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Implementation of a multi-level optimisation methodology within the e-design of a blended wing body
Aerospace Science and Technology 8 (2004) 145–153 www.elsevier.com/locate/aescte
Implementation of a multi-level optimisation methodology within the e-design of a blended wing body ✩ Implementierung einer hierarchischen Optimierungs-Methodologie im Entwurfsprozess eines Nurflüglers Heiko Engels a , Wilfried Becker a,∗ , Alan Morris b a Universität Siegen, Institut für Mechanik und Regelungstechnik-Mechatronik, Paul-Bonatz-Str. 9-11, 57068 Siegen, Germany b Cranfield University, School of Engineering, Department of Engineering Mechanics & Structures, Bedfordshire MK43 0AL, UK
Received 24 February 2003; received in revised form 3 July 2003; accepted 7 August 2003
Abstract The modern requirement for low weight/high strength aircraft structures is placing an every increasing emphasise on the direct use of optimisation methods in the overall design process. In certain cases, such as that of the Blended Wing-Body (BWB) aircraft, the design cannot be successfully completed without the application of optimisation methods. This type of complex design has inevitably led to the growth in the size of the optimisation problem with large numbers of design variables and constraints being required in a design with strong interactions between the various structural components. Treating the problem in the conventional manner with all components considered simultaneously leads to excessive computer run times. In order to control this growth in problem size a multi-level approach has to be used in order to break down the problem into several sub-problems taking into account the structural coupling effects. Such an approach enables the use of parallel computer processing leading to a significant reduction of the computer run time and decreases the design cycle time. 2003 Elsevier SAS. All rights reserved. Zusammenfassung Im Hinblick auf ein möglichst geringes Gewicht bei möglichst hoher effektiver Festigkeit erfordert der moderne Flugzeug-Leichtbau immer mehr den gezielten Einsatz algorithmischer Strukturoptimierung im gesamten Entwurfsprozess. In bestimmten Fällen, wie etwa bei Nurflüglern (Blended Wing Bodies, BWB), ist der Einsatz von Optimierungsmethoden sogar fast unumgänglich. Dabei wächst mit der Anzahl gegebener Entwurfsvariablen und zu beachtender Nebenbedingungen die Größe eines Optimierungsproblems schnell, und es sind starke Interaktionen zwischen den beteiligten Teilstrukturen zu berücksichtigen. Die gleichzeitige detaillierte Analyse und Optimierung aller Strukturkomponenten verbietet sich in der Regel vom Berechnungsaufwand her. Das Aufwandsproblem lässt sich jedoch durch eine Aufspaltung in Teilprobleme und eine geeignete hierarchische Optimierung bewältigen, wobei alle wichtigen Interaktionseffekte zu berücksichtigen sind. Nicht zuletzt ermöglicht ein derartiger Zugang den Einsatz verteilten Rechnens mit einer entsprechenden Reduktion des erforderlichen Zeitaufwandes. 2003 Elsevier SAS. All rights reserved. Keywords: Optimisation methodology; Multi-level optimisation; Multidisciplinary optimisation; Blended wing body; Parallel computing Schlüsselwörter: Optimierungsmethodologie; Hierarchische Optimierung; Multidisziplinäre Optimierung; Nurflügler; Verteiltes Rechnen
1. Introduction
✩
This article was presented at the German Aerospace Congress 2002.
* Corresponding author.
E-mail address: [email protected] (W. Becker). 1270-9638/$ – see front matter 2003 Elsevier SAS. All rights reserved. doi:10.1016/j.ast.2003.10.001
Motivated by the increasing economic competition and impact of aircraft on the environment as well as the limited energy resources the European Union has put forward a number of research targets for the Aerospace Industry
146
H. Engels et al. / Aerospace Science and Technology 8 (2004) 145–153
under Framework 5. One is to derive aircraft designs and methodologies which are environmentally friendly. A second is recognition that the European aircraft industry has to confront the fact of technology drift which is opening the aerospace market to emerging countries with lower costs. Finally, Europe has to compete with the US and thus the development of more innovative aircraft designs which are low cost and require minimum maintenance is of main interest [2,3]. The main aim of the European funded project “MultiDisciplinary Design and Optimisation for the Blended Wing Body Configuration (MOB)” is to develop a distributed e-design system with a Blended Wing Body (BWB) as the driving scenario. This system incorporates expertise from different design groups distributed across Europe. The e-design system enables it to operate as a multi-disciplinary design group where the involved groups employ their own design software tools. In this way a distributed and interactive set of multi-disciplinary programs can be constructed by the individual partners incorporating appropriate optimisation software. Thus it is possible to develop new aircraft designs with a distributed optimisation software system allowing a strong interaction between relevant disciplines: aerodynamics, structural design, flight mechanics, aeroelasticity, etc. The purpose of the MOB project is to set up a Computational Design Engine (CDE) enabling the development of efficient and highly innovative aircraft designs by a team of engineers distributed across Europe using the internet to operate as one single design group. This new design software is being demonstrated, as already indicated, by applying it to the design of a sophisticated aircraft design – the Blended Wing Body aircraft. MOB is recognising that the interaction between the different disciplines can no longer be neglected when undertaking the design and optimisation of complex designs such as BWB. Furthermore the decomposition of a specific main discipline, for example the aircraft structure, and the subsequent independent analysis of its separate components is equally inadmissible. This combination of requirements creates a major problem when the optimisation and analysis of large engineering designs is undertaken due excess computational requirements needed to handle the large number of design variables and constraints. To solve these problems recourse has to be made to a multi-level approach to decompose the entire system problem into several sub-problems taking into account the various coupling effects. The multi-level approach allows the optimisation of individual system components thereby reducing the computer run time and design cycle time significantly. In the literature various concepts have been proposed for breaking large optimisation problems into subproblems. Most of them are specialized for the multi-level optimisation of structural engineering problems. In the case of the Blended Wing Body a more general approach for the optimisation of multi-disciplinary applications is necessary. Such an approach has already been developed and suggested
by Sobieski [5]. In the following, in essence, we follow the conceptual methodology suggested by Sobieski. Thus the considered optimisation problem is subdivided into several subsystems and a single coordination problem. The mutual interdependence of the subsystems is taken into account by introducing additional constraints. Thus the uncoupled subsystems can be considered and optimised individually.
