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MDO analyses of wing structures for a complete aeroelastically constrained aircraft

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Abstract

A multidisciplinary design optimization (MDO) approach for airplane structures is presented which integrates modeling used within the structures, aerodynamics, flight dynamics, and aeroelasticity disciplines. The MDO procedure uses a numerical optimizer which includes a finite element (FE) analysis for structures, a panel method analysis for steady and unsteady aerodynamics, and an aeroelastic solver for stability and static and dynamic response. The space discretizations used in the structural and aerodynamic meshes are dynamically updated during the optimization process according to wing planform and wing structural variables. This MDO approach is primarily based on the first principles; therefore, the set of possible optimal solutions has no particular limit. The optimization capabilities of the wing planform variables compared with standard structural design variables are highlighted in this paper. Moreover, the use of composite objective functions has demonstrated the further capabilities of the presented MDO procedure. These results show that the MDO approach provides a significant, numerically efficient, and reliable tool within the framework of preliminary aircraft design.

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Abbreviations

a, b, c :

Weight coefficients for the objective function

\(A\!\! R\) :

Wing aspect ratio

c :

Specific fuel consumption

C D :

Drag coefficient

C L :

Lift coefficient

DLM:

Doublet lattice method

E :

Aerodynamic efficiency

FE :

Finite element

H :

Endurance

M C :

Cruise Mach number

MDO:

Multidisciplinary-design optimization

R :

Range

S :

Wing area

SQP:

Sequential quadratic programming

V :

Velocity

W :

Weight

W 0f :

Zero fuel weight

W f :

Fuel weight

α :

Angle of attack

δ e :

Elevator angle

ζ:

Aeroelastic damping ratio

ρ ∞ :

Air density at flight altitude

σ:

Stress

References

  1. Moore, G.J.: MSC/NASTRAN design seisnitivity and optimization. User Guide, V67. The MacNeal-Schwendler Corporation, USA (1992)

  2. Ashley, H.: On making things the best-aeronautical uses of optimization. J. Aircr. 19(1), 5–28 (1982)

    Article  MathSciNet  Google Scholar 

  3. Nell, D.J., Johnson, E.H., Canfield, R.: Astros, a multidisciplinary automated structural design tool. J. Aircr. 27(12), 1021–1027 (1990)

    Article  Google Scholar 

  4. Brama, T.: The structural optimization system Optsys-current status and applications. In: Agard Report R-784, Integrated Design Analysis and Optimisation of Aircraft Structures, 72nd Meeting of the Agard Structures and Materials Panel, pp. 6.1–6.9 (1991)

  5. Wakayama, S.: Blended-Wing-Body Optimization Problem Setup, AIAA Paper 2000-4740 (2000)

  6. Österheld, C.M., Heinze, W., Horst, P.: Preliminary design of a blended wing body configuration using the design tool PrADO. In: Proceedings of the CEAS Conference on Multidisciplinary Aircraft Design and Optimisation, Köln, June 25–26, 2001

  7. Fudge, D.M., Zingg, D.W., Haimes, R.: A CAD-Free and a CAD-Based Geometry Control System for Aerodynamic Shape Optimization, AIAA Paper 2005-0451 (2005)

  8. Alonso, J.J., LeGresley, P., Pereyra, V.: Aircraft design optimization. Math. Comput. Simul. 79(6),1948–1958 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Azamatov, A.I., Lee, J.W., Byun, Y.H., Kim, S.H.: Advanced configuration generation technique for the complex aircraft geometry. In: Proceedings of the 2008 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Xian, China, pp. 1141–1146 (2008)

  10. Mastroddi, F., Tozzi, M., Capannolo, V.: On the use of geometry design variables in the MDO analysis of wing structures with aeroelastic constraints on stability and response. Aerospace Sci Technol 15(3), 196–206 (2011)

    Article  Google Scholar 

  11. Haftka, R.T., Gurdal, Z.: Elements of Structural Optimization. Kluwer, The Netherlands (1992)

    Book  MATH  Google Scholar 

  12. Zhang, K.S., Han, Z.H., Li, W.J., Song, W.P.: (2008) Coupled aerodynamic/structural optimization of a subsonic transport wing using a surrogate model. J. Aircr. 45(6), 2167–2171

    Article  Google Scholar 

  13. Alexandrov, N., Hussaini, M.Y.: Multidisciplinary design optimization: state of the art. In: Proceedings of the ICASE/NASA Langley Workshop on Multidisciplinary Design Optimization, SIAM Proceedings Series (1997)

  14. Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA-II. In: PPSN VI: Proceedings of the 6th International Conference on Parallel Problem Solving from Nature, pp. 849–858 (2000)

  15. Obayashi, S.: Multidisciplinary design optimization of aircraft wing planform based on evolutionary algorithms. In: Proceedings of the 1998 IEEE International Conference on Systems, Man, and Cybernetics, La Jolla, California, IEEE, October, 1998

