Int. J. Simul. Multidisci. Des. Optim. 2, 187–192 (2008) Available online at:c© ASMDO, EDP Sciences 2008 http://www.ijsmdo.orgDOI: 10.1051/ijsmdo:2008025

Development of a collaborative optimization tool for the sizingdesign of aerospace structures

L. Guadagni1,a

CNES, Rond-point de l’Espace, 91023 Evry, France

Received 30 October 2007, Accepted 15 February 2008

Abstract – The work introduces a computational method for the optimization of aerospace preliminarydesigns. It was developed considering a collaborative approach to solve the sizing optimization of a structuremodel defined by finite element method and by a large number of subsystems. A brief introduction explainshow the collaborative optimization method can be used for general structural problem and how thisapproach can offer many advantages to the computation analyses. Central discussion is the description ofan automatic procedure defined by three deterministic optimization codes and their interface systems withthe MSC.Nastran environment. They decompose the structure complexity executing an interface algorithmfor FE models searching an optimized solution for the structural subsystems respecting different kinds ofconstraints. Furthermore, in order to show the uses of the procedure in an industrial context, two realisticapplications for the minimum design are also discussed. The results show a good comparison with thecommercial solvers, taking out better results in less time processing and finding new alternative designconfigurations.

Key words: Collaborative optimization method; FE analysis; aerospace application

1 Introduction

Aerospace engineering is a complex system of differentsciences working towards the definition of an aerospacedesign. Since the advent of aviation the structural prob-lem was one of the more critical tasks for the engineers.In general a good structural solution was a good startingpoint from which all the other disciplines could adapt.The earliest studies, acting on the interaction between allthe aerospace branches, show that a different approach isnecessary. As the aerospace design is a multidisciplinaryproblem, the single disciplines are inserted in an itera-tive design process: any decision or choice made on a dis-cipline has an effect on the other ones. Nowadays, thisfact is well known in the engineering area and with theincrease of the aerospace activities, more complex com-putational methods are been developed. Some good sam-ples and solutions founded to solve complex phisical sys-tems in the aerospace demain are available in differentworks [1–3].

In a structural approach this means to take into ac-count more detailed model in order to consider the phe-nomena inherent to all structural aspects; consequentlythe structural complexity of the design become an impor-tant aspect to face because of its influence on the solutionmethod. In the aerospace industry, for example, looking

a Corresponding author: luca.guadagni@gmail.com

for a structural solution often means considering a largenumber of design requirements that can heavily modifythe solution during the computation. In a mathematicalcontext the design process turns out to be an optimiza-tion task definition; defining the structural design witha mathematical model, the target becomes to reach anoptimal condition (i.e. a lighter structural configurationin a structural task) where the performances and the re-quirements have to be feasible and satisfied. There area lot of programs available today and most of them aregeneral purpose software based on finite element method(FEM) working with non-specific models. Sometimes theresponse of the optimization is too generic and a morespecific solution is required.

In this article an optimization procedure for prelimi-nary aerospace design is presented. The activity is focusedon the sizing optimization of complex system defined by alarge number of structural subsystems that are improvedwith dedicated external solvers using the finite elementanalysis (FEA) only for the static equilibrium determi-nation. The process is iterative and in order to guaranteethe effects of each subsystem analysis, the overall model isupdated with the previous local results for each iteration.The procedure is a tool of external software working un-der the control of Multi Level Architectures (MLA) calledCollaborative Optimization (CO). The last section of thiswork is dedicated to the analyses of complex aeronauticaland space structures and to the results discussion.

Article published by EDP Sciences

188 International Journal for Simulation and Multidisciplinary Design Optimization

Fig. 1. The flow chart for the global procedure OPT.TOOL (a) and for the local optimization software: RAD.Opt (b), BAD.Opt(c) and PAD.Opt (d).

2 The OPT.TOOL procedure

In this article a Multidisciplinary Design Optimization(MDO) procedure with a CO architecture is used offeringmany advantages. The main idea is to disassemble thesystem to different structural subsystems and to considerthese as single disciplines. In a CO context the theoryimposes that the discipline solvers work as stand-alone,changing the whole process as well as a system of inde-pendent subsystem software [4]. The procedure developedhere is an OPTimization TOOL (OPT.TOOL) dedicatedto the aerospace applications. The software is not a gen-eral purpose optimizer, but a manager for local optimiza-tion solvers. The procedure was created to deal with sizingoptimization tasks where: (1) the global structure is de-fined by a FEM with high level of complexity; (2) localsolvers for optimal sizing are developed for specific sub-systems; (3) the local optimal solutions are derived with-out using the FEA; (4) the optimization goal is the globalweight minimization; (5) a large number of design vari-ables and constraints are taken into account; (6) the FEmodel is updated with all optimal solutions from each ex-ternal solvers. At the first step of its flow chart (Fig. 1a) aFEM properties reading is provided and in order to evalu-ate the stress conditions, a static equilibrium of the globalmodel is performed using MSC.Nastran. Furthermore theexecution of some external solvers in a CO environmentare activated and the process ends with the optimal re-