2. The MOB project The multi national project team consists of 3 airframe design and manufacturing companies, 4 national research institutes and 8 universities from four European countries. Partners are Cranfield University as the main contractor and project coordinator, BAE Systems, QinetiQ and Rutherford Appleton Laboratory (RAL) from the United Kingdom; Saab Aerospace and Royal Institute of Technology (KTH) from Sweden; Technische Universitoit Delft and National Aerospace Laboratory (NLR) from the Netherlands; Deutsches Zentrum für Luft- und Raumfahrt (DLR), European Aeronautic Defence and Space Company (EADS), Technische Universität Braunschweig, Technische Universität München, Technische Universität Berlin, Universität Stuttgart and Universität Siegen from Germany. The main target of the project is the development of tools and methodologies allowing the design of large-scale aeronautical products by a group of teams distributed across Europe. Each team employs individual discipline based software programs to create a distributed Computational Design Engine based on multi-level concepts employing multidisciplinary design and optimisation methods. Due to the physical distribution of the teams within Europe the CDE has to couple the respective software tools to ensure the necessary information flow through all design levels from conceptual to main phase with increasing accuracy of physical models (finite element models, aerodynamic models, etc.) [2]. Thus the created CDE mirrors the actual situation where different engineering teams, located at various sites, have to develop new and innovative aircraft designs in a co-operative manner with their own specific design tools and methodologies.
3. The blended wing body design The second purpose of the project is the application of the developed CDE to an actual problem of interest. The chosen design of the Blended Wing Body (Fig. 1) is a modern type of aircraft design with the potential for high efficiency. The development of the BWB design requires a multidisciplinary approach incorporating advanced optimisation techniques. Distributed teams of specialist engineers provide the knowledge required from the wide range of disciplines needed for this complex design. Thus the BWB, as the driving scenario, demonstrates the benefits of the flexible
H. Engels et al. / Aerospace Science and Technology 8 (2004) 145–153
Fig. 1. Blended Wing Body configuration [2].
CDE methodology. The focus of the project is to point out the practicability of the CDE process rather than developing a BWB design with respect to real life accuracy of the physical models.
4. Multi-level optimization methodology The scenario described above requires the overall multidisciplinary optimisation problem being decomposed into several sub-problems. Thus, the entire problem is divided into a system level, intermediate level and several subsystem levels depicted by boxes shown in Fig. 2. This procedure has been described in the computational design engine specification above. At the system level the preliminary design of the aircraft is optimised. The optimisation of the preliminary design of the aircraft can be performed by the optimisation procedure PrADO; a preliminary design and optimisation tool for aircraft applications provided by the University of Braunschweig [4]. With respect to the leading design criterion such as flight performance, direct operating costs, etc. a first design of the aircraft can be determined by the PrADO
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software tool. Typical design variables are structural aspect ratios, skin thicknesses, span width etc. Possible constraints are the landing performance, climb performance, and maximum takeoff weight etc. and the objective function may be minimum total weight, minimum direct operating costs or an alternative. The intermediate level considers the pure mono disciplines like structural design, aerodynamics, flight mechanics and aero-servo elastic analysis. Thus, there is one intermediate level for each discipline. The design variables on this level are aspect ratios and other sizing variables for structures and the profile thickness of the 2D-airfoil for aerodynamics possibly. Intermediate level constraints for the structural optimisation are stresses, strains, displacements etc. and for aerodynamic applications prescribed pressure distributions. Typical objective functions are the minimal structural weight and minimal drag for aerodynamics. At the lower levels (subsystem levels) the design is considered in more detail. The branch for these subsystem levels in the case of the structure’s discipline might be extended from a particular structural component (wing, etc.) down to individual stringers or even joints. Possible design variables at this level are various geometrical dimensions such as skin thicknesses, stringer dimensions etc. The interaction between each sublevel has to be taken into account during the design process. Changing the design variables during the optimisation process on the subsystem level will influence the upper level with respect to the constraints (subsystem level, intermediate level) and vice versa. Thus most of the constraints are implicit functions of the design variables of different levels and disciplines. The different levels can be uncoupled by an appropriate approximation of the constraints and then optimised individually. In the following section a two-level optimisation approach for structures is discussed which in principle can be extended easily to a more general multi-level optimisation
Fig. 2. Multi-level approach [5].
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procedure. It is emphasized that the approach might be generalized in an arbitrary manner in principle. This methodology can be applied to aerodynamics or even other multidisciplinary engineering problems. Within the two-level approach the considered structural problem is decomposed into the intermediate level and several subsystem levels. The design problem is posed in terms of the Blended Wing Body structure where the fuselage has a door and the target is to create a minimum weight design. The problem has two levels involving the entire BWB structure and the cutout for the freight door. The subsystem level is a single component represented by the door cutout and the intermediate level is the whole assembled aircraft structure. In order to optimise each level individually it is necessary to set up an appropriate optimisation model. The mathematical formulation of the optimisation problem for the intermediate level reads: Min fI (xI ) | gjI (xI , xII ) 0, gjII (xI , xII ) 0 , (1) XI
where xI is the vector of the intermediate design variables, xII is the vector of the subsystem design variables, fI (xI ) is the intermediate objective function, gjI (xI , xII ) is the vector of the intermediate inequality constraints as functions of the intermediate and subsystem design variables xI , xII , gjII (xI , xII ) is the vector of the subsystem inequality constraints as functions of the intermediate and subsystem design variables xI , xII . Thus, the aim of the optimisation is to minimize the objective function fI (xI ) through an appropriate selection of the design variables xI , while satisfying the inequality constraints gjI (xI , xII ): gjI (xI , xII ) 0,
j = 1, . . . , n,
(2)
these are the behavioural constraints which are, for example, the strength constraints in each element of the FEM-model given by σequ,j I − 1 0, (3) gj (xI , xII ) = max σu where σequ is the von Mises equivalent stress and σu is the ultimate strength. The subsystem inequality constraints have also to be taken into account in the form: gjII (xI , xII ) 0,
j = n + 1, . . . , m.
(4)
In order to consider each level individually the design variables xII of the subsystem are kept constant during the optimisation of the intermediate level. The respective side constraints of the problem are xI l xI xI u ,
(5)
where xI l is the lower bound of the design variable vector, xI u is the upper bound of the design variable vector. Typical design variables are the overall skin thickness, aspect ratios and other sizing variables.
Fig. 3. Interlevel flow of information [5].
