In our study, analyzing aircraft’s wing with the old assumptions will not give an exact solution but this solution (total deformation) changes according to the geometry of the cross-section of the beam, so the total deformation of the beam may be greater or lower than the exact solution. In these two cases, the solution is not acceptable as in the first case which the deformation is greater than the exact solution will make more weight and cost, and Engineers design aircraft at minimum weight and less cost. But in the second case which will make lower deformation than exact solution will be much risky as the aircraft could fail at any time, and this case much dangerous because it threatens the life of people.

1. MODELING AND STRUCTURAL ANALYSIS
OF A WING WITH HISTORICAL
PERSPECTIVE
[PAST VS PRESENT]
SUBMITTED TO: PROF. SAMAH
SUBMITTED BY:
AHMED SAMIR, BAHAA IBRAHIM, ABD-ELHALEEM OMARA,
MOHAMED NOFAL, MOHAMED HELMY, MUHAMMAD SAYED

2. Abstract
• The most important goal for structural study is evaluation deformations
and stresses on the structural body.
• A comparison between structure analysis of different wings in past and in
the present.
• We solve aircraft’s wing as a cantilever beam by using Matlab software.
• And modeling and structural analysis on Real aircraft’s wing using finite
Element Method (FEM) and finite Volume Method (FVM) that gives exact
solution.
• Also illustrate Fluid Structure interaction (FSI) and how to connect
between them on Ansys with System coupling to make Stress analysis and
see the deformation on wing due to the fluid.

3. What we refer to is…
• We aim to study a 3D aircraft’s wing which subjected to flowing
fluid with specific velocity and calculate the aerodynamic forces ,
stresses and deformations by two ways. Using a Matlab Code and
ANSYS.
• And compare the results to see will approximations used in first way
is valid or not and displays favor and priority of the development of
computers and IT resources on the world by now.
• As it decrease time-cost of analyzing and find best compromise
between safety and cost for any design.

5. 4321 5
Analysis of a wing as a cantilever beam
ANALYZING WITH OLD ASSUMPTION USING MATLAB SOFTWARE
WHY we
approximate
real wing as
cantilever
beam?
HOW to
solve this
problem
including
linear algebra?
What is
the software
available in
past to apply
our method on
it?
When is
the solution of
problem to be
acceptable?
What else
to work on it
to find out
proper
Approximation
to be
acceptable?

6. 1 WHY we approximate real wing as
cantilever beam?
 At the beginning of airplane industry it was difficult for Engineers to calculate
aerodynamic forces.
 stresses and deformations on the wing as its cross-section gives nonlinear
equations that very hard to be handy calculated, as these equations lead to
unsolvable integrations and formulas.
 So they have to consider that the aircraft’s wing to be analyzed is a
cantilever beam to ease the calculations.

7. 2 HOW to solve this problem including
linear algebra?
 By looking to the methods to solve the problem :-
we find that the Stiffness Method is the best method to achieve both
solving the problem and including Linear Algebra which we summarizes it
steps in this simple flow chart.

8. Start
Calculate number of
member m then
number of nodes
n=m+1
Tabulate the joint
information
Tabulate the
member
information
Write Stiffness matrix after
elimination rows and columns
corresponding to axial forces and
displacements
Write Stiffness matrix Sj after
elimination rows and columns
corresponding to axial forces and
displacements
Rearrangement Sj such that the
numbering system indicates first all
off the displacement are free to occur
, and second the possible
displacements corresponding to
support constraints
Partition the Stiffness Matrix
according to whether the
displacement are free to displace
or restrained by supports
Construct the
nodal load
vector [A]
Construct Fixed end action Due to
member loads [AML] for both
constant distributed load
[AML]rec and linear distributed
load[AML]tri.
Calculate
Equivalent
nodal load [AE]
[AE]=
[AML]rec - [AML]tri.
Calculate
Combined
nodal vector
[Ac] = [A]+ [AE]
Calculate
Combined
nodal vector
[Ac] = [A]+ [AE]
Rearrangement the combined nodal
vector [Ac] using numbering system
in this form
[Ac] = [ AD | ARL]
Calculate the
unknown nodal
displacement vector
[D] = [S]^-1 [AD]
End

9. 3 What is the software available in past to
apply our method on it?
 We got the MATLAB code from Mathworks .
It visualizes the deflection in beam with changing the properties of the material
and cross section.
 We did some changes to suit our problem and to get the required output.
 We also summarize the steps of code in this flow chart.

10. Start Definex &y
Determine displacement and
rotationangle
0 meansfixed
Non-zerovalue means unknown
B.C,
Determineforces
atpoints of every
element.Ifno
pointload exist
leavezero.
For eachmember cal.E,I,A, distributedload.Solve thebeam problemPlotdeflectioninthewholebeam
Wecananimatethesolution. End

11. 4 When is the solution of problem to be
acceptable?
 Analyzing aircraft’s wing with the old assumption on matlab will not give an exact
solution .
the total deformation of the beam may be greater or lower than the exact solution
 In past this solution was acceptable because they uses less technology and many
assumptions to obtain the solution .
 But now the matter is different , this solution in not acceptable as threatens lives of
people, as the wing could fail at any time.
computers and IT resources has a great development in recent years which uses a very
high technology with nearly no assumptions to obtain the exact solution.

