Final Structure - Copy
Transcript of Final Structure - Copy
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ISTANBUL TECHNICAL UNIVERSITY
FACULTY OF AERONAUTICS AND ASTRONAUTICS
UCK 328E-STRUCTURAL DESIGN
Instructor: Prof. Dr. Zahit Mecitoglu
Term Project: Structural Design And Analyses Of A Wing Of ATA
Unmanned Aircraft
110090052 Kaan Berki KARABAY
110090053 Cemre UNAL
110110083 Selahattin GOKCEN
Spring, 2013
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INDEX
Page No
INDEX ..................................................................................................................................... 2TABLE LIST .......................................................................................................................... 2
FIGURE LIST ........................................................................................................................ 3
1. INTRODUCTION .............................................................................................................. 5
2. GEOMETRY and MATERIAL ........................................................................................ 6
2.1 Geometry ....................................................................................................................... 6
2.2 Material ....................................................................................................................... 10
3. LOADING CONDITIONS .............................................................................................. 11
4. FINITE ELEMENT METHOD ...................................................................................... 16
5. RESULTS OF ANALYSES ............................................................................................. 20
6. EVALUATION ................................................................................................................. 34
BIBLIOGRAPHY ................................................................................................................ 36
ATTACHMENTS...................................................................................................................37
TABLE LIST
Page No
Table 2.1 : Material Numbers..........................................................................................9
Table 2.2 : Properties Of Components...........................................................................10
Table 2.3: Mechanical Properties of Balsa ...............................................................10
Table 2.4: Mechanical Properties of Carbon Pipe ....................................................11
Table 3.1: The Parameters Of The ATA Aircrafts.........................................................12
Table 5.1: Convergency Of Meshes...............................................................................28
Table 5.2 :Vibration Frequencies Of 5 Modes Of The Wing(Hz)................................28
Table 5.3: The Result Of Buckling Analysis For First Modes.......................................31
Table 5.4: The Reaction Forces In Y Direction..............................................................33
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FIGURE LIST Page No
Figure 1.1 : A Sample Image Of ATA Unmanned Aircraft .................................6
Figure 2.1: Top View Of The Wing And Dimensions Of First Geometry...................6
Figure 2.2 : Side View Of The Wing And Dimensions Of First Geometry]................7
Figure 2.3 : The General Image Of Wing................................................................7
Figure 2.4: Top View Of The Wing And Dimensions Of Final Geometry..................8
Figure 2.6: Cross Section Of Carbon Pipe (Thickness : 1 mm)................................8
Figure 2.7 : Cross Section Of Spar (Thickness : 4 mm)...........................................9
Figure 2.8 :Display of Components According To Real Constant Numbers...............9
Figure 3.1: Lift Distribution Of The Single Wing..................................................13
Figure 3.2 : The Calculation Of Parasite Drag Coefficient......................................14
Figure 3.4 : The Pressure Distribution On Wing....................................................15
Figure 3.5: Pressure Distribution On The Rib At The Root.....................................15
Figure 4.1: SHELL 63 Elastic Element ...........................................................16
Figure 4.2: The Meshed Carbon Pipe...................................................................17
Figure 4.3: The Meshed Spar...............................................................................17
Figure 4.4: The Meshed Structure Containing All Components...............................18
Figure 4.6 : Boundry Conditions..........................................................................19