At the subsystem level the corresponding formulation of the optimisation problem is in accordance to the intermediate level: Min fII (xII ) | gjII (xI , xII ) 0, gjI (xI , xII ) 0 , (6) XII
where as before xI and xII are the vectors of the intermediate and subsystem design variables, fII (xII ) is the objective function of the subsystem level and gjII (xI , xII ), gjI (xI , xII ) are the respective inequality constraints. The respective inequality constraints of the subsystem level are formulated as follows gjII (xI , xII ) 0,
j = 1, . . . , r,
(7)
which again might be strength constraints as a function of the subsystem design variables σequ,j II gj (xI , xII ) = max − 1 0. (8) σu The design variables xII can influence the intermediate inequality constraints gjI (xI , xII ) which have to be considered during the optimisation process in the form: gjI (xI , xII ) 0,
j = r + 1, . . . , s.
(9)
Once more the design variables xI of the intermediate level are kept constant during the optimisation of the subsystem level. Within the presented two-level approach the intermediate level is coupled to the subsystem level in two ways. The subsystem level receives the boundary conditions Q, the valid design variables xI and the approximated constraints gjI (xI , xII ) of the intermediate system. The data passed from the subsystem level to the intermediate level carry the information of the approximated constraints gjII (xI , xII ) as a function of the design variables xI as illustrated in Fig. 3. The structural behaviour of the door cutout design at the subsystem level is represented within the intermediate level by effective stiffnesses, e.g. in the form of superelement stiffnesses. In order to accomplish the respective decomposition of the optimisation problem an appropriate approximation for the subsystem constraints on the intermediate level has to be chosen. In the present case the approximation is given by a Taylor-series expansion:
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149
Fig. 4. Data flow and subtask management.
gjII (xI , xII ) = gjII
k ∂gjII (xkI , xII ) xI , xII + xI − xkI , ∂xI
j = 1, . . . , n,
∂gjI (xI , xkII ) ∂xII (10)
xkI
where the design vector corresponds to the actual design of iteration k. The respective first derivatives of the subsystem constraints are calculated numerically by finite differencing: ∂gjII (xkI , xII ) ∂xI
=
gjII (xkI + xI , xII ) − gjII (xkI , xII ) xI
.
(11)
For the intermediate level constraints at the subsystem level an approximation can be employed in the analogous manner: ∂gjI (xI , xkII ) gjI (xI , xII ) = gjI xI , xkII + xII − xkII , ∂xII j = 1, . . . , r,
(12)
where xkII is the design variable vector of the actual design for iteration k. The necessary first derivative is again given by finite difference scheme:
=
gjI (xI , xkII + xII ) − gjI (xI , xkII ) xII
.
(13)
Thus, the intermediate level, as well as the subsystem level can be considered individually in correspondence to Fig. 4. The implementation of this procedure enables a parallel optimisation procedure for each individual level. The optimisation of the intermediate level provides the necessary boundary loads and deformations as well as the approximation of the intermediate level constraints for the subsystem level (Eq. (12)). The solution of the optimisation problem for the subsystem level and calculation of the respective sensitivities yields the approximation of the subsystem constraints for the intermediate level (Eq. (10)). The implementation of the derived multi-level approach in terms of the computational design engine (CDE) is illustrated in Fig. 4. The overall product data in terms of structural aspect ratios, geometry, structural mass, structural stiffness, eigen modes, maximum lift coefficient etc. is stored on a data base generated and managed by the data base software DEVA. The defined intermediate levels
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can access this data base in order to get the necessary information for respective optimisations and analysis. On the other hand the intermediate levels store new data and results on the data base reversibly. There is one intermediate level for each of the mono disciplines: • • • •
Structural Design, Aerodynamics, Flight Mechanics, and Aero-Servo Elastic Analysis.
These use particular analysis tools like the pre-processor PATRAN as a structural model generator or the finite element code NASTRAN to analyse the present problem. The different intermediate levels themselves interact through the objective functions and constraints which are functions of the design variables. As an example the aerodynamic analysis provides the necessary aerodynamic loads for the structural analysis whereas the structural analysis supplies the structural mass and stiffness for the flight mechanics analysis. This concept of multi-disciplinary analysis has also been implemented by NLR in the higher levels of the CDE. In the sequel the multi-level optimisation is discussed in more detail for the structural intermediate level. As already noted the structure is decomposed into an intermediate level and several subsystem levels. The geometry of the blended wing body is given by an ICAD-model provided by the DEVA database. Importing this geometry model enables the generation of an appropriate finite element model by PATRAN. Within the optimisation procedure for the intermediate level the structural model is now represented by an appropriate FEM-model, which can be analysed by the commercial FEM-code NASTRAN. The aerodynamic loads are provided by the aerodynamic analysis. The actual numerical implementation of the optimisation procedure requires a well-organised data transfer and can be visualized as outlined by the optimisation loop shown in Fig. 4. Starting from an initial design x0 the iterative procedure leads to an improved design variable vector xk after each iteration k. The optimisation procedure is stopped as soon as a convergence criterion becomes active at which stage the final or optimal design x∗ is achieved. Considering the subsystem level, the geometry again is defined by an ICAD-model or might be generated by the user in PATRAN. The respective finite element model is also generated in PATRAN and the optimisation procedure is implemented in terms of the optimisation loop illustrated in Fig. 5. The data transfer with regard to ICAD-models or other information as well as analysis processes are managed by SPINEware provided by the National Aerospace Laboratory (NLR). SPINEware is an object-oriented system that enables the construction of user-defined working environments in heterogeneous computer networks. The decomposition of the intermediate level and subsystem level is achieved by the stated Taylor-series expansion (Eqs. (10)–(13)). The
Fig. 5. Optimisation loop [1].
structural multi-level optimisation procedure consists of the following steps: 1. Optimisation of the intermediate level and provision of the boundary loads, deformations and the approximated intermediate level constraints for the subsystem level. 2. Approximation of the intermediate level constraints with respect to the subsystem design variables. 3. Solution of the optimisation problem for the subsystem level. 4. Approximation of the subsystem constraints with respect to the intermediate level design variables for the intermediate level. 5. The reduced stiffnesses and the approximated constraints are supplied for the intermediate level. In this procedure, the optimisation in step 1 and 3 is iterative and nested in the overall procedure, steps 1 through 5. The optimisations in steps 1 and 3 are performed separately, which enables parallel computer processing.
