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DETECTION OF DAMAGE IN STIFFENERS OF AIRCRAFT WING STRUCTURE BASED ON INDUCED SKIN STRAINS AND LATERAL DEFLECTIONS

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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 03, March 2019, pp. 110-126. Article ID: IJMET_10_03_011
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=3
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication
Scopus Indexed
DETECTION OF DAMAGE IN STIFFENERS OF
AIRCRAFT WING STRUCTURE BASED ON
INDUCED SKIN STRAINS AND LATERAL
DEFLECTIONS
Dr. Hatem Hadi Obeid
Faculty of Engineering/ Department of Mechanical Engineering
University of Babylon
ABSTRACT
In this paper, the technique of structure health monitoring was applied to detect
damage occurrence in the stiffeners of wing structure. A wing structure of airfoil
shape according to digital NACA 0015 was considered for modelling the aerodynamic
wing shape. Finite element models of the wing structure were created included
undamaged and damage wing structures using high order eight nodes and six nodes
shell elements. The damaged wing models included damaged at the main spar at 20%,
40%,60% and 80% the distance than the root chord. A mathematical model was
developed using high order shell elements and programmed via MATLAB. The load
cases were predicted experimentally using wind tunnel test on a wood airfoil
prototype such that the pressure distributions through upper and lower wing skins
measured at different attack angles. The static solutions were achieved for each finite
element model under action of maximum pressure distribution at attack angle of 100.
Strains distributions and lateral deflections through lower skin were estimated. The
results of strains through lower skin showed occurring of climax in strain values
initiated in the distribution at the location of the damage for all the cases of damaged
structures, which not appeared in the undamaged wing structure. The results of lateral
deformations through lower skin showed indicating variations in the shape of the
curves, such that the curve appeared to be gradually increased the region between the
chord and the damage. Semi to rapid increasing in the lateral deformation occurred in
region between the damage and the end tip of wing. The difference in the behavior of
the induced strains and lateral deformation between undamaged and damaged wing
structures is intended to a technique predicting of the occurrence of the damage in the
wing structure. The present of a climax in the strain distribution lead to presence of
damage near the climax value of strain. Also, the indicating of variations in the shape
of the lateral deformations of skins semi or rapid increasing lead to presence of
damage near the rejoin of that variation. It is concluded the possibility of using the
strain and deflection analysis for the wing structure to investigate occurring damage
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Detection of Damage in Stiffeners of Aircraft Wing Structure Based On Induced Skin Strains and
Lateral Deflections
in the structure due to variation in the strains and lateral deflections between different
damage locations.
Key Words: Wing structure, Structural health monitoring, finite element method,
structural analysis, airfoil pressure distributions, strain, stress, deflection, damage in
wing structure.
Cite this Article: Dr. Hatem Hadi Obeid, Detection of Damage in Stiffeners of
Aircraft Wing Structure Based On Induced Skin Strains and Lateral Deflections,
International Journal of Mechanical Engineering and Technology, 10(3), 2019, pp.
110-126.
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=3
1. INTRODUCTION
The Structural Health Monitoring of failures in aircraft and other flying equipment is very
important because its concerned with the safety of their users or the risks that may be
occurred due to falling on the ground. This analysis is applicable in wide range of engineering
fields spanning from mechanical, aerospace, military, building, to bridge and transportation
applications. Needs for prediction of failure in the aerospace structures are rapidly increasing
due to demands of enhance safety, reduce inspection time and cost but maintaining structural
function and uses. This field is also providing smart prognosis and diagnosis of failure
instantaneously. The deployment and development of structural health monitoring system is
required to ensuring the safe operation of any engineering structure or system. The execution
of the structural health monitoring is mainly considering the following processes: [1]
- Using sensors and instrumentation devices for sensing and tracing the interpretation of
an engineering system or structure under operational loads.
- Assessment the performance of the system or structure for any propagation of damages
or defects by the analysis of the measured values analytically or numerically.
- Indicating a notification or an alarm when the desired system parameters are exceeded.
The base on parameters or criteria that the structural health monitoring system executed
are varied depending on the nature of the system responses or performance. Although the
importance of structural health monitoring but their researches are relatively young if
compared to other engineering fields, thus most of the researches have been conducted at
universities or research and development centers of companies.
The applications of structural health monitoring in engineering fields included different
problems such detection of damage in steel structure, aerospace, concrete structures, precast
concrete, box girders in railroads, composite materials, dikes and pipelines of water and
wastewater. Also, evaluation bridge deflection; stress or strain analysis in petroleum pipes,
dam structures, or suspension bridge cables. In addition to more complicated problems such
