimization proceeded with optimization of the stacked number and the
stacking angle as a result of primary optimization, the stacking angle was rearranged from 32
to 22 sheets, and the stacking angle was rearranged to [+45/
−
45/
−
45/
−
45/0/0/0/0/0]s,
reducing the thickness and weight to 0.24 kg. From the initial shape to the secondary
optimization, the number of stacked layers and the stacking angle were optimized, and the
weight was reduced to about 20%.
Moreover, Figure 10 shows the mass optimization response according to generation
and can be divided into two areas based on 30,000 evolutions. From 1 to 30,000 evolutions,
the number of stacks changed significantly to find the optimal thickness, resulting in a
width of significant changes in thickness and weight, while finding the optimal lamination
angle ratio. When the design variable and the objective function begin to converge without
changing from approximately generation 80, little weight change occurs, and the ratio
of the optimal stacking water to the stacking angle is obtained. After that, the optimal
stacking order was found by mixing the same stacking water and stacking angle up to
375 generations.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 15 of 23
lamination angle ratio. When the design variable and the objective function begin to con-
verge without changing from approximately generation 80, little weight change occurs,
and the ratio of the optimal stacking water to the stacking angle is obtained. After that,
the optimal stacking order was found by mixing the same stacking water and stacking
angle up to 375 generations.
Figure 10. Optimization result, failure index (Tsai-wu).
As the population progresses, Figure 10 shows the process of converging to the fail-
ure index, one of the design variables. Since it was in the process of finding the optimal
thickness within the area of approximately 80 generations, the change in the number of
stacks and the ratio of the stacking angle changed significantly, so the values were widely
distributed in areas lower than the convergence value. As 80 generations passed, the num-
ber of stacked products with a certain thickness and stacking angle ratio was found, and
the stacking order was optimized within the failure index convergence value area up to
30,000 entities. As a result, the outer shell of the unmanned aerial vehicle wing was opti-
mized according to the design variables and objective functions to realize a weight reduc-
tion of about 20% and was designed in an optimal stacked structure. All restrictions were
also satisfied. As shown in Figure 11, there were many substantial difficulties in compar-
ing the convergence of genetic algorithms with other numerical algorithms. Because many
variables exist due to the setting of various operators used in genetic algorithms, it cannot
be determined which genetic algorithm is most promising. Therefore, it was compared to
the convergence of design variables accordingly through optimization algorithms of the
response surface methodology algorithm (RSM) and kriging algorithm other than the ge-
netic algorithm. The response surface method is one of the statistical methods for model-
ing and analyzing the relationship between multiple variables and response variables,
and is an approach to designing an experiment appropriately to determine the optimum
of multiple variables. Kriging is an approach that calculates the average value of an al-
ready known function and predicts the value of the function at the point of interest.
Figure 10. Optimization result, failure index (Tsai-wu).
As the population progresses, Figure 10 shows the process of converging to the failure
index, one of the design variables. Since it was in the process of finding the optimal
thickness within the area of approximately 80 generations, the change in the number
of stacks and the ratio of the stacking angle changed significantly, so the values were
widely distributed in areas lower than the convergence value. As 80 generations passed,
the number of stacked products with a certain thickness and stacking angle ratio was
found, and the stacking order was optimized within the failure index convergence value
area up to 30,000 entities. As a result, the outer shell of the unmanned aerial vehicle
wing was optimized according to the design variables and objective functions to realize
a weight reduction of about 20% and was designed in an optimal stacked structure. All
restrictions were also satisfied. As shown in Figure 11, there were many substantial
difficulties in comparing the convergence of genetic algorithms with other numerical
algorithms. Because many variables exist due to the setting of various operators used in
genetic algorithms, it cannot be determined which genetic algorithm is most promising.

