MMAE545-Final Report-Analysis of Aircraft Wing

Final report

Members (as the presentation order): Li He, Jinliang Zhao and Shijie Song.

Contribution of each member: We did it together, and everyone made a great effort for

each section of the project.

Our project consist of 4 parts: CAD model, mesh model, static analysis and dynamic

analysis.

CAD Model

We have used Inventor to establish the geometry model of aircraft. In the CAD model,

we elected NACA 0012 wing type as our analysis object. We considered the Taper of

Wing, as 0.9, and Anhedral Angle, as 2○. Moreover, due to the weight of motor &

aircraft body and distribution of force, we set the thickness and place of ribs along with

the mass and force distribution. As shown in the following two pictures.

As to the materials, we have selected Ply-Wood (2&3mm) as Ribs, Balsa (1mm) as

Skin and Carbon Fiber (2mm) as Tubes. According to the practical application, once

the material has reshaped plastically, Analysis of wing isn’t meaningful, so we haven’t

applied the plastic data into the material card for analyzing.

Mesh Model

In the mesh model, we have tried to use 3D mesh model. However, it’s too difficult to

fix out the contacting problem between two contacting solids. Finally, we chose the

shell mesh model: the element size is 10mm, element type is S3/S4, the element count

is 36339, and the node count is 22654. The mesh model is showing in the following

two pictures.

Static Analysis

For the static analysis, there are 3 part needed to mention, which are boundary

conditions, loading and results and analysis.

1. Boundary Conditions

Considered the real situation of aircraft wings, the part of wings which connects to the

body of the aircraft are needed to be fixed.

2. Loading

The principle of force distribution principle:

And the curve of the force distribution: 𝐹 = √𝑙2 − 𝑥2 where 𝑥 is the distance from

the position to the fixed part of the wing.

For the real situation of wings, 3 different situations’ loading are needed to analyze

which are steady flying, overloading and rolling.

For the first two situations, the loading method is the same. The only difference is the

value of the force. As for adding lifting force, in order to satisfy the distribution of

lifting force, we need to add all different value of force on each node of the wing which

is not easy to achieve. Therefore, we can add the same force on the nodes of each period.

That makes force distribution approximately conforming to the equation of the

distribution.

Then we add the general value of 15N loading on the wing. Because it is the half mass

of the aircraft we designed. And the loading of the overloading situation is the 3 times

of the steady flying’s which is 45N.

As for rolling, not only do we need add 15N on the wing, but also we have to add a

torque to make it rolling. And we decided the general value of the torque is 3N·m. As

for the torque’s loading area, we add two forces which are the same value and the

directions are opposite but not in the same line to the connection between ribs and tubes.

Then we use the boundary conditions and loading conditions to edit the *inp file. And

then use Abaqus to analyze it.

3. Result and Analysis

1) For the steady flying

The peak stress of the tubes=11.15 MPa

The peak stress of the skin=1.04 MPa

The peak stress of the ribs=7.64 MPa

Considering all the materials’ ultimate stress, peak stresses are safe for the wings.

The force- time curve at the fixed reference node. (In Y-direction)

The displacement-time curve at the end of the tube. (In Y-direction)

2) Overloading

The peak stress of the tubes=25.35 MPa

The peak stress of the tubes=2.465 MPa

The peak stress of the tubes=1.462 MPa

Considering all the materials’ ultimate stress, peak stresses are safe for the wings.

The force- time curve at the fixed reference node. (In Y-direction)

The displacement-time curve at the end of the tube. (In Y-direction)

3) Rolling

The peak stress of the tubes=11.48 MPa

The peak stress of the tubes=1.072 MPa

The peak stress of the tubes=74.21 MPa

Considering all the materials’ ultimate stress, peak stresses are safe for the wings.

The force magnitude curve fixed reference nodes (two different nodes in different tubes).

The force in X direction curve of fixed reference nodes (two different nodes in different tubes).

The force in Y direction curve of fixed reference nodes (two different nodes in different tubes).