Figure 5.1: Displacement Values Of First Design (Max:53 mm).............................20
Figure 5.2: Von Mises Stress Values Of First Design(Max:40 MPa)........................20
Figure 5.3: Tsai-Wu Failure Criteriation Values Of First Design.............................21
Figure 5.4: Displacement Values ( Max:67 mm)....................................................22
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FIGURE LIST Page No
Figure 5.5: Tsai-Wu Failure Criteria (Max: 0,87)...................................................22
Figure 5.6: Von Mises Stress Values Of Carbon Pipe For Nodes..............................23
Figure 5.7 : Von Mises Stress Values Of Carbon Pipe For Elements.........................24
Figure 5.8 : Von Mises Stress Values For Spars For Nodes ( Max:12 MPa)...............24
Figure 5.9 : Von Mises Stress Values Of Ribs For Elements.....................................25
Figure 5.10: Von Mises Stress Values Of The Spar For Nodes(Max:6.3MP................26
Figure 5.11: Von Mises Stress Values Of The Spar For Elements(Max:6.3 MPa.........26
Figure 5.12: General Image Of Distribution Of Von Mises Stress Values For
Nodes (Max:46 MPa).........................................................................................27
Figure 5.13: General Image Of Distribution Of Von Mises Stress Values For
Elements (Max:47 MPa).........................................................................................28
Figure 5.14: Image Of 1th Mode Of Wing (Max Displacement: 207.3 mm).................29
Figure 5.15: Image Of 2nd Mode Of Wing (Max Displacement: 197 mm)...................29
Figure 5.16: Image Of 3rd Mode Of Wing (Max Displacement: 199 mm)....................30
Figure 5.17: Image Of 4th Mode Of Wing (Max Displacement: 199 mm)....................31
Figure 5.18: Image Of 5th Mode Of Wing (Max Displacement: 277 mm).....................31
Figure 5.19: Front View Of Buckling Analysis For 1st Mode.........................................32
Figure 5.20: Isometric View Of Buckling Analysis For 1st Mode...................................32
Figure 5.20: Side View Of Buckling Analysis For 1st Mode............................................3
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1.INTRODUCTION
An unmanned aerial vehicle (UAV), commonly known as a drone, is an aircraft
without a human pilot on board. Its flight is controlled either autonomously by computers in
the vehicle, or under the remote control of a pilot on the ground or in another vehicle. [1]
ATA unmanned aircraft was designed and built for the competition named Desing
/Build/Fly that was organized by the supports of American Cessna Aircraft Company and
Rahytheon Rocket Systems in 2012, April. ATA Team was all consisted of students of
Istanbul Technical University, Faculty of Aeronautics and Astronautics. In this competition,
ATA Team became 4th that was the best success ever among very popular univercities like
MIT, Illnois, Virginia Technical Univercity.
In this study, the wing of the aircraft was designed and analyzed in CATIA V5 and
ANSYS 14.5, respectively. All the calculations were done in Microsoft Office EXCEL.
First geometry of wing was designed. Because of importance of lightness, balsa and
carbon are choosen as materials for skin and ribs, respectively. SHELL 63 Elastic Shell
element was used for finite element model. Lift and drag forces was calculated by appropriate
equations. These processes were discussed in next chapters in details. Von Mises stress values
were compared to allowable stresses values. The convergency of meshes was examined and
found proper. After providing stress and displacement conditions, Tsai-Wu failure criteriation
and modal analysis under just gravitational load were done. At the end, total weight of the
wing was calculated. Results of analyses were examined in evaluation part. The sources that
were researched were indicated in the bibliography part. A sample image of ATA unmanned
aircraft was shown in Figure 1.1 .
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Figure 1.1 : A Sample Image Of ATA Unmanned Aircraft [2]
2. MATERIAL AND GEOMETRY
2.1. Geometry
2.1.1 First Geometry
For airfoil geometry, MH114 was chosen by designer . With the given data, first geometry
was created. The first geometry of the wing was shown in Figure 2.1, 2.2, 2.3 .
Figure 2.1: Top View Of The Wing And Dimensions Of First Geometry
65 mm 715 mm
59.2 mm
177.3 mm
65 mm
RootTip
61.1 mm
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Figure 2.2 : Side View Of The Wing And Dimensions Of First Geometry
Figure 2.3 : The General Image Of Wing
2.1.2. Final Geometry
After analyzing the first wing, there were found unnecessary parts and some parts were
substracted, then the length of carbon pipe was shorten. The final geometry of the wing was
shown in Figure. There used totally 13 ribs.
