Chapter 6
obtaining afterwards the 2D definition of the von Mises general stress:
σV M=
qσ2x−σxσy+σ2y+3τ2x y (6.3)
Note that the most demanding phenomena occurs around the leading edge wing-box boundary, specially at the corners of it because of the stress-concentration factor (that is why the wing-box corners have been rounded), not because of the shockwave appearance nor the pressure distribution itself. When embedding an object inside a flow, the first intrusion which will be the stagnation point, suffers from a higher pressure value on its boundary because of the flow’s speed reduction. Therefore, at the leading part of the aerofoil there is a higher structural demand due to the pressure’s distribution. Moreover, the obtained magnitudes are lower than the elastic failure parameters of the selected material (Aluminum al- low 6061σyi el d=276M P a). Thus this distribution can deal perfectly with the flight conditions established.
Figure 6.1: Von Mises distribution for the RAE 2822 case study.
Differently for the displacements in Figure (6.2), the maximum value is found at the leading edge of the aerofoil, which is expected as it is the most further way from the non-displacement constraint applied at the wing-box, analog to the standard case of a cantilever beam. Nevertheless, the magnitude of the displacement is small (∼10µc) and will not have a direct influence in the aerodynamic behaviour.
Figure 6.2: Displacements for the RAE 2822 case study.
From this point, and by checking the stress distribution inside the aerofoil plus the micro-displacements generated, one can guess that there is unnecessary material in this model. This is why a topology optimisation is actually applied to just use the optimal and necessary quantity of material in order to make the design efficient. The goal is to reduce weight such that few fuel is consumed, thus being more efficient from the operational/performance point of view.
In this case study, as one of the most critical parameters in the aeronautical field is the weight of the component, the structural safety of the aerofoil is being modified and analysed following a minimising procedure for the weight of the aerofoil. For instance, the following descriptions and results are directed towards the maximisation of the structural stiffness-to-weight ratio, also known as the minimisation of the compliance-to-weight of the object. Therefore, the expected results will show structural voids in differ- ent inner areas of the aerofoil which do not have a noticeable influence on the stiffness of the geometry, meaning that they can be neglected as the rest of the structure can absorb perfectly the respective loads.
Moreover, the topology study was carried out using the same Aluminum-6061 material stated previously in Table 4.1 as it has a wider interval of safety rather than other materials named in section 4. In Figure (6.3) the path followed by the solver in order to reach the specific weight goals of the optimisation is shown.
(a) Weight reduction target: 50%. (b) Weight reduction target: 35%.
(c) Weight reduction target: 25%. (d) Weight reduction target: 10%.
Figure 6.3: Topology optimisation procedure development for the case study.
Note that the wing-box constraint and the skin have been untouched by the solver and that the primor- dial structure lies just below the skin of the aerofoil, then, to avoid large deformations due to pressure, inner truss structures are required. Given the chosen mesh definition, the optimised structure is neither smooth nor easy to manufacture, thus a post-processing is required. On the upper side of the wing-box surface, a more reinforced structure is needed following the stress distribution showed in Figure (6.1), which could be solved by stringers. Even though the stresses are similar in the leading edge, connected bars have been understood to be the most optimal element to withstand the loads transferred by the skin.
Apart from that, the trailing edge inner areas are empty. It does not mean that it should be designed in such a way but any structure in that sub-region is negligible towards the final behaviour thus avoidable.
Nevertheless, this void should be filled with a lighter material or other attachments so as to maintain the aerodynamic shape of the aerofoil; then, a secondary material could carry that function.
Regarding the optimised geometries given by the solver, the 25% weight constraint looks like an ideal shape for the design as, it is noticeably efficient in terms of mass reduction but not as simple and fragile- looking as the 10% case. To demonstrate its proper design, the following set, shown in Figures (6.4) and (6.5), analyses the failure index of the structure and the von Mises stress distribution. Note how, for the highest weight reduction target, theFI is higher and some parts of the resulting structure suffer from high demanding stresses, specially at the upper-left part of the aerofoil. In order to avoid ruptures or unexpected failures, it is better to reinforce the general layout even though the final weight is higher as one can observe in the result shown in Figure (6.5b).
(a)
(b)
Figure 6.4: (a) Failure index distribution and (b) Von Mises stress distribution of the test case for a 10%
mass reduction.
(a)
(b)
Figure 6.5: (a) Failure index distribution and (b) Von Mises stress distribution of the test case for a 25%
mass reduction.