as detection of impact effects in wind turbine blades and water leaks. The vibration of highrise reinforced structures such as towers can be evaluated and assessment.
In this paper the structural health monitoring is applied for detection failure at the
stiffeners of aircraft wing structure. The performance of an aircraft structure can be
characterized by various factors, essentially the response (i.e. strain mapping, shape
determination etc.) due to applied loading that can be evaluated by health monitoring
technique [2]. Finite element method is powerful to be used to modelling the wing structure
for estimation the effects in the structures due to the applied loading. The most wing structural
stiffness comes from the interior stiffeners. The stiffeners included main, auxiliary spars and
ribs. Having stiffeners (spars and ribs) attaing structure increases the load resistance of the
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Dr. Hatem Hadi Obeid
structure without further increasing in the weight. To further reduce the weight, a certain
arrangement of stiffener on structure is being necessary to increase the rigidity with less
material. The construction of both stiffeners and outer skin gives the overall wing structural
stiffness. The response of wing structure into the loading depending mainly on the overall
stiffness of wing. Then the present of damage in any location in the stiffeners will be affecting
on the response of the wing to the applied loading.
2. FINITE ELEMENT MODELLING
2.1. Geometric Parameters:
In this work, a wing structure of a guided aircraft laboratory prototype was modelled via finite
element method. Different finite element models were created each represent a case of
damage in spar. The purpose of these finite element models is performing static analysis
under action of static load and obtain strains induced in the skins and the lateral deformation
at the tip of wing. Then the health monitoring technique is applied to estimate relations
between damage of stiffeners and the static induced strains and deformations. The geometry
configurations and dimensions are illustrated in figure (1), such that the wing consisting of
upper and lower skins, spars and ribs. The wing stiffeners are constructed as eight spars and
ten ribs connected for giving the wing structure the required stiffness. The four digits
symmetrical NACA 0015 airfoil was used as an aerodynamic shape for the considered wing.
The (00) number of the NACA indicating that it has no camber. The (15) number of the
NACA indicates that the airfoil has a “thickness to chord length ratio” of 15% as shown in
figure (2). The equation describing the geometric shape of a NACA 0015 foil is [4,5]:
(1)
x: is the location along chord from ranged (0 to 100%).
y(x) is the half thickness at any location x .
t: is maximum thickness of the wing as a fraction of the chord.
The chords of the wing structure were assigned as 1m and 0.4m at the root and tip
respectively with length 1.75m.
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Detection of Damage in Stiffeners of Aircraft Wing Structure Based On Induced Skin Strains and
Lateral Deflections
2.2. Mesh Generation of wing structure:
In order to study the effect of damage that occurred in the spars, finite elements models were
created for each damage case. The damage was assumed to be as a cut in the connection of the
main spar which is located at the maximum thickness of wing, such that it assumed that the
damage occurred at five locations in the spar nearest to the maximum wing thickness. High
order SHELL 8-node quadrilateral element and 6-nodes triangular element ware selected for
the generation finite element model of the wing structures. Figure (3) is shown the high order
SHELL 8-Node element parameters and degrees of freedom. The upper and lower skins were
discretized into ten divisions, to be generate one hundred shell elements at each skin. The
spars and ribs were discretized into ten divisions in order to connected with both and skins
element at the contracted nodes to maintain continuous element connections as shown in
figure (4). The thickness of all of skins, spars and ribs were assigned to 0.4 mm. Aluminum
2024 alloy -T3 was used as the material of all parts their mechanical properties are shown in
table (1). [7]
3. DEFINITION OF THE ELEMENT COORDINATE SYSTEMS [8,9,10]
For the typical shell elements as shown in Figure (3), the external faces (surfaces) of the
element are curved, while the thickness is generated by straight lines. Many coordinate sets
employed in the formulation of degenerated shell element. These coordinate systems are
described in the following sections.
3.1. Global Coordinate System - (Xi)
It is the global Cartesian coordinate system, used to describe the wing geometry in the space.
The coordinates and deflections of nodes can be described using this coordinates system. In
addition to describe the assembled global stiffness matrix and assembled force vector. The
following notation is used:
Xi
(I=1,3) and X1 =X , X2=Y , X3=Z
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,
113
Ui
(I=1,3) and U1=U, U2 =V, U3=W
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Dr. Hatem Hadi Obeid
(i=1,3) is a unit vector in the X i direction.
This system is used to define global stiffness matrix and applied force vector and in the
structure geometry, as well as nodal coordinate and displacements are referred to this system.
Xi
3.2. Nodal Coordinate System (V1f , V2f , V3f )
This system type can be established at each nodal point as shown in Figure (3) with origin
located at reference surface (shell mid-surface), V3f is a vector formulated from nodal
coordinate of shell surfaces at node f,
V3 f  X f Yf Z f  top  X f Yf Z f  bot
T
V3 f  X ftop  X fbot
,
T
2
The unit vector V3f can normalize from the vectorV3f, thus:
V3 f 
hf 
V3 f
hf
V
x
3f
V3yf
V3zf  T
3
 ΔX