10 mm
177,3 mm59,2 mm
Carbon Pipe
Rib
Spar
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Figure 2.4: Top View Of The Wing And Dimensions Of Final Geometry
Figure 2.5: Side View Of The Wing And Dimensions Of Final Geometry
Chord length and wing span were 236.5 mm and 780 mm, respectively.According to
these dimensions, wing area equals to 0,185 m. The carbon pipe had offset. Because the
offset was mounted to fuselage and connection point for the wing.
Figure 2.6: Cross Section Of Carbon Pipe (Thickness : 1 mm)
The cross sections of the carbon pipe and spar were shown in Figure 2.6 and 2.7,
respectively.
This part was substracted. The new length
of carbon pipe was 260 mm.
36.4 mm 23 mm 29.1 mm 48 mm 100 mm
RootTip
9 mm 10 mm15 mm
7 mm
10 mm
8 mm
61.1 mm
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Figure 2.7 : Cross Section Of Spar (Thickness : 4 mm)
The cross section areas were considered same for all the structure because of easiness in
designing process.The thickness of the skin was also considered 1 mm for all the structure.
The properties of the components were shown in Table 2.1 , 2.2 and Figure 2.8.
Table 2.1 : Material Numbers
Material Number 1 Balsa
Material Number 2 Carbon Tube
Figure 2.8 :Display of Components According To Real Constant Numbers
4 mm24.97 mm
1
2
3
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Table 2.2 : Properties Of Components
Structure Real Constant Number Thickness
Rib 1 3 mm
Skin 2 1 mm
Spar 3 4 mm
2.2.Material
Model aircraft had to be very light and resistent because of the missions of the competition.
Because of that carbon tube was choosen for the pipe where the wing connected to the
fuselage. The other parts of the wing was made from Balsa that had very high elasticity
modulus in x direction. Safety factor was considered 1,3 because of the importance of
lightness. The mechanical properties of the carbon tube and balsa were shown in Table 2.3
and Table 2.4, respectively. Also the allowable stresses in different directions were calculated
in these tables.
Table 2.3: Mechanical Properties of Balsa [3]
Elasticity Modulus in X Direction 4600000 MPa
Elasticity Modulus in Y Direction 110 MPa
Elasticity Modulus in Z Direction 110 MPa
Poisson Ratio in XY Plane 0,3Poisson Ratio in YZ Plane 0,00717
Poisson Ratio in XZ Plane 0,00717
Shear Modulus in XY Plane 600 Mpa
Shear Modulus in YZ Plane 600 Mpa
Shear Modulus in XZ Plane 360 Mpa
Density 150 kg/m Allowable Stress
Tensile Yield Strength in X Direction 32,5 MPa 32,5/1,3=25 MPa
Tensile Yield Strength in Y Direction 27,5 MPa 25,7/1,3=19,8MPa
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Tensile Yield Strength in Z Direction 27,5 MPa 25,7/1,3=19,8MPa
Compression Yield Strength in X Direction 19,5 MPa 19,5/1,3=15 MPa
Compression Yield Strength in Y Direction 16,5 MPa 16,5/1,3=12,7MPa
Compression Yield Strength in Z Direction 16,5 MPa 16,5/1,3=12,7MPa
Table 2.4: Mechanical Properties of Carbon Pipe [4]
Elasticity Modulus in X Direction 142000 Mpa
Elasticity Modulus in Y Direction 10300 MPa
Elasticity Modulus in Z Direction 10300 Mpa
Poisson Ratio in XY Plane 0,27
Poisson Ratio in YZ Plane 0,0195
Poisson Ratio in XZ Plane 0,0195
Shear Modulus in XY Plane 7200 MPa
Shear Modulus in YZ Plane 7200 MPa
Shear Modulus in XZ Plane 4824 MPa
Density 1500 kg/m Allowable Stresses
Tensile Yield Stress in X Direction 1035 MPa 1035/1,3=796,2 MPa
Tensile Yield Stress in Y Direction 41 MPa 41/1,3= 31,6 MPa
Tensile Yield Stress in Z Direction 41 MPa 41/1,3=31,6 MPa
Compression Yield Stress in X Direction 689 MPa 689/1,3= 530 MPa
Compression Yield Stress in Y Direction 117 MPa 117/1,3=90 MPa
Compression Yield Stress in Z Direction 117 MPa 117/1,3= MPa
3.LOADING CONDITIONS
Because of the manueveirs of the aircraft the load factor was considered 1.5 . Load factor
is defined as the as the ratio of the lift of an aircraft to its weight. The total lift for for the one
wing can be calculated from Formula 1. The total weight of the structure was 18 N.