5. Example: multi-level optimisation of a door reinforcement As an actual example in the following the structural multi-level optimisation of the blended wing body is discussed in more detail and represents the optimisation/analysis MDO process for a door reinforcement. Undertaking a full structural optimisation for a large aircraft such as a BWB taking into consideration each individual detail like doors, windows, spars etc. within the finite element model of the blended wing body design (Fig. 6) would represent a too large computational problem. Therefore the structural system has to be decomposed into different levels. With respect to the derived multi-level methodology the finite element model of the blended wing body structure represents the intermediate level whilst the model of a door cutout shown in Fig. 7 represents the subsystem level. This optimisation problem is used here
H. Engels et al. / Aerospace Science and Technology 8 (2004) 145–153
151
Fig. 6. Finite element model of the blended wing body generated by BAE systems.
where mI (xI ) is the structural mass. The respective constraints gjI (xI , xII ) are given by the von Mises equivalent I in each finite element: stress σequ I σu , σequ,j
j = 1, . . . , n, I σequ,j (xI , xII ) gjI (xI , xII ) = max − 1 0, σu
Fig. 7. Finite element model of the door cutout generated by University of Siegen.
as a driving scenario to demonstrate the efficiency of the introduced multi-level optimisation approach. The generation procedure of the FE-models is an automated process in accordance to the paradigm shown in Fig. 4. FE models for the BWB structure and the door model employ eight-node displacement-based shell elements with six degrees of freedom at each node. In addition, a door reinforcement has been generated along the door boundary by appropriate laminate elements with the first ply modelling the overall skin and the second layer the door reinforcement. Distributed aerodynamic pressure loads load the BWB-structure and the door. The aim is to minimize the structural mass by an appropriate selection of the design variables while simultaneously fulfilling the strength constraints. Thus the mathematical formulation of the optimisation problem for the intermediate level (BWB) is as follows in accordance to Eq. (1): (14) Min mI (xI ) | gjI (xI , xII ) 0, gjII (xI , xII ) 0 , XI
(15) (16)
where σu is the ultimate strength. The design variables xII of the subsystem level are kept constant during the optimisation process on the intermediate level. The solution of the optimisation problem for the subsystem level and calculation of the respective sensitivities yields the approximation of the subsystem constraints for the intermediate level in accordance to Eq. (10). Thus the von Mises II is a function of the intermediate design equivalent stress σequ variables xI in each finite element of the door reinforcement and is approximated as follows k II II σequ,j (xI , xII ) = σequ,j xI , xII +
II ∂σequ,j (xkI , xII )
∂xI
xI − xkI σu ,
j = n + 1, . . . , m, which again can be rearranged II σequ,j (xI , xII ) gjII (xI , xII ) = max − 1 0. σu
(17)
(18)
The design vector xkI corresponds to the actual design for iteration k. The optimisation model for the intermediate level is completed by the skin thicknesses of the BWB design as design variables. Thus the overall skin of the BWB design is subdivided into 33 domains with variable thicknesses and q = 1, . . . , 33 design variables respectively. The respective side constraints of the problem are
152 q
H. Engels et al. / Aerospace Science and Technology 8 (2004) 145–153 q
q
xI l xI xI u ,
q = 1, . . . , 33,
(19)
q
where xI l is the lower bound of the design variable vector, q xI u is the upper bound of the design variable vector. As mentioned earlier, no structural details are considered in the finite element model of BWB. In the present case the cutout of a door (Fig. 7) is investigated, which leads to undesired stress concentrations in the corner vicinities. The respective local strength degradation has to be assessed cautiously. In order to reduce the stress concentrations, to prevent premature failure and to reattain sufficient effective strength a local reinforcement is employed. In accordance to the intermediate level the optimisation problem is defined by the subsequent mathematical formulation: Min mII (xII ) | gjI (xI , xII ) 0, gjII (xI , xII ) 0 . XII
(20)
The strength constraints are formulated by the von Mises II in each finite element of the reinforceequivalent stress σequ ment: II σu , σequ,j
j = 1, . . . , r,
which can be rewritten σ II (x , x ) equ,j I II gjII (xI , xII ) = max − 1 0. σu
(21)
(22)
The thickness of the local reinforcement as the design variable completes the optimisation model for the subsystem level. The intermediate design variable vector xI which is defined by the different skin thicknesses is kept constant during the optimisation of the door reinforcement. Fig. 8 illustrates the results of the objective function, the design variable and the constraint for both the intermediate
Fig. 8. Optimisation results for the objective function, design variable and constraints of the intermediate and subsystem level for each global iteration k.
H. Engels et al. / Aerospace Science and Technology 8 (2004) 145–153
and subsystem level for each iteration k. The actual numerical results are normalized by the value of the initial design (k = 0) for the objective functions as well as the design variables as follows: mIk mII , k; mI0 mII 0
tks tkr , , t0s t0r
(23)
where mIk , mII k is the structural mass of the intermediate and subsystem level for iteration k, mI0 , mII 0 is the structural mass of the intermediate and subsystem level for the initial design (k = 0), tks , tkr is the local skin and reinforcement thickness for iteration k, t0s , t0r is the local skin and reinforcement thickness for the initial design (k = 0). The illustrated results demonstrate the effective performance of convergence for the multi-level optimisation procedure. Obviously there is no further improvement of the objective functions after the fourth global iteration.
6. Conclusions The application of a multi-level MDO process is seen to be an essential component in the implementation of a realistic design and optimisation system for large-scale aircraft. The effectiveness of the approach is clearly demonstrated when the methodology is applied to a reduced size problem involving the multi-level structural optimisation of a BWB structure incorporating a reinforced cutout for a freight door. The advantages shown by this application can be read across to the larger scale problem, which is the focus of the MOB
153
project. It is shown that the larger problem could not be handled without the use of some form of decomposition of the overall design problem. Acknowledgements This work was financially supported by the Commission of the European Union under the GROWTH Programme for the Research project MOB “Multi-Disciplinary Design and Optimisation for the Blended Wing Body Configuration” which is gratefully acknowledged. (Contract number: G4RD-CT1999-0172.) References [1] H.A. Eschenauer, J. Geilen, H.J. Wahl, SAPOP – An optimisation procedure for multicriteria structural design, in: H.R.E.M. Hörnlein, K. Schittkowski (Eds.), International Series of Numerical Mathematics, Birkhäuser, Basel, 1993, pp. 207–227. [2] A. Morris, The MOB project an European Union funded project aimed at creating methods to support e-design across Europe, Aeronautics Days 2001, European Commission, Hamburg, 29–31 January 2001. [3] A. Morris, Distributed MDO: the way of the future, in: Proceedings of the CEAS Conference on Multidisciplinary Aircraft Design and Optimisation, Köln, Germany, 2001. [4] C. Oesterheld, W. Heinze, Concept of the aircraft design tool PrADO for the assessment of BWB configurations, MOB/1.1/IFL/BDAT/001 Report of the MOB Project. [5] J. Sobieszczanski-Sobieski, Structural optimisation by multilevel decomposition, AIAA Paper No. 83-0832, Proceedings AIAA/ASME/ ASCE/AH 24th Structures, Structural Dynamics and Materials Conference, Lake Tahoe, Nevada, May 2–4, 1983.
