Robert Tanner FEA CW2 (final)

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Finite Element Analysis of a Helicopter Floor Panel
Robert Tanner
EXECUTIVE SUMMARY
This report covers the Finite Element (FE) analysis of a Titanium panel used to replace the floor of a rescue
helicopter in order to determine the suitability of the replacement panel. The suitability of the panel was tested
by determining the maximum deflection, in millimetres (mm), and stress, in megapscals (MPa), experienced
by the panel in three mission scenarios. The scenarios were: built in to the helicopter with a 100 kilogramme
(kg) winch attached; simply supported with the winch attached; and built into the helicopter with the weight of
a 10kg grain sack distributed across it. FE models were generated for each scenario and the results verified
by comparing them to analytical calculations for plates of a similar geometry and loading regime. The models
were found to accurately demonstrate the displacement and stress fields of each scenario. The models
determined that the winch could be safely deployed in either of the first two scenarios, and that the helicopter
could carry at least 250 grain sacks. Some additional analyses that could be carried out were also suggested.
OUTLINE OF PROBLEM
The FE problem which this report explores was to determine the maximum stress and deflection of a
replacement floor panel for a rescue helicopter in three different mission scenarios, and therefore determine
the suitability of the panel for those scenarios. A diagram of the panel is shown below in Fig. 1. The diagram
is not to scale, but is a useful indicator of the problem geometry. All the dimensions are in mm.
Fig. 1 Diagram of helicopter floor panel [1]
The panel was cut from alpha, annealed Titanium available on the scene. The Titanium had a Young’s modulus
of 116 gigapascals (GPa), a Poisson’s ratio of 0.34 and a yield stress of 800MPa.
The first two mission scenarios were concerned with the deflection and stress of the panel caused by a 100kg
winch, assumed to have a circular footprint, as shown in Fig. 1, with the weight evenly distributed across it.
Scenario 1 modelled the deflection and stress if the panel edges were “built in”, i.e. fixed in place. Scenario 2
was similar to Scenario 1, but with the panel resting at the base of the helicopter, simply supported around the
edges. The purpose of these models was to determine if the safety factors to avoid yield in both scenarios are
acceptable. Scenario 3 modelled the deflection and stress caused by a single 10kg grain sack on the panel.
The panel was assumed to be “built in” and the weight uniformly distributed across the panel. The purpose of
this analysis was to determine the maximum number of sacks the rescue helicopter could safely transport [1].
ANALYTICAL CALCULATIONS
In order to verify the FE models used in this problem, the maximum deflection, 𝛿 𝑚𝑎𝑥, and stress, 𝜎 𝑚𝑎𝑥, for
each loading scenario were compared to analytical calculations for rectangular plates under similar loading
regimes. The rectangular plates were used to model the large section of the panel where the winch is fixed.
The analytical calculations are approximations, however, the problem geometries are similar enough that the
FE models are considered valid if the analytical and FE calculations are similar. The calculations for 𝛿 𝑚𝑎𝑥 and
𝜎 𝑚𝑎𝑥, of a rectangular plate, dimensions 𝑎 × 𝑏, under a load distributed across a central circular area, radius
𝑟0, such as in Fig. 2, were used as the analytical calculations for Scenario 1 and Scenario 2, due to similar
problem geometries.
Fig. 2 Diagram of rectangular panel with load applied to a central circular area [2]

