Multi-scale Least-Weight Design of a Wing-Box Through a Global/Local Modelling Approach


In this work, a multi-scale optimization strategy for lightweight structures, based on a global-local modelling approach is presented. The approach is applied to a realistic wing structure of a civil aircraft. The preliminary design of the wing can be formulated as a constrained optimization problem, involving several requirements at the different scales of the structure. The proposed strategy is characterized by two main features. Firstly, the problem is formulated in the most general sense, by including all design variables involved at each problem scale. Secondly, two scales are considered: (i) the structure macroscopic scale, where low-fidelity numerical models are used; (ii) the structure mesoscopic scale (or component-level), where enhanced models are involved. In particular, the structural responses are evaluated at both global and local scales, avoiding the use of approximated analytical methods. To this end, fully parametric global and local finite element models are interfaced with an in-house genetic algorithm. Refined models are created only for the most critical regions of the structure, and linked to the global one by means of a dedicated sub-modelling approach.

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  1. 1.

    Wignot, J., Combs, H., Ensrud, A.: Analysis of circular shell-supported frames. Technical note 929. NACA (1944)

  2. 2.

    Kuhn, P., Peterson, J., Levin, L.: Summary of diagonal tension. Technical note 2661. NACA (1952)

  3. 3.

    Gerard, G.: The crippling strength of compression elements. J. Aerosp. Sci. 25(1), 37–52 (1958).

    Article  Google Scholar 

  4. 4.

    Niu, M.: Airframe structural design: practical design information and data on aircraft structures. Conmilit Pr (1988)

  5. 5.

    Bruhn, E.: Analysis and Design of Flight Vehicle Structures. Tri-State Offset Co., Cincinnati (1973)

    Google Scholar 

  6. 6.

    Grihon, S., Samuelides, M., Merval, A., Remouchamps, A., Bruyneel, M., Colson, B., Hertel, K.: Fuselage structure optimisation. In: Advances in Collaborative Civil Aeronautical Multidisciplinary Design Optimization. Progress in Astronautics and Aeronautics, AIAA (2009).

  7. 7.

    Hughes, O., Ghosh, B., Chen, Y.: Improved prediction of simultaneous local and overall buckling of stiffened panels. Thin Walled Struct. 42(6), 827–856 (2004)

    Article  Google Scholar 

  8. 8.

    Stamatelos, D., Labeas, G., Tserpes, K.: Analytical calculation of local buckling and post-buckling behavior of isotropic and orthotropic stiffened panels. Thin Walled Struct. 49(3), 422–430 (2011)

    Article  Google Scholar 

  9. 9.

    Sobieszczanski, J., Loendorf, D.: A mixed optimization method for automated design of fuselage structures. J. Aircr. 9(12), 805–811 (1972)

    Article  Google Scholar 

  10. 10.

    Fischer, M., Kennedy, D., Featherston, C.: Multilevel framework for optimization of lightweight structures. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng. 226(4), 380–394 (2012)

    Article  Google Scholar 

  11. 11.

    Venkataraman, S., Haftka, R.: Structural optimization complexity: What has moore’s law done for us? Struct. Multidiscip. Optim. 28(6), 375–387 (2004)

    Article  Google Scholar 

  12. 12.

    Hirai, I., Wang, B., Pilkey, W.: An efficient zooming method for finite element analysis. Int. J. Numer. Methods Eng. 20(9), 1671–1683 (1984)

    MATH  Article  Google Scholar 

  13. 13.

    Sun, C., Mao, K.: A global–local finite element method suitable for parallel computations. Comput. Struct. 29(2), 309–315 (1988)

    MATH  Article  Google Scholar 

  14. 14.

    Mao, K., Sun, C.: A refined global–local finite element analysis method. Int. J. Numer. Methods Eng. 32(1), 29–43 (1991)

    MATH  Article  Google Scholar 

  15. 15.

    Whitcomb, J.: Iterative global/local finite element analysis. Comput. Struct. 40(4), 1027–1031 (1991)

    Article  Google Scholar 

  16. 16.

    Cormier, N., Smallwood, B., Sinclair, G., Meda, G.: Aggressive submodelling of stress concentrations. Int. J. Numer. Methods Eng. 46(6), 889–909 (1999)

    MATH  Article  Google Scholar 

  17. 17.

    Dababneha, O., Kipouros, T.: A review of aircraft wing mass estimation methods. Aerosp. Sci. Technol. 72, 256–266 (2018)

    Article  Google Scholar 

  18. 18.

    Benaouali, A., Kachel, S.: Multidisciplinary design optimization of aircraft wing using commercial software integration. Aerosp. Sci. Technol. 92, 766–776 (2019)

    Article  Google Scholar 

  19. 19.

    Zhao, A., Zou, H., Jin, H., Wen, D.: Structural design and verification of an innovative whole adaptive variable camber wing. Aerosp. Sci. Technol. 89, 11–18 (2019)

    Article  Google Scholar 

  20. 20.

    Dababneha, O., Kipouros, T.: Influence of high fidelity structural models on the predicted mass of aircraft wing using design optimization. Aerosp. Sci. Technol. 79, 164–173 (2018)

    Article  Google Scholar 

  21. 21.

    Arrieta, A., Stritz, A.G.: Optimal design of aircraft structures with damage tolerance requirements. Struct. Multidiscp. Optim. 30, 155–163 (2005)

    Article  Google Scholar 

  22. 22.