(1)
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The lift force was for two wings. Since one wing was analyzed, the lift force was divided
by 2. So the total lift force was 13,5 N.
First, some parameters were needed. The calculated parameters were shown in Table 3.1:
Table 3.1: The Parameters Of The ATA Aircrafts
The lift distribution of lift and drag distributions were calculated as follows:
Lift DistributionThe wing span and the magnitute of circulation an the root of a three dimensional
wing were 2s and 0. The formulas used in calculations were below:
With the data of coordinates given, circulation was found. Then inserting the lift force
formula lift force was found. The details of the calculations were given in attachments. The
graph of the lift distribution was shown in Figure 3.1.
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Figure 3.1: Lift Distribution Of The Single Wing
Drag DistributionFor a wing with an eliptical lift distribution, induced drag is calculated as follows:
[6]
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For a wing with an eliptical lift distribution, parasite drag was calculated and shown
in Figure 3.2 .
Figure 3.2 : The Calculation Of Parasite Drag Coefficient
The total drag force was calculated from the formula given below:
For all the calculations, the freestream density was taken 1,226 kg/m3 and total drag was
calculated as 2,5653 N. The wing was divided into 12 zones and these zones were divided
into 4 areas. The areas were shown in Figure 3.3.
Figure 3.3 : The Different Divided Areas
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The distributions of drag and lift forces were applied as pressures and shown in Figure
3.4 and 3.5.
Figure 3.4 : The Pressure Distribution On Wing
Figure 3.5: Pressure Distribution On The Rib At The Root
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4.FINITE ELEMENT MODEL
After determining the geometry and appropriate element was choosen as SHELL 63 Elastic
Element. SHELL63 is well suited to model linear, warped, moderately-thick shell structures.
The element has six degrees of freedom at each node: translations in the nodal x, y, and z
directions and rotations about the nodal x, y, and z axes. The deformation shapes are linear in
both in-plane directions. For the out-of-plane motion, it uses a mixed interpolation of tonsorial
components.The geometry, node locations, and the coordinate system for this element are
shown in Figure 4.1.
Figure 4.1: SHELL 63 Elastic Element [7]
The element is defined by four nodes, four thicknesses, and the orthotropic material
properties. A triangular-shaped element may be formed by defining the same node number for
nodes K and L as described in Triangle, Prism and Tetrahedral Elements. The element has
plasticity, creep, stress stiffening, large deflection, and large strain capabilities.The meshed
Figures are shown in Figure 4.2, 4.3 and 4.4.
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Figure 4.2: The Meshed Carbon Pipe
Figure 4.3: The Meshed Spar
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Figure 4.4: The Meshed Structure Containing All Components
Figure 4.5: The Meshed Ribs
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In the wing structure there used totally 19307 nodes and 19961 elements. Because of
limitation on the number of elements, there could not be used another mesh. For that reason
the most appropriate mesh was choosen and element length was 5 mm. So the convergency of
different meshes could not be examined also.