sults updating in a FEM file. Three optimization analysesfor aerospace structures are available at the local level:(1) wing and fuselage frame (RAD.Opt); (2) beam andstringer elements (BAD.Opt); (3) stiffened and curvedpanels (PAD.Opt). All the external codes, the softwaremanager and the algorithms were written by the authorin C language using the Numerical Recipes Library in C 1.

2.1 The external optimization software

In this paragraph a description of the main common andspecific properties for the external optimizators is re-ported. Each optimization program operates on the suit-able elements only: after the property reading from theFE input file and the recovery of the stress conditions, aoptimization solution is performed. At the end of the pro-cess the optimal results are updated into a new FEM. Theflow charts are an assembly of modules defined by sev-eral complex algorithms interfacing with the FEM. Thecodes can distinguish between different type of FE ele-ments (with one and two dimensions only) and automat-ically translates the mechanical properties for the solver.As the optimization considers the forces acting on the ele-ments, the rest of the data are taken from the static FEAperformed at the beginning. Afterwards the codes search

1 Numerical Recipes Library in C (2nd ed.) is a registeredtrade-mark by Cambridge University Press.

L. Guadagni: Development of a collaborative optimization tool for the sizing design of aerospace structures 189

an optimal configuration using the feasible direction al-gorithm (based on the gradient method) [5] respectingspecific requirements. As a commercial software gives asingle solution of the optimization problem, the codes areprovided with an external library of cross section shapes.When needed it can be used to change the mechanicalcharacteristics (i.e. for a stringer or stiffener element),besides having an improvement on the original modela set of alternative configurations is also available. Theprocess ends with the updating of the optimal data intothe global FEM properties. The first local software is aRing frame Analysis and Design Optimizer (RAD.Opt),its target is to determie an optimal sizing of a framewith a specific shape without using the FEA computa-tion, but resolving inherent closed formulation. As thestructural analysis is tightly linked to the frame shape,and to give to the procedure more generality, two closedshapes are taken into account (Fig. 1b): (1) circular shape(ringframe) and (2) non-circular shape (frame). For bothcases a specific structural analysis for the stress distribu-tion determination is available and discussed in a previouswork [6]. The second local solvers is the Beam Analysisand Design Optimizer (BAD.Opt) for the computationof structural optimization of longitudinal beam elements,like wing stringers or stiffened panel stiffeners (Fig. 1c).The last code is a Panel Analysis and Design Optimizer(PAD.Opt). The program’s goal is the sizing optimiza-tion of stiffener panels in the case of a preliminary design(Fig. 1d). This means the software hasn’t a complete the-ory for panel analysis, but it is only a way to predict anoptimal configuration considering: (1) several geometrical(flat and curved panels, stiffened panels with a orthogonalgrid) and load configurations; (2) different material char-acteristics (isotropic and composite material defined withthe smeared theory); (3) failure modes for local skin, stiff-ener and global buckling (performed solving handbookformulas). Three groups of variables designs are consid-ered for the optimum panel weight: (1) the skin thickness;(2) the stiffener cross sections; (3) the stiffener distance(between two subsequent stiffeners). For each program anoptimization task on the specific structural components isperformed. The algorithm can be defined by the followingcommon system of equations:

⎧⎪⎪⎪⎨⎪⎪⎪⎩

W (ρ, di, le) → Wmin objective functiondi,min ≤ di ≤ di,max geometric constraintsσe(s) ≤ σamm stress constraintsσe(s) ≤ σl,cr local stability constraintsσe(s) ≤ σg,cr global stability constraints

(1)

where ρ is the material density, e the number of subsys-tem finite elements (located by the geometrical variable s)and le the FE element lengths. The target of the opti-mization is to minimize the subsystem weight W withrespect to the design variables di of the cross section andto geometrical (di,min and di,max is the dimensional rangeby user’s defined) and structural constraints, comparingthese last ones with the ultimate yield stress of the ma-terials (σamm). There is also a third group of constraintsrelative to the instability conditions. Each solver has some

specific features to evaluate the local critical load σl,cr onparticular elements (i.e. the local instability of a panelstiffener) or the global one σg,cr on the overall subsys-tems (i.e. the global instability of a stiffened panel). Atthe present time the software capabilities are limited tothe structural analysis of metal alloy with isotropic oranisotropic properties.