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The primary difference between the plate in Fig. 2 and the panel in Fig. 1 is the absence of the additional
filleted portion on the right hand edge of the panel. However, since no load is applied to those areas in Scenario
1 and 2, it is still appropriate to use the plate shown in Fig. 2 as an approximation to the problem. The
calculations for 𝛿 𝑚𝑎𝑥and 𝜎 𝑚𝑎𝑥 at the centre of a plate such as the one shown in Fig. 2 are:
𝛿 𝑚𝑎𝑥 = 𝛼𝑊𝑏2
𝐸𝑡3⁄ (1)
𝜎𝑐,𝑚𝑎𝑥 =
3𝑊
2𝜋𝑡2
[(1 + 𝑣) ln
2𝑏
𝜋𝑟0
+ 𝛽] (2)
where 𝑊 is the applied load in Newtons (N), 𝐸 and 𝑣 are the Young’s modulus and Poisson’s ratio of the plate
material, 𝑡 is the thickness and 𝛼 and 𝛽 are constants dependent on scenario and the ratio 𝑎 𝑏⁄ . For instance
𝛼 for a square, built in plate is 0.0611 and 0.1267 for a simply supported plate. Additionally, the maximum edge
stress of a built in plate is:
𝜎𝑒𝑑𝑔𝑒,𝑚𝑎𝑥 = 𝛾𝑊 𝑡2⁄ (3)
where 𝛾 is another dimensionless constant [2]. However, the analytical calculations for Scenario 1 predict that
the maximum stress will be in the centre of the circular footprint of the winch, not along the long edge.
In order to perform these calculations, several key assumptions were made: first, the values for each variable
defined in the problem were used, so as to model the helicopter floor panel. Second, the force due to gravity
was assumed to be 10 Newtons per kilogram (N/kg), to simplify the calculations and provide a limited safety
factor. Finally, since the values for 𝛼, 𝛽 and 𝛾 for each regime are only recorded for certain ratios of 𝑎 𝑏⁄ , none
of which apply to the large portion of the floor panel, so the values for 𝑎 𝑏⁄ = 1.0 were used as an approximation
to problem geometry, as the large portion is approximately square.
In the analytical solution for Scenario 3, the helicopter panel was modelled as a built in rectangular panel with
a uniformly distributed load across the entire panel. The bending equations of such a panel are:
𝛿 𝑚𝑎𝑥 = 𝛼𝑤𝑏4
𝐸𝑡3⁄ (4)
𝜎𝑐,𝑚𝑎𝑥 = 𝛽𝑤𝑏2
𝑡2⁄ (5)
𝜎𝑒𝑑𝑔𝑒,𝑚𝑎𝑥 = 𝛾𝑤𝑏2
𝑡2⁄ (6)
where 𝑤 is the applied load per unit area across the panel [2], which was calculated from the total area of the
panel, not an equivalent rectangular plate. Using the same assumptions as in Scenario 1 and 2, the analytical
calculations predicted the maximum stress on the floor panel in Scenario 3 would be in the centre of the long
edge of the panel.
FINITE ELEMENT MODELLING
The helicopter floor panel was modelled in MSC Patran, using shell elements. The decision was made to use
shell elements as the panel is thin and because membrane elements are suitable only to model situations in
the xy plane [3]. Scenario 1 and Scenario 2 were analysed using the same model and mesh, which can be
seen in Fig. 3. Due to the symmetry of the panel, a half model would have been possible, however, the
symmetry constraint of a half model interfered with the load on the circular region, and a full model was used.
The components elements of the model were individually meshed and equivalenced using the Tolerance Cube
method. This was done to maintain the individual meshes of the circular region, which would have been
eliminated if the elements were combined into a composite. The mesh was constructed from Quad4 mesh
elements created by a Hybrid mesher, which was selected as the mesh elements therefore generally maintain
a quadrilateral shape, tending to perfect squares away from the circular region in the centre or the curved
edges, closely resembling the problem geometry. Refining the mesh resulted in a difference between iterations
of less than 1% for both Scenario 1 and 2, indicating that the model had already reached the stable solution.
Fig. 3 Final mesh for FE model of Scenario 1 and Scenario 2

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To model Scenario 1, all the edges of the model were constrained to have no translational or rotational degrees
of freedom. The weight of the winch was modelled by a pressure of 8 kilopascals (kPa) applied to the finite
elements within the circular region. The deflection and stress fields of the FE model are shown in Fig. 4(a) and
Fig. 4(b). The values of 𝛿 𝑚𝑎𝑥 and 𝜎 𝑚𝑎𝑥 are similar to the analytical solutions, and the shapes of the fields
resemble those predicted by theory: the deflection field shows a maximum near the centre of the panel,
decreasing outwards from the centre in concentric regions tending to a rectangular shape, the expected
deflection profile of a centre-loaded plate with fixed edges. Meanwhile, the stress is a maximum near the centre
of the panel, with stress decreasing outwards from the centre, before increasing again towards at the fixed
edges, as predicted by the analytical calculations. Therefore, the FE results are considered accurate.
(a) (b)
Fig. 4 Deflection field (a) and Von Mises stress field (b) of Scenario 1
The model of Scenario 2 is similar to the model of Scenario 1, except the panel edges were permitted to freely
rotate. The resultant deflection and stress fields are shown in Fig. 5(a) and Fig. 5(b). As in Scenario 1, the
fields closely correspond to theory. The deflection field shows a similar pattern to Scenario 1, but with
significant deflection present closer to the edges, as expected of a simply supported plate. Also, the stress
field corresponds to theory in that it shows a maximum near the centre of the panel, decreasing outwards from
the centre, with no significant stress in the centre of the panel edges, supporting the analytical calculations.
These FE results are also considered accurate.
(a) (b)
Since the load in Scenario 3 was evenly distributed across the panel, rather than in a specific region, it could
therefore be constructed from fewer elements and a half model could be used, with the lower edge constrained
by a symmetry constraint. The mesh was constructed in the same fashion as in Scenario 1 and Scenario 2,
and refinement of the mesh produced no significant change in the values of 𝛿 𝑚𝑎𝑥 and 𝜎 𝑚𝑎𝑥, indicating the
model was at a stable solution. The final model and mesh used to analyse Scenario 3 is shown in Fig. 6.
Fig. 6 Final mesh for FE model of Scenario 3
The edges of the panel in Scenario 3 were constrained to have no translational or rotational degrees of freedom
and a pressure of 25.2 pascals (Pa) was applied across the surface. The deflection and stress fields are shown
in Fig. 7(a) and Fig. 7(b), the maximum values are close to values predicted by the analytical calculations, and
the shapes of the fields correlate with the analytical predictions. The displacement field shows a maximum in
the approximate centre of the panel, decreasing in concentric regions outwards tending to the shape of the
panel, as predicted by the theory of plates in bending. The stress field shows high stress along the fixed edges
with a region of lesser stress in the approximate centre of the panel, just as the analytical solutions predicted
that the edge stresses would exceed the centre stress. Therefore, the FE model of Scenario 3 is likely accurate.