For fixing the sutructure spar and carbon pipe were connected to wing. For that reason,
boundry conditions were applied on spar and carbon pipe. The degree of freedom or the
surfaces were limited in every direction. It was shown in Figure 4.6.
Figure 4.6 : Boundry Conditions
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5.RESULTS OF ANALYSIS
Results Of Analyses Of First Design
Figure 5.1: Displacement Values Of First Design (Max:53 mm)
Figure 5.2: Von Mises Stress Values Of First Design(Max:40 MPa)
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Displacement and Von Mises Stress values of first design were shown in Figure 5.1
and 5.2, respectively. The results were found appropriate. But because of the competition
rules and the missions that ATA unmanned aircraft would do, the lightness was very
important property. For that reason, the length of the carbon pipe whose density was very high
compared to balsa material was shorten and the unnecessary parts of the ribs were substracted.
After these prosesses, desired geometry was created. Also Tsai-Wu failure criteriation of first
design was shown in Figure 5.3. The structure was stable that failure criteriation value did not
exceed 1 under the loading conditions.
Figure 5.3: Tsai-Wu Failure Criteriation Values Of First Design
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Results Of Analyses Of Final DesignIn this study, static and modal analysis of the components of the wing structure were
examined. For each component the analysis results were shown below.
Figure 5.4: Displacement Values ( Max:67 mm)
Figure 5.5: Tsai-Wu Failure Criteria (Max: 0,87)
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The displacement values are appropriate for the structure. Maximum displacement
occured at the tip and the value was found 67 mm. After that Tsai-Wu criteriation was
examined and found maximum 0,87. Tsai-Wu criteriation values was under 1 and there was
no problem in the wing structure. The displacement and Tsai-Wu results were shown in
Figure 5.4 and 5.5 respectively.
Figure 5.6: Von Mises Stress Values Of Carbon Pipe For Nodes
Figure 5.6 and 5.7 showed the Von Mises Stress values for nodes and elements,
respectively. The maximum stress values were found 46 MPa and 47 MPa. Maximum stresses
were under the allowable stress values and occured at near the middle of the tube as expected.
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Figure 5.7 : Von Mises Stress Values Of Carbon Pipe For Elements
Figure 5.8 : Von Mises Stress Values For Spars For Nodes ( Max:12 MPa)
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Figure 5.9 and 5.10 showed the Von Mises Stress values of spars for nodes and elements,
respectively. The maximum stress values were found 12 MPa and 17.9 MPa. Maximum
stresses were under the allowable stress values and occured at the hole of the root rib as
expected. The great difference between nodal and element solution is the cause of mesh. As
mentioned before, because of limitation of the number of elements there could not be used
more elements. Here could not be found exact value. But the locations where the maximum
stress occured were same. Also the convergency of the meshes were not appropriate for the
results for ribs. In fact, the geometry of the ribs was the main reason for the irregularity of the
meshes.
Figure 5.9 : Von Mises Stress Values Of Ribs For Elements
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Figure 5.10: Von Mises Stress Values Of The Spar For Nodes(Max:6.3MPa)
Figure 5.11: Von Mises Stress Values Of The Spar For Elements(Max:6.3 MPa)
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Von Mises stress values of the spar for nodes and elements were shown in Figure 5.10 and
5.11 respectively. The maximum stress values were found 6.3 MPa and same. It did not
exceed the allowable values. As the geometry was rectangle prism and smooth, the meshes
was excellent. Because of that the convergency of the meshes was good.
Figure 5.12: General Image Of Distribution Of Von Mises Stress Values For Nodes (Max:46 MPa)
As understood from the figures none of the Von Mises stress values exceeded the
allowable values. The values of the carbon pipe were the same with general distribution. So
the maximum stress occured on the carbon pipe. Because of that reason the skin thickness was
considered as thin as possible and 1 mm. In addition, the rib on the tip of wing was not same
with the others. It remained same with first geometry for easiness in the covering prosess.