Implementation of a multi-level optimisation methodology within the e-design of a blended wing body ✩ Implementierung einer hierarchischen Optimierungs-Methodologie im Entwurfsprozess eines Nurflüglers Heiko Engels a , Wilfried Becker a,∗ , Alan Morris b a Universität Siegen, Institut für Mechanik und Regelungstechnik-Mechatronik, Paul-Bonatz-Str. 9-11, 57068 Siegen, Germany b Cranfield University, School of Engineering, Department of Engineering Mechanics & Structures, Bedfordshire MK43 0AL, UK
Received 24 February 2003; received in revised form 3 July 2003; accepted 7 August 2003
Abstract The modern requirement for low weight/high strength aircraft structures is placing an every increasing emphasise on the direct use of optimisation methods in the overall design process. In certain cases, such as that of the Blended Wing-Body (BWB) aircraft, the design cannot be successfully completed without the application of optimisation methods. This type of complex design has inevitably led to the growth in the size of the optimisation problem with large numbers of design variables and constraints being required in a design with strong interactions between the various structural components. Treating the problem in the conventional manner with all components considered simultaneously leads to excessive computer run times. In order to control this growth in problem size a multi-level approach has to be used in order to break down the problem into several sub-problems taking into account the structural coupling effects. Such an approach enables the use of parallel computer processing leading to a significant reduction of the computer run time and decreases the design cycle time. 2003 Elsevier SAS. All rights reserved. Zusammenfassung Im Hinblick auf ein möglichst geringes Gewicht bei möglichst hoher effektiver Festigkeit erfordert der moderne Flugzeug-Leichtbau immer mehr den gezielten Einsatz algorithmischer Strukturoptimierung im gesamten Entwurfsprozess. In bestimmten Fällen, wie etwa bei Nurflüglern (Blended Wing Bodies, BWB), ist der Einsatz von Optimierungsmethoden sogar fast unumgänglich. Dabei wächst mit der Anzahl gegebener Entwurfsvariablen und zu beachtender Nebenbedingungen die Größe eines Optimierungsproblems schnell, und es sind starke Interaktionen zwischen den beteiligten Teilstrukturen zu berücksichtigen. Die gleichzeitige detaillierte Analyse und Optimierung aller Strukturkomponenten verbietet sich in der Regel vom Berechnungsaufwand her. Das Aufwandsproblem lässt sich jedoch durch eine Aufspaltung in Teilprobleme und eine geeignete hierarchische Optimierung bewältigen, wobei alle wichtigen Interaktionseffekte zu berücksichtigen sind. Nicht zuletzt ermöglicht ein derartiger Zugang den Einsatz verteilten Rechnens mit einer entsprechenden Reduktion des erforderlichen Zeitaufwandes. 2003 Elsevier SAS. All rights reserved. Keywords: Optimisation methodology; Multi-level optimisation; Multidisciplinary optimisation; Blended wing body; Parallel computing Schlüsselwörter: Optimierungsmethodologie; Hierarchische Optimierung; Multidisziplinäre Optimierung; Nurflügler; Verteiltes Rechnen
1. Introduction
✩
This article was presented at the German Aerospace Congress 2002.
* Corresponding author.
E-mail address: [email protected] (W. Becker). 1270-9638/$ – see front matter 2003 Elsevier SAS. All rights reserved. doi:10.1016/j.ast.2003.10.001
Motivated by the increasing economic competition and impact of aircraft on the environment as well as the limited energy resources the European Union has put forward a number of research targets for the Aerospace Industry
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under Framework 5. One is to derive aircraft designs and methodologies which are environmentally friendly. A second is recognition that the European aircraft industry has to confront the fact of technology drift which is opening the aerospace market to emerging countries with lower costs. Finally, Europe has to compete with the US and thus the development of more innovative aircraft designs which are low cost and require minimum maintenance is of main interest [2,3]. The main aim of the European funded project “MultiDisciplinary Design and Optimisation for the Blended Wing Body Configuration (MOB)” is to develop a distributed e-design system with a Blended Wing Body (BWB) as the driving scenario. This system incorporates expertise from different design groups distributed across Europe. The e-design system enables it to operate as a multi-disciplinary design group where the involved groups employ their own design software tools. In this way a distributed and interactive set of multi-disciplinary programs can be constructed by the individual partners incorporating appropriate optimisation software. Thus it is possible to develop new aircraft designs with a distributed optimisation software system allowing a strong interaction between relevant disciplines: aerodynamics, structural design, flight mechanics, aeroelasticity, etc. The purpose of the MOB project is to set up a Computational Design Engine (CDE) enabling the development of efficient and highly innovative aircraft designs by a team of engineers distributed across Europe using the internet to operate as one single design group. This new design software is being demonstrated, as already indicated, by applying it to the design of a sophisticated aircraft design – the Blended Wing Body aircraft. MOB is recognising that the interaction between the different disciplines can no longer be neglected when undertaking the design and optimisation of complex designs such as BWB. Furthermore the decomposition of a specific main discipline, for example the aircraft structure, and the subsequent independent analysis of its separate components is equally inadmissible. This combination of requirements creates a major problem when the optimisation and analysis of large engineering designs is undertaken due excess computational requirements needed to handle the large number of design variables and constraints. To solve these problems recourse has to be made to a multi-level approach to decompose the entire system problem into several sub-problems taking into account the various coupling effects. The multi-level approach allows the optimisation of individual system components thereby reducing the computer run time and design cycle time significantly. In the literature various concepts have been proposed for breaking large optimisation problems into subproblems. Most of them are specialized for the multi-level optimisation of structural engineering problems. In the case of the Blended Wing Body a more general approach for the optimisation of multi-disciplinary applications is necessary. Such an approach has already been developed and suggested
by Sobieski [5]. In the following, in essence, we follow the conceptual methodology suggested by Sobieski. Thus the considered optimisation problem is subdivided into several subsystems and a single coordination problem. The mutual interdependence of the subsystems is taken into account by introducing additional constraints. Thus the uncoupled subsystems can be considered and optimised individually.
