# The engineering sector

### 1.0 Introduction and Theory

In the engineering sector, numerous cases relates to the ability of a structural components to withstand factors such as stresses and strains from a given load without failing. In order to solve these problems, mathematics can be applied but as more complex data are produces, errors are more likely to occur. To eliminate this error factor, the components can be design and simulated from computer software by algorithms; furthermore the results can be analysed in graph to draw a faster conclusion before the manufacture stage, which works out to be more cost effective. Due to computer software, the designs can be as complex as required since the forces can be applied at any position and in any direction.

In this study, the software I-DEAS will be used with a Finite Element Method (FEM) to investigate the stresses on an aerofoil based on an external forces applied near the leading edge.

### 1.1 FEM

FEM is a numerical method used to get approximate solutions by solving partial equations. Even though the results are approximates, they are accurate to very high degrees and usually shows remarkable similarities to real life solutions. FEM can be used to cover most regions of where failures would occur, such as in this study: stresses strains and displacements. This method has proven to be extremely reliable, and on today's engineering market, this tool is used prior to manufacture and has proven to be cost effective.

This study consists only of a simple 2D problem, therefore the constraint forces can only be used in the x and y direction, furthermore the mesh can be generated only on one face.

By the use of FEM, 2.5D and 3D problems can also be solved. 2.5D situations consist of a z direction as well for the acting force, [2] but are still restricted to a one face mesh. Whereas in a 3D case, the forces can be applied in all directions as well as any face can be meshed.

A careful creation of a mesh is important in FEM, since the more refine the mesh, the greater the chances of convergence. This is because approximations are produced in each element of the mesh, which are defined by a certain degree of freedom. So from a larger degree of freedom (a smaller mesh) more values can be obtained within a certain area, which therefore produces more accurate approximations.

The software I-DEAS generates mesh sizes based on the user's requirements, but for best result they need to be refined accordingly.

Some designs can produce complex shapes, and in some situations the element of the mesh are found to be skewed. We should aim to avoid this factor, since it produces inaccurate results. This could be avoided by changing the mesh type, such as from squares to triangles.

### 1.2 The selected design

The design of and aerofoil with an external force (a bird) acting on its leading edge was chosen, as this is related to my third year project from DEN 118 (Bird impact: a comprehensive review). A section of a wing was selected, because wings have one of the highest rate of damage from bird impacts. So by selecting this design I hope to achieve a better understanding of how the forces vary across the 2D cross section. Figure 1 shows a wing cross section, on which the forces will be applied.

For this design, in order to produce the most accurate result possible, the bottom surface of the wing was clamped and forces totalling 180N were applied on the aerofoil. The some of the force is 180N, so if the force is being applied by 5 separate nodes, then at each node a force of 35N will be applied. Refer to Figure 2.

The aim of this study is to apply a range of different element length, as well as different type of meshes to produce the most accurate results based on a bird impact colliding with an aerofoil.

### 2.0 Procedure

By selecting the Master modeller tab from the drop down menu, the general shape of the aerofoil can be formed. This consisted of a semi circle, connected by two lines representing the lower and upper surface up until the trailing edge.

From the extrusion option, a 3D shape was then produced. The contours of the aerofoil was selected and extruded by a 100 units. Refer to Figure 1, section 1.2.

From the drop down menu, the Meshing tab was selected. The aerofoil was selected and the define shell mesh tap was chosen. The element length then was chosen (which changes from 0.5, 2, 5 and 10) and the element family was changed to plane stress. Furthermore, for each element length, the element type was changed to square and then to triangle to give different sets of results. Refer to graph 1 and 2, section 3.0.

From the drop down menu, the Boundary condition tab was then selected. The displacement restraints were applied by selecting the value zero from the menu before pressing enter. The restraints were set for only the lower surface of the aerofoil. By selecting zero this meant that the lower surface was clamped.

From the Boundary condition tab, a force totalling 180N was applied to the nodes near the leading edges. Refer to Figure 2.

From the drop down menu, the Model simulation tab was then selected. Since all the variable has been defined, the solution set button was selected, followed by the solve tab. This then produces the solutions.

From the drop down menu, the Post Processing tab was then selected. By selecting the display button followed by enter, the solution could finally be viewed. Refer to Figure 3.

NB. The material was changed from the default material of Steel to Aluminium, since Aluminium is used aircraft components.

The following Aluminium properties were used:

Young's modulus = 70 GPa

Shear Stress = 26 Gpa

Poisson's Ratio = 0.35

0.5

20647

2.0

658

5.0

103

10.0

31

### Triangle

0.5

10041

2.0

1323

5.0

206

10.0

56

Table 1: Analysed data from I-DEAS

### 4.0 Discussion

The aim of this study was to find which configuration gives the most accurate result due to a bird impact on the wing.

From graph 1, a general trend for the two curves shows that, as the mesh width (element length) decreases the maximum stress increases. This is because there are more elements in the mesh; therefore more approximations can be obtained to provide a accurate result.

Comparing the square shape mesh to that of the triangular; it can be observed that for all four coordinates, the square mesh produces a larger maximum stress. So it can be suggested that the triangular mesh is less accurate than the square mesh for an aerofoil.

Looking at element length for 0.5 and 2.0 only, the pattern for both lines shows a levelling-off of the curves. That region shows that if the element length was to be further decreased, this would result in little or no change in the value of the maximum stress. So if this study was to be further researched, it would be pointless to have element lengths below 0.5.

Overall from graph 1, it can be suggested that more accurate data from a bird impact could be obtained from a square mesh of length 0.5.

From graph 2, it is surprising to find that a smaller element length of 5 produces less accurate data than that of length 10; for both square and triangular mesh. This could be due to error from the skewedness of the elements near the surface of the aerofoil and especially at the trailing edge.

Comparing the square shape mesh to the triangular mesh; again the general pattern shows that the square mesh is more accurate, since all the coordinates are above that of the triangular mesh.

Looking at the general trends, the two element length of 2.0 has the most accurate values for both curves, since they produce the highest maximum displacements. for the square mesh and for the triangular mesh.

If this study was to be further researched, it could be worth increasing the element length above 10 to about 12 and 15 to see if they produce a higher maximum displacement; since at element length 10, both lines are going upwards.

Overall from graph 2, it can be suggested that more accurate data can be retrieved from a square mesh of length 2.

Looking at both graph 1 and 2, it can be observed that a square mesh is more accurate, but most accurate data based on the element length could be retrieved at about 1.5.

Although the results show trends that would be expected, the obtained values are not fully accurate since there are some factors of error.

The cell structures around the inner edge of the aerofoil and specially at the trailing edge are more skewed, therefore the mesh point (nodes) are further away from one another and this influences the truncation error (the difference between computer estimation and real life).

Another factor is the program I-DEAS is not suitable for this design. I-DEAS assumes that both the aerofoil and the bird are at fixed position for any given time. But in reality the force changes as the birds collides with the wing, at any given time. A more appropriate software to use would be ABACUS.

This study could be further improved by considering more element types, such as the 6 point triangle mesh or by the use of more element length or by even considering other factors apart from stress, strain and displacement due to an applied force.

On the whole, the aim of this study was to provide an accurate result of a bird strike on an aerofoil using I-DEAS and this was met.

### 5.0 Conclusion

• The study was a success
• A square shape mesh produces more accurate results that the triangular mesh
• Most accurate results based on element length is near 1.5
• An error factor from meshing is skewed elements near the trailing edge of the aerofoil

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