Volume 7, Issue 3, March – 2022 International Journal of Innovative Science and Research Technology

ISSN No:-2456-2165

Topology Optimization of Aircraft Wing Fuselage

Lug Attachment Bracket
R S Harish, K Veda Abhishek, Harish U V, Tharundeep K G. Sakthivel, N Raghukiran
School of Mechanical Engineering Centre for Automation, School of Mechanical
Vellore Institute of Technology, EngineeringVellore Institute of Technology,
Chennai, India. Chennai, India.

Abstract:- Topology optimization has become an effective design [2,3]. The wings and the fuselage are the most integral
tool for light-weight and performance design, especially structural components of an aircraft. Wings are subjected to a
in the aeronautics and aerospace industry. It has proved spectrum of flight loads. During every flight, the airplane
to meet the requirement to produce intricate parts that takes off, flies to certain altitudes which pressurizes the
are more robust and lightweight. This technology has wings and the fuselage, and as a result metal fatigue is
proved costeffectiveness, improved payload capacity, and created. So in all the operable conditions, the wing and the
increased fuel economy in the aerospace sector, and fuselage must be rigidly attached together and in case of
enabled structural components to deliver the same or failure might lead to adverse accidents [4]. The lug is a part
enhanced performance while using less material. Among that connects the wing and the fuselage. Sometimes, the
the aircraft, the fuselage and the wings are important consequences of the failure of the lug can be very severe that
structural components. Wing fuselage lug attachment it might lead to the separation of the aircraft structure. Thus,
bracket is the connecting element that connects the wings it is important to establish damage-tolerant design criteria
and the fuselage. Catastrophic failure of the bracket may and analysis methods to ensure high performance and
sometimes lead to the separation of the aircraft structure. reliability of aircraft lug attachments [4,5,6]. To maintain the
This work is focused on modelling, shape optimization, load-carrying capacity and performance of the bracket, the
and analysis of an aircraft wing-fuselage lug attachment lug design must be optimized for a better strength to weight
bracket. The methodology involves modelling and shape ratio. A detailed study must be carried out on the load cases
optimization of the bracket using different sets of and the load to which the bracket is subjected must be
materials. Finite elemental modelling and structural calculated. Shape optimization must be performed on the
analysis were done to study the stresses and deformation structural domain of the lug according to the load path
on the bracket. Fatigue damage estimation is carried out criticality to achieve an optimal design. The structural
to study the behavior of bracket for repeated cyclic analysis must be carried out on the shape optimized bracket
loading. and comparison must be made between conventional design
and topology optimized design in aspects of the factor of
Keywords:- Topology optimization, wing-fuselage attachment safety (FOS) and deformation. Design decisions must be
bracket, fatigue damage, static structural, load factor, mass made without compromising on performance and load-
reduction. carrying capability to arrive at an optimal design. To validate
the design for repeated loading conditions, fatigue damage
I. INTRODUCTION estimation to crack initiation has to be carried out for a
An aircraft is a machine capable of flying by gaining typical flight load spectrum [6]. In this current work, an
support from the air. It has a complex structure comprising of attempt has been made to design and optimize the structure
basic components such as fuselage, wing, tail units, and of the wing-fuselage lug attachment bracket for a better
control system. Advancements in aircraft development have strength to weight ratio and estimate the fatigue damage
been rapid over the years. One of the active areas of factor for a typical flight load spectrum.
technological advancements is to meet the rising II. METHODOLOGY
environmental concerns dealing with pollution and global
warming due to aircraft emissions. This has led to various This paper is focused on 3D modelling and shape
research for alternative clean energy sources as well as to optimization of the bracket. Finite elemental modelling and
increase fuel efficiency [1]. Weight is one of the most structural analysis are done to study the stresses and
important factors affecting the efficiency of aircraft and flight deformation on the bracket. To understand the dynamic
endurance. Significant weight reduction can result in characteristics of the bracket under repeated cyclic loading
improvised efficiency, increased fuel economy thus and to validate the safety and reliability of the design, fatigue
increasing flight endurance. Reducing the mass of the aircraft damage estimation is done to calculate the life to crack
has proved to be an effective method in increasing the fuel initiation.
efficiency as lower mass requires lesser lift force and thrust
during flight [2]. Topology optimization has proved to be an
effective tool for mass reduction and performance design in
the aerospace industry. Topology optimization is an
algorithmic method of optimizing the distribution of material
within a specified structural domain according to the load
cases and boundary conditions to achieve the most efficient

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Volume 7, Issue 3, March – 2022 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
Ultimate load = 169050×1.5 = 253575 N

Load distribution of on fuselage and wings = 25% and

75%.

Total load acting on the wings = 253575×0.75 =

190181.25 N

Load acting on each of the wings = 190181.25/2 =

95090.625 N

Number of spars in the wing = 3

Load should be shared by each of the spars:

i) spar 1 = 15% ii) spar 2 = 40% iii) spar 3 = 45%
For this analysis, spar 2 is chosen.

