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also demonstrates how a topology optimisation followed by a detailed sizing and shape
optimisation may be used to provide efficient aircraft component designs satisfying
manufacturing, stability and stress constraints.
Figure 1: Topology, Sizing and Shape Optimisation Process for
Design of Aircraft Components
This optimisation process includes the full process from finite element model
generation through to the generation of a final design and import of this design back
into a CAD system.
Copyright © Altair Engineering Ltd, 2002 11/3
2.0 OPTIMISATION OF MAIN WING BOX RIBS
The traditional design of Airbus main wing box ribs incorporates a shear web,
stabilised against buckling by adding a rectangular grid of stiffeners. The added grid of
stiffeners serves both to increase the buckling load by splitting the shear web into
smaller panels and to provide the rib with its post-buckling strength but also serves to
resist loads such as the compressive rib brazier loads and lateral fuel pressure loads.
The shear web gives a good general design allowing the component to carry loads
acting in different directions. A finite element model illustrating this traditional Airbus
rib design is shown in Figure 2.
Figure 2: Typical Shear Web Design as Used for Airbus Main Wing Box Ribs
The design depicted in Figure 2 is not too different from the result that could be
expected from a compliance based topology optimisation, if obtained using optimally
layered microstructures1. Examples of topology optimised designs obtained via
different formulations of the topology optimisation problem may be found in [1] and [2].
A topology optimisation performed using layered microstructures would typically
suggest a design with a stiff exterior edge of solid isotropic material and with an interior
web made from a low-density anisotropic material. Such a solution could be realised
via a design with a thick external flange and with a thin internal anisotropic shear web.
Hence, a design concept somewhat similar to a traditional Airbus rib, only without the
stabilising stiffeners.
Topology optimised designs obtained using optimal layered microstructures are often
claimed not to be manufacturable, as the stiffness and the orientation of the layered
composite are allowed to change from point to point in the structure. The same thing
holds for other formulations of the topology optimisation problem allowing formation of
areas with intermediate material densities. Topology optimised designs are therefore
often forced into isotropic truss-like designs by artificially penalising the formation of
regions with anisotropic materials/intermediate material densities. Figure 3 below
shows an example of the use of such a penalisation technique to avoid formation of
1 The traditional compliance based topology optimisation method determines an optimal structure by distributing a fixed amount of
an isotropic material in an available design space. The design description is in terms of a material density function that varies
across the design space. A zero material density represents a hole in the structure while a density of 1 represents solid isotropic
material, but intermediate densities are also allowed. More optimal designs may be obtained by allowing the formation of optimal
composite materials. Certain classes of layered microstructures, formed from a mixture of two isotropic materials, can be shown to
be optimal for the compliance formulation that minimise the total elastic energy stored in the structure.
Copyright © Altair Engineering Ltd, 2002 11/4
areas with intermediate densities, and clearly demonstrates the topology optimisation
methods ability to predict both shear web and truss like designs.
The example in Figure 3 considers topology optimisation of an outboard wing box rib,
subject to both local air pressure loads and running wing box loads diffusing into the rib
from several wing bending/twist cases. For the example in Figure 3 the upper and
lower channel sections with stringer cut-outs and skin attachments have been frozen,
in order to allow an easy implementation of a suggested solution. Figure 3 shows the
available design space and topology optimisation results without/with penalisation.
Figure 3: Topology Optimised Main Wing Box Rib
(Top picture shows the designable and non-designable areas of the rib. Middle
picture shows a shear web type design obtained by not penalising intermediate
material densities. Bottom picture shows a more truss-like design obtained by
penalising the formation of areas with intermediate material densities)
Non Design Area
Design Area
Copyright © Altair Engineering Ltd, 2002 11/5
Determining a topology optimised design, such as the results shown in Figure 3, may
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