  16. Venter, G., Sobieszczanski-Sobieski, J.: Multidisciplinary optimization of a transport aircraft wing using particle swarm optimization. Struct. Multidiscip. Optim. 26(11), 121–131 (2004)

    Article  Google Scholar 

  17. Venter, G., Sobieszczanski-Sobieski, J.: Particle swarm optimization. AIAA J. 41(8), 1583–1589 (2002)

    Google Scholar 

  18. Jeon, K.S., Lee, J.W., Byun, Y.,H.: Multidisciplinary design approach using repetitive response surface enhancement and global optimization. In: SNPD ’08: Proceedings of the 2008 Ninth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing, pp. 25–28 (2008)

  19. Martins, J.R.R.A., Marriage, C.: An object-oriented framework for multidisciplinary design optimization. In: 3rd AIAA Multidisciplinary Design Optimization Specialist Conference (2007)

  20. Alexandrow, N.M., Lewis, R.M.: Algorithmic perspectives on problem formulations in MDO. In: 8th AIAA/NASA/USAF/ISSMO multidisciplinary analysis and optimization symposium AIAA 2000-4719, Long Beach, California, September, 2000

  21. Cramer, E.J., Dennis, J.E. Jr., Frank, P.D., Lewis, R.M., Shubin, G.R.: Problem formulation for multidisciplinary optimization. SIAM J. Optim. 4, 754–776 (1993)

    Article  MathSciNet  Google Scholar 

  22. Balling, R., Wilkinson, C.: Execution of multidisciplinary design optimization approaches on common test problems. AIAA J. 35(1), 178–186 (1997)

    Article  MATH  Google Scholar 

  23. Braun, R.D., Kroo, I.M.: Development and application of the collaborative optimization architecture in a multidisciplinary design environment. In: Alexandrov, N.M., Hussaini, M.Y. (eds.) Multidisciplinary Design Optimization: State of the Art, SIAM (1997)

  24. Wujek, B.A., Renaud, J.E., Batill, S.M.: A concurrent engineering approach for multidisciplinary design in a distributed computing environment. In: Alexandrov, N.M., Hussaini, M.Y. (eds.) Multidisciplinary Design Optimization: State of the Art, SIAM (1997)

  25. Sobieszczanski-Sobieski, J., Kodiyalam, S.: BLISS/S: a new method for two-level structural optimization. Struct. Multidiscip. Optim. 21, 1–13 (2001)

    Article  Google Scholar 

  26. Geilen, M.C.W., Basten, T., Theelen, B.D., Otten, R.H.J.M.: An algebra of Pareto points. Fundam. Inform. 78(1), 35–74 (2007)

    Google Scholar 

  27. Pareto, V.: Manuale di Economia Politica, Piccola Biblioteca Scientifica, Milan, 1906; Translated into English by A.S. Schwier, Manual of Political Economy. MacMillan, London (1971)

  28. Caixeta, P.R. Jr., Marques, F.D.: Neural network metamodel-based MDO for wing design considering aeroelastic constraints. In: 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, vol. 2762 (2010)

  29. Cavagna, L., Riccobene, L., Ricci, S., Brard, A., Rizzi, A.: A fast MDO tool for aeroelastic optimization in aircraft conceptual design. In: 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, vol. 5911 (2008)

  30. Reuther, J.J., Alonso, J.J., Martins, J.R.R.A., Smith, S.C.: A coupled aero-structural optimization method for complete aircraft configurations. AIAA 37th Aerospace Sciences Meeting (1999)

  31. Gill, P.E., Murray, W., Saunders, M.A.: User’s Guide for Snopt Version 6, a Fortran Package for Large-Scale Nonlinear Programming (2002)

  32. Rodden, W.P., Johnson, E.H.: MSC/NASTRAN Aeroelastic Analysis User’s Guide V68. The MacNeal-Schwendler Corporation, USA (1994)

    Google Scholar 

  33. Butler, R., Hansson, E., Lillico, M., Van Dalen, F.: Comparison of multidisciplinarary design optimization codes for conceptual and preliminary wing design. J. Aircr. 35(6), 934–940 (1999)

    Article  Google Scholar 

  34. Fransen, S.H.J.A.: Conceptual Design of a 70 Passenger Airliner Propelled by Fuel-Efficient Turbofan Engines, Memorandum M725, Technical University of Delft, March (1996)

  35. Nygren, K.P., Schulz, R.R.: Breguet’s formulas for aircraft range and endurance. An application of integral calculus. In: United States Military Academy, ASEE Annual Conference Proceedings (1996)

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Rome “La Sapienza”, via Eudossiana, 18, 00184, Rome, Italy

    Franco Mastroddi, Marco Tozzi & Emanuele Mastrella

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  1. Franco Mastroddi
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  2. Marco Tozzi
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  3. Emanuele Mastrella
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Correspondence to Franco Mastroddi.

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Mastroddi, F., Tozzi, M. & Mastrella, E. MDO analyses of wing structures for a complete aeroelastically constrained aircraft. CEAS Aeronaut J 3, 67–77 (2012). https://doi.org/10.1007/s13272-012-0041-0

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