AEE 464 Fall 2008 PROJECT # 2 IMPORTANT NOTES 1- Indicate ...

AEE 464 Fall 2008
PROJECT # 2
IMPORTANT NOTES
1- Indicate your group members on the front page of your project report
2- Submit pdf format of the project report in soft form. DO NOT PREPARE HARD
COPY !!
This project is about the finite element analysis of the torque box of a wing configuration
which is introduced in detail in the subsequent sections. The project document is composed of
the following sub-sections.
1- Wing geometry and structural Layout
2- Displacement boundary conditions applied
3- Material used in the sub-elements of the wing
4- External load acting on the wing structure
5- Project requirements
1- WING GEOMETRY and STRUCTURAL LAYOUT
Consider the torque box of a NACA2412 wing given in Figure 1 below. The profile data of
NACA 2412 is given in the Appendix.
Figure 1 Torque box of a NACA 2412 wing

The wing has the following overall geometric properties:
Chord length : 1.524 m
Semi span length: 4.572 m (excludes the spar root extensions !!!)
The wing is composed of two spars and 4 ribs as shown in Figure 2. Front spar is located at
25% chord from the leading edge of the wing, whereas rear spar is located at 70% chord from
the leading edge. Four ribs divide the wing into 3 equal section of length 1.524 m. The root
extensions of the front and rear spars are of 0.5 m in length.
Front spar
Figure 2 Structural layout of the wing
The spar flanges and upper and lower skin stiffener details are shown in Figure 3. Spar
flanges are composed of L profiles whereas upper and lowe skin stiffeners have T shaped
corss-sectional areas.
Root extension of spars
Rib 1
Rib 2
Rib 3
Rib 4
Rear spar

Figure 3 Spar flanges and upper and lower skin stiffeners
The upper and lower skin thicknesses, front and upper spar webs thicknesses, rib thicknesses,
front and rear spar flanges details and upper and lower skin stiffener details are given in detail
below. These geometric parameters change discretely between the rib stations.
Upper and lower skin thicknesses (same for both)
Between rib 1-2: 2 mm
Between rib 2-3: 1.6 mm
Between rib 3-4: 1.2 mm

Front and rear spar web thicknesses (same for both)
Rib thicknesses
Root extension: 4 mm
Between rib 1-2: 3 mm
Between rib 2-3: 2.5 mm
Between rib 3-4: 2 mm
Rib 1: 4 mm
Rib 2: 3 mm
Rib 3: 2.4 mm
Rib 4: 1.5 mm

Front and rear spar flanges cross-sectional details (same for both)
Rib 1-2
Rib 2-3
Rib 3-4
Root extension
Section W (mm) H (mm) t1 (mm) t2 (mm)
Root extension 35 35 12 12
between Rib 1-2 30 30 10 10
Between Rib 2-3 25 25 8 8
Between Rib 3-4 20 20 5 5
Upper and lower skin stiffener cross-sectional details (same for both)
Rib 2-3
Rib 3-4
Rib 1-2
H
W
t2
t1

Section W (mm) H (mm) t1 (mm) t2 (mm)
between Rib 1-2 20 25 6 6
between Rib 2-3 15 20 4 4
between Rib 3-4 10 15 2.5 2.5
2- DISPLACEMENT BOUNDARY CONDITIONS APPLIED
The translational displacements of all the nodes on the spar flanges and spar webs of the front
and rear spar root extensions shown in Figure 4 will be fixed and rotations will be let free.
Front spar
extension
Figure 4 Displacement boundary conditions to be applied
3- MATERIAL USED IN THE SUB-ELEMENTS OF THE WING
All the sub-elements of the wing is assumed to be composed of Aluminum 2024-T3 with the
following properties:
Young’s modulus: 73.1 GPa
Poisson’s ratio: 0.3
Density: 2780 kg/m 3
Tensile and compressive allowable limit: 250 MPa
Shear allowable: 200 MPa
Rear spar
extension

4- EXTERNAL LOAD ACTING ON THE WING STRUCTURE
The spanwise distribution of the external lift and pitching moment acting on the wing
structure is shown in Figures 5 and 6, respectively. The chordwise distribution of the external
loading is neglected and the external load is assumed to be acting along the front spar.
List Distribution(N/m)
9000.00
8000.00
7000.00
6000.00
5000.00
4000.00
3000.00
2000.00
1000.00
0.00
0 0.2 0.4 0.6 0.8 1
Figure 5 Spanwise lift distribution
Pitching Moment Distribution (N.m/m)
0.00
-50.00
-100.00
-150.00
-200.00
-250.00
-300.00
-350.00
-400.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Figure 6 Spanwise pitching moment distribution