    Ciampa, P., Nagel, B., Tooren, M.: Global local structural optimization of transportation aircraft wings. In: 51st AIAA/ASME/ASCE/AHS/ASC Structures., Structural Dynamics, and Materials Conference (2010)

  23. 23.

    Chedrik, V.: Two-level design optimization of aircraft structures under stress, buckling and aeroelasticity constraints. In: 10th World Congress on Structural and Multidisciplinary Optimisation (2013)

  24. 24.

    Liu, Q., Mohamed, J., Sameer, B.M., Rakesh, K.K.: Integrated global wing and local panel optimization of aircraft wing. In: 56th AIAA/ASCE/AHS/ASC Structures. Structural Dynamics, and Materials Conference (2015)

  25. 25.

    Montemurro, M.: A contribution to the development of design strategies for the optimisation of lightweight structures, Hdr thesis, Université de Bordeaux. URL (2018)

  26. 26.

    Montemurro, M., Vincenti, A., Vannucci, P.: A two-level procedure for the global optimum design of composite modular structures–application to the design of an aircraft wing. Part 1: theoretical formulation. J. Optim. Theory Appl. 155(1), 1–23 (2012)

    MathSciNet  MATH  Article  Google Scholar 

  27. 27.

    Montemurro, M., Vincenti, A., Vannucci, P.: A two-level procedure for the global optimum design of composite modular structures–application to the design of an aircraft wing. Part 2: numerical aspects and examples. J. Optim. Theory Appl. 155(1), 24–53 (2012)

    MathSciNet  MATH  Article  Google Scholar 

  28. 28.

    Montemurro, M., Catapano, A., Doroszewski, D.: A multi-scale approach for the simultaneous shape and material optimisation of sandwich panels with cellular core. Compos. Part B Eng. 91, 458–472 (2016)

    Article  Google Scholar 

  29. 29.

    Montemurro, M., Catapano, A.: A new paradigm for the optimum design of variable angle tow laminates. In: Buttazzo, G., Frediani, A. (eds.) Variational Analysis and Aerospace Engineering: Mathematical Challenges for the Aerospace of the Future. Springer Optimization and Its Applications, vol. 116. Springer, New York (2016).

    Google Scholar 

  30. 30.

    Costa, G., Montemurro, M., Pailhès, J.: A general hybrid optimization strategy for curve fitting in the non-uniform rational basis spline framework. J. Optim. Theory Appl. 176(1), 225–251 (2018)

    MathSciNet  MATH  Article  Google Scholar 

  31. 31.

    Montemurro, M., Catapano, A.: On the effective integration of manufacturability constraints within the multi-scale methodology for designing variable angle-tow laminates. Compos. Struct. 161, 145–159 (2017)

    Article  Google Scholar 

  32. 32.

    Montemurro, M., Izzi, M.I., Yagoubi, J.E., Fanteria, D.: Least-weight composite plates with unconventional stacking sequences: design, analysis and experiments. J. Compos. Mater. 53(16), 2209–2227 (2019)

    Article  Google Scholar 

  33. 33.

    Panettieri, E., Montemurro, M., Catapano, A.: Blending constraints for composite laminates in polar parameters space. Compos. Part B Eng. 168, 448–457 (2019)

    Article  Google Scholar 

  34. 34.

    Montemurro, M., Pagani, A., Fiordilino, G.A., Pailhès, J., Carrera, E.: A general multi-scale two-level optimisation strategy for designing composite stiffened panels. Compos. Struct. 201, 968–979 (2018)

    Article  Google Scholar 

  35. 35.

    Airbus A320 aircraft characteristics for airport and maintenance planning, Tech. rep., AIRBUS S.A.S., Customer Services Technical Data Support and Services (2010).

  36. 36.

    Raymer, D.P.: Aircraft Design: A Conceptual Approach. Educ Series, American Institute of Aeronautics and Astronautics (1989)

  37. 37.

    Goranson, U.G.: Fatigue issues in aircraft maintenance and repairs. Int. J. Fatigue 20(6), 413–431 (1998)

    Article  Google Scholar 

  38. 38.

    Technical note 2751, National Advisiory Committee for Aeronautics

  39. 39.

    Gerard, G.: Minimum Weight Analysis of Compression Structures. New York University Press, New York (1956)

    Google Scholar 

  40. 40.

    Montemurro, M., Vincenti, A., Vannucci, P.: The automatic dynamic penalisation method (ADP) for handling constraints with genetic algorithms. Comput. Methods Appl. Mech. Eng. 256, 70–87 (2013)

    MathSciNet  MATH  Article  Google Scholar 

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This paper presents part of the activities carried out within the research project PARSIFAL (Prandtlplane ARchitecture for the Sustainable Improvement of Future AirpLanes), which has been funded by the European Union under the Horizon 2020 Research and Innovation Program (Grant Agreement No. 723149).

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Correspondence to Marco Montemurro.

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Panettieri, E., Montemurro, M., Fanteria, D. et al. Multi-scale Least-Weight Design of a Wing-Box Through a Global/Local Modelling Approach. J Optim Theory Appl 187, 776–799 (2020).

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  • Optimization
  • Genetic algorithms
  • Wing
  • Stiffened panels
  • Global/local modelling approach

Mathematics Subject Classification

  • 90C26
  • 90C30
  • 90C31
  • 90C90
  • 74S05
  • 74K99