msc aeronautical engineering aerospace structures...

MSc Aeronautical Engineering

Aerospace Structures & Numerical Analysis

Assignment B

Lecturer: Dr. R J Grant

Student: Rodrigo Folgueira (S10004004)

Submission date: 11/04/2012

Similarity score: %

Glyndwr University Assignement B

Rodrigo Folgueira (S10004004)

2

Table of contents Table of contents ........................................................................................................................... 2

Introduction .................................................................................................................................. 4

Background Theory ....................................................................................................................... 5

Finite element theory ................................................................................................................ 5

Alluminum alloy 7075 ............................................................................................................... 7

Hand calculation ............................................................................................................................ 8

Shear force and bending moment ............................................................................................ 8

Second moment of area of the cross section .......................................................................... 11

Reserve Factor ......................................................................................................................... 13

Calculation with Abaqus .............................................................................................................. 14

First and basic design .............................................................................................................. 14

Loads ................................................................................................................................... 15

Mesh .................................................................................................................................... 18

Visualization ........................................................................................................................ 19

Results ................................................................................................................................. 20

S. Mises ............................................................................................................................ 20

Pressure ........................................................................................................................... 22

Second improved design ......................................................................................................... 24

Loads ................................................................................................................................... 25

Mesh .................................................................................................................................... 26

Visualization ........................................................................................................................ 27

Results ................................................................................................................................. 28

S. Mises ............................................................................................................................ 28

Pressure ........................................................................................................................... 30

Third design without torsion load ........................................................................................... 32

Loads ................................................................................................................................... 33

Mesh .................................................................................................................................... 34

Visualization ........................................................................................................................ 35

Results ................................................................................................................................. 36

S. Mises ............................................................................................................................ 36

Pressure ........................................................................................................................... 38

Third design with torsion load ................................................................................................ 40



3

Loads ................................................................................................................................... 42

Mesh .................................................................................................................................... 43

Visualization ........................................................................................................................ 44

Results ................................................................................................................................. 45

S. Mises ............................................................................................................................ 45

Pressure ........................................................................................................................... 47

Conclusions ................................................................................................................................. 49

References ................................................................................................................................... 51



4

Introduction The present report consists in the analysis of a wing box structure using

finite element method and hand calculation.

The requirement is to, after that analysis; investigate the torsional properties of

this and similar wing box structures by modifying the design.

The wing box is designed in Abaqus 6.10-1. Finally the aim of the project is to

study how the forces acts in the wing box structure and compare the results

obtained in Abaqus between that obtained by hand calculation.

First step is to design the basic wing and calculate the stresses with Abaqus,

after this calculations, the results will show where and how is possible to

change the design of the wing in order to improve its mechanical properties.

After the first improvement, is necessary to compare the new results with that

one’s made in the first step. As the torsional is study is also necessary a new

and last design is made, that is the definitely and better design that must hold

all the forces, including the sensible torsional load.

Through the paper, the process and comparation will be explained more clearly

with the help of more than 60 pictures.

Finally the most important part of the project is to see the different results that

have been obtained and to make some conclusions about them.



5

Background Theory

Finite element theory

The finite element method (FEM) has become very important in solving

engineering problems, physical, etc.., Allowing to solve cases that until recently

were virtually impossible to solve by traditional mathematical methods.

This required to prototype, test them and go to make improvements in an

iterative fashion, which came with a high cost in both economic and

development time.

The MEF enables a mathematical model for calculating the real system, the

easier and economic change than a prototype. But it remains a method

approximate calculation because the basic assumptions of the method. The

prototypes, therefore, still necessary, but in smaller numbers, since the former

can approach the optimum design significantly more.

The finite element method and mathematical formulation and relatively new,

although its basic structure has been known for some time, in recent years

undergone a great development due to advances in computer technology. They

have been precisely these computer advances that have been made available

to users lot of programs that can perform calculations with finite elements, but

do not be deceived, the management of such programs requires a thorough

knowledge not only of the material with which it works, but also of the principles

of FEM. Only in this case we will be able to guarantee that the results obtained

in the analysis are consistent with reality.