2.2 The collaborative approach

OPT.TOOL is a multilevel software manager for the ex-ecution of the local optimizers working on specific sub-structures. The use of this method is based on the in-tuition to consider a problem classified as disciplinarywith a multidisciplinary approach. This idea should ap-pear in contradiction and counterproductive, but the COcan bring a lot of advantage to the structural optimiza-tion for complex FE systems. The three programs work onthe same disciplines, but on different components. Theyappear to be independent, but as the components are to-gether assembled and the global structure must be stat-ically determined, a set of shared parameters are iden-tifiable (i.e. all the forces and flows at the interface FEgrids). These parameters influence the behaviour of thelocal optimizers acting on the local stress and instabil-ity constraints and realizing a little interdisciplinary dataexchange. In relation to two different definitions of the in-terdisciplinary consistency constraints, two different COmethods (CO1 and CO2) are developed by Alexandrovand Lewis [7, 8]. In this work a CO1 approach is used(Fig. 2) bringing several benefits: (1) the local optimiza-tion always obtains a feasible design; (2) the interdisci-plinary parameters are seen at the local level only (inde-pendent disciplines); (3) the interdisciplinary consistencyconstraints are defined with a linear function allowing theuse a gradient based algorithm.

3 OPT.TOOL analyses

In this paragraph two OPT.TOOL analyses are discussed.As the software tool is developed to deal with realisticstructural designs, the results are based on complex FEmodel and show the main OPT.TOOL features: (1) pro-viding a multiconfiguration structural solution; (2) satis-fying the requirements initially defined. The first problemrefers to an aeronautical application, the second one to aspace module and, in order to evaluate the procedure, acomparison analysis with a commercial optimizer is alsopresented on the last problem.

3.1 Aeronautical wing structure

The example presents a wing structure of a utility aircraft(Fig. 3a), loaded with a set of realistic loads: aerodynamicpressure, gravitational forces and inside system weights.The loads are performed defining the load factor n in dif-ferent flight condition as: normal (n = + 1), upside down

190 International Journal for Simulation and Multidisciplinary Design Optimization

Fig. 2. The OPT.TOOL collaborative architecture. it readsthe local design varables {f}ini and takes out the optimalvalues {f}opt.

Fig. 3. Outline of an aircraft wing (a) with the details ofthree structural groups: the panels (b), the stringers (c) andthe wing ribs (d).

(n = − 1), hard landing (n = + 2.5) and over the maxi-mum load factor (n = + 3.9). The following substructuresare present in the model: 48 panels (Fig. 3b), 17 longitu-dinal stringers (Fig. 3c), 23 wing frames (Fig. 3d). Forthis last group only the cross section of the closed-shapedframe around the wing web is taken into account for theanalysis because of the small value of the wing web thick-ness. No ring frames or stiffened panels are in the model.The material is an aluminium alloy for all groups. In rela-tion to a simuilar application developed by Piperni [9] andCraig [10], the aim of these examples is to show the fea-ture of the OPT.TOOL procedure to determine a optimalconfiguration in relation to the following requirements: (1)all the load cases are acting (improbable situation); (2)specific range of values defined on the cross section andpanel thickness (respectively 9 mm2 ≤ Ai (di) ≤ 900 mm2

and 1 mm ≤ tp ≤ 100 mm); (3) ultimate yield stressimposed to 270 MPa; (4) different safety factors for thestructural (s1) and stability constraints (s2) (respectively|σ(di)| ≤ σmat

s1for the stress constraint and σ(di) ≤ σcr

s2

for stability one). A total number of 288 design vari-ables are available for the optimization. Three analysiscases are performed in relation to different security fac-tors: s1 = s2 = 1.0 (case 1), s1 = s2 = 1.2 (case 2)and s1 = s2 = 1.3 (case 3), where the graphs in Fig-ure 4 are drawing respect to the computational iterationsnedeed for the objective function convergence. Because ofthe acting loads, the global weight increase for the threecases (Tab. 1), while a light increase is available for the“set 1”, a reference analysis with single load n = +1 andsecurity factors s1 = s2 = 1.2. The result shows that, in

Table 1. OPT.TOOL wing analysis: results for multi-load andsingle (set 1) load cases.

case 1 case 2 case 3 set 1

Start [kg] 81.21 81.21 81.21 81.21OPT.TOOL [kg] 128.03 128.06 128.52 105.79time 1h02m 1h05m 1h03m 0h25m

Fig. 4. OPT.TOOL analyses for a wing aircraft. Global weightgraphs for different cases.

