DETECTION OF DAMAGE IN STIFFENERS OF AIRCRAFT WING ...€¦ · Detection of Damage in Stiffeners of...

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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 10

0.

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

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 high-

rise 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



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.


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:

iX (I=1,3) and X1 =X , X2=Y , X3=Z , iU (I=1,3) and U1=U, U2 =V, U3=W



iX (i=1,3) is a unit vector in the iX 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.

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,

bot

f

top

ff3 XXV ,

T

bot f f f

T

topf f ff3ZYXZYXV

2

The unit vector f3Vcan normalize from the vectorV3f, thus:

Tz

f3

y

f3

x

f3

f

f3

f3 V V V

h

VV

3

2/12

f3

2

f2

2

f1fΔXΔXΔX h

4

1,2,3iXXΔX bot

if

top

ifif

5

The vector 3fV 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:x

3f

z

1f

y

1f

z

3f

x

1f V-V , 0.0 V , V V

Or, if the vector is in the Y-direction 0.0 V V

z

3f

x

3f

x

3f

z

1f

y

1f

z

3f

x

1f V-V , 0.0 V , V V

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 3fV , 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 ηξ, 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.

3.4. Local Coordinate System (''''

i Z, Y , X or X )

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 ), ''

Y and X tangent it as shown in Figure (3). The vectors '

1V ,'

2V ,'

3Vdefine

'''Z and Y,X direction of mid-surface respectively, and it should be noted that,


Lateral Deflections


ξ

z

ξ

y

ξ

x

ξ

,

η

z

η

y

η

x

η

,

ξ

z

ξ

y

ξ

x

ξV1

,

ξ

z

ξ

y

ξ

x

ηξV3

x

η

Z

η

Y

η

X

6

[T] = '

1V , '

2V , '

3V 7

'

1V , '

2V , '

3V : unit vectors on '''

Z and Y,X .

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:

2

1bot

'

f top

'

f

'

fXXX

, botf

f

f

topf

f

f

f

f

f

Z

Y

X

Z

Y

X

2

1

Z

Y

X

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:

if

n

1ffi X , NX

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:

botf

f

f

topf

f

f

f3f

Z

Y

X

Z

Y

X

Vh

10

The distance between the arbitrary point (p) and the node f (at mid-surface) can be written as follows:

Unit Distance = 2

ζ h f

11



Since the i

f3f Vh means the coordinates of the arbitrary point, the equation (11) can be rewritten with

the application of the two-dimensional interpolation function ηξ,N f from Table () so that:

i

f3

n

1ffi

V2

ζηξ,NX

12

The general formulation of the coordinate defines the geometry of the shell element which

represents the rotations between the coordinate ( ζηξ ) and coordinates (X, Y, Z). It is

obtained by the summation of the previous two parts (equation (8) & equation (12)) so that:

botif

n

1fftopif

n

1ffi X

2

ζ1),(NX

2

ζ1),(NX

13

z

f3

y

f3

x

f3

fn

1ff

mid

n

1ff

V

V

V

2

h ζ),(N

Z

Y

X

),(N

Z

Y

X

iX is the elemental Cartesian coordinate, ( XX1 , YX 2 , ZX 3 ), 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.

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 f1V and the corresponding rotation ( f1α ). The other directions is f2V and the

corresponding rotation is ( f2α ), and it is the displacements ( f2f1 δ,δ ) of a point at unit distance

(h) from node f on the “normal” resulted from the two rotations ( f1α , f2 ) are calculated as

follows:

h

δα f1

f1 or f1f1 αh δ

14

h

δα f2

f2 or f2f2 αh δ

where 2

hh f

, f1δ is the displacement in the direction of f1V , f2δ is the displacement

in the negative direction of f2V . Equation (13) can be written as follows:

f2

f1

f2

f1

α

αh

δ

δ

15

The global displacement can be found from:

i '

οff

n

1fmid

i

οffiuNuNu

16


Lateral Deflections


iu : the nodal displacement through element thickness. i

fu : nodal displacement through

Cartesian coordinate.

i '

fu :nodal displacement through “normal” of the cross product of

rotations f1 and f2 .

Since; '

f2

'

f1

i

οf δδu 17

where the corresponding displacement components ('

f1 ,'

f2 ) of '

fu can be calculated as

follows:

i

f1f1f'

f1 V2

h

and

i

f1f1f'

f1 V2

h

18

Since the global displacement can be found as shown before in equation (16) as the

simulation of the mid-surface nodal displacement (i

fu ) and the relative displacements are

caused by the rotations of the normal (i'

fu ), then the element displacement field can be

expressed by:

)α Vα V(2

h . ζuu

f2

i

f2f1

i

f1fi

οfif

19

f2

f1

z

f2

z

f1

y

f2

y

f1

x

f2

x

f1

fn

1ff

f

f

fn

1ff α

α

VV

VV

VV

2

h ζηξ,N

w

v

u

ηξ,Nwvu

20

The contribution to the global displacement from a given node f in the general form and

for complete element is:

f

S ζη,ξ,Nun

1ffi

21

f2

f1

f

f

f

z

f2

f

f

z

f1

f

ff

y

f2

f

f

y

f1

f

ff

x

f2

f

f

x

f1

f

ff

α

α

w

v

u

V2

h ζNV

2

h ζNN00

V2

h ζNV

2

h ζN0N0

V2

h ζNV

2

h ζN00N

wvu

22

Nf is the shape function matrix of the degenerated shell element.

