MECH 3900 Coursework 1
Example report
A C Jones
Group 0
01/01/18
1. Method
Four models will be generated, building from a simple theoretical approximation which assumed that the structure is a uniform cross section, uniformily loaded cantilever beam, through to a three-dimensional model which describes some of the geometric features in detail and allows the stress field to be visualised. Planned comparisons are listed in Table 1 and are designed to provide confidence in the final results of the plate model.
The maximum von Mises stress in the plate model will be compared to the yield stress of the aviation aluminimum to make an assessment of the chances of material failure. A maximum stress which is 20% below the material yield stress will be considered to indicate that the stabiliser is “fit for purpose” under the flight conditions tested.
Table 1: Models, measurements and planned comparisons.
Model Outputs / measurements Comparisons with other models
Theoretical Tip deflection and maximum stress. It is expected that the theoretical and simple beam results will be the same. This comparison is to ensure that there are no mistakes in the basic calculations. The ball-park deflection and stress found here can be used as a sanity check for the more complex models.
Simple beam Tip deflection and maximum stress.
Complex beam Tip deflection and maximum stress. The complex model would not be expected to produce the same results as the simple model.
The deflection of this representation may be in between the simple model and the plate model, depending on the choices made.
Plate model Tip deflection, measured at the nose of the profile.
Deflection and strain fields.
Maximum stress, anywhere in the stabiliser, excluding the first layer of elements next to the boundary conditions. It is expected that the deflection will be in the same range as for the complex beam.
The strain field will be used to observe the overall deformation of the structure and check that this is sensible.
The stress field is much more sophisticated and therefore may not be directly comparable to any of the other models.
2.1 The theoretical beam model
Classic theoretical calculations for the tip deflection and and maximum stress values in a cantilever beam with a distrubuted load, were used to generate baseline values. The inputs and methods are summarised in Table 2.
Table 2: Concise methodology for the cantilever beam with a distributed load.
Input Value and units Notes
[Rationale; method summary; source of information.]
Structural values
Spanwise length of stabiliser 524 mm
(0.524 m)
Cross sectional profile representation
Seven segments, including the upright, were used to represent the cross sectional profile.
Position of upright component: 178.5 mm from tail edge at root and 108.5 from tail edge at tip.
Skin thickness 1 mm Assumed uniform thickness for all line segments.
Centroid position Unit chord:
(0.4765, 0) At y=0 and 47.65% of the chord length in the x-direction.
Tip – Chord length 155 mm
Tip – Ixx value 20,025 mm4
Root – Chord length 260 mm
Root – Ixx value 94,514 mm4
Midpoint – total area 457.94 mm2 Actually not needed if the centroid was calculated on the unit chord length and then scaled.
Midpoint – Ixx value 57,270 mm4
Load calculations
Height 4267.2 m Converted from 14000 feet in flight information.
Speed 49.2 m/s Converted from …
Air density ~0.76 kg/m^3 Found from … [ref]
Mid-point chord length 207.5 mm
Coefficient of pressure for unit chord 1.242
Lift per unit length for mid point of stabiliser. 235.09 N/m Which is 0.00023509 kN/mm. Conversion so that units match with the structural aspects above.
Material properties
Young’s modulus 69 GPa Given.
Cantilever beam theory outputs
Max moment 31.863 kNmm
Y-position of max stress 16.6 mm Unit length chord data, max y/c=0.08
