AE410FEMAP_PROJ

Aerospace Engineering 410 Aerospace Structural Dynamics 17 December 2014, San Diego, California

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American Institute of Aeronautics and Astronautics

AE410 FEMAP/NASTRAN Finite Element Analysis

Project

Julian Bagtas1 and Lea Ricci2

San Diego State University, San Diego, California 92182

[Abstract] The objective of the assignment is to utilize

FEMAP/NASTRAN finite element analysis software to analyze model and

analyze normal modes and linear static analyses on a wing box structure.

The wing bodies to be analyzed will have two interior rib setups, one without

ribs and the other without. The models will be used to compare the

structural performance differences accompanied with using ribs in a wing

body.

Nomenclature E = Elastic modulus ν = Poisson’s ratio ρ = Density ωn = Natural frequency σ = Bending T = Torsion troot = top/bottom skin at root tcenter = top/bottom skin at center ttip = top/bottom skin at tip tweb = spar web thickness trib = rib thickness Aspar = spar cap area Hz = hertz p = pressure I. Introduction This report will analyze the use of ribs in a wing body using FEMAP/NASTRAN finite

element analysis software. Linear static analysis will be performed on the two unswept wing

bodies in addition to normal modes to compare and contrast the data with and without wing rib

usage. The differences in data being observed are in regards to the following topics:

● Bending modes ● Torsional modes ● Natural frequencies

________________________________________ 1 Undergraduate student, Aerospace Engineering, 5500 Campanile Drive, San Diego, CA 92182,

and AIAA Student Member. 2 Undergraduate student, Aerospace Engineering, 5500 Campanile Drive, San Diego, CA 92182,

and AIAA Student Member.


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With elliptical loading scenario: ● Tip deflection ● Tip rotation ● Von-Mises stress distribution

The observed wing body was constructed using the following parameters and dimensions:

Figure 1Given dimensions of the modeled unswept wing

The wing also has the following material properties:

E = 70GPa

ρ = 2700Kg/m3

ν = 0.33

II. Normal Modes Analysis

Firstly, the wing box structure with no ribs was used to tabulate the natural frequencies ωn and

mode shapes. The following data will correspond to model A (without ribs) and model B (with

ribs) respectively.

A. Model A

1. First 30 natural frequencies and mode shapes


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The following tables and figures show the first 30 natural frequencies and mode shapes of the

wing box structure with the absence of ribs. As seen in the figures, the deformations along the

wing body are primarily rotational and translational. The biggest change in deformation occurs

starting from the seventh mode. As seen in figure 8 the model seems to deform due to a

combination of torsion and bending. The following figures depict the original structure in a wire

frame, and the deformed structures are plotted with their respective frequencies along the body.

Table 1 Tabulated Natural frequencies with corresponding mode number


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Figure 2 Translational deformation in mode 1

Figure 3 Translational and rotational deformation in mode 2


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Figure 4 Rotational deformation in mode 3

Figure 5 Translational deformation in mode 4


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Figure 6 Translational and rotational deformations in mode 5

Figure 7 Rotational deformation in mode 6


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2. First bending and torsional mode

Figure 8 shows the plot of the frequencies on the wing in the first bending and torsion mode. The

frequencies range from high in the wing root area to low in towards the wing tip area as seen in

the visual representation of the deformed wing.

3. Fixed boundary condition

Once the frequencies and modes of the non-fixed wing model were tabulated and observed, the root of the wing was then fixed to a boundary condition. The fixed root wing body was then used to observe the same modes and frequencies as seen in the unconstrained wing body. The following table is a tabulation of the natural frequencies of the fixed wing.

Figure 8 Torsional and bending deformation in mode 7


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In comparison to the unconstrained wing body, one can expect different frequencies and vast differences in regards to deformations. It can be inferred that majority of the deformations seen in fixed wing will occur at the tip and have no translational deformations due to its constraints. These next figures are the visuals provided by FEMAP for the fixed boundary conditions.

Table 2 First 30 modes and corresponding frequencies for fixed boundary condition


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Figure 9 Torsional deformations in mode 1

Figure 10 Plate deformations in mode 2


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Figure 111 Bending deformations in mode 3

Figure 12 Plate and torsional deformations in mode 4


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4. First three bending and torsional modes and corresponding frequencies

The first three bending and torsional modes occur at modes 2, 3, 4 and 1, 5, 6 respectively. The

plate deformations seen in the visual representations of the deformed wing are due to bending.

The deformed wing bodies can be seen in figures 9 through 13. The table 2 displays each natural

frequency for their respective bending or torsional mode.

5. Mesh refinement

Next, the number of elements was doubled along the wing to refine the mesh of the structure. The

causes of error are primarily due to the number of elements on the structure itself. As the number

of elements increases, so does the models ability to simulate a more finite analysis on the wing

body. Given that the simulation done by FEMAP will be more finite due to the increase in

elements, the accuracy of all other measurements and visualization of deformation modes should

increase as well. The table shown is the data collected pertaining to the mesh refinement for the

wing body. The following is the table of the frequencies and modes of the refined mesh wing.

Table 3 Natural frequencies and corresponding modes for mesh refinement


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6. Plots of mode shapes for the first three bending and torsion models using converged mesh

The shapes for the 6 modes (3 bending and 3 torsional) should remain the same with the use of

the converged mesh. Although the shape looks the same, the converged mesh is more accurate

due to the reasons mentioned previously in part 5. The refined mesh models are as follows:

Figure 14 Mode 1 refined mesh



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B. Model B 1. First 30 natural frequencies and mode shapes.

