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be seen as a problem of finding a structure with optimal load paths to transfer a
number of well defined loads to well defined supports. Aircraft components are often
part of a larger structure and the applied component interface loads cannot be fixed.
The stiffness of the component will change how loads diffuse into the component, and
the loading is therefore a function of design. The designs shown in Figure 3 were
obtained by initially condensing all loads/supports delivered by the surrounding
structure into boundary load vectors and a boundary stiffness matrix, and then solving
the topology optimisation problem for fixed external loading. The boundary loads could
have been updated after each iteration, allowing the loads in the skin to redistribute
and thereby allowing the rib loading to change.
Figure 4, below illustrates the importance of the boundary support conditions for the
rib design and also the importance of exploring the design space using the topology
optimisation tool. The main wing box rib has in this example been optimised, removing
the stiff non-designable upper and lower channel sections. This creates a very
different and possibly more optimal topology, but also a design that could prove difficult
to implement due to final assembly issues around rib/skin bolting.
Figure 4: Topology Optimised Main Wing Box Rib.
(The formation of intermediate material densities have been penalised and a
minimum member size constraint has been used to obtain a well-defined design.
Load cases include both local air pressure loads and running loads from several
wing-bending cases)
Non Design Area
Design Area
Copyright © Altair Engineering Ltd, 2002 11/6
The effectiveness of the shear web design and the truss like design in Figure 3, are
generally not very different. The optimum configuration for a component like a wing
box rib is therefore likely to be determined by the amount of weight that needs to be
added to stabilise the design in buckling. This question unfortunately is not addressed
by the topology optimisation and can only be answered by a detailed sizing and shape
optimisation. Current studies at Airbus UK therefore consider detailed sizing and
shape optimisation of both traditional shear web rib designs and of truss like rib
designs generated from topology optimisation results. Figure 5 shows how the
topology optimisation result in Figure 4 may be used to form an initial design for a
sizing and shape optimisation. The interpretation of the topology optimisation result
includes adding stiffeners to stabilise the rib against out of plane buckling before a final
sizing and shape optimisation is performed including both stress and stability designs.
The use of sizing/shape optimisation is discussed in Section 3.
Figure 5: Initial Design for Sizing/Shape Optimisation
Obtained by Engineering the Solution from a Topology Optimisation.
3.0 OPTIMISATION OF A380 LEADING EDGE DROOP NOSE RIBS
The following describes the first real application of topology optimisation methods at
Airbus UK to assist the design of aircraft components. A set of leading edge droop
nose ribs for the Airbus A380 aircraft was designed and optimised using Altair’s
topology, sizing and shape optimisation tools. An initial design study incorporating a
stiffened shear web design, had suggested difficulties reaching a very demanding
weight target. Discrete force inputs on the droop nose ribs, which are used to hinge
and activate two high-lift surfaces, made the set of ribs ideal candidates for topology
optimisation. A work program was therefore launched to design and optimise the 13
droop nose ribs using topology optimisation followed by a detailed sizing and shape
optimisation. The 13 droop nose ribs were optimised during a very concentrated “fiveweek”
work program involving engineers from Airbus UK’s structural optimisation team
and A380 inboard outer fixed leading edge team but also engineers from both Altair
Engineering and BAE SYSTEMS Aerostructures. The work program resulted in a set of
conceptually different ribs, shown in Figure 6, which met the weight target and
satisfied all stress and buckling criteria included in the optimisation.
At the start of the droop nose optimisation program Airbus UK and Altair Engineering
both had very limited experience applying the topology, sizing and shape optimisation
to the design of aircraft components. The very short work program left very little time to
Copyright © Altair Engineering Ltd, 2002 11/7
investigate how to best represent load/boundary conditions and how to best handle
local and global buckling criteria in the detailed sizing/shape optimisation. A lot of
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