Structural Analysis ReportDecember 5th, 2014

Jonathon Miller

Abstract:Using finite element analysis software, ANSYS, the structural strength of a NACA

0024 wing under specific loading conditions will be determined. The wing was modeled in ANSYS and the forces from lift, drag and engine weight were applied to the model. Linear, non-linear, buckling and modal analysis were performed on the model. This was done to determine if the current wing design can withstand normal flight conditions or if it needs to be redesigned. After analyzing the results this wing needs to be redesigned, it fails during multiple analysis types.

Introduction:The wing design is a set of 15, 0.005m thick ribs which span every meter of the

wing and is covered in 0.003m thick skin that has twelve stringers that run the length of the wing. The wing itself is a swept dihedral with a taper, and the engine is mounted roughly a little more than a third of the way down the wing from the root. The wing is to be analyzed with regular loads to find places prone to failure that may need reinforcement or to find possible failures from typical loading of the wing.

Wireframe displaying internal structure

Approach:Making the model:

The script for making the model itself was split up into many sections. The first was defining the material properties for the skin, then the ribs, and then the stringers, each with different properties. Next the thickness for the skin, ribs, and stringers was added to create volumes out of the areas that will be created in later sections. Then the keypoints for the ribs at the base(side closest to the fuselage) and end(side farthest from the fuselage) of the wing along with the critical rib where the turbine is located, were created to outline the shape of the wing. Lines can then be made from the keypoints to create visually connected airfoil outlines. The stringers can then be attached to the airfoil outlines using the already defined keypoints. Next more keypoints are created and connected by lines which are made to squares for the different airfoil cross sections. These areas will make up the basic surfaced shape of the airfoil. Then areas are made by connecting 4 lines created from 4 keypoints. These areas are key as they will divide the current airfoil structure into 15 different sections. Once the structure is divided into 15 different sections, the locations of the keypoints that will be used to create the areas for the other ribs will be know and can be utilized. Next the oval cut out sections are made. This is done by creating individual circular areas on each rib and scaling them to the correct elliptical size which have a long diameter of 0.4 of the chord length. We also make sure that the center of each oval is ⅓ of the chord length away from the leading edge. These areas are then essentially added to the rib areas and each area is deleted individually in order to create the elliptical holes in each rib. Finally in order to recombine all the previously separated areas, the whole piece is meshed in sections with respect to its element type which will be discussed in detail later. This creates the wing in which we will apply our boundary conditions, loads, and conduct our analysis upon. Assumptions:

- Drag: It is assumed the drag is applied to the leading edge of the aircraft. This assumption is made to simplify the problem of trying to distribute the load across all surfaces with exposure to the flow, and finding the resulting forces. Then determining whether or not they are perpendicular to the flow. This assumption can safely be made because the purpose of this analysis is analyzing the structural strength of the wing. By applying the same amount of force that would be distributed by the skin it simplifies the problem both computationally and conceptually.

- Lift: It is assumed that the lift acts through the quarter chord of each airfoil. The aerodynamic center is assumed to be on the quarter chord of an airfoil and this is what all moments and forces are assumed to act on for an airfoil. This assumption simplifies the calculation and distribution of force across the entire area of a wing. Once again this is an assumption that is safe to make because this test is about the structural integrity of the wing, not local skin strength.

- Engine Weight: The weight of the engine is applied to four stringers on the bottom of the wing. This is a way of applying the force directly to the structure of the wing and allows the weight to affect the overall bending of the wing. The values that this loading gives us are slightly incorrect due to the fact that obviously on a real wing the engine is not simply attached to 4 stringers. This allows the entire force of the engine to be concentrated in four spots however due to the fact that the stringers are attached to the ribs we still receive plausible results.

Boundary Conditions:The end of the wing that is attached to the aircraft body has the boundary

condition of zero degrees of freedom. This is because the wing will be riveted, welded or otherwise sturdily attached to the aircraft. In the model it has zero degrees of freedom at the end of each stringer and along all lines that are the root edge of the wing.

Loads:- Drag: Sixteen individual loads were chosen over a pressure because of the

taper. If a pressure was applied to the wing it would be incorrect because a pressure is applied perpendicular to the surface. On a tapered wing the drag force, due to airflow, is applied to the wing at some angle. The individual forces were able to be applied entirely in the negative X direction. The sixteen individuals loads were calculated by finding the equations of the linear lines of the distributed loads. After the loads were calculated at each Z coordinate corresponding to a rib(including the root) they were scaled to allow the sum of all the forces to equal that of the integral of the two equations that represented the distributed loads. The loads were applied to the ribs because this applies the forces to the main supporting structure of the wing. Incorrect failure of the skin could be found if the force was applied to the midpoint between the ribs because it would concentrate the load too much, over representing the force on the weakest point.