The following tables and figures show the first 30 natural frequencies and mode shapes of the

wing box structure with the presence of ribs. As seen in the figures, the deformations along the

wing body are primarily bending and torsional as opposed to the rotational and translational

deformations seen in the rib-less wing body. The biggest change in deformation occurs starting

from the seventh mode. As seen in figure 25 the model seems to deform due to a combination of

bending and torsion. The following figures depict the original structure in a wire frame, and the

deformed structures are plotted with their respective frequencies along the body. The next table

shows the ribbed model’s natural frequencies and their respective modes.

Table 4 Ribbed natural frequencies and corresponding modes


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Figure 19 Ribbed model mode 1



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2. First three bending and torsional modes with corresponding frequencies

Figures 19 through 24 show the plots of the frequencies on the wing on the first three bending and

torsional modes. Figures 19, 21 and 23 represent torsional deformations and figures 20, 22 and 24

represent the bending deformation modes.

3. Double spar cap area effects on natural frequencies for the first three bending and first

three torsional modes

Table 5 represents the natural frequencies of the wing body with a doubled spar cap area. Using

table 5 as a reference, one can see that the natural frequencies are relatively similar in comparison

to the original spar cap area. However, the increase in spar cap area is expected provide more

bending stiffness and rigidity due to the fact that the spar caps are placed longitudinally. Although

the data does not directly display this relation, it can be inferred that the bending stiffness should

increase with larger spar caps. Conversely, the spar cap area increase does not have the same

effect with torsional stiffness. The following figures are the first 7 modes with a doubled spar cap

area.


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Table 5 Double spar cap area frequencies

Figure 26 Double spar cap area mode 1


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4. Double rib thickness effects on natural frequencies for the first three bending and

torsional modes

It is to be expected that the rib thickness corresponds directly to the relationship with that of the

spar cap area. However, as opposed to increasing bending stiffness, the rib thickness adds

structural rigidity along the width of the wing, therefore increasing torsional stiffness. However,

the data does not represent this relationship. Instead, the frequency data is again similar to that of

the original ribbed wing model. The effect of the increase rib thickness can be seen in the

following table of natural frequencies.

III. Linear Static Analysis of Elliptical Loading

For this section, an elliptical loading scenario is given to observe tip deflections and behaviors.

The loading scenario given in figure 33 with a pressure of p=4.0 N/cm2.

1. Comparison and Analysis of wing box with and without ribs, in terms of max tip deflection

and rotation In terms of max tip deflection, the model with the ribs shows more tip deflection compared to that of the model without ribs. Conversely the model with ribs has less tip rotation than the model with no ribs. The differences with the tip deflections is correlated with the wing skin’s ability to deform. The wing skin is also constrained with the ribs in conjunction with the spars. The pairing of ribs and spars creates a body stiffer in torsion, thereby reducing tip rotation.

Figure 33 Elliptical loading scenario. Chord wise pressure distribution (top). Span wise pressure distribution (bottom)

Table 6 Double rib thickness effect on natural frequencies


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2. Von-Mises Stress Distribution analysis

It is assumed that the contour plots for the Von-Mises stress distribution on the top and bottom

skin is not symmetric. Since the pressure distribution is acting on the top skin only, the force is

based on only one side making the distribution non-symmetric. In comparison to the wing body

without ribs, it can be inferred that the wing body with ribs has an added constraint to the wing

skin which causes the middle of the wing skin sections to deform more than the outside edges

constrained by the ribs and spars. The non-ribbed model has a more even deformation due to the

wing skin’s lack of constraints. The following figures represent the deformations across the wing.

Figure 34 Von-Mises distribution due to pressure force, ribbed model

Figure 35 Von-Mises distribution, non-ribbed model


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3. Double spar cap area max deflection, max tip rotation and max stress analysis

Counterintuitively, when the spar cap area is doubled, the max deflection increases while the rotation and stress remain the same as previously tested. One may assume that an increase in the spar cap area will increase the tip deflection rigidity, however that is not the case

Figure 36 Doubled spar cap area, Von-Mises plot ribbed model

Figure 27 Double spar cap area, Von-Mises plot, non-ribbed model


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4. Double rib thickness max deflection, max tip rotation and max stress analysis

Doubling the rib thickness also has little changes to the previously tested model in terms of deflection, rotation and max stress. The changes that occurred are due to the increase in the area in which the wing skin is constrained to the ribs.

Figure 3828Von-Mises with double rib thickness


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Figure 29 Von-Mises, double rib area, non-ribbed model

IV. Conclusion

When analyzing this particular wing body, the data proves that wing ribs are a primary wing

structure when constructing a stable and rigid wing body. As seen in the data collected above, the

wing ribs add structural rigidity and increase torsional stiffness. Although it can be argued that

wing ribs have a non-uniform Von-Mises stress distribution, it can be noted that the positive

structural performance of the ribs outweigh the negative aspects associated with including ribs in

a wing structure. Lastly, after investigating the effects of ribs on structural deformations under

static loads and on natural frequencies and modes, one may conclude that wing ribs are crucial to

wing structures.


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References

Book 1P Singiresu S. Rao, Mechanical Vibrations, 5th ed., Prentice Hall, New York, 1 Lake Street, Upper Saddle River, NJ 07458. 2011

Student Workload Distribution

The student work load was evenly distributed amongst the FEMAP modeling and analysis as well

as the report formatting and content. Report formatting, wing body modelling, meshing and

normal mode analysis was done by Lea Ricci. The FEMAP model analysis, meshing and various

parts of normal mode analysis and linear static analysis was conducted by Julian Bagtas.

Although certain sections of the assignment are listed as the duties of a particular student, each

section was checked and reviewed by each partner to ensure that the whole assignment is a

collaborative effort.

Documents

AE410FEMAP_PROJ