2. The MOB project The multi national project team consists of 3 airframe design and manufacturing companies, 4 national research institutes and 8 universities from four European countries. Partners are Cranfield University as the main contractor and project coordinator, BAE Systems, QinetiQ and Rutherford Appleton Laboratory (RAL) from the United Kingdom; Saab Aerospace and Royal Institute of Technology (KTH) from Sweden; Technische Universitoit Delft and National Aerospace Laboratory (NLR) from the Netherlands; Deutsches Zentrum für Luft- und Raumfahrt (DLR), European Aeronautic Defence and Space Company (EADS), Technische Universität Braunschweig, Technische Universität München, Technische Universität Berlin, Universität Stuttgart and Universität Siegen from Germany. The main target of the project is the development of tools and methodologies allowing the design of large-scale aeronautical products by a group of teams distributed across Europe. Each team employs individual discipline based software programs to create a distributed Computational Design Engine based on multi-level concepts employing multidisciplinary design and optimisation methods. Due to the physical distribution of the teams within Europe the CDE has to couple the respective software tools to ensure the necessary information flow through all design levels from conceptual to main phase with increasing accuracy of physical models (finite element models, aerodynamic models, etc.) [2]. Thus the created CDE mirrors the actual situation where different engineering teams, located at various sites, have to develop new and innovative aircraft designs in a co-operative manner with their own specific design tools and methodologies.
3. The blended wing body design The second purpose of the project is the application of the developed CDE to an actual problem of interest. The chosen design of the Blended Wing Body (Fig. 1) is a modern type of aircraft design with the potential for high efficiency. The development of the BWB design requires a multidisciplinary approach incorporating advanced optimisation techniques. Distributed teams of specialist engineers provide the knowledge required from the wide range of disciplines needed for this complex design. Thus the BWB, as the driving scenario, demonstrates the benefits of the flexible
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Fig. 1. Blended Wing Body configuration [2].
CDE methodology. The focus of the project is to point out the practicability of the CDE process rather than developing a BWB design with respect to real life accuracy of the physical models.
4. Multi-level optimization methodology The scenario described above requires the overall multidisciplinary optimisation problem being decomposed into several sub-problems. Thus, the entire problem is divided into a system level, intermediate level and several subsystem levels depicted by boxes shown in Fig. 2. This procedure has been described in the computational design engine specification above. At the system level the preliminary design of the aircraft is optimised. The optimisation of the preliminary design of the aircraft can be performed by the optimisation procedure PrADO; a preliminary design and optimisation tool for aircraft applications provided by the University of Braunschweig [4]. With respect to the leading design criterion such as flight performance, direct operating costs, etc. a first design of the aircraft can be determined by the PrADO
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software tool. Typical design variables are structural aspect ratios, skin thicknesses, span width etc. Possible constraints are the landing performance, climb performance, and maximum takeoff weight etc. and the objective function may be minimum total weight, minimum direct operating costs or an alternative. The intermediate level considers the pure mono disciplines like structural design, aerodynamics, flight mechanics and aero-servo elastic analysis. Thus, there is one intermediate level for each discipline. The design variables on this level are aspect ratios and other sizing variables for structures and the profile thickness of the 2D-airfoil for aerodynamics possibly. Intermediate level constraints for the structural optimisation are stresses, strains, displacements etc. and for aerodynamic applications prescribed pressure distributions. Typical objective functions are the minimal structural weight and minimal drag for aerodynamics. At the lower levels (subsystem levels) the design is considered in more detail. The branch for these subsystem levels in the case of the structure’s discipline might be extended from a particular structural component (wing, etc.) down to individual stringers or even joints. Possible design variables at this level are various geometrical dimensions such as skin thicknesses, stringer dimensions etc. The interaction between each sublevel has to be taken into account during the design process. Changing the design variables during the optimisation process on the subsystem level will influence the upper level with respect to the constraints (subsystem level, intermediate level) and vice versa. Thus most of the constraints are implicit functions of the design variables of different levels and disciplines. The different levels can be uncoupled by an appropriate approximation of the constraints and then optimised individually. In the following section a two-level optimisation approach for structures is discussed which in principle can be extended easily to a more general multi-level optimisation
Fig. 2. Multi-level approach [5].
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procedure. It is emphasized that the approach might be generalized in an arbitrary manner in principle. This methodology can be applied to aerodynamics or even other multidisciplinary engineering problems. Within the two-level approach the considered structural problem is decomposed into the intermediate level and several subsystem levels. The design problem is posed in terms of the Blended Wing Body structure where the fuselage has a door and the target is to create a minimum weight design. The problem has two levels involving the entire BWB structure and the cutout for the freight door. The subsystem level is a single component represented by the door cutout and the intermediate level is the whole assembled aircraft structure. In order to optimise each level individually it is necessary to set up an appropriate optimisation model. The mathematical formulation of the optimisation problem for the intermediate level reads: Min fI (xI ) | gjI (xI , xII ) 0, gjII (xI , xII ) 0 , (1) XI
where xI is the vector of the intermediate design variables, xII is the vector of the subsystem design variables, fI (xI ) is the intermediate objective function, gjI (xI , xII ) is the vector of the intermediate inequality constraints as functions of the intermediate and subsystem design variables xI , xII , gjII (xI , xII ) is the vector of the subsystem inequality constraints as functions of the intermediate and subsystem design variables xI , xII . Thus, the aim of the optimisation is to minimize the objective function fI (xI ) through an appropriate selection of the design variables xI , while satisfying the inequality constraints gjI (xI , xII ): gjI (xI , xII ) 0,
j = 1, . . . , n,
(2)
these are the behavioural constraints which are, for example, the strength constraints in each element of the FEM-model given by σequ,j I − 1 0, (3) gj (xI , xII ) = max σu where σequ is the von Mises equivalent stress and σu is the ultimate strength. The subsystem inequality constraints have also to be taken into account in the form: gjII (xI , xII ) 0,
j = n + 1, . . . , m.
(4)
In order to consider each level individually the design variables xII of the subsystem are kept constant during the optimisation of the intermediate level. The respective side constraints of the problem are xI l xI xI u ,
(5)
where xI l is the lower bound of the design variable vector, xI u is the upper bound of the design variable vector. Typical design variables are the overall skin thickness, aspect ratios and other sizing variables.
Fig. 3. Interlevel flow of information [5].
At the subsystem level the corresponding formulation of the optimisation problem is in accordance to the intermediate level: Min fII (xII ) | gjII (xI , xII ) 0, gjI (xI , xII ) 0 , (6) XII
where as before xI and xII are the vectors of the intermediate and subsystem design variables, fII (xII ) is the objective function of the subsystem level and gjII (xI , xII ), gjI (xI , xII ) are the respective inequality constraints. The respective inequality constraints of the subsystem level are formulated as follows gjII (xI , xII ) 0,
j = 1, . . . , r,
(7)
which again might be strength constraints as a function of the subsystem design variables σequ,j II gj (xI , xII ) = max − 1 0. (8) σu The design variables xII can influence the intermediate inequality constraints gjI (xI , xII ) which have to be considered during the optimisation process in the form: gjI (xI , xII ) 0,
j = r + 1, . . . , s.
