Chapter 1 Introduction
8.2 Results
model had 2552 panels and the FE model had 2668 shell elements (the correspondent to the outer skin shell elements plus the beams' web shell elements).
Regarding the analysis of one particular individual in the swarm, it is clear in g. 8.2 that an individual maintains its objective function as apparently constant, from step 1 to step 19. Because of the way range is calculated, precautions must be made in order to guarantee that fuel fraction is not a negative number, a situation that may occur if lift is lower than structural mass. In these situations, fuel fraction is set to zero, which in turn results in a null range, hence the constant value. From step 26 onwards, the individual has moved in the design space towards a point that allows for a non null fuel fraction and a non null range.
Table 8.3 compares the best initial solution, i.e., the best random individual in the initial population and the nal best solution in the population regarding Range, Lift, L/D, structural mass, maximum stress, payload (dened as liftable weight other than structural mass and fuel) and objective function.
Best Initial Individual Final Solution Variation
Range(km) 2285 3772 65%
Lif t(N) 2465 2267 −8.00%
L/D 24.15 24.57 1.70%
mstructural(kg) 117.5 38.1 −68%
P ayload(kg) 107.2 154.6 44%
σmax(M P a) 25.5 97.7 283%
Objective F unction −110.1 −184.5 68%
Table 8.3: Gains from the optimisation process.
From the analysis of these values, it is clear that there was optimisation in both aerody- namic and structural elds, but most importantly, optimisation in a coupled environment.
Analysing only aerodynamic performance in lift and L/D ratio shows two similar solu- tions but their dierences arise when the results of the structure are considered. The optimised solution shows a maximum stress value very close to the allowed maximum, guaranteeing that the structure is capable of handling the aerodynamic loads, yet light enough to allow for a long range. The notion of optimisation in a coupled environment becomes even clearer when intermediate results are analysed, as during the optimisation process some solutions had higher lift or L/D or lower mass, but always with a higher value of the aggregate objective function than the found optimal solution.
The other important results of the optimized solution are a wing tip rotation of 0.12o, low enough not to inuence the aerodynamic solution (as no coupled aero-structural analysis is performed), a wing tip deection of 31 mm and a pitch down moment of 70 Nm. Recall that a statically stable solution is the goal and the aircraft should present a null pitching moment. Although the achieved result for this conguration was not null, it is very low for an aircraft of these dimensions and mass, being easily compensated by
control surfaces or the slight shift of the center of gravity.
Figures 8.4 and 8.5 show spanwise chord and incidence distributions. As can be seen in the chord distribution graphic, chord is almost constant throughout the wing. Even though this may not favor the best L/D ratio, it adds area to the wing, having a more signicant eect on range (by means of a higher fuel mass) than another distribution.
Regarding incidence, the graphic shows a decrease towards the wing tip, which favors not only the L/D ratio by means of a more favorable lift distribution (somewhat overcoming the lower than optimal lift distribution given by the almost constant chord distribution) but also has signicant eects in terms stability. As noted before, the chosen airfoil is not a reex airfoil, which would be a more natural choice for ying wing conguration, due to its lower pitching moment. However, the optimal incidence distribution combined with the accentuated backward sweep of the wing have a balancing eect on the aircraft regarding pitching moment, guaranteeing static stability.
Figure 8.4: Spanwise chord distribution.
The aerodynamic design variables value distributions result in the Cp distribution on the aircraft shown in g. 8.6. It is clear in this picture that the central body has a signicant contribution to lift and it is also clear that the 3D Panel Method is capable of capturing the tridimensional eects of the ow, as the wing root is the section with the lowest Cp value, result of the induced circulation of the body area onto the wing.
Fig. 8.7 shows the stress intensity on the optimised solution. As expected, the wing root area shows higher stresses than the rest of the structure, particularly near the leading edge, as not only upwards bending occurs due to lift, but also backwards bending, result of drag.
Fig. 8.8 shows the thickness distribution from which the FEM solution was obtained,
Figure 8.5: Spanwise incidence distribution.
Figure 8.6: Cp distribution in the upper camber of the aircraft.
Figure 8.7: Stress intensity (top and bottom views, left and right, respectively; in Pa).
miser's ability to create an structure that is adequate to the aerodynamic loadings.
Figure 8.8: Shell thickness distribution (in m).
Solving this problem showed that the application is capable of handling a multidisci- plinary design optimisation problem, demonstrating the advantages of this methodology applied to preliminary aircraft design. The modularity approach also proved useful as changing the model's complexity or the analysis tools has no implications in the rest of the application.
As already referred in 7.3, the tests described in chapter 7 proved extremely useful in understanding the issues related to the construction of proper AOFs in the context of multiobjective optimisation, as the results shown in this chapter prove that the tool is able to fulll all the requirements that are prescribed for the problem.