2
1f
 ΔX 2 f   ΔX 3 f 

2 1/ 2
2
4
i  1,2,3
ΔXif  X iftop  X ifbot
5
The vector V 3f is the direction of “normal” at the node f, which is not necessarily
perpendicular to the mid-surface at f.
The vector V2f is normal to plane of vectors V1f and V3f: V2f = V1f  V3f .
The mathematical characteristic of vector V1f is perpendicular to V3f and parallel to the
global X – Z plane, thus:
V1fx  V3fz
, V1fy  0.0
,
V1fz  -V3fx
 x z

Or, if the vector is in the Y-direction V3f  V3f  0.0
V1fx   V3fz
, V1fy  0.0
,
V1fz  -V3fx
3.3. Curvilinear Coordinate System (  )
The description of this system is established by the definition of three coordinates, each one
has its characteristic as shown in Figure (3). The  coordinate is an intrinsic coordinate
through thickness direction.  coordinate is defined as a function of V , the  -direction is
considered normal to the shell mid-surface. It is assumed that the curvilinear coordinate varies
between (-1 and +1), which represent the top and bottom surfaces of the element respectively.
The two other coordinates are ξ, η which are curvilinear coordinate in the middle plane of the
shell element and are also assumed to vary between (-1 and +1) which represent the faces of
the element.
3f
3.4. Local Coordinate System ( X
'
i
or X ' , Y ' , Z ' )
This system is a cartesian coordinate system defined at the sampling points wherein stresses
'
and strains are to be calculated. The direction Z is taken perpendicular to the mid-surface (
  constant ),
X ' ,Y ' and Z '
'
'
' V
it as shown in Figure (3). The vectors V1 ,V 2 , 3 define
direction of mid-surface respectively, and it should be noted that,
X ' and Y ' tangent
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Detection of Damage in Stiffeners of Aircraft Wing Structure Based On Induced Skin Strains and
Lateral Deflections
 x 
ξ 