(9)
Once more the design variables xI of the intermediate level are kept constant during the optimisation of the subsystem level. Within the presented two-level approach the intermediate level is coupled to the subsystem level in two ways. The subsystem level receives the boundary conditions Q, the valid design variables xI and the approximated constraints gjI (xI , xII ) of the intermediate system. The data passed from the subsystem level to the intermediate level carry the information of the approximated constraints gjII (xI , xII ) as a function of the design variables xI as illustrated in Fig. 3. The structural behaviour of the door cutout design at the subsystem level is represented within the intermediate level by effective stiffnesses, e.g. in the form of superelement stiffnesses. In order to accomplish the respective decomposition of the optimisation problem an appropriate approximation for the subsystem constraints on the intermediate level has to be chosen. In the present case the approximation is given by a Taylor-series expansion:
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Fig. 4. Data flow and subtask management.
gjII (xI , xII ) = gjII
k ∂gjII (xkI , xII ) xI , xII + xI − xkI , ∂xI
j = 1, . . . , n,
∂gjI (xI , xkII ) ∂xII (10)
xkI
where the design vector corresponds to the actual design of iteration k. The respective first derivatives of the subsystem constraints are calculated numerically by finite differencing: ∂gjII (xkI , xII ) ∂xI
=
gjII (xkI + xI , xII ) − gjII (xkI , xII ) xI
.
(11)
For the intermediate level constraints at the subsystem level an approximation can be employed in the analogous manner: ∂gjI (xI , xkII ) gjI (xI , xII ) = gjI xI , xkII + xII − xkII , ∂xII j = 1, . . . , r,
(12)
where xkII is the design variable vector of the actual design for iteration k. The necessary first derivative is again given by finite difference scheme:
=
gjI (xI , xkII + xII ) − gjI (xI , xkII ) xII
.
(13)
Thus, the intermediate level, as well as the subsystem level can be considered individually in correspondence to Fig. 4. The implementation of this procedure enables a parallel optimisation procedure for each individual level. The optimisation of the intermediate level provides the necessary boundary loads and deformations as well as the approximation of the intermediate level constraints for the subsystem level (Eq. (12)). The solution of the optimisation problem for the subsystem level and calculation of the respective sensitivities yields the approximation of the subsystem constraints for the intermediate level (Eq. (10)). The implementation of the derived multi-level approach in terms of the computational design engine (CDE) is illustrated in Fig. 4. The overall product data in terms of structural aspect ratios, geometry, structural mass, structural stiffness, eigen modes, maximum lift coefficient etc. is stored on a data base generated and managed by the data base software DEVA. The defined intermediate levels
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can access this data base in order to get the necessary information for respective optimisations and analysis. On the other hand the intermediate levels store new data and results on the data base reversibly. There is one intermediate level for each of the mono disciplines: • • • •
Structural Design, Aerodynamics, Flight Mechanics, and Aero-Servo Elastic Analysis.
These use particular analysis tools like the pre-processor PATRAN as a structural model generator or the finite element code NASTRAN to analyse the present problem. The different intermediate levels themselves interact through the objective functions and constraints which are functions of the design variables. As an example the aerodynamic analysis provides the necessary aerodynamic loads for the structural analysis whereas the structural analysis supplies the structural mass and stiffness for the flight mechanics analysis. This concept of multi-disciplinary analysis has also been implemented by NLR in the higher levels of the CDE. In the sequel the multi-level optimisation is discussed in more detail for the structural intermediate level. As already noted the structure is decomposed into an intermediate level and several subsystem levels. The geometry of the blended wing body is given by an ICAD-model provided by the DEVA database. Importing this geometry model enables the generation of an appropriate finite element model by PATRAN. Within the optimisation procedure for the intermediate level the structural model is now represented by an appropriate FEM-model, which can be analysed by the commercial FEM-code NASTRAN. The aerodynamic loads are provided by the aerodynamic analysis. The actual numerical implementation of the optimisation procedure requires a well-organised data transfer and can be visualized as outlined by the optimisation loop shown in Fig. 4. Starting from an initial design x0 the iterative procedure leads to an improved design variable vector xk after each iteration k. The optimisation procedure is stopped as soon as a convergence criterion becomes active at which stage the final or optimal design x∗ is achieved. Considering the subsystem level, the geometry again is defined by an ICAD-model or might be generated by the user in PATRAN. The respective finite element model is also generated in PATRAN and the optimisation procedure is implemented in terms of the optimisation loop illustrated in Fig. 5. The data transfer with regard to ICAD-models or other information as well as analysis processes are managed by SPINEware provided by the National Aerospace Laboratory (NLR). SPINEware is an object-oriented system that enables the construction of user-defined working environments in heterogeneous computer networks. The decomposition of the intermediate level and subsystem level is achieved by the stated Taylor-series expansion (Eqs. (10)–(13)). The
Fig. 5. Optimisation loop [1].
structural multi-level optimisation procedure consists of the following steps: 1. Optimisation of the intermediate level and provision of the boundary loads, deformations and the approximated intermediate level constraints for the subsystem level. 2. Approximation of the intermediate level constraints with respect to the subsystem design variables. 3. Solution of the optimisation problem for the subsystem level. 4. Approximation of the subsystem constraints with respect to the intermediate level design variables for the intermediate level. 5. The reduced stiffnesses and the approximated constraints are supplied for the intermediate level. In this procedure, the optimisation in step 1 and 3 is iterative and nested in the overall procedure, steps 1 through 5. The optimisations in steps 1 and 3 are performed separately, which enables parallel computer processing.