6

Fig 1 First step. Design.

Fig 3 Third step. Calculate.

Fig 2 Second step. Create the mesh.



7

Alluminum alloy 7075 General 7075 characteristics and uses: Very high strength material used for

highly stressed structural parts. The T7075 temper offers improved stress-

corrosion cracking resistance.

Applications: Aircraft fittings, gears and shafts, fuse parts, meter shafts and

gears, missile parts, regulating valve parts, worm gears, keys, aircraft,

aerospace and defense applications; bike frames, all-terrain vehicle (ATV)

sprockets.

Physical Properties Metric English

Density 2.81 g/cc 0.102 lb/in³

Hardness, Brinell 150 150

Hardness, Rockwell A 53.5 53.5

Hardness, Rockwell B 87 87

Hardness, Vickers 175 175

Ultimate Tensile Strength 572 MPa 83000 psi

Tensile Yield Strength 503 MPa 73000 psi

Elongation at Break 11 % 11 %

Elongation at Break 11 % 11 %

Modulus of Elasticity 71.7 GPa 10400 ksi

Poisson's Ratio 0.33 0.33

Fatigue Strength 159 MPa 23000 psi

Fracture Toughness 20 MPa-m½ 18.2 ksi-in½



Machinability 70 % 70 %

Shear Modulus 26.9 GPa 3900 ksi

Shear Strength 331 MPa 48000 psi

Electrical Resistivity 5.15e-006 ohm-cm 5.15e-006 ohm-cm

Specific Heat Capacity 0.96 J/g-°C 0.229 BTU/lb-°F

Thermal Conductivity 130 W/m-K 900 BTU-in/hr-ft²-°F

http://asm.matweb.com/search/GetUnits.asp?convertfrom=43&value=2.81

http://asm.matweb.com/search/GetUnits.asp?convertfrom=79&value=83

















8

Hand calculation

Shear force and bending moment

A1) Shear force NmmNLW )/(

1. Aerodynamic Load

0 verticalF

01/14001/140028002

1

1/28001/280032002

11/3200

1/320038002

13/38003/38004500

2

1

mmNmmN

mmNmmNmmN

mmNmmNmmNV

NV 21050140070028002003200300114001050

2. Wing Structure Load

0 verticalF

06/3006/3007002

1 mmNmmNV

NV 018001200

NV 3000

3. Fuel Load

02/400 mmNV

NV 800



9

4. Engine Load N3000

Total Shear Force = Aerodynamic Load + Wing Load

N

N

14250

3000800300021050

Total Shear Force X Load Factor N57000414250

A2) Bending Moment Nmmmm

NxLW )(

x distance from root

1. Aerodynamic Moment

0 AM

mmmNmmmN

mmmNmmmNmmmN

mmmNmmmNmmmNM

2

151/1400

3

151/1400

2

1

2

141/2800

3

141/400

2

1

2

131/3200

3

131/600

2

1

2

33/3800

3

33/700

2

1

NmM 55250

2. Wing Structure Moment

0 AM

02

66/300

3

66/300700

2

1

mmmNmmmNM

NM 054002400

NmM 7800



10

3. Fuel Moment

02

22/400

mmmNM

0800 NM

NmM 800

4. Engine Moment

02/3000 mmNM

NmM 6000

Total Bending Moment Nm406506000800780055250

Total Bending Moment X Load Factor Nm162600440650



11

Second moment of area of the cross section

71 BB

82 BB

93 BB

104 BB

115 BB

126 BB

1

21 2

6

btB

Boom Area

100

1222

6

200312

6

21005825

26

20032

6

21005825

1

2

1

7

1

B

2

71 1647322500825 mmBB

30036697.281122

1222

6

200312

6

21223

122

1002

6

2003

26

20032

6

212232

6

2003

2

3

2

8

2

12

B

2

82 948mmBB

9.29536630011726

200312

6

2122312

6

2003

26

20032

6

212232

6

2003

3

4

3

9

3

23

B

2

93 9.961 mmBB



12

4.28130607.304117

102210012

6

21173

117

1222100

26

20032

6

211732

6

2003

4

5

4

10

4

3

4

B

2

115 1.902 mmBB

249.322625126

2833

83

1022

6

2003625

26

28332

6

2003625

6

12

6

5

6

B

2

126 9.1196 mmBB

Second Moment of Area

222222 839.11961021.90211745.9421229.96112294810016472 zzI4084,858,150 mmI zz



13

Reserve Factor

3wt 50wb

3st 200sb

1s

w

t

t 25.0