 y
ξ
ξ 
z


  ξ 
[T] = 
V
'
1
,
V1'
,V ,V
'
2
'
3
 x 
 η


 y
η
 η
z


  η 
'
, V2 ,
V3'
 x 
ξ 


 y
V1  ξ  
ξ 
z


  ξ 
,
 x 
ξ 


 y
V3  ξ η  
ξ 
z


ξ 
,
 X 
 η 


 Y 
 η 
Z


x η 
6

: unit vectors on
7
'
'
X ,Y and Z
'
.
3.5. Geometry of Elements [10]
To obtain the formulation of the coordinates of any point within the element, it is simpler to
divide the general formulation of coordinate in two parts. The first part is to establish the term
of formulation, which represents the intercept of the “normal” with the mid-surface. If there is
a node (f) at the “normal” at  =0 surface and this “normal” has a top and bottom nodes at 
=+1 and  =-1 surfaces respectively, the coordinates of node (f) can be obtained as follows:
1
X 'f   X 'f  top  X 'f  bot
2

,
X f 
 1

Yf   2
Z f 


X f

Yf
Z f





 top

X f

Yf
Z f





 bot
8
Since node (f) is in the mid-surface (at  =0 surface), the two dimensional interpolation
function N f  ,  can be applied from Table (2) , to obtain relationship between the Cartesian
point and the curvilinear coordinate as follows:
X i   N f  ,  X if
n
f 1
9
The second part is to establish the second term of the general formulation, which defines
the position of the point along this “normal”. But to establish that, it is necessary to define
arbitrary point (p) on the “normal” at node (f), therefore the vector V3f which represents the
thickness of the shell hf, can be written ass:
X f 
X f 


h f  V3 f  Yf
  Yf 
Z 
Z 
 f  top
 f  bot
10
The distance between the arbitrary point (p) and the node f (at mid-surface) can be written as follows:
Unit Distance =
hf ζ
2
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Dr. Hatem Hadi Obeid
h f  V3i f
Since the
means the coordinates of the arbitrary point, the equation (11) can be rewritten with
the application of the two-dimensional interpolation function N f ξ, η from Table () so that:
n
ζ
X i   N f ξ, η V3i f
2
f 1
12
The general formulation of the coordinate defines the geometry of the shell element which
represents the rotations between the coordinate ( ξηζ ) and coordinates (X, Y, Z). It is
obtained by the summation of the previous two parts (equation (8) & equation (12)) so that:
n
X i   N f (, )
f 1
n
1 ζ
X if top   N f (, ) 1  ζ X if bot
2
2
f 1
X 
X 
n
ζ hf
  n
 
Y

N
(

,

)
   f
Y    N f (, )
2
f 1
f 1
Z
Z
 
  mid
V

V
V

x
3f
y
3f
z
3f
13





is the elemental Cartesian coordinate, ( X 1  X , X 2  Y , X 3  Z ), n: is the number of
nodes per element, hf is the element thickness at node f, i.e. the respective “normal” length,
Xif is the Cartesian coordinate of nodal point f, and N f (  , ) is the two dimensional
interpolation functions. ( ζ =constant) at nodal point f.
Xi
3.6. Displacement Field [10]
Each node of the high order element has five degrees of freedom representing the
displacement along local coordinates. It is assumed that the strains in the directions to the
mid-surface is assumed to be negligible. The deflections through the element mid surface can
be defined by the three displacements (u,v,w), and two rotations of the nodal vector V3f about
orthogonal directions normal to it. One of the two orthogonal directions is represented by unit
vector V and the corresponding rotation ( α 1 f ). The other directions is V 2 f
and the
δ
,
δ
α
corresponding rotation is ( 2 f ), and it is the displacements ( 1 f 2 f ) of a point at unit distance
1f
(h) from node f on the “normal” resulted from the two rotations ( α 1 f ,  2f ) are calculated as
follows:
α1f 
δ1 f
h
δ1f  h α1 f
or
δ2f
h
α2f 
where
h
δ2f  h α2f
or
hf 
2
14
, δ1f
is the displacement in the direction of V 1 f , δ 2 f
is the displacement
in the negative direction of V 2 f . Equation (13) can be written as follows:
δ1f   h α1f 
δ 
α 
 2f 
 2f 
15
The global displacement can be found from:
u    N u 
n
i
f 1
f
i
οf
mid
 