Fig. 5. OPT.TOOL wing analysis. Cross section (case 2) forinitial (a) and optimal configuration (b).

order to consider a safe configuration and respecting allloads taken into account, a 20 kg of structure mass mustbe added. Another OPT.TOOL feature is the performingof a multiconfiguration solution. In this example the OPT.TOOL can generate different cross section typologies forthe design variables of the wing section. From a homoge-neous condition (Fig. 5a, rectangular cross sections) thesolver goes towards a heterogeneous one (Fig. 5b rectan-gular and “C” cross section).

3.2 Space module

The example shows the OPT.TOOL computation perfor-mances for space applications. The structure is a spacemodule of the International Space Station (ISS) designedby ALCATEL ALENIA Space. An example of the useof a CO approach to the aerospace application is avail-able in Brown [11] (where a more generic optimization on

L. Guadagni: Development of a collaborative optimization tool for the sizing design of aerospace structures 191

Fig. 6. Space structure model (a) with the panels (b) and thebar elements (c) details.

the global design of a space vehicle, with a comparison ofthree different methods, is reported) and in Wallace [12],where the philosophy of the CO design is applied as wellas it was done for this work. The FE model2 has an highdefinition degree and was created taking into account (1)the primary structure (no inside structures are presented)and (2) a large set of loads (Fig. 6a). These are takenfrom a realistic situation of typical space mission: lift- offand cargo bay loads, internal pressure, berthing condi-tions and static connection forces to the Space Station.Two results are performed: (a) a sample computation ofthe optimal configuration and (b) a comparison with acommercial optimizer. The first analysis is based on thesizing optimization of the following three design struc-tural groups: 44 biaxial blade stiffened panels (Fig. 6b),32 longitudinal stringers, 13 ring frames and general shapeframes (Fig. 6c). All the materials are aerospace isotropicalloy and composites. As reported before, for the wingexample, also for this problem different requirements areimposed: (1) all the load cases are activated; (2) specificrange defined on the design variables of the cross sec-tion of stringers, frames, panel stiffeners and panel thick-ness (respectively 8 mm ≤ dst, dfr, dps, tp ≤ 50 mm);(3) ultimate yield stress imposed to 270 MPa; (4) struc-tural and stability security factors fixed respectively tos1 = s2 = 1.0. Overall the procedure has to solve anoptimization problem with 666 variables designs. In Fig-ure 8a two lines are reported to indicate the initial FEmodel weight (dotted line) and the actual one consid-ering the mass of the all component features that, re-quiring a high FEM definition, they are described intothe OPT.TOOL input file (i.e. the stiffened panels etc.).The results show a small increase of the global model

2 ALCATEL ALENIA Space is the owner of the FE modelused for the analyses.

Fig. 7. Result comparison of the global weight on a spacestructure.

weight. The single code behaviours show (Fig. 8b) an in-crease of the panel group weight (dotted line), on thecontrary a decrease for the stringer and frames groupsappears (Tab. 2a). Some considerations about this anal-ysis follow. The optimal result is achieved with not vi-olated constraints, so the new configuration is feasiblein relation to the load cases and the requirement. TheOPT.TOOL ends generating a optimal FEM with 0.74%mass increased. The last consideration is about the pro-cessing time: because of the high complexity of the solu-tion and the type of optimization task activated (in par-ticular on the panel stiffeners), the analysis lasts almostfive hours. This processing time doesn’t last so long as theMSC.Nastran run. In order to validate the OPT.TOOLprocedure a comparison with MSC.Nastran’s optimiza-tion solver is performed. The comparison between theMSC.Nastran and OPT.TOOL solution on the same FEmodel is based. As the finite element software can notsupport a sizing optimization of the distance between thepanel stiffeners, the theory of equivalent stiffness is usedto define the properties of the panels in the model andthe panel stiffeners optimization is omitted. In compar-ison with to the previous example a different definitionof the requirements are report: (1) all the load cases areactivated; (2) specific range defined on the cross sectionof stringers and frames and panel thickness (respectively64 mm2 ≤ Ai(di) ≤ 2500 mm2 and 8 mm ≤ tp ≤ 50 mm);(3) ultimate yield stress imposed to 270 MPa; (4) struc-tural and stability security factors fixed respectively tos1 = s2 = 1.0: (5) because of the absence of the stiffenerpanel the local stability constraint is not taken into ac-count on these elements. The comparison results show(Fig. 7) a small difference (about 20 kg) between thetwo global weights (Tab. 2b), with a long processing timefor the FE software. This is why the MSC.Nastran timeprocessing will be longer if the time for writing the exe-cution (Sol 200) will be considered; OPT.TOOL doesn’tneed this kind of user’s attention because of its FE inter-facing algorithm. A different mass distribution betweenthe groups is reached because of the stability conditionsthat increase the panels weights giving out the remaininggroups mass.