Table 1 Lift and pitching moment distribution acting
Lift per unitSpan
Pitching moment per unit span
(positive leading edge up)
Span
(N/m)
(N.m / m)
0 8149.40 -379.18
0.1 8129.39 -378.35
0.2 8068.81 -375.88
0.3 7962.26 -370.93
0.4 7798.37 -362.69
0.5 7559.84 -350.33
0.6 7214.76 -329.72
0.7 6707.42 -295.92
0.8 5922.61 -239.05
0.9 4571.50 -141.78
0.95 3401.58 -75.84
0.98 2230.58 -33.80
0.9999 206.62 -2.47
Table 1 tabulates the lift and pitching moment distribution. It is assumed that the half of the
load is acting along the front spar lower flange and the other half is assumed to be acting
along the front spar upper flange as shown in Figure 7. Spanwise load distribution has to be
decided by the students. Some options are:
• Learn how to use ‘Fields’ in generating the distributed load along the upper and lower
spar flanges (Students who chooses this option will receive 5% bonus)
• Consider the external load section by section by taking sectional average and applying
constant sectional average along the section you generated. Do not forget by taking
large number of sections you can approximate the true load better.
Half lift and moment
acts along upper
flange
Half lift and moment
acts along lower
flange
Figure 7 Load share

In addition to the aerodynamic load also include the weight effect. The direction of the
gravitational acceleration is given in Figure 8.
5- PROJECT REQUIREMENTS
Figure 8 Direction of gravitational acceleration
i- Using PATRAN model the structure. Use the contour points for the NACA2412
profile given in Appendix and scale it until the chord is 1.524 m.
ii- Generate the stiffener location edges and ribs
iii- Using PATRAN create shell meshes (QUAD4 elements) on all the surfaces (upper
and lower skins, ribs and front ant rear spar webs) and apply the displacement
boundary conditions. Verify element normals of the shell element groups that is
defined in part v. Make sure that for each groups element normal point in the same
direction. Plot the element normals.
iv- Generate beam elements (CBEAM) to model the spar flanges and stiffeners on the
upper and lower skin. Use offset feature to position the spar flanges and upper and
lower skin stiffeners as shown in Figure 3 !!.
g=9.81
m/s 2

Hint:
For spar flanges if you use arbitrary beam shape generation feature utilizing
boundary loops, you can orient the profile properly by rotating the beam cross-
section. Do not forget to assign stress output locations at the corners of the profile.
For the upper and lower skin stiffeners you can use the T cross-section from the
available beam cross-sections in Patran.
v- Use FEM group capability to group the shell elements and beam elements into the
following groups:
- Upper skin
- Lower skin
- Front and rear spar webs
- Front and rear spar flanges
- Ribs
- Upper and lower skin stiffeners
(DO NOT INCLUDE SPAR EXTENSIONS IN THE GROUPS !!!)
vi- Perform the solution for three different mesh sizes. Plot at the variation of the
maximum displacement.
vii- Plot the variation of the combined bending plus axial stress on one of the front spar
upper flange beam element at approximately mid wing span for the three mesh
sizes. Indicate the element in your report.
viii- Plot the variation of the Von-Misses stress on one of the shell elements on the
lower wing skin at approximately mid wing span for the three mesh sizes. Indicate
the element in your report.
ix- Based on the three plots in vi, vii, and viii make comments about the convergence
of the results based on the displacement and stress results.
x- Create contour plots for the Von-Misses stresses on the shell elements and
comb,ned axial and bending stress for beam elements for the finest mesh size
only. (DO NOT CONSIDER THE STRESSES IN THE SPAR EXTENSIONS !!!)
Plots Von Misses stresses for the shell elements for the following groups:
- Upper skin
- Lower skin
- Front and rear spar webs
- Ribs
Plots combined bending and axial stresses for the beam elements for the following

groups:
- Front and rear spar flanges
- Upper and lower skin stiffeners
xi- Create displacement plot for the whole wing structure.
xii- Make a note of the following in a table
- Maximum displacement and its location ( which node)
- Maximum Von Misses on the shell elements (which group and which element)
- Maximum shear stress on the shell elements (which group and which element)
- Maximum combined axial and bending stress on the spar flanges (which
element)
- Maximum combined axial and bending stress on the skin stiffeners (which
element)
xiii- Comment on the structural integrity of the wing torque box based on your stress
results and stress allowable for the aluminum material.
IMPORTANT NOTE:
Your outputs should be in a report format and including the
* Description of the problem
* Description of the finite element modeling technique of the structure (Element types
used, number of elements, number of nodes etc.) accompanied with relevant figures of
the finite element mesh

APPENDIX: Profile data of NACA 2412 for unit chord length
1.0000 ......
1.0000 (0.0013)
0.9500 0.0114
0.9000 0.0208
0.8000 0.0375
0.7000 0.0518
0.6000 0.0636
0.5000 0.0724
0.4000 0.0780
0.3000 0.0788
0.2500 0.0767
0.2000 0.0726
0.1500 0.0661
0.1000 0.0563
0.0750 0.0496
0.0500 0.0413
0.0250 0.0299
0.0125 0.0215
0.0000 ......
0.0000 0.0000
0.0125 -0.0165
0.0250 -0.0227
0.0500 -0.0301
0.0750 -0.0346
0.1000 -0.0375
0.1500 -0.0410
0.2000 -0.0423
0.2500 -0.0422
0.3000 -0.0412
0.4000 -0.0380
0.5000 -0.0334
0.6000 -0.0276
0.7000 -0.0214
0.8000 -0.0150
0.9000 -0.0082
0.9500 -0.0048
1.0000 (-0.0013)