  N f u 'οf
i
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Detection of Damage in Stiffeners of Aircraft Wing Structure Based On Induced Skin Strains and
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u i : the nodal displacement through element thickness. u if : nodal displacement through
i
'
Cartesian coordinate. u f :nodal displacement through “normal” of the cross product of
rotations  1f and  2 f .
i
Since;
u οf  δ 1' f  δ '2 f
17
'
'
where the corresponding displacement components (  1f ,  2f ) of u
follows:
i
hf 
 1f V 1f
2
 1' f 
and
 1' f 
'
f
can be calculated as
i
hf 
 1f V 1f
2
18
Since the global displacement can be found as shown before in equation (16) as the
i
simulation of the mid-surface nodal displacement ( u f ) and the relative displacements are
'i
caused by the rotations of the normal ( u f ), then the element displacement field can be
expressed by:
u if  u iοf 
i
i
ζ . hf
(V 1 f α 1 f  V 2 f α 2 f )
2
19
 uf  n

ζ hf
u 
 n
 
 v    N f ξ, η v f    N f ξ, η
2
f 1


w 
 f 1
w f 

V

V
V

x
1f
y
1f
z
1f
V
V
V
x
2f
y
2f
z
2f

  α1 f 
α 
 2 f 

20
The contribution to the global displacement from a given node f in the general form and
for complete element is:
u i   N f ξ, η, ζ  Sf
n
f 1

N f
 u  
v  0
w  
0

Nf
Sf
0
0
Nf
0
0
Nf
ζ hf x
V1f
2
ζ hf y
Nf
V1f
2
ζ hf z
Nf
V1f
2
Nf
21
ζ hf x
V2 f
2
ζ hf y
 Nf
V2 f
2
ζ hf z
 Nf
V2 f
2
 Nf

  uf 
  vf 
 w f 
  α1 f 
 α 
  2 f 
22
is the shape function matrix of the degenerated shell element.
is transformation matrix of the displacement vector at node f of shell element
u f , vf , w f , 1f ,  2f T .
3.7. State of Stress [10]
The stress and strain components for the shell assumption of zero local stress through shell
'
'
mid-surface along Z -direction (  z  0 ) and using Hooks law enables the stresses vector to
be reduced to following five stress components,
 ζx 
ζ 
 y 
ζ   η x y   Dε  ε ο 
η 
ηx z 
 yz 
'
'
' '
' '
23
' '
  is the initial strain vector.
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 is the strain vector.
[D] is the elasticity matrix given by,
0
0 
1 ν 0
0
0 
E ν 1 0
0
0 
0 0 G
D 
2
1  ν  0 0 0 K 1G
0 
0 0 0
0
K 2 G 
24
G: modulus rigidity, E: modulus of elasticity,  : Poisson’s ratio,
K1, K2 is the shear correction factors.
3.8. State of Strains [10]
The normal strain in the Z -direction (  z ) is neglected. Therefore, the general vector of green
strains it will be reduced to the following five components,
'
'
 u
 x

  v
  y
  u v


 y x
  u  w
 z  x

 v  w
z   y

'
'
ε
ε

ε  




'
x'
'
y'
x'y'
x 'z'
y'z'
'
'
'
'
'
'
'
'
'
'
'
'