200

50

s

w

b

b

According to graph, 35.4sk

2

905.0

s

ssB

b

tEk

2

2

3

2

/62200

3107035.4905.0905.0 mmN

b

tEk

s

ssB

Actual Stress / Stress caused by Ultimate Load =

Maximum Bending Stress X Ultimate Factor =

(Wing Root Bending Moment X Average Height X Ultimate Factor) / Second Moment of Area

2

3

/07.174150858084

5.16

8310211712210010162600

mmN

Reserve factor in tension 201.207.174

350

Reserve factor in compression 3562.007.174

62

07.174 B



14

Calculation with Abaqus

First and basic design

The first idea, in order to make the best possible design was to design with a

design program, Solid Works, Inventor and Catia were used with this purpose,

but all the designs failed when they were transfer to Abaqus, so the last

decision was to make all the disgns with Abaqus 6.10-1.

This is the first and more basic design:

Fig 5 Design I. Front view.

Fig 4 Design I.



15

Loads

After the design process and when all the partitions, sets, assemblies, etc. are

ready is time to put the loads into the wing box.

These loads are:

Fuel: Distributed load of the weight of the fuel.

Value: -400N.m x load factor = -1600N.m

Situation: Along the first two partitions (along 2m from the encastre).

Engine: Concentrated load of the weight of the engine.

Value: -3000N

Situation: In the second partition (2m from the encastre).

Structure: Distributed load of the weight of the structure.

Value:

Distance (m)

Structure loading

1 2 3 4 5 6 Total

33.335 33.335 33.335 33.335 33.335 33.335 200.01

633.33 566.66 500 433.32 366.65 300 2799.96

666.665 x 4

600 x 4 533.35 x

4 466.655

x 4 349.485

x 4 333.35 x

4

Total 2666.6

6 2400 2133.34 1862.62 1397.94 1333.34 11793.9

Situation: Along the wing structure



16

Aerodynamic: This is the aerodynamic load.

Value:

Distance (m)

Aerodynamic loading

1 2 3 4 5 6 Total

116.67 116.67 116.67 300 200 700 1550.01

4267 4033 3800 3200 2800 1400 19500

4383.67 x 4

4144.67 x 4

3416.67 x 4

3500 x 4

3000 x 4

2100 x 4

Total 17534.08

16548.08 15666.08 14000 12000 8400 69254.24

Situation: Along the wing structure.



17

For the distributed loads (fuel, structure and aerodynamic) is necessary to make

partitions – in this case it was decided to make six like in the plot of the

exercise-and insert the data obtained in the hand calculation, shown previously.

In the front view is also possible to see the Boundary Conditions, there is an

Encastre in the left part of the wing box, the location is that because this is the

connection between the wing and the aircraft.

Fig 6. Loads I.

Fig 6. Loads I. Front view.



18

Mesh

For the first design, as is a simple one, the mesh does not give any problem.

Fig 7 Mesh I.

Fig 8 Mesh I. Front view.



19

Visualization

After meshing and when all the loads are defined, is time to create a job and

view the results. That is the visualization of the designed wing box prepare for

the results:

Fig 9 Visualization design I.



20

Results

S. Mises

As it is possible to see in the following pictures, the data to the "S. Mises" are

pretty bad, this is because the design was not good, is very weak in its internal

structure and cannot withstand stress, which is why at the back (as seen in the

figure 13) it is possible to see a significant deformation.

In the first 2-3 meter the deformation is acceptable, but this is because of the

encastre in the left side.