There was one hole that carbon pipe connected as understood from Figure 5.12 and 5.13.
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Figure 5.13: General Image Of Distribution Of Von Mises Stress Values For Elements (Max:47 MPa)
Table 5.1: Convergency Of Meshes
Component Element Solution(MPa) Nodal Solution (MPa) Convergency(%)
Carbon Pipe 47.2 45.9 2.75
Rib 17.9 11.9 33
Spar 6.37 6.37 0
The convergency of meshes were shown in Table 5.1. After Von Mises stress analyses,
modal analyses of 5 modes of the wing were examined and the vibration frequencies were
found as shown in Table 5.2. The displacements for 5 modes were shown in Figure 5.14, 5.15,
5.16, 5.17, 5.18.
Table 5.2 :Vibration Frequencies Of 5 Modes Of The Wing(Hz)
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Figure 5.14: Image Of 1th
Mode Of Wing (Max Displacement: 207.3 mm)
Figure 5.15: Image Of 2
nd
Mode Of Wing (Max Displacement: 197 mm)
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Figure 5.16: Image Of 3rd
Mode Of Wing (Max Displacement: 199 mm)
Figure 5.17: Image Of 4th
Mode Of Wing (Max Displacement: 199 mm)
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Figure 5.18: Image Of 5th
Mode Of Wing (Max Displacement: 277 mm)
After examining the modal analysis, also buckling analysis of the wing was done for one
mode. The reason of the negative value in the frequency was reasearched and consulted to
instructors, but could not be found. The value was shown in Table 5.3 and the images of the
buckling analyses were shown in Figure 5.19, 5.20 and 5.21.
Table 5.3: The Result Of Buckling Analysis For First Mode
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Figure 5.19: Front View Of Buckling Analysis For 1st
Mode
Figure 5.20: Isometric View Of Buckling Analysis For 1st
Mode
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Figure 5.20: Side View Of Buckling Analysis For 1st
Mode
Maximum displacement for buckling analysis for first mode was found 1mm. It was
considered appropriate.
Weight Of The StructureTable 5.4: The Reaction Forces In Y Direction
With Gravity Without Gravity
First Design -12.208 N -13.530 N
Final Design -12.501 N -13.530 N
As understood from Table 5.4, in the first design, the weight of the structure was
found 1.32N, 137.6 g. After idealizing the wing total weight was found 1.029N, 105 gr.
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6.EVALUATION
In this study, design and analyses of the wing of ATA unmanned aircraft that
participated in 'Design/Build/Fly' competition that was held by the supports of American
Cessna Aircraft Company and Rahytheon Rocket Systems in 2012, April.
Design, analyses and calculations were done in CATIA V5 , ANSYS 14.5 and
Microsoft Office EXCEL program, respectively.
Firstly, the wing was designed then analyses were done.Lightness was very important
parameter for ATA aircraft.Because of that load and safety factor were taken 1.5 and
1.3,respectively.Under these conditions, Displacement and Von Mises stress values were
found 53 mm and 40 MPa. Results were considered appropriate. But that was not ideal one.
For finding the desired design the wing was optimized. Because of importance of lightness,
balsa and carbon are choosen as materials for skin and ribs, respectively. SHELL 63 Elastic
Shell element was used for finite element model.Structure was modeled with 5 mm-length
elements. There used 19307 nodes and 19961 elements. Because of limitation on the number
of elements, there could not be used another mesh. Total lift and drag forces were 13,5 N.
Dividing the wing 14 zones, again dividing zones into 4 areas, the pressures were applied.
The wing was attached from spar and carbon pipe to fuselage. Because of that the movement
of areas that were connected was limited in translation and rotation in x, y, z directions. In the
results part, displacement values were found suitable for 76cm wing. Then none of Von Mises
values exceeded the allowable stress values for different components. The convergency of
meshes were good except mesh of ribs. Because of the geometry of ribs meshes were irregular
and convergency was too high. Tsai-Wu failure criteriation values were under 1 as expected.