Drag Vectors(Scaled x3) Lift Vectors(Scaled x3)

- Lift: Lift was applied using the same process of drag by dividing it into sixteen individual forces and applying them to each individual rib. The lift forces had the same distribution as the drag but a factor of ten times larger.

- Engine Weight: The engine weight was distributed across 4 keypoints on the underside of the wing. Each keypoint is along a stringer. This allows the engines weight to be directly applied to the frame and not the skin. This is desired because when an engine of this mass is attached to a wing it is not just bolted on through the skin. This loading allows for accurate calculation of the effect the engine has on the structural integrity of the wing but not the local strength of the wing or even the local rib. This is because the design does not have a defined way to attach the engine and ideally it would be directly supported by multiple ribs.

Engine Weight Vectors (Newtons)

Mesh:

All 3 parts of the wing were meshed separately to ensure that each part had its correct material properties. The most efficient way to mesh the created wing the way it was modeled was to use “amesh” commands for each subsection. The “amesh” command allows the user to select 2 separate areas and mesh everything in between including the chosen areas themselves. This command also allows the user to specify a step size to create desired accuracy. For maximum accuracy we decided to use the finest step size of 1. The skin was meshed first using 5 separate “amesh” commands ensuring that the entire outer shell of the wing’s area was meshed together to create one cohesive structure that would not disconnect when loading was applied. Next both the ribs and the stringers were meshed with 4 “amesh” commands which cover every rib in between the wing cap rib to the rib closest to connecting with the fuselage. Meshing both the stringers and the ribs together allow us to apply forces directly to the stringer’s keypoints and know that the structure of the ribs will also bare the load conjointly with the stringers, even if the load is not directly applied to the ribs.

Materials:Three different types of materials were used for the model. The ribs stringers and

skin all had different types of aluminum used, the below table shows the material properties.

Part Material Type

Elastic Modulus (GPa)

Poisson's Ratio

Tensile Yield Strength (MPa)

Skin 2024-T3 73.1 .33 345

Stringer 7075-T6 71.7 .33 503

Rib 6061-T4 68.9 .33 145

Results & Discussion: Linear Analysis:

- Nodal Displacement: The max nodal displacement is .1446 meters and happens at the tip of the wing. The skin also has a spike in displacement where the engine is attached, the engine is attached to four different stringers with four different point loads. In reality the engine load would be spread over the wing structure with a bracketing structure, this would reduce the local stress concentrations at these points.

Displacement at Engine Location (meters) Vector sum of Nodal Displacement (meters)

- Von Mises Stress: The maximum stress of 1.28 GPa occurs where the engine is attached. This is greater than the yield strength of all three materials, but as stated previously, the engine would be attached differently in practice. The stress in the rest of the wing is 197 KPa which is much less than the yield strength of the materials.

Von Mises Stress (Pascals) Von Mises Stress At Engine Location (Pascals)

Nonlinear Analysis:- Stepped Analysis Results: The following table shows the time steps that were

used to analyze the wing using large displacement (Nonlinear) analysis.

Set Time/Freq Load Step Substep Cumulative

1 0.0500 1 1 3

2 .10000 1 2 7

3 .17500 1 3 15

4 0.25000 1 4 25

5 0.30625 1 5 34

6 1.0000 1 999999 56

- Leading Edge Wingtip Displacement: The displacement of the leading edge of the wingtip was analyzed and is shown in the following graph.

Displacement over time on leading edge of wingtip (meters)

Nodal Displacement: In the nonlinear analysis five different modes were analyzed. The following images show the displacements at substeps one and five, with displacements of 0.007 meters and 0.0495 meters respectively.

Top Surface Bottom Surface

Nodal Displacement at substep 1 (meters)

Z Displacement of Rib Closest to Engine (meters)

Top Surface Bottom Surface

Nodal Displacement at substep 5 (meters)- Von Mises Stress: The Von Mises Stresses are largest where the engine weight

forces are located. Similar to the linear analysis this can be ignored as the engine will most likely be attached using a bracket system. Therefore, the first

and fifth modes have maximum stresses of 8.574 KPa and 61.834 KPa respectively.