Fig 10 S. Mises I. Up view.

Fig 11 S. Mises I. Down view.



21

Fig 12 S. Mises I. Front view.

Fig 13 S. Mises I. Back view.



22

Pressure

As it happens with the Mises stress, it is possible to detect that the data from

the pressure is also bad. In the figure 17 is possible to observe that the

structure does not withsand these pressures

Fig 14 Pressure I. Up view.

Fig 15 Pressure I. Down view.



23

Fig 16 Pressure I. Front view.

Fig 17 Pressure I. Back view.



24

Second improved design The following design is the first improved design based in the results obtained in

the previous one, we detected that the structure was weak inside, in order to

solve this decision; the internal structure size was increased. The aim of this

decision, was to try to solve the problem increasing as minimum as possible the

weight of the structure.

Fig 18 Design II.

Fig 19 Design II. Front view.



25

Loads

The loads are still the same for this second design. The only change is to

increase a bit the structure load because we increase the weight adding

material in the strings.

Fig 21 Loads II. Front view.

Fig 20 Loads II.



26

Mesh

In the second design, as the improvements consist in add material (make bigger

the internal structure), the mesh needs to be smaller and it start to be

complicated to mesh the wing.

After a few designs, finally the decision is to make the same number of stringers

but longer, which will give to the wing more consistency.

That is the mesh obtained for this design:

Fig 22 Mesh II.

Fig 23 Mesh II. Front view.



27

Visualization

Visualization of the second design structure before proceed to the calculation.

Fig 24 Visualization design II.



28

Results

S. Mises

As it is possible to see in the following pictures, the problem is still not solved,

the structure is still being deformed because of the stresses. That shows that

the design still needs to be improved.

Also it is possible to observe that the obtained data for the stress is better, this

gives the clue that the process is right, it is necessary to make the internal

structure stronger. The point now is to try to make this taking care about the

total weigh.

Fig 25 S. Mises II.

Fig 26 S. Mises II. Down view.



29

Fig 27 S. Mises II. Front view.

Fig 28 S. Mises II. Back view.



30

Pressure

The same happens with the pressure, it is possible to observe the deformation in the figures

31 and 32, it is improved, it is less, but it is still there.

Fig 29 Pressure II. Up view.

Fig 30 Pressure II. Down view.



31

Fig 31 Pressure II. Front view.

Fig 32 Pressure II. Back view.



32

Third design without torsion load Trying to solve the problem of the deformation without forgetting about the

weigh, that is the last design. The internal structure is completely different, as

observed in the last two designs; the small stringers are useless that is why the

idea now is to change them instead of two connected beams in the middle.

The problem now is the stress in both sides of the structure that gives the idea

of crossing two beams that will hardly improve the consistency against torsion

and compression forces.

Fig 34 Design III. Front view.

Fig 33 Design III.



33

Loads

The only change in the loads now is the weight of the structure which was significantly

increased.

Fig 35 Loads III.

Fig 36 Loads II. Front view.



34

Mesh

Mesh this structure becomes now a problem, because there are now so many

internal pieces that make it hard. The idea was to make partitions and make a

different mesh for each one, but the difficulty of assembly later all the partitions

made it impossible.

Finally with a 12 size type of mesh it was possible to mesh the piece as a solid,

but this small mesh increase so much the time for the calculations, because it

has now so much elements and nodes to check.

Fig 37 Mesh III.

Fig 38 Mesh III. Front view.



35

Visualization

Visualization of the third design:

Fig 39 Visualization design III.



36

Results

S. Mises

As it is possible to see in the following pictures, the last design is successful;

the structure is now able to withstand all the loads and as it was guessed the

new cross ribs in both sides are working properly increasing the strength of the

structure in the sides where it was weak against torsional and compression

forces.

Fig 40 S. Mises III. Up view.

Fig 41 S. Mises III. Downn view.



37

Fig 42 S. Mises III. Front view.

Fig 43 S. Mises III. Back view.



38

Pressure

The same happens with the pressure, as now the structure is well designed is

able to withstand the deformation.