25
'
'
'
The local derivatives above of the displacement components u , v and w in the local
'
coordinates system ( X 1 ) can be obtained as:
 u'
 x'
 u'
 '
 y
 u'
 '
z
 v'
 x'
 v'
 y'
 v'
 z'
 w' 
 u
 x
 x' 

 w ' 
T u
   
'
y 
 y
 u
 w' 


z
 z' 
v
x
v
y
v
z
w
x 
w
  
y 
w

z 
26
[  ] is the transformation matrix given by,
 x
 x'

y
[ ]   '
 x
 z
 '
 x
 u
 x
 u

 y
 u

z
v
x
v
y
v
z
 x
ξ

x
[J]  
 η
 x

ζ
x
 y'
y
 y'
z
 y'
x 
 z' 

y
'
z 
z 

 z' 
 u
w
ξ

x

w
1   u
  J 
 η
y 
 u
w


z 
ζ
y
ξ
y
η
y
ζ
z
ξ

z
 η
z

ζ 
27
v
ξ
v
η
v
ζ
w
ξ 

w
η 
w

ζ 
28
[J] is Jacobian matrix
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Detection of Damage in Stiffeners of Aircraft Wing Structure Based On Induced Skin Strains and
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The transpose of the Jacobian matrix results from equation (12) can be expressed as
follow:
 X f 
 
h
T
[J]    Yf N f , N f, 0  f
2
f 1
 Z f 
 
n

V3xf 
V3xf 

hf   y 
 y
V3f 0 0 N f  
V3f N f , N f, 0
2  z
V z 

 3f 
V3f 

30
n is the number of node per element,
hf is the element thickness at node f, and
N f , 
N f , 
N f , 

N f , 
;

31
are the derivatives of the global displacements referred to the curvilinear coordinates are
obtained from equation (18), such as
u

. . .etc.
n
hf  x
hf  x


u
   N f , u f 
V1 f N f ,  1f 
V2 f N f ,  2f 
 f  1 
2
2

32
The strain matrix B can be formulated from equations (21), (29) and (31) as:
  B
where,
33
δ  u , v , w , α
a
 i
0
 bi

0

[B]=  ci
0
, α2 
T
1


eiV 1 y
- eiV 2 x

(eiV i1 x  diV i 1 y) (- eiV i 2 x  diV i 1 y) 

(giV i 1 y  eiV i 1 z) (- giV i 1 y  eiV i 2 z) 
(diV i 1 z  giV i 1 x) (- diV i 2 z  giV i 2 x)
d iV i 1 x
0
bi 0
ai 0
ci bi
0 ai
34
- di V i 2 x
i
i
35
ai  J11* Ni, ζ  J12* Ni, η
bi  J *21 Ni, ζ  J *22 Ni, η
ci  J *31 Ni, ζ  J *32 Ni, η
di  hi (aiz ,  J *31 Ni)
2
ei  hi (biz ,  J *23 Ni)
2
g i  hi (ciz ,  J *23 Ni)
2
Consequently, it is used in the calculation of the stiffness matrix [K] using the midcoordinate rule. Hence [K] can be defined as follows:
[K] 
1 1

1 1
 1 T

 1[B] [D][B] J ξ, η, ζ  dζ  dξ d η
36
Then K can be written as summing up the contribution of each layer at the gauss points,
1 1
2 Δh j 
 nL
[K]    [B j ]T [D j ][Bj ] Jξ, η, ζ 
dξ dη
h 
1 1  j1
37
[K] : stiffness matrix, [D] : elasticity matrix, [Bj]: strain-displacement matrix.
J (, ,  )
is the determinant of the Jacobian matrix for layer ( j ).
h j
is the thickness of the jth layer.
nL is the total number of layers.
e
In the same way, the internal force vector { f } can be determined as follows:
{f e }   [B]T {} J dV
38
v
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Dr. Hatem Hadi Obeid
2 Δh j 
 nL 1 1
{f e }     [B j ]T {ζ j } J(ξ(η, ζ)
dξ dη
h 
 j1 1 1
39
e
{f }
{ j }
: is current stress vector,
: is the internal force vector.
It should be noted that, it is essential in nonlinear analysis to determine the internal force
vector (or equivalent nodal forces) at the end of each iteration. The transformation to the local
coordinates system ( X  Y ) using the following relation:
'
'
[Ds' ]  [S]T [Ds ][S]
 l