Top Surface Bottom SurfaceVon Mises Stress at substep 1 (Pascals)

Top Surface Bottom Surface Von Mises Stress at substep 5 (Pascals)

Buckling:- Stepped Analysis Results: The following table shows the time steps that were

used to analyze the wing using buckling analysis.

Set Time/Freq Load Step Substep Cumulative

1 0.97317 1 1 1

2 0.97621 1 2 2

3 0.98047 1 3 3

4 0.98763 1 4 4

5 0.99251 1 5 5

6 1.0013 1 6 6

7 1.0066 1 7 7

8 1.0151 1 8 8

9 1.0165 1 9 9

10 1.0221 1 10 10

- Nodal Displacement: In the buckling analysis ten different modes were analyzed. The following images show the displacements at substeps one and ten, with displacements of 0.134 meters and 0.146 meters respectively.

Nodal Displacement at substep 1 (meters) Nodal Displacement at substep 10 (meters)

- Von Mises Stress: The Von Mises Stresses for the first buckling mode are largest where the engine weight forces are located. The Von Mises Stresses for the tenth buckling mode are concentrated around the engine weight forces, but there are also buckling failures in other isolated areas. The first and tenth modes have maximum stresses of 1.53 GPa and 2.45 GPa respectively. In the first failure mode the point forces applied for the engine weight are believed to cause the extreme stress concentrations and show a false failure. If the wing had a more distributed engine weight, the wing could support the given loading scenario. If these stress concentrations are ignored, the buckling stresses for the first and fifth modes would be 227.15 KPa and 814.11KPa respectively.

Von Mises Stress at substep 1 (Pascals) Von Mises Stress at substep 10 (Pascals)

Modal Analysis- Stepped Analysis Results: The following table shows the time steps that were

used to analyze the wing using Modal analysis.

Set Time/Freq Load Step Substep Cumulative

1 15.285 1 1 1

2 15.893 1 2 2

3 16.068 1 3 3

4 16.228 1 4 4

5 16.509 1 5 5

6 16.681 1 6 6

7 17.093 1 7 7

8 17.363 1 8 8

9 17.871 1 9 9

10 17.980 1 10 10

- Nodal Displacement In the modal analysis ten different modes were analyzed. The following images show the displacements at substeps one and ten, with displacements of 0.371 meters and 0.291 meters respectively.

Nodal Displacement at substep 1 (meters) Nodal Displacement at substep 10 (meters)

- Von Mises Stress: The Von Mises Stresses are largest at the root of the wing. The following images show these stresses at the first and tenth modal mode, the stresses are 0.709 GPa and 0.654 GPa respectively.

Von Mises Stress at substep 1 (Pascals) Von Mises Stress at substep 10 (Pascals)

- Harmonic Analysis: The following graph is the harmonic analysis showing the displacement of the leading edge of the wingtip. One hundred modes were analyzed to create the graph, in comparison to the other modal analyses which use ten. The spike at 19.55 Hertz is the natural frequency and should be avoided during operation.

Harmonic Analysis Displacement of Displacement of Wing at Natural Frequency Leading Edge Wingtip

Von Mises Stress of Wing at Natural Frequency

Conclusion: Many modes of failure were to be analyzed, including displacement and Von

Mises stresses using linear, nonlinear, buckling, modal and harmonic. Using ANSYS to run finite element analysis, it was discovered that the wing would support typical loading if the engine did not cause local failure where it is attached to the wing. The wing structure can support the load of the engine, but in this model the engine does not have a proper bracketing system and causes local failure where the loads are applied. The wing also failed in the vibrational analysis when the frequencies were in the range of fifteen to twenty hertz, and the wing has a natural frequency of 19.55.

One major source of error was how the engine was attached to the wing. The model was able to represent the effect the engine would have on the overall structural integrity of the wing, but locally where it is attached it makes the stringers and skin fail. This failure is disregarded because the engine would not be attached just to the skin. The loads being point loads on the leading edge and the ¼ cord will cause error. Loads in these locations prevent any type of twist that happens to the wing due to uneven loading. Twist of the wing was not analyzed because it would greatly increase the complexity of the loading on the wing. To strengthen the wing some type of stiffener other than the stringers would be needed. An I beam that runs the length of the wing would be helpful in strengthening the wing.