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detailed sizing and shape optimisation, incorporating both stress and buckling
constraints.
Figure 8: Design Variables for Cruciform-Section and T-Section Truss Members.
The Variables w1 and w2 were Fixed in the Sizing and Shape Optimisation
Figure 9: Initial Design for Sizing and Shape Optimisation
Created by Interpreting the Topology Optimisation Result
w2
h3
t2 t1
t3
t1 t2
h3
t3
w1
w1 w2
Plane
of Rib
Copyright © Altair Engineering Ltd, 2002 11/10
Ideally, all of the dimensions of the truss-member cross-sections as well as the shear
web thickness should be allowed to vary as design variables in the optimisation,
allowing a detailed optimisation of the in-plane and out-of-plane stability of the ribs. In
practice the height/thickness of the vertical stiffeners were allowed to vary, but only the
thickness of the horizontal segments. Allowing the width of the horizontal segments
(w1 and w2) to vary would involve changing the shape of the cut-outs in the ribs, and
design variables would have to be linked to ensure for example that the vertical
stiffeners remained along the centreline of the truss-members. With the current shape
optimisation pre-processing tools for OptiStruct this would have been time consuming
to set up, and with the short time scales of the project this complexity was not
implemented.
Having constructed finite element models for detailed sizing and shape optimisation,
optimisation was now performed designing for minimum mass with both manufacturing
requirements and stress and buckling allowables as design criteria in the optimisation
process. For stress, a Von Mises stress allowable was used with a reduction factor for
fatigue. For buckling, the design philosophy was not to allow buckling of the structure
below ultimate loads. The buckling constraints for the optimisation were defined
requiring the buckling load factor in linear eigenvalue buckling to be greater than unity
for all ultimate loads. To avoid optimisation convergence problems, due to buckling
mode switching, buckling constraints were formulated for the five lowest buckling
eigenvalues in each load case.
The optimisation as it stood converged to a feasible design for all thirteen ribs, with the
final masses summing to a total close to the weight target specified for the work
package. Subsequent to the optimisation, the new rib designs have had to be
analysed / tested for several other criteria including local flange buckling, fatigue and
birdstrike. Both fatigue tests and machining trials are currently ongoing. Figure 10
shows a prototype rib for the A380 droop nose rib.
Figure 10: Topology, Sizing and Shape Optimised A380 Prototype
Leading Edge Droop Nose Rib Machined from High Strength Aluminium Alloy.
Copyright © Altair Engineering Ltd, 2002 11/11
4.0 CONCLUSIONS
The present work illustrates how topology, sizing and shape optimisation tools may be
used in the design of aircraft components. The technology has been successfully used
in an industrial environment with short industrial time scales and has on a single
application proved to be able to provide efficient stress and stability component
designs.
Initial studies have shown that care should be taken in the modelling of the load and
boundary conditions of the components. For aircraft component design it is also
important to be aware of the impact of changing loading situations. The truss type
designs obtained using the topology optimisation are highly specialised designs
optimised for certain loading situations.
Load definitions generally change as the design of an aircraft mature, and this could
seriously affect the optimality of the structure. It could therefore prove important to
carefully select applications for topology optimisation and only use the technology on
structures with well defined loading conditions.
5.0 REFERENCES
[1] ‘Topology Design of Structures’, M P Bendsøe and C A Mota Soares, NATO ASI
Series, Kluver Academic Publishers, Dortdrecht, The Netherlands, 1993.
[2] ‘Optimisation of Structural Topology, Shape and Material’, M P Bendsøe,
Springer-Verlag, Heidelberg, Germany, 1995
This technical paper was first presented at an Altair Engineering event.
About Altair Engineering
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