Therefore, load acting on it is = 95090.625×0.45 =

42790.78 N

Total load the bracket is subjected to, W = 42790.78 N

This load will induce the bending moment acting at the

Fig. 1: Workflow root of the bracket. Thus, it will act as a cantilever beam.
A. Geometric Parameterization and CAD Modelling Distance of the root of bracket from the lug node =
The wing-fuselage attachment bracket was modelled in 727.2 mm
Solidworks 2019 and the below figure shows the different
configurations of the model. Various structural components Bending moment created at the root of the bracket =
of the wing-fuselage lug attachment bracket are: 42790.78 N × 727.2 mm
 Lug: A component with pin holes that connects the wing
with the fuselage. BM = 31108.89 Nm
 I-spar: Integral part of wings which carries the weight of C. Material Specification
the wings and is subjected to flight loads. Wing surfacing is The material chosen for lug is heat-treated Steel alloy
done on the I-spar. AISI 4340 due to its high strength, toughness, and fatigue
 Rivets: Permanent mechanical fasteners of the cylindrical strength [4,5,6]. For I-spar, the suitable material was decided
structure. as aluminum alloy 2024 T351 as it has an excellent strength-
to-weight ratio. It also has good machinability and surface
finish capability [4,5,6].

Sl. Parameters Steel Alloy Aluminium Alloy

No. AISI-4340 2024-T351
1 Young’s 203000 72400
Modulus (MPa)
2 Poisson’s ratio 0.32 0.33
3 Ultimate tensile 1835 483
strength (MPa)
4 Yield stress,σy 1550 345
(MPa)
Table 1: Material property table for chosen materials for lug
and I-spar.

D. Topology Optimization
Topology optimization is an algorithmic method of
Fig. 2: Geometric configuration of the wing fuselage lug
optimizing the distribution of material within a specified
attachment bracket
structural domain according to the load cases and boundary
B. Load Case Study and Calculations conditions to achieve the most efficient design [1,2,3].
Airplane type = medium size aircraft Topology optimization of the bracket was carried out in
Weight of Aircraft (MTOW) = 5750 kg = 56350 N Autodesk Fusion 360. The optimization process is as follows:
Load factor considered in design = 3g Initially, the shape optimization target needs to be set. In our
Limit load on the structure = 169050 N case, the lug part of the wingfuselage attachment bracket is
Factor of safety = 1.5 set as the optimization target. Under the material study
feature, respective materials for lug (steel alloy AISI 4340)

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Volume 7, Issue 3, March – 2022 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
and I-spar (aluminum alloy 2024 T351) was applied. A
model-based size mesh is generated for the bracket with
26348 nodes and 105260 elements. Under optimization
settings, target mass is set as below or equal to 60% with
maximizing stiffness as the goal objective. The entire I-spar
region is set as a preserved region as we aim to optimize the
lug part of the bracket. And a 40 mm offset from both the lug
holes is set as a preserved region considering safety aspects.
The load case needs to be specified for the model. Both the
lug holes of the bracket are structurally constrained with all
six degrees of freedom. A vertical load of 42791 N is applied
at one end of the I-spar acting upwards which creates the
required bending moment. Contacts type is set as bonded Fig. 4: Finite elemental model of the bracket
contact.
III. RESULTS AND DISCUSSIONS

A. Static Structural Analysis Load and Boundary Conditions

The below figure shows the load and boundary conditions
applied on the topology optimized bracket. Both the nodes of
the lug section of the bracket are structurally constrained with
all six degrees of freedom. A vertical load of 42791 N is
applied at one end of the I-spar acting upwards (Y-direction)
which creates the required bending moment [6,8].

Fig. 3: Optimal topology design for the lug portion of the

bracket

A significant mass reduction of nearly 30% was

achieved. Mass of the lug was reduced from 27.99 kg to
19.64 kg after shape optimization. The above figure shows
the load path criticality of the lug for the applied load case.
Fig. 5: Load and boundary conditions applied on the bracket
Name Value B. Analysis Readings
Mass before 27.999 kg The maximum deformation was found to be 0.46 mm and
it occurred on the edge of the I-spar region. The below figure
Mass after 19.640 kg shows the total deformation contour of the bracket when
Mass Ratio 70.15% subjected to a bending load of 42791 N. The observed
Table 2: Topology Optimization Summary displacement (0.46 mm) lies within 1.3% of the total length
of the bracket. This is permissible according to the aircraft
E. Finite Elemental Modelling industry standards [5].
The finite element modelling (FEM) is a discretization
technique in structural mechanics. It uses a numerical method
to approximate the solution of boundary and/or initial value
problems characterized by partial differential equations
(PDEs) [7]. A finite elemental model of the topology
optimized bracket was carried out in ANSYS Workbench
19.0. Meshing is the process where the structural domain is
subdivided into smaller domains or elements known as
meshes. The entire structural domain was meshed with
tetrahedron type meshing. The fine mesh was accomplished
in high-stress gradient domains and the coarse mesh was
accomplished in low-stress gradient domains. As a result of
meshing 1666570 nodes and 826297 elements were
developed.