192 International Journal for Simulation and Multidisciplinary Design Optimization

Fig. 8. OPT.TOOL space module analysis. Global (a) and local group weights (b) for the initial FE (dotted line) and theactual (continuous line) models.

Table 2. OPT.TOOL analysis (a) vs. MSC.Nastran comparison (b) results on a space structure.

Start OPT.TOOL(a) OPT.TOOL(b) MSC.Nastran(b)

global weight [kg] 3864.99 3891.82 3819.36 3798.69panels [kg] 422.28 581.59 584.85 328.27str., fra. [kg] 548, 64 416.16 340.08 576, 38time − 4h48m 2h21m 6h05m

4 Conclusions

The work presents a multilevel optimization method forthe preliminary design based on the CO architecture.It has been showed how the OPT.TOOL procedure canbe a good approach for the sizing optimization of real-istic structures defined by a FE model and consideringsome structural and stability local effects. Some featureshave been presented in two examples on aeronautical andaerospace structures, where: (1) a good comparison witha commercial optimization solver has been demostrated(with better results, in a shorter processing time); (2) newstructural local configurations (wing example) and lightermodel (aerospace example) have been founded respect tothe initial conditions; (3) the process is completely au-tomatic and no FE modifications are requested; (4) theOPT.TOOL local results are entirely uploaded in a FEmodel and available for further analyses.

References

1. R. Braun, R.W. Powell, R.A. Lepsch, I.M. Kroo, inComparison of two multidisciplinary optimization strate-gies for launch-vehicle design, Journal Of Space AndRocket, Vol. 52, Nov. 2, May (2006)

2. O. Kalden, U.M. Schottle, in A software tool for anal-ysis of future launch vehicle concepts, internationalAstronautical Congress Paper, IAC -03-V.5.08

3. N. Durante, A. Dufour, V. Pain, in Multidisciplinaryanalysis and optimization approach for the design of ex-pendable launchers, 10th AIAA/ISSMO Multidisciplinary

Analysis and Optimization Conference, AIAA 2004-4441,30 August–1 September, 2004

4. R. Braun, A. Moore, I. Kroo, in Use of the collaborativeoptimization architecture for launch vehicle design, AIAAPaper 96-4018, 1996

5. G.N. Vanderplaats, in An efficient feasible direction algo-rithm for design synthesis, AIAA Journal, Vol. 22, No. 11(1984)

6. L. Guadagni, in Development of multilevel procedures forthe optimal design of aerospace vehicles, Ph.D. Thesis,Politecnico di Torino, 2005

7. N.M. Alexandrov, R. M. Lewis, in Analytical and com-putational aspects of collaborative optimization, NASAPaper TM-2000-210104, 2000

8. N.M. Alexandrov, R.M. Lewis, In Analytical andcomputational properties of distributed approaches toMDO, 8th AIAA/USAF/NASA/ISSMO Symposium OfMultidisciplinary Analysis & Optimization, September2000

9. P. Piperni, M. Abdo, F. Katyeke, in The building blocks ofa multi-disciplinary wing design method, General Meetingand Conference (Toronto), April 26 and 27, 2005

10. S. Craig, P.E. Collier, in Next generation structuraloptimization today, Colier Research & DevelopmentCorporation, September 1997

11. N.F. Brown, J.R. Olds, in Evaluation of multidisciplinaryanalysis tecniques applied to a reusable launch vehicle,Journal Of Space And Rocket, Vol. 43, No. 6, (2006)

12. J. Wallace, J.R. Olds, A.C. Charania, G. Woodcock,in A studi of arts: a dual-fuel reusable launch vehiclewith launch assist, 39th AIAA/ASME/SAE/ASEE JointPropulsio Conference And Exibit, July 2003