The force in Z direction curve of fixed reference nodes (two different nodes in different tubes).

The displacement magnitude curve of reference node of the end of the tube (two different nodes in different tubes).

The displacement in Y direction curve of reference nodes at the end of the tube (two different nodes in different tubes).

The displacement in X direction curve of reference nodes at the end of the tube (two different nodes in different tubes).

The displacement in Z direction curve of reference nodes at the end of the tube (two different nodes in different tubes).

4) Analysis

All three different conditions are satisfied to be lower than ultimate stress of 3

different materials. Hence, it is safe in all 3 conditions. And from the curve of

displace-time and force-time, we can easily get the displacement of the end of the

wing and the force of the connecting part. And that’s is important for further analysis

of aircraft wings

Dynamic Analysis

1. Natural Frequency

There could be a severe resonance-related problem during aircraft operation is flutter.

Even though the initiation of flutter may be much more complex than resonance

excitation, resonance is still one of the contribution to structural failure when flutter

occurs.

Based on the geometry we created before, we use Abaqus to detect the first 5 nature

frequency and see its deflection. (Base on precious experience, the first 5 modes have

the most important influence on the structure).

Fig.1 Original Aircraft Wing Model

Fig.2 Displacement at Frequency of 5.5864Hz

Fig.3 Displacement at Frequency of 32.117Hz

Fig.4 Displacement at Frequency of 33.222Hz

Fig.5 Displacement at Frequency of 42.250Hz

Fig.6 Displacement at Frequency of 49.710Hz

From the result we can see that the deflection is small, around 1mm, but we still need

to pay attention with it. Because the deflection may be small, it may cause the fatigue

issue.

After the analysis, we want to know the structure’s influence on the nature frequency.

So we add some stringers through the wing, and do the analysis again.

The following is our model.

Fig.7 Geometry of Added Stringers

After adding the stringers, we ran the simulation and got the following results (Fig. 8-

12).

Fig.8 Displacement at Frequency of 5.0029Hz

Fig.9 Displacement at Frequency of 29.517Hz

Fig.10 Displacement at Frequency of 32.550Hz

Fig.11 Displacement at Frequency of 44.574Hz

Fig.12 Displacement at Frequency of 74.606Hz

As can be seen from the above, the structure of the wing does not influence deflection

at nature frequency much. While shape is the significant factor.

The table below shows the nature frequency and its deflection.

2. Impact imitation

It is usual that aircraft’s wings might have an impact with unknown objects, most of

which are birds. In order to explore the damage made by this kind of impact. We did an

impact dynamic analysis.

In order to research different situations, we set different locations and weight of mass,

run 6 situations.

6 Situations: End of Wing & 0.5Kg,

End of Wing & 1.0 Kg,

End of Wing & 1.0 Kg,

Middle of Wing & 0.5Kg,

Middle of Wing & 1.0Kg,

Middle of Wing & 5.0Kg

Velocity: 20 m/s

Fig.12 End of Wing & 0.5Kg

Fig.13 End of Wing & 1.0Kg

Fig.12 End of Wing & 5.0Kg

Fig.12 Middle of Wing & 0.5Kg

Fig.12 Middle of Wing & 1.0Kg

Fig.12 Middle of Wing & 5.0Kg

And the rib’s allowable stress is 31MPa.

From the result of the analysis, we draw the following conclusion:

The max stress are all under the allowable stress (1000Mpa) of the carbon-fiber in

all of the simulation.

The ribs are easily broken when the mass is above 1kg.

We have not considered the impacting on skin, because it is vulnerable.

IN THE FUTURE

The most important factor of an aircraft is its weight, so in the future, we are considering

losing structure weight.

Ribs. From the static analysis, we can see that the ribs still has a lot of rooms to

improve, it still has many blue area, that we can drill a hole to reduce its weight.

Carbon-fiber. The carbon-fiber does not play is role effectively. Max stress are all

under 200Mpa, while the allowable stress of carbon-fiber is 1000Mpa. We are

considering use a cheap one or reduce its thickness to reduce the cost.