Then 5 modes of modal analyses were done. The vibrations were evaluated as normal. Then
buckling analysis was done for one mode and maximum displacement for that mode was 1
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mm. The sources used and calculations were given in bibliography and attachments,
respectively. For under all these conditions, the structure can be tought as resistent and could
do missions successfully.
This study was just an approximation to real case. In theory, under some assumptions,
the structure had no problem. But to get exact results, the aircraft had to be flied and tested by
experts.
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BIBLIOPGRAPHY
[1]Url-1 Taken Date : 01.05.2013
[2]Url-2 Taken Date : 01.05.2013
[3]Url-3 Taken Date : 06.05.2013
[4]Url-4
[5]Url-5
[6]Url-6
[7] ANSYS 14.5 Help Topics
ATTACHMENTS
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ATTACHMENTS
Area(mm2) Pressure (Mpa) Applied Pressure(Mpa)
1. Area (upper) 8071 0,00008784927 0,000114204
2.Area (upper) 8018 0,00008727239 0,000113454
3. Area (Lower) 7760 - 0,0000263554.Area (Lower) 7825 - 0,000026182
1. Area (upper) 8071 0,00008614798 0,000111992
2.Area (upper) 8018 0,00008558227 0,000111257
3. Area (Lower) 7760 - 0,000025844
4.Area (Lower) 7825 - 0,000025675
1. Area (upper) 8071 0,00008538880 0,000111005
2.Area (upper) 8018 0,00008482807 0,000110276
3. Area (Lower) 7760 - 0,000025617
4.Area (Lower) 7825 - 0,000025448
1. Area (upper) 8071 0,00008419116 0,000109449
2.Area (upper) 8018 0,00008363830 0,0001087303. Area (Lower) 7760 - 0,000025257
4.Area (Lower) 7825 - 0,000025091
1. Area (upper) 8071 0,00008247669 0,000107220
2.Area (upper) 8018 0,00008193509 0,000106516
3. Area (Lower) 7760 - 0,000024743
4.Area (Lower) 7825 - 0,000024581
1. Area (upper) 8071 0,00008012876 0,000104167
2.Area (upper) 8018 0,00007960258 0,000103483
3. Area (Lower) 7760 - 0,000024039
4.Area (Lower) 7825 - 0,000023881
1. Area (upper) 8071 0,00007697721 0,0001000702.Area (upper) 8018 0,00007647172 0,000099413
3. Area (Lower) 7760 - 0,000023093
4.Area (Lower) 7825 - 0,000022942
1. Area (upper) 8071 0,00007276948 0,000094600
2.Area (upper) 8018 0,00007229162 0,000093979
3. Area (Lower) 7760 - 0,000021831
4.Area (Lower) 7825 - 0,000021687
1. Area (upper) 8071 0,00006711053 0,000087244
2.Area (upper) 8018 0,00006666983 0,000086671
3. Area (Lower) 7760 - 0,000020133
4.Area (Lower) 7825 - 0,0000200011. Area (upper) 8071 0,00005931621 0,000077111
2.Area (upper) 8018 0,00005892669 0,000076605
3. Area (Lower) 7760 - 0,000017795
4.Area (Lower) 7825 - 0,000017678
1. Area (upper) 8071 0,00004793766 0,000062319
2.Area (upper) 8018 0,00004762287 0,000061910
3. Area (Lower) 7760 - 0,000014381
4.Area (Lower) 7825 - 0,000014287
1. Area (upper) 8071 0,00002714268 0,000035285
2.Area (upper) 8018 0,00002696445 0,000035054
3. Area (Lower) 7760 - 0,0000081434.Area (Lower) 7825 - 0,000008089
9.Zone
10.Zone
11.Zone
12.Zone
8.Zone
3.Zone
4.Zone
5.Zone
6.Zone
7.Zone
1.Zone
2.Zone
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