12. 5 What else to work on it to find out
proper Approximation to be acceptable?
 Using ANSYS.

13. Results of
MatLab Code
Consider a simply supported
cantilever beam that is
loaded by a liner-distributed
load, which represents the
lift applied vertically upward
along the beam, and a
constant distributed load,
which represents the weight
of the wing applied vertically
downward along the beam,
as shown.
Wing Structure Idealization

14. X (m) It means that the length of divided beams. As you notice the node 11 equal to all the
beam length.
Y (m) Because there is no another members so the col. all the values equal to 0.
dy (m) This is the vertical deflection as you notice at node 11 the deflection equal to 0.178 m
at the tip and that is close to the deflection of results of ANSYS.
Fy (N) The force at every node as you notice at the first node the vertical reaction at the root
is equal to -4.2226e+05 N and that is close to the vertical reaction of results of ANSYS.
Mz (N.m) The moment at every node as you notice at the first node the moment at the root is
equal to -7.7920e+05 N.m and that is close to the moment of results of ANSYS.

15. Maximum Deformation at the tip (m)
.1784
Angle of twist on wing
Cantilever beam
Length
Chord
Mass
Density
𝑳 = 𝟒. 𝟖 𝒎
𝒄 = 𝟏. 𝟔𝟑𝟔𝟏
𝒎 = 𝟐𝟖𝟓. 𝟔𝟕 𝒌𝒈
𝝆 = 𝟐𝟕𝟎𝟎 𝒌𝒈. 𝒎−𝟑
Fluid
Density
Inlet velocity
Outlet pressure
𝝆 = 𝟏. 𝟐𝟐𝟓 𝒌𝒈. 𝒎−𝟑
𝝂𝒊𝒏𝒍𝒆𝒕 = 𝟐𝟎𝟎 𝒎. 𝒔−𝟏
𝑷 𝑮𝒂𝒖𝒈𝒆 = 𝟎 𝑷𝒂
Inputs in code

16. Results of
ANSYS
First Ansys Design modeler used to
model the aircraft’s wing with
specified dimensions, the wing have
been designed to have a constant
configuration along its length. The
wing is freely to deform at the tip
but fixed at the root as clamped to
the fuselage.
Meshing the fluid region generated
about 467716 element and 84885
node for Computational Fluid
Dynamics (CFD) it contains
tetrahedral cells in the boundary
layer. The static structure wing finite
element meshing has 53156
element and 102300 node.
Wing Structure Meshing

17. Fluid Region Meshing

18. Domain of the Boundary Conditions
Structure
Length
Poisson’s ratio
Wing’s density
Young’s Modulus
𝑳 = 𝟏𝟎 𝒎
𝝂 =. 𝟑𝟑
𝝆 = 𝟐𝟕𝟎𝟎 𝒌𝒈. 𝒎−𝟑
𝑬 = 𝟕 × 𝟏𝟎 𝟏𝟎
𝑷𝒂
Fluid
Length
Fluid’s density
Viscosity
𝑳 = 𝟏𝟎 𝒎
𝝆 = 𝟏. 𝟐𝟐𝟓 𝒌𝒈. 𝒎−𝟑
𝝁 = 𝟏. 𝟔 × 𝟏𝟎 𝟓
𝒌𝒈/(𝒎. 𝒔)
Inputs in Ansys

19. Maximum Tip Deformation (m)
.239
Total deformation on the wing

20. Von Mises stress variation

21. Min Principal stress variation

22. Fluid Velocity Variation

23. Fluid pressure Variation (2D)

24. Fluid pressure Variation (3D)

25. Conclusions
•From the comparisons of results above it can see that the approximation which
considers aircraft’s wing as a cantilever gives less –deformation along the wing–
than exact one (FSI on ANYS), so that we could say powerfully without any doubt
that approximation is non-acceptable nowadays cause it threatens lives of
people, as the wing could fail at any time.
•the results shows the importance development of IT resources (New softwares)
like ANSYS software especially Fluid-Structure Interaction (FSI) part which ease
the solution of the wing by using System Coupling which safe time, cost and give
exact solution.
•Conflicts of interest: The authors not declare any conflicts of interest.

26. Future Work
•Determine vibratory Reliability Analysis of an Aircraft’s Wing via Fluid–Structure
Interactions.
•Find the best compromise between cost and safety in order to supply guidelines
for carrying out reliable and cost-effective projects.
•Try to find out a proper approximation to get a closer value of deformation to
the real value.
•Update the Matlab code to consider the other effects which was neglected .