5. Example: multi-level optimisation of a door reinforcement As an actual example in the following the structural multi-level optimisation of the blended wing body is discussed in more detail and represents the optimisation/analysis MDO process for a door reinforcement. Undertaking a full structural optimisation for a large aircraft such as a BWB taking into consideration each individual detail like doors, windows, spars etc. within the finite element model of the blended wing body design (Fig. 6) would represent a too large computational problem. Therefore the structural system has to be decomposed into different levels. With respect to the derived multi-level methodology the finite element model of the blended wing body structure represents the intermediate level whilst the model of a door cutout shown in Fig. 7 represents the subsystem level. This optimisation problem is used here
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151
Fig. 6. Finite element model of the blended wing body generated by BAE systems.
where mI (xI ) is the structural mass. The respective constraints gjI (xI , xII ) are given by the von Mises equivalent I in each finite element: stress σequ I σu , σequ,j
j = 1, . . . , n, I σequ,j (xI , xII ) gjI (xI , xII ) = max − 1 0, σu
Fig. 7. Finite element model of the door cutout generated by University of Siegen.
as a driving scenario to demonstrate the efficiency of the introduced multi-level optimisation approach. The generation procedure of the FE-models is an automated process in accordance to the paradigm shown in Fig. 4. FE models for the BWB structure and the door model employ eight-node displacement-based shell elements with six degrees of freedom at each node. In addition, a door reinforcement has been generated along the door boundary by appropriate laminate elements with the first ply modelling the overall skin and the second layer the door reinforcement. Distributed aerodynamic pressure loads load the BWB-structure and the door. The aim is to minimize the structural mass by an appropriate selection of the design variables while simultaneously fulfilling the strength constraints. Thus the mathematical formulation of the optimisation problem for the intermediate level (BWB) is as follows in accordance to Eq. (1): (14) Min mI (xI ) | gjI (xI , xII ) 0, gjII (xI , xII ) 0 , XI
(15) (16)
where σu is the ultimate strength. The design variables xII of the subsystem level are kept constant during the optimisation process on the intermediate level. The solution of the optimisation problem for the subsystem level and calculation of the respective sensitivities yields the approximation of the subsystem constraints for the intermediate level in accordance to Eq. (10). Thus the von Mises II is a function of the intermediate design equivalent stress σequ variables xI in each finite element of the door reinforcement and is approximated as follows k II II σequ,j (xI , xII ) = σequ,j xI , xII +
II ∂σequ,j (xkI , xII )
∂xI
xI − xkI σu ,
j = n + 1, . . . , m, which again can be rearranged II σequ,j (xI , xII ) gjII (xI , xII ) = max − 1 0. σu
(17)
(18)
The design vector xkI corresponds to the actual design for iteration k. The optimisation model for the intermediate level is completed by the skin thicknesses of the BWB design as design variables. Thus the overall skin of the BWB design is subdivided into 33 domains with variable thicknesses and q = 1, . . . , 33 design variables respectively. The respective side constraints of the problem are
152 q
H. Engels et al. / Aerospace Science and Technology 8 (2004) 145–153 q
q
xI l xI xI u ,
q = 1, . . . , 33,
(19)
q
where xI l is the lower bound of the design variable vector, q xI u is the upper bound of the design variable vector. As mentioned earlier, no structural details are considered in the finite element model of BWB. In the present case the cutout of a door (Fig. 7) is investigated, which leads to undesired stress concentrations in the corner vicinities. The respective local strength degradation has to be assessed cautiously. In order to reduce the stress concentrations, to prevent premature failure and to reattain sufficient effective strength a local reinforcement is employed. In accordance to the intermediate level the optimisation problem is defined by the subsequent mathematical formulation: Min mII (xII ) | gjI (xI , xII ) 0, gjII (xI , xII ) 0 . XII
(20)
The strength constraints are formulated by the von Mises II in each finite element of the reinforceequivalent stress σequ ment: II σu , σequ,j
j = 1, . . . , r,
which can be rewritten σ II (x , x ) equ,j I II gjII (xI , xII ) = max − 1 0. σu
(21)
(22)
The thickness of the local reinforcement as the design variable completes the optimisation model for the subsystem level. The intermediate design variable vector xI which is defined by the different skin thicknesses is kept constant during the optimisation of the door reinforcement. Fig. 8 illustrates the results of the objective function, the design variable and the constraint for both the intermediate
Fig. 8. Optimisation results for the objective function, design variable and constraints of the intermediate and subsystem level for each global iteration k.
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and subsystem level for each iteration k. The actual numerical results are normalized by the value of the initial design (k = 0) for the objective functions as well as the design variables as follows: mIk mII , k; mI0 mII 0
tks tkr , , t0s t0r
(23)
where mIk , mII k is the structural mass of the intermediate and subsystem level for iteration k, mI0 , mII 0 is the structural mass of the intermediate and subsystem level for the initial design (k = 0), tks , tkr is the local skin and reinforcement thickness for iteration k, t0s , t0r is the local skin and reinforcement thickness for the initial design (k = 0). The illustrated results demonstrate the effective performance of convergence for the multi-level optimisation procedure. Obviously there is no further improvement of the objective functions after the fourth global iteration.
6. Conclusions The application of a multi-level MDO process is seen to be an essential component in the implementation of a realistic design and optimisation system for large-scale aircraft. The effectiveness of the approach is clearly demonstrated when the methodology is applied to a reduced size problem involving the multi-level structural optimisation of a BWB structure incorporating a reinforced cutout for a freight door. The advantages shown by this application can be read across to the larger scale problem, which is the focus of the MOB
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project. It is shown that the larger problem could not be handled without the use of some form of decomposition of the overall design problem. Acknowledgements This work was financially supported by the Commission of the European Union under the GROWTH Programme for the Research project MOB “Multi-Disciplinary Design and Optimisation for the Blended Wing Body Configuration” which is gratefully acknowledged. (Contract number: G4RD-CT1999-0172.) References [1] H.A. Eschenauer, J. Geilen, H.J. Wahl, SAPOP – An optimisation procedure for multicriteria structural design, in: H.R.E.M. Hörnlein, K. Schittkowski (Eds.), International Series of Numerical Mathematics, Birkhäuser, Basel, 1993, pp. 207–227. [2] A. Morris, The MOB project an European Union funded project aimed at creating methods to support e-design across Europe, Aeronautics Days 2001, European Commission, Hamburg, 29–31 January 2001. [3] A. Morris, Distributed MDO: the way of the future, in: Proceedings of the CEAS Conference on Multidisciplinary Aircraft Design and Optimisation, Köln, Germany, 2001. [4] C. Oesterheld, W. Heinze, Concept of the aircraft design tool PrADO for the assessment of BWB configurations, MOB/1.1/IFL/BDAT/001 Report of the MOB Project. [5] J. Sobieszczanski-Sobieski, Structural optimisation by multilevel decomposition, AIAA Paper No. 83-0832, Proceedings AIAA/ASME/ ASCE/AH 24th Structures, Structural Dynamics and Materials Conference, Lake Tahoe, Nevada, May 2–4, 1983.