Fig. 6: Total deformation contour of the bracket

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Volume 7, Issue 3, March – 2022 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
The maximum equivalent stress value was observed to D = ∑ (N𝑖/𝑁𝑓) = C
be 137 MPa occurring at the flange portion of the lug. The Where D = damage accumulate factor; Ni = applied
below figure shows the stress contour of the bracket when number of cycles; N𝑓 = number of cycles to failure; C =
subjected to a bending load of 42791 N. constant equal to 1.

Cycles Range of Stresses in lug portion

applied Load factor (MPa)
(Ni) g Minimum Maximum
stress stress
1000000 0.5g - 1.0g 20 73
712740 1.0g - 1.5g 30 109
156850 1.5g - 2.0g 39 145
69534 2.0g - 2.5g 49 181
35619 2.5g - 3.0g 60 218
Fig. 7: Stress contour of the bracket 20234 3.0g - 3.5g 70 254
12798 3.5g - 4.0g 80 290
The minimum factor of safety (FOS) for the optimal 8680 4.0g - 4.5g 90 326
topology design was found to be 1.82. Thus, we can conclude 4.5g - 5.0g
6268 100 363
that our design is safe.
4668 5.0g - 5.5g 109 399
3568 5.5g - 6.0g 120 435
Table 4: Stress values in the lug for flight load spectrum

The total damage accumulate (D) was calculated for

different load factors in the flight load spectrum and the total
damage accumulate factor is found to be 2.030959e-1 < 1.
According to Palmgren-Miner’s rule, the design is safe if the
damage accumulation factor happens to be less than unity
[6,10]. The result obtained is much lesser than unity and thus
we can validate that our design is safe and reliable. So, under
all the flight load spectrum the wing-fuselage lug attachment
bracket is safe and no crack initiation happens.

Fig. 8: The factor of safety [FOS] of the bracket Failure

Amplitude Mean Stress Damage
no.
stress stress ratio accumulate
C. COMPARISON BETWEEN CONVENTIONAL AND cycles
(MPa) (MPa) R D
TOPOLOGY OPTIMIZED DESIGN Nf
>10^7 26.50 46.50 0.27 0.1000000
Topology Optimized >10^7 39.50 69.50 0.28 0.0712740
Conventional Design
Design >10^7 53.00 92.00 0.27 0.0156850
Factor of Factor of >10^7 66.00 115.00 0.27 0.0069534
1.81 1.82
safety [FOS] safety [FOS] >10^7 79.00 139.00 0.28 0.0035619
Total Total >10^7 92.00 162.00 0.28 0.0020234
0.46 mm 0.46 mm
deformation deformation >10^7 105.00 185.00 0.28 0.0012798
Maximum Maximum >10^7 118.00 208.00 0.28 0.0008680
138 137
stress (MPa) stress (MPa) >10^7 131.50 231.50 0.28 0.0006268
Table 3: Design comparison >10^7 145.00 254.00 0.27 0.0004668
D. Fatigue Damage Estimation ∑D 0.2030959
From the results of static structural analysis of wing- Table 5: Fatigue damage accumulate factor under typical
fuselage lug attachment bracket, it is observed that the flight load spectrum
maximum stress occurs at the lug part whose material is steel
IV. CONCLUSION
AlSl 4340. Fatigue damage estimation of the bracket to crack
initiation was carried out in accordance with a typical flight Mass reduction is of major interest in improving aircraft
load spectrum [6,9]. A damage-tolerant design criterion and performance. In this work, we have designed and optimized
stress-life approach has been followed for carrying out the structure of the aircraft wing-fuselage bracket with
fatigue damage estimation [6,10]. Fatigue failure primarily topology optimization tools by studying the load paths and
occurs in three stages, i.e. crack initiation, crack propagation, validated the design by estimating the fatigue damage for
and final rupture. Calculation of fatigue life to crack repeated cyclic loading. A significant mass reduction in the
initiation is carried out by using Palmgren-Miner’s Rule. lug part of nearly 30% (27.99 kg to 19.64 kg) was achieved
According to Miner’s rule, by the topology optimization technique. Maximum

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Volume 7, Issue 3, March – 2022 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
deformation of 0.46 mm, maximum equivalent stress of 137 [7.] Gokhale N. S. 2008. Practical finite element analysis.
MPa was observed and the minimum factor of safety of 1.82 Finite to infinite.
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static structural analysis, the maximum stresses observed was Attachment Bracket Lug for Fighter Aircraft.
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[9.] Rigby R. and Aliabadi M. H. 1997. Stress intensity
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Fatigue crack growth analysis can be performed on the
[12.] Tarun Kumar B. Jain, Boopathi Raja G, and Meenakshi
bracket to calculate its life from crack initiation to the
Sundaram. 2016. Stress Analysis for Wing Attachment
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bracket to study its performance under varied frequency
ranges. The use of composite material may result in
improvised strength to weight ratio. Structural testing of the
bracket can be carried to validate the theoretical calculation
and software analysis results.

ACKNOWLEDGMENT

We would like to extend our gratitude to Dassault

Systèmes and Autodesk for supporting and equipping us with
the educational licensed software.

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