Appl. Sci. 2022,12, 9436 16 of 23
Therefore, it was compared to the convergence of design variables accordingly through
optimization algorithms of the response surface methodology algorithm (RSM) and kriging
algorithm other than the genetic algorithm. The response surface method is one of the
statistical methods for modeling and analyzing the relationship between multiple variables
and response variables, and is an approach to designing an experiment appropriately to
determine the optimum of multiple variables. Kriging is an approach that calculates the
average value of an already known function and predicts the value of the function at the
point of interest.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 16 of 23
Figure 11. Comparison results of algorithms.
Figure 11 compares the convergence of genetic algorithms, reaction surface methods,
and kriging. Compared to other algorithms, the reaction surface method has a signifi-
cantly smaller range of changes in convergence and converges approximately 250 times
as the optimization process proceeds within a constant convergence. Kriging has the most
extensive range of initial convergence changes, and after 100 times, optimization pro-
ceeded within an inevitable convergence and converged from 270 times. Genetic algo-
rithms have a lower initial convergence than croaking, occur within a higher range than
reaction surface methods, and converge at 80 iterations, which are relatively fewer cycles
than other optimization algorithms. The reasons why genetic algorithms can have faster
convergence conditions are as follows. Compared to the RSM algorithm and Kriging al-
gorithm, there were no restrictions on design variables, limitations, repeatability, and in-
itial input values. It is possible to randomly select factors within the range of design vari-
ables and to select higher factors that best match the objective function and converge
through generations. The results of each optimization algorithm may be different depend-
ing on constraints, but as a result of approaching the current design variable condition, it
was verified that the genetic algorithm converged relatively faster than the other optimi-
zation algorithms.
5. Verification of Optimum Design through Local and Global Analysis
In order to verify the optimal design results calculated by the genetic algorithm,
structural analysis was performed by applying the stacked ply and stacking angle calcu-
lated by the framework using the genetic algorithm. Figure 12 shows the composition of
finite element modeling; 650 shell elements and 1951 nodes were applied to the web;
[+45/−452/+452/902]s were applied to the outer skin, and
[+45/−45/−45/−45/0/90/0/+45/−45/0/90/0]s were calculated through genetic algorithms. The
boundary condition was that both ends of the outer shell were held as fixed ends, and the
side was set as free ends. Finally, the load was analyzed through NASTRAN by applying
a compression load on both sides of the outer shell and applying one of the flight condi-
tions.
Figure 11. Comparison results of algorithms.
Figure 11 compares the convergence of genetic algorithms, reaction surface methods,
and kriging. Compared to other algorithms, the reaction surface method has a significantly
smaller range of changes in convergence and converges approximately 250 times as the
optimization process proceeds within a constant convergence. Kriging has the most ex-
tensive range of initial convergence changes, and after 100 times, optimization proceeded
within an inevitable convergence and converged from 270 times. Genetic algorithms have
a lower initial convergence than croaking, occur within a higher range than reaction sur-
face methods, and converge at 80 iterations, which are relatively fewer cycles than other
optimization algorithms. The reasons why genetic algorithms can have faster convergence
conditions are as follows. Compared to the RSM algorithm and Kriging algorithm, there
were no restrictions on design variables, limitations, repeatability, and initial input values.
It is possible to randomly select factors within the range of design variables and to select
higher factors that best match the objective function and converge through generations.
The results of each optimization algorithm may be different depending on constraints, but
as a result of approaching the current design variable condition, it was verified that the
genetic algorithm converged relatively faster than the other optimization algorithms.
5. Verification of Optimum Design through Local and Global Analysis
In order to verify the optimal design results calculated by the genetic algorithm, structural
analysis was performed by applying the stacked ply and stacking angle calculated by the
framework using the genetic algorithm. Figure 12 shows the composition of finite element
modeling; 650 shell elements and 1951 nodes were applied to the web; [+45/
−
45
2
/+45
2
/90
2
]s
were applied to the outer skin, and [+45/
−
45/
−
45/
−
45/0/90/0/+45/
−
45/0/90/0]s were
calculated through genetic algorithms. The boundary condition was that both ends of the

Appl. Sci. 2022,12, 9436 17 of 23
outer shell were held as fixed ends, and the side was set as free ends. Finally, the load was
analyzed through NASTRAN by applying a compression load on both sides of the outer
shell and applying one of the flight conditions.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 17 of 23
Figure 12. Finite element modeling of the blade-stiffened panel.
5.1. Verification of Optimum Design through Static Analysis
In this section, the design verification of the reinforced composite laminates was per-
formed through static strength analysis. For static strength, the damage index was deter-
mined based on the Tsai-wu failure index in Figure 13, which was a constraint condition.
For an outer shell made of anisotropic material, it was necessary to determine whether to
yield concerning the stress and the direction of the member.
Figure 13. Failure index results according to laminate sequence.
Figure 12. Finite element modeling of the blade-stiffened panel.
5.1. Verification of Optimum Design through Static Analysis
In this section, the design verification of the reinforced composite laminates was
performed through static strength analysis. For static strength, the damage index was de-
termined based on the Tsai-wu failure index in Figure 13, which was a constraint condition.
For an outer shell made of anisotropic material, it was necessary to determine whether to
yield concerning the stress and the direction of the member.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 17 of 23
Figure 12. Finite element modeling of the blade-stiffened panel.
5.1. Verification of Optimum Design through Static Analysis
In this section, the design verification of the reinforced composite laminates was per-
formed through static strength analysis. For static strength, the damage index was deter-
mined based on the Tsai-wu failure index in Figure 13, which was a constraint condition.
For an outer shell made of anisotropic material, it was necessary to determine whether to
yield concerning the stress and the direction of the member.
Figure 13. Failure index results according to laminate sequence.
Figure 13. Failure index results according to laminate sequence.
Figure 13 compares the Tsai-wu failure index values according to stacking order. In
the case of the initial model, it existed at a position lower than the convergence value,