2
 m
[S]    2lm

0


0

2
40
m
2
lm
0
 lm
0
2lm
l 2  m2
0
0
0
l
0
0
m
l
2
0

0
0

m
l 

41
3.7. Boundary conditions
The wing is clamped through the root chord such that all the degrees of freedom of the
regarded nodes are fixed to be zeros. While all other nodes are freely to be of three
translations and three rotations along the corresponding local coordinates.
3.8. EXPERIMENTAL PREDICTION OF PRESSURE DISTRIBUTION:
In order to predict the load that applied on the wing structure, a prototype for the airfoil was
manufactured using wood material according to the digital naca number 0015. Then the
prototype was amounted in the wind tunnel section as shown in figure (5). Its required to
measure the pressure distribution through the airfoil, thus twelve manometers were used for
this purpose. The wind tunnel is flowing air at 50 m/s over the airfoil. The airfoil was
mounted with different attack angles (0 to 10 degrees). Figures (6),(7) showed the pressure
distributions through upper and lower skins with different attack angles. The net pressure
distribution is equal to the difference between the pressures through upper and lower skins.
The pressure distribution was measured for each attack angle which is represent the effect of
aerodynamic lifting of the wing.
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Detection of Damage in Stiffeners of Aircraft Wing Structure Based On Induced Skin Strains and
Lateral Deflections
3.9. STATIC ANALYSIS [10]
Static analysis solution has been included the calculation of the effects of the applied load
under steady loading conditions on a structure. The pressure distributions through upper and
lower skins were applied as normal pressures on the elements. The static analysis is governing
by the following equilibrium equation:
K  q  F
42
The above equilibrium equation is solved by jacobi iterative method to obtain the
displacement [q] vector.
4. RESULTS AND DISCUSION
Naman Jain [11,12] was created a Finite element code to solve shell structure under action of
static loads. In this work, a development was achieved for using Naman Jain code to generate
stiffened shell structure using quadrilateral eight nodes shell element and triangular six nodes
shell element. Jacobi iterative method was used to solve equation (42) to obtain the
deformations along global coordinates. Then the deformations transformed using equation
(41) to the local coordinates. The local deformations were transformed into global coordinates
x,y and z directions. The strains were estimated through local coordinates and substituted in
the stress strain relations to obtain elemental stresses through local coordinates. The first run
included the healthy structure that did not subjected into damage. Figure (8) showed the safe
strains induced in the lower skin along the intersection of the skins and main spar. Its noted
that the strains in the healthy wing were decreased gradually in the rejoins moved away than
the wing chord. The same behavior was noted in the strains induced in the upper and lower
skins. Figure (9) showed the safe lateral deformations induced in the lower skin along the
intersection of the skins and main spar. The lateral deformations of both the lower and upper
skins at the intersection of skins with main spar were approximately coincident. Also, the
lateral deformations were increased gradually in the rejoins moved away than the wing chord.
A similar behavior was noted in the study of Salu Kumar Das and Sandipan Roy [13]. The
second run included the static solution of the finite element model subjected to damage at the
main spar at the location apart 20% than the chord. The damage simulated as a cut in the
element connection of the spar and skins. The strain distributions are illustrated in figure
(10), where noted that a climax is initiated in the distribution at the location of the damage. In
addition to variation in the shape of the distribution of the strains in the rejoin between the
damage and the end tip of the wing. Figure (11) showed the distribution of the lateral
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Dr. Hatem Hadi Obeid
deformations of the lower skin at the intersection of the main spar with skins. The distribution
indicated that there are two shapes, the first shape in the rejoin between the chord and the
damage where the distribution was gradually increased. The second shape is between the