Fig 44 Pressure III. Up view.

Fig 45 Pressure III. Down view.



39

Fig 46 Pressure III. Front view.

Fig 47 Pressure III. Back view.



40

Third design with torsion load The following design is the same than the last one. As it was successful and the

increase on the weight was big, the decision was to not change it and try to see

what happen with the structure when the tensional load is add.

It will be possible to improving it adding another rib or two strings in the left side,

as it is in this side where the deformation is bigger but this will have two

consequences: The weight will be increased even more and it will not be

possible to mesh it (the size of the mesh is now in its limit).



41

Fig 48 Design IV.

Fig 49 Design IV. Front view.



42

Loads

The loads are the same in the previous design. The only difference is that now

a torsional load of 300N is applied to the structure. It is required a significant

load that is the reason of adding 300N. It is possible to see the torsional load in

the figure 51 in the right side.

Fig 50 Loads IV.

Fig 51 Loads IV. Front view.



43

Mesh

The mesh is the same than in the previous design, it is in the limit size because

of the complex of the structure. Minimum size for the capacity of calculation of

the i7 processor that was used; adding more material an error about the

necessity of more virtual memory appear.

Fig 52 Mesh IV.

Fig 53 Mesh IV. Front view.



44

Visualization

Fig 54 Visualization design IV.



45

Results

S. Mises

It is possible to observe that even adding the torsional moment the structure is

still withstanding the loads. Now it is posibble to appreciate in the figure 55 a

deformation in the middle of the structure.

Fig 55 S. Mises IV. Up view.

Fig 56 S. Mises IV. Down view.



46

Fig 57 S. Mises IV. Front view.

Fig 58 S. Mises IV. Back view.



47

Pressure

Like in the S. mises calculations a deformation in the middle of the structure

appears now, but the design is still good and able to withstand it.

Fig 59 Pressure IV. Up view.

Fig 60 Pressure IV. Down view.



48

Fig 61 Pressure IV. Front view.

Fig 62 Pressure IV. Back view.



49

Conclusions The aim of this project was to calculate some stresses of a wing structure,

through the paper it was explained how to compare and improve this structure.

The first design is a basic design with a few strings in it, as it is observed, this

strings are not strong enough to withstand the loads applied in it. It is necessary

to improve the design.

The first though it was to add material in that strings to make them stronger, but

after calculating the structure, the conclusion is that it is better, but is not

enough good.

Improving the wing is not a problem but as it is necessary to take care also

about the total weight of the structure, it is necessary to improve the design with

the minimum increase of material.

The main deformation is in the middle of the structure so two ribs are added in

the middle instead of the weak strings, also two cross ribs are added into both

sides in order to work against the torsional and compression that was observed

in the sides.

The problem now appears with the mesh, but it is solved making these ribs

thinner and suppressing all the strings; so finally we have a design with no

strings but with some ribs.

After the calculations, the design is able to withstand the loads, so this design is

successful, another restriction is applied now, a torsional load. As said

previously any change in the material or any change in the design will made

impossible to mesh the structure as is designed like a solid structure, not an

assembly of different parts; but the design was well done and successfully so

the torsional load is applied to the same design.

After the calculations, the S. Mises and the pressure, shows that the structure is

successful, is able to stand all the loads, a deformation appears now in the

middle of the structure.

This deformation could be solved applying a horizontal rib in the middle of the



50

structure, but this will increase significantly the total final weight, that is why is

not a good solution for this problem.



51

References

Books

Getting Started with ABAQUS / Standard (Interactive version) Hibbitt,

Karlson & Sorensen, Inc.

Theory about Finite Element method:

O.C. Zienkiewicz, R.L. Taylor. “El Método de los Elementos Finitos”.

Vols 1 y 2.

CIMNE-Mc Graw Hill, 1994.

Inernet

Technical information about the aluminum alloy:

Aerospace Specification Metals, Inc. (). Aluminum 7075-T6; 7075-T651.

http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA7075

T6

http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA7075T6

http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA7075T6

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