Appl. Sci. 2022,12, 9436 18 of 23
and when only thickness optimization was performed while the optimization proceeds,
the value exists at a position higher than the convergence value, so there was a broken
ply. When the thickness and stacking order are optimized, it can be seen that a value
close to the convergence value exists and satisfies the constraint of the 0.8 failure index.
Figure 14 visually expresses the results of the failure index and shows the maximum
failure index value for each model. Figure 15 compares whether the allowable stresses of
compression and tension are satisfied. In the case of the initial model, the stress generated
in the optimization model generated a stress value lower than the allowable stress, and as
the optimization progressed, the stress value received by the envelope gradually increased.
Therefore, it can be confirmed that a stress value occurred. Each stress distribution is
confirmed in Figures 16 and 17. Although there was a difference in the stress values, the
overall stress distribution of the composite laminate had a similar shape.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 18 of 23
Figure 13 compares the Tsai-wu failure index values according to stacking order. In
the case of the initial model, it existed at a position lower than the convergence value, and
when only thickness optimization was performed while the optimization proceeds, the
value exists at a position higher than the convergence value, so there was a broken ply.
When the thickness and stacking order are optimized, it can be seen that a value close to
the convergence value exists and satisfies the constraint of the 0.8 failure index. Figure 14
visually expresses the results of the failure index and shows the maximum failure index
value for each model. Figure 15 compares whether the allowable stresses of compression
and tension are satisfied. In the case of the initial model, the stress generated in the opti-
mization model generated a stress value lower than the allowable stress, and as the opti-
mization progressed, the stress value received by the envelope gradually increased.
Therefore, it can be confirmed that a stress value occurred. Each stress distribution is con-
firmed in Figures 16 and 17. Although there was a difference in the stress values, the over-
all stress distribution of the composite laminate had a similar shape.
Figure 14. Comparison of each model’s failure index results.
Figure 14. Comparison of each model’s failure index results.

Appl. Sci. 2022,12, 9436 19 of 23
Appl. Sci. 2022, 12, x FOR PEER REVIEW 19 of 23
Figure 15. Comparison of each model’s applied stress results.
Figure 16. Comparison of stress σxx results (left: tension, right: compression).
Figure 15. Comparison of each model’s applied stress results.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 19 of 23
Figure 15. Comparison of each model’s applied stress results.
Figure 16. Comparison of stress σxx results (left: tension, right: compression).
Figure 16. Comparison of stress σxx results (left: tension, right: compression).

Appl. Sci. 2022,12, 9436 20 of 23
Appl. Sci. 2022, 12, x FOR PEER REVIEW 20 of 23
Figure 17. Comparison of stress σxy results (left: tension, right: compression).
5.2. Verification of Optimum Design through Stability Analysis
To verify the structural stability of the wing, buckling analysis was performed using
a finite element average internal load. Due to optimization, the outer skin was applied to
the plate thinner, resulting in overall or local buckling more easily. Table 4 summarizes
the eigenvalues and margins from the first to the fourth mode for each model as the results
of the buckling analysis of the skin applying the optimal design. It can be seen that the
initial buckling value of the initial model is 1.016 eigenvalue, and the minimum margin is
0.02. As the optimization proceeded, in the case of a model with only thickness optimiza-
tion, the eigenvalue was 1.022, the minimum margin was 0.02, and it was confirmed that
it did not converge to the minimum margin of 0.05, which is the constraint. This is because
it can be seen that the minimum margin is 0.05, which converges to the minimum margin
of 0.05, which is the buckling design requirement. Figure 18 visualizes and compares the
primary mode results in the envelopes of each shape model. Figure 18 compares the
Figure 17. Comparison of stress σxy results (left: tension, right: compression).
5.2. Verification of Optimum Design through Stability Analysis
To verify the structural stability of the wing, buckling analysis was performed using a
finite element average internal load. Due to optimization, the outer skin was applied to
the plate thinner, resulting in overall or local buckling more easily. Table 4summarizes the
eigenvalues and margins from the first to the fourth mode for each model as the results of
the buckling analysis of the skin applying the optimal design. It can be seen that the initial
buckling value of the initial model is 1.016 eigenvalue, and the minimum margin is 0.02.
As the optimization proceeded, in the case of a model with only thickness optimization,
the eigenvalue was 1.022, the minimum margin was 0.02, and it was confirmed that it did
not converge to the minimum margin of 0.05, which is the constraint. This is because it can
be seen that the minimum margin is 0.05, which converges to the minimum margin of 0.05,
which is the buckling design requirement. Figure 18 visualizes and compares the primary
mode results in the envelopes of each shape model. Figure 18 compares the buckling results