damage and the end tip of the wing, where the distribution appeared to be semi gradually
comparative with the first region. This is behavior due to the present of damage at the location
20% than the chord. In which the stiffness if reduced rapidly at that location. So, this behavior
can be used as a key to detect the damage location. The other runs were executed for the finite
element models that included the damages at the locations apart than the chord by 40%, 60%
and 80%. The behavior of the strain distribution indicates a decreasing towards the end tip of
the wing such that initiated a sudden climax at the location of the damage as shown in figures
(12, 14, and 16). The behavior of the lateral deformations indicated variations the shape of the
curve, such that the curve appeared to be gradually increased the region between the chord
and the damage. Semi to rapid increasing in the lateral deformation occurred in region
between the damage and the end tip of wing as shown in figures (13, 15, and 17).
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Detection of Damage in Stiffeners of Aircraft Wing Structure Based On Induced Skin Strains and
Lateral Deflections
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Dr. Hatem Hadi Obeid
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Detection of Damage in Stiffeners of Aircraft Wing Structure Based On Induced Skin Strains and
Lateral Deflections
CONFLICT OF INTERESTS
Declare that there is no “conflict of interests” regarding the publication of this paper.
ACKNOWLEDGMENTS
My thankful for the assistance from the staff of post graduate laboratory at Department of
Mechanical Engineering ,College of Engineering, Babylon University ,Iraq.
DATA AVAILABILITY
All data concerned with the fixation and performing the test of pressure distributions
through wing in wind tunnel are available in the author and can be obtained via mailing.
The codes of the finite element analysis can be obtained after publication of the research
and can be contacting with author for this purpose.
REFERENCES
[1]
Structural Health Monitoring for Civil Structures: From the Lab to the Field, Piervincenzo
Rizzo, Yi Qing Ni, and Jinying Zhu Volume 2010, Article ID 165132.
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Dr. Hatem Hadi Obeid
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
Experimental modal analysis and dynamic strain fiber Bragg gratings for structural health
monitoring of composite antenna sub-reflector, Aikaterini Panopoulou, S. Fransen's,
Vicente Gomez-Molinero, Vassilis Kostopoulos
E.N. Jacobs, K.E. Ward, & R.M. Pinkerton. NACA Report No. 460, "The characteristics
of 78 related airfoil sections from tests in the variable-density wind tunnel". NACA, 1933.
Fundamentals of aerodynamics", John D. Anderson,Jr, third ed, chap 4
Moran, Jack (2003). An introduction to theoretical and computational aerodynamics.
Dover. p. 7. ISBN 0-486-42879-6.
Payne, Greg (8 Jul 1994), NACA 6, 7, and 8 series, archived from the original on April
27, 2009
An experimental investigation into the high velocity penetration resistance of CFRP and
CFRP/aluminium laminates, Ming-ming Xu, Guang-yan Huang, Yong-xiang Dong, Shunshan Feng, Composite Structures, Volume 188, 15 March 2018, Pages 450-460.
The Finite Element Method Using MATLAB, Second Edition 2nd Edition, Young W.
Kwon, Hyochoong Bang,
Programing the Finite Element Method with Matlab, Jack Chessa, 3rd October 2002
William Weaver, Jr. and Paul R. Johnston,"Finite Element Programs for Structural
Analysis", Standford University, Printice-Hall Inc, N. J., 1984.
MATLAB Code for Structural Analysis of 2-D Structures Subjected to Static and SelfWeight Loading Conditions, Naman Jain, International Journal of Trend in Research and
Development, Volume 4, 2017.
EFFECT OF HIGHER ORDER ELEMENT ON NUMERICAL INSTABILITY IN
TOPOLOGICAL OPTIMIZATION OF LINEAR STATIC LOADING STRUCTURE, N
AMAN JAIN, Journal of Theoretical and Applied Mechanics, Sofia, Vol.48 No.3 (2018)
pp. 78-94.
Finite element analysis of aircraft wing using carbon fiber reinforced polymer and glass
fiber reinforced polymer, Salu Kumar Das , Sandipan Roy, 2nd International conference
on Advances in Mechanical Engineering (ICAME 2018), IOP Conf. Series: Materials
Science and Engineering 402 (2018) 012077.
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