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(a) (b)
RESULTS SUMMARY
Analytical Finite element
Scenario 1
Maximum deflection (mm) 26.67 25.10
Maximum stress (MPa) 62.70 63.40
Scenario 2
Scenario 3
DISCUSSION AND RECOMMENDATIONS
While the maximum analytical and FE values in all scenarios are similar, the FE solutions are almost all of
lesser magnitude, indicating that the different geometry generally reduces deflection and relaxes stress, except
for the deflection of built in panels. The FE models correlate strongly with analytical models, however, due to
differing problem geometries, there are differences. In the FE models, the centres of the fields are offset from
the centre of the large section of the panel, where the field would be centred if the section was a separate
plate. Also, the fields were distorted, tapering towards the filleted portion of the panel. Finally, the curved edges
act as regions of stress concentration, in the case of Scenario 3, acting as the site of the maximum stress,
instead of the region predicted by the analytical solution, which indicates how the analytical solutions are
approximations and cannot fully model the floor panel.
The yield stress of the Titanium of the floor panel is 800MPa [1], therefore, the safety factor of Scenario 1 is
approximately 12.6, and the safety factor of Scenario 2 is approximately 9.7. These safety factors are
acceptable as, assuming that the average mass of a person is 80kg [4], and two people will be carried by the
winch at a time [5], the average additional load on the panel in Scenario 1 or 2 is 1600N. Assuming the
maximum additional load is twice that to account for factors such as heavy loads or improper use of the winch,
the maximum stress on the panel would be increased by a factor of roughly 4.2, and the safety factors of the
scenarios could accommodate this additional load.
Furthermore, assuming that the maximum stress the panel can safely support is half the yield stress, then, as
each 10kg sack exerts a stress of 1.44MPa on the panel, the maximum number of sacks the helicopter can
carry before yield is 277. This would result in a maximum deflection which is likely around the same deflection
that the panel would experience while using the winch in rescue operations. Nonetheless, in the interest of
safety, the maximum number of sacks should be rounded down to approximately 250.
CONCLUSION
In conclusion, the FE models of the replacement floor panel used in this problem indicate that there are
significant safety factors for loading Scenario 1 and Scenario 2, and also indicate that the helicopter can carry
a large number of the grain sacks as defined in Scenario 3. Since the panel can safely accommodate significant
loads beyond the mass of the winch, and could carry a large number of grain sacks without causing the floor
panel to yield, this suggests that the loading regimes specified in the problem outline are appropriate.
There are additional loading scenarios which could be analysed to gain a fuller picture of how the floor panel
could be deployed in the real world, for instance, modelling the effects of one of the plate edges becoming
detached from its supports. As well as this, it could be advantageous to model how the stress and displacement
of the helicopter floor affects the walls of the helicopter.
REFERENCES
1. University of Bristol, “Finite Element Coursework Exercise 2”, https://www.ole.bris.ac.uk/bbcswebdav/, accessed 26 November
2015
2. Young, W. C., “Roark’s formulas for stress and strain”, Mc Graw-Hill, Chapter 10, Table 26, 2002
3. Kansara, K., “Development of membrane, panel and flat shell elements in Java”, http://scholar.lib.vt.edu/theses/available,
accessed 17 December 2015
4. Walpole, S. C. et al, “The weight of nations”, BMC Public Health, 12 (439), pp. 1-6, 2012.
5. Trapp, D., “Working with search and rescue helicopters”, http://www.raf.mod.uk/rafsearchandrescue/, accessed 17 December
2015.

Robert Tanner FEA CW2 (final)

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Robert Tanner FEA CW2 (final)