SIZING AND SHAPE OPTIMIZATION METHODS TO OPTIMAL DESIGN OF AIRCRAFT COMPONENTS
**** Hidden Message ***** Copyright © Altair Engineering Ltd, 2002 11/1APPLICATION OF TOPOLOGY,
SIZING AND SHAPE OPTIMIZATION METHODS
TO OPTIMAL DESIGN OF AIRCRAFT COMPONENTS
Lars Krog, Alastair Tucker and Gerrit Rollema
Airbus UK Ltd
Advanced Numerical Simulations Department
Bristol
BS99 7AR
lars-a.krog@bae.co.uk
Abstract : Topology optimisation has for a considerable time been applied successfully in the automotive
industry, but still has not become a mainstream technology for the design of aircraft components. The
explanation for this is partly to be sought in the larger problem sizes and in the often quite
complicated support and loading conditions for aircraft components. Also, aircraft components are
often stability designs and the compliance based topology optimisation method still lacks the ability to
deal with any buckling criteria. The present paper considers the use of the compliance formulated
topology optimisation method and detailed sizing/shape optimisation methods to the design of aircraft
components but also discusses the difficulties in obtaining correct loading and boundary conditions for
finite element based analysis/optimisation of components that are integral parts of a larger structure.
Keywords : Leading Edge Ribs, Wing Box Ribs, OptiStruct, Topology, Size and Shape
1.0 INTRODUCTION
Aggressive weight targets and shortened development time-scales in the civil aircraft
industry naturally calls for an integration of advanced computer aided optimisation
methods into the overall component design process. Airbus has in a number of recent
studies used Altair’s topology, sizing and shape optimisation tools in an attempt to
achieve lighter and more efficient component designs. Considered components
include wing leading edge ribs, main wing box ribs, different types of wing trailing edge
brackets as well as fuselage doorstops and fuselage door intercostals. The designs for
most of these components are to some extent driven by buckling requirements but also
by for example stress and stiffness requirements.
Finite element based topology, sizing and shape optimisation tools are typically used
as part of a two-phase design process. Firstly, a topology optimisation is performed to
obtain a first view on an optimal configuration for the structure – an initial design with
optimal load paths. Next, the suggested configuration is interpreted to form an
engineering design and this design is then optimised using detailed sizing and shape
optimisation methods with real design requirements. Numerous examples from the
automotive industry have demonstrated the ability of such an approach to quickly
generate optimum components for stiffness, stress and vibration designs.
The success of the above optimisation scheme relies on a topology optimisation to
suggest a good initial design. Numerous examples have shown that the major weight
savings are achieved when selecting the type of design and not when doing the
detailed design optimisation. The aerospace industry is very aware of this and often
Copyright © Altair Engineering Ltd, 2002 11/2
spends considerable time studying different design alternatives. Efficient designs have
therefore evolved through decades of manual optimisation. However, topology
optimisation methods may still have a place as new sizes/types of aircraft are designed
and as new materials and manufacturing processes continue to appear.
This paper studies the use of Altair’s finite element based topology, sizing and shape
optimisation tools for design of aircraft components. Aircraft components are often
stability designs and topology optimisation methods still completely lack the ability to
deal with buckling criteria. The present work therefore uses the traditional compliance
based topology optimisation method to suggest an optimal design configuration, which
is engineered to provide the design with some stability. Finally, a detailed sizing/shape
optimisation is performed including both stability and stress constraints.
This design process (Figure 1) has been used for optimisation of various aircraft
components. The examples included in the following sections shows how topology
optimisation may be used to suggest good initial designs for aircraft components, but
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 and .
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
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
problems were encountered during the work, and not all of the problems could be
resolved in the short time frame. The work therefore was followed up by a validation of
the designs via traditional hand stressing methods, and qualification of the
ribs/structure against fatigue and bird strike is still ongoing.
Figure 6: Topology, Sizing and Shape Optimised A380 Droop Nose Ribs.
3.1 Topology Optimization of A380 Leading Edge Droop Nose Ribs
The first question that arose when considering topology optimisation of the droop nose
ribs was how to best represent the attachment of the ribs to their surrounding leading
edge structure (droop nose skin, main wing box front spar and skin overhang) and also
how best to model the diffusion of air pressure loads into the droop nose ribs. In the
section on optimisation of main wing box ribs, this was done applying super element
techniques. However, for the optimisation of the A380 droop nose ribs we had not
investigated such modelling techniques and therefore had no experience on how they
would work with topology optimisation.
Some preliminary studies had been undertaken at Airbus UK, studying issues with
boundary conditions. Leading edge droop nose ribs had been topology optimised
considering the ribs in isolation and considering the ribs as part of the leading edge
droop nose structure. The global compliance formulation used in the traditional
formulation of the topology optimisation method had shown difficulties giving any
structure, when optimising ribs as an integral part of the leading edge droop nose
structure.
Copyright © Altair Engineering Ltd, 2002 11/8
This problem was put down to the global compliance objective function, which included
the total elastic energy in both the droop nose rib being designed but also in all of the
surrounding structure. Better results had been obtained optimising ribs in isolation, but
again the topology optimisation was shown to be very sensitive to stiffness of the
rib/droop nose skin attachment flange. This problem was put down to the global
compliance objective function used in the traditional topology optimisation method. The
objective function now included both the energy in the designable area of the rib but
also the energy in the rib flange that was generally considered to be non-designable.
From the very start of the new droop nose optimisation program, the decision was
taken not to attempt to model the surrounding structure, as this would result in several
detailed modelling issues and also increase the optimisation run times. Instead
simplifying assumptions were made and all attachments to the surrounding structure
were modelled using single point constraints. All lateral translations around the edge
of the ribs were for example restrained to represent the very stiff span wise support
from the main wing box front spar, sub spar and the droop nose skin. Constrained
degrees of freedom in the plane of the ribs were also used to represent the
attachments to the main wing box front spar and skin overhang.
The topology optimisation was again seen to be quite sensitive to the constrained
degrees of freedom, and several studies was performed to accurately model the load
transfer between the rib and the main wing box front spar and skin overhang. These
boundary condition modelling issues have since been resolved using super element
techniques. An example of a result of a topology optimisation is shown in Figure 7.
Figure 7: Topology Optimisation of Leading Edge Rib.
(The left picture shows the designable and non-designable areas for the rib while
the right picture shows the design suggested by topology optimisation. A total
of between 6-12 load cases were used for the topology optimisation of the
leading edge ribs)
Copyright © Altair Engineering Ltd, 2002 11/9
3.2 Sizing and Shape Optimization of A380 Leading Edge Droop Nose
Based on the topology optimisation results, which are used to determine a design with
optimal load paths, engineering solutions were created. Interpreting regions with high
density of material as structure and regions with low density of material as holes, the
topology optimised designs could be interpreted as truss-like structures.
Engineering designs incorporating a mixture of truss-design and shear-web design
were now formed in collaboration with the A380 designers. The ribs were also given
some out of plane stability by adding vertical stiffeners at the centre of the truss
members, resulting in T-sections for single-sided machined ribs and cruciform shaped
sections for double-sided machined ribs (Figure 8). The engineering designs were
initially built as finite element models (Figure 9) which served as initial designs for a
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
‘Topology Design of Structures’, M P Bendsøe and C A Mota Soares, NATO ASI
Series, Kluver Academic Publishers, Dortdrecht, The Netherlands, 1993.
‘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.
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