Appl. Sci. 2022,12, 9436 21 of 23
of the outer shell in primary mode with the initial and optimization models. Figure 18a
shows the shape of buckling by twisting outward from the area under compression load
due to the thick outer skin, and Figure 18b shows the shape of buckling in the entire outer
skin, not in some areas.
Table 4. Comparison results of each model’s stability analysis.
Mode Level
(a) (b) (c)
Eigenvalue (λ)
/M.S(λ-1)
Eigenvalue (λ)
/M.S(λ-1)
Eigenvalue (λ)
/M.S(λ-1)
Mode I 1.016/0.016 1.022/0.022 1.054/0.054
Mode II 1.016/0.016 1.022/0.022 1.095/0.095
Mode III 1.419/0.419 1.050/0.050 1.095/0.095
Mode IV 1.419/0.419 1.056/0.056 1.116/0.116
Appl. Sci. 2022, 12, x FOR PEER REVIEW 21 of 23
buckling results of the outer shell in primary mode with the initial and optimization mod-
els. Figure 18a shows the shape of buckling by twisting outward from the area under com-
pression load due to the thick outer skin, and Figure 18b shows the shape of buckling in
the entire outer skin, not in some areas.
Figure 18. Comparison of Buckling results, 1st Mode.
Table 4. Comparison results of each model’s stability analysis.
Mode Level
(a)
(b)
(c)
Eigenvalue (λ)
/M.S(λ-1)
Eigenvalue (λ)
/M.S(λ-1)
Eigenvalue (λ)
/M.S(λ-1)
Mode I
1.016/0.016
1.022/0.022
1.054/0.054
Mode II
1.016/0.016
1.022/0.022
1.095/0.095
Mode III
1.419/0.419
1.050/0.050
1.095/0.095
Mode IV
1.419/0.419
1.056/0.056
1.116/0.116
Figure 18. Comparison of Buckling results, 1st Mode.

Appl. Sci. 2022,12, 9436 22 of 23
6. Conclusions
In this paper, the following conclusions were obtained using genetic algorithms to
achieve weight optimization by carrying out the optimal stiffness design for numerous
design areas of slender and long-wing structures. First, the design variables were calculated
to quickly meet the prevailing design conditions, strength, and stability conditions of
composite wing structures with variable stacking. As a result, the variable stiffness of the
composite stacking optimization procedure was developed in the design of UAV wing
structures. Furthermore, the stacking sequence of the proposed optimization process by
applying genetic algorithms was able to obtain a reasonable distribution of stiffness while
complying with the critical guidelines related to individual laminated ply designs.
The stiffness optimization process of the proposed composite wing structure was
applied to the UAV wings. It was implemented as a partial model and validated through
NASTRAN. The function of the stiffness optimization process was demonstrated by enter-
ing the response conditions set in many design areas of the wing structure, i.e., satisfying
static strength and stability.
Author Contributions:
Formal analysis, J.-H.J.; Investigation, J.-H.J.; Project administration, S.-H.A.;
Software, J.-H.J.; Writing—original draft, J.-H.J.; Writing—review & editing, S.-H.A. All authors have
read and agreed to the published version of the manuscript.
Funding:
This research was funded by Shinhan University Research Fund, grant number [2021-0007].
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Acknowledgments: This work was supported by the Shinhan University Research Fund, 2021.
Conflicts of Interest: The authors declare that there is no conflict of interest.
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