Sf is transformation matrix of the displacement vector at node f of shell element

T

f2f1fff ,,w,v,u .

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 ( 0'

z ) and using Hooks law enables the stresses vector to

be reduced to following five stress components,

ο

zy

zx

yx

y

x

εεD

η

η

η

ζ

ζ

ζ

''

''

''

'

'

23

is the initial strain vector.



is the strain vector.

[D] is the elasticity matrix given by,

GK0000

0GK00000G000001ν000ν1

ν1

ED

2

1

2

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,

'

'

'

'

'

'

'

'

'

'

'

'

'

'

'

'

zy

zx

yx

y

x

y

w

z

vx

w

z

u

x

v

y

u

y

vx

u

ε

ε

ε

''

''

''

'

'

25

The local derivatives above of the displacement components ''' wand v,u in the local

coordinates system ('

1X ) can be obtained as:

z

w

z

v

z

u

y

w

y

v

y

ux

w

x

v

x

u

z

w

z

v

z

u

y

w

y

v

y

ux

w

x

v

x

u

T

'

'

'

'

'

'

'

'

'

'

'

'

'

'

'

'

'

'

26

[ ] is the transformation matrix given by,

'''

'''

'''

z

z

y

z

x

z

z

y

y

y

x

y

z

x

y

x

x

x

][

27

ζ

w

ζ

v

ζ

u

η

w

η

v

η

u

ξ

w

ξ

v

ξ

u

J

z

w

z

v

z

u

y

w

y

v

y

ux

w

x

v

x

u

1

28

ζ

z

ζ

y

ζ

x

η

z

η

y

η

x

ξ

z

ξ

y

ξ

x

[J]

[J] is Jacobian matrix 29


Lateral Deflections


The transpose of the Jacobian matrix results from equation (12) can be expressed as

follow:

n

1ff,,f

z

f3

y

f3

x

f3

ff

z

f3

y

f3

x

f3

ff,,f

f

f

f

T 0 N N

V

V

V

2

hN00

V

V

V

2

h0 N N

Z

Y

X

]J[

30

n is the number of node per element,

hf is the element thickness at node f, and

,NN ;

,NN f

,ff

,f

31

are the derivatives of the global displacements referred to the curvilinear coordinates are

obtained from equation (18), such as

u

. . .etc.

n

1f

2f,f

x

f2

f

1f,f

x

f1

f

f,f N V2

h N V

2

hu N

u

32

The strain matrix B can be formulated from equations (21), (29) and (31) as:

B 33

where, T

21α , α , w, v,u δ

34

[B]=

)VgVd(-)VgV(da0c

)VeVg(-)VeV(gbc0

)VdVe(-)VdV(e0ab

Ve-Ve0b0

Vd-Vd00 a

x2iz2ix1iz1iii

z2iy1iz1iy1iii

y1ix2iy1ix1iii

x2iy1ii

x2ix1ii

iiii

iiii

iiii

ii

ii

35

η,NJζ,NJa i*

12i

*

11i η,NJζ,NJb i

*

22i

*

21i

η,NJζ,NJc i

*

32i

*

31i

)NJz(a2

hd i*

31

,i

ii

)NJz(b

2he i

*

23

,i

ii

)NJz(c

2h

i*

23

,i

ii g

Consequently, it is used in the calculation of the stiffness matrix [K] using the mid-

coordinate rule. Hence [K] can be defined as follows:

ηdξ dζ ζη,ξ,J [D][B][B] [K]1

1

1

1

1

1

T d

36

Then K can be written as summing up the contribution of each layer at the gauss points,

dη dξ h

Δh2ζη,ξ,J ]][B[D][B [K]

1

1

1

1

nL

1j

j

jj

T

j

37

[K] : stiffness matrix, [D] : elasticity matrix, [Bj]: strain-displacement matrix.

),,(J is the determinant of the Jacobian matrix for layer ( j ).

jh is the thickness of the jth layer.

nL is the total number of layers.

In the same way, the internal force vector {e

f } can be determined as follows:

dV J }{]B[}f{v

Te

38



dη dξ h

Δh2 ζ)η,J(ξ( }{ζ][B}{f

nL

1j

1

1

1

1

j

j

T

j

e

39

}{ j: is current stress vector,

}f{ e

: 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 ( ''YX ) using the following relation:

][S][D[S]][Ds

T'

s

40

lm

ml

mllmlm

lmlm

lmml

000

000

0022

00

00

[S] 22

22

22

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.


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:

FqK 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



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).


Lateral Deflections



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.

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