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Aeroelastic topology optimization of membrane structures for micro air vehicles

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Abstract

This work considers the aeroelastic optimization of a membrane micro air vehicle wing through topology optimization. The low aspect ratio wing is discretized into panels: a two material formulation on the wetted surface is used, where each panel can be membrane (wing skin) or carbon fiber (laminate reinforcement). An analytical sensitivity analysis of the aeroelastic system is used for the gradient-based optimization of aerodynamic objective functions. An explicit penalty is added, as needed, to force the structure to a 0–1 distribution. The dependence of the solution upon initial design, angle of attack, mesh density, and objective function are presented. Deformation and pressure distributions along the wing are studied for various load-augmenting and load-alleviating designs (both baseline and optimized), in order to establish a link between stiffness distribution and aerodynamic performance of membrane micro air vehicle wings. The work concludes with an experimental validation of the superiority of select optimal designs.

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References

  • Albertani R, Stanford B, Hubner J, Ifju P (2007) Aerodynamic coefficients and deformation measurements on flexible micro air vehicle wings. Exp Mech 47(5):625–635

    Article  Google Scholar 

  • Anagnostou G, Rønquist E, Patera A (1992) A computational procedure for part design. Comput Methods Appl Mech Eng 97(1):33–48

    Article  MATH  Google Scholar 

  • Balabanov V, Haftka R (1996) Topology optimization of transport wing internal structure. J Aircr 33(1):232–233

    Article  Google Scholar 

  • Beckers M (1999) Topology optimization using a dual method with discrete variables. Struct Multidisc Optim 17(1):14–24

    Google Scholar 

  • Bendsøe M, Sigmund O (2003) Topology optimization. Springer, Berlin, Germany

    Google Scholar 

  • Bendsøe M, Lund E, Olhoff N, Sigmund O (2005) Topology optimization: broadening the areas of application. Control Cybern 34(1):7–35

    Google Scholar 

  • Borrvall T, Petersson J (2003) Topology optimization of fluids in stokes flow. Int J Numer Methods Fluids 41(1):77–107

    Article  MATH  MathSciNet  Google Scholar 

  • Chen T, Wu S (2008) Multiobjective optimal topology design of structures. Comput Mech 21(6):483–492

    Article  Google Scholar 

  • Cook R, Malkus D, Plesha M, Witt R (2002) Concepts and applications of finite element analysis. Wiley, New York, NY

    Google Scholar 

  • Deb K, Goel T (2001) A hybrid multi-objective evolutionary approach to engineering shape design. In: International conference on evolutionary multi-criterion optimization, 7–9 March, Zurich, Switzerland

  • Eschenauer H, Olhoff N (2001) Topology optimization of continuum structures: a review. Appl Mech Rev 54(4):331–390

    Article  Google Scholar 

  • Gersborg-Hansen A, Sigmund O, Haber R (2005) Topology optimization of channel flow problems. Struct Multidisc Optim 30(3):181–192

    Article  MathSciNet  Google Scholar 

  • Gomes A, Suleman A (2008) Topology optimization of a reinforced wing box for enhanced roll maneuvers. AIAA J 46(3):548–556

    Article  Google Scholar 

  • Haftka R, Gürdal Z (1992) Elements of structural optimization. Kluwer, Dordrecht, The Netherlands

    MATH  Google Scholar 

  • Hsu M, Hsu Y (2005) Interpreting three-dimensional structural topology optimization results. Comput Struct 83(4):327–337

    Article  Google Scholar 

  • Katz J, Plotkin A (2001) Low-speed aerodynamics. Cambridge University Press, Cambridge, UK

    MATH  Google Scholar 

  • Krog L, Tucker A, Kemp M (2004) Topology optimization of aircraft wing box ribs. In: AIAA/ISSMO multidisciplinary analysis and optimization conference, 30 August–1 September, Albany, NY

  • Lee S, Bae J, Hinton E (2000) Shell topology optimization using the layered artificial material model. Int J Numer Methods Eng 47(4):843–867

    Article  MATH  Google Scholar 

  • Luo Z, Yang J, Chen L (2006) A new procedure for aerodynamic missile designs using topological optimization approach of continuum structures. Aerosp Sci Technol 10(5):364–373

    Article  Google Scholar 

  • Lyu N, Saitou K (2005) Topology optimization of multicomponent beam structure via decomposition-based assembly synthesis. J Mech Des 127(2):170–183

    Article  Google Scholar 

  • Martins J, Alonso J, Reuther J (2001) Aero-structural wing design optimization using high-fidelity sensitivity analysis. In: Confederation of European aerospace societies conference on multidisciplinary analysis and optimization, 25–26 June, Cologne, Germany

  • Maute K, Allen M (2004) Conceptual design of aeroelastic structures by topology optimization. Struct Multidisc Optim 27(1):27–42

    Article  Google Scholar 

  • Maute K, Reich G (2006) Integrated multidisciplinary topology optimization approach to adaptive wing design. J Aircr 43(1):253–263

    Article  Google Scholar 

  • Maute K, Nikbay M, Farhat C (2002) Sensitivity analysis and design optimization of three-dimensional non-linear aeroelastic systems by the adjoint method. Int J Numer Methods Eng 56(6):911–933

    Article  Google Scholar 

  • Ormiston R (1971) Theoretical and experimental aerodynamics of the sail wing. J Aircr 8(2):77–84

    Article  Google Scholar 

  • Pingen G, Evgrafov A, Maute K (2007) Topology optimization of flow domains using the Lattice Boltzmann method. Struct Multidisc Optim 34(6):507–524

    Article  MathSciNet  Google Scholar 

  • Stanford B, Abdulrahim M, Lind R, Ifju P (2007a) Investigation of membrane actuation for roll control of a micro air vehicle. J Aircr 44(3):741–749

    Article  Google Scholar 

  • Stanford B, Sytsma M, Albertani R, Viieru D, Shyy W, Ifju P (2007b) Static aeroelastic model validation of membrane micro air vehicle wings. AIAA J 45(12):2828–2837

    Article  Google Scholar 

  • Stegmann J, Lund E (2005a) Nonlinear topology optimization of layered shell structures. Struct Multidisc Optim 29(5):349–360

    Article  Google Scholar 

  • Stegmann J, Lund E (2005b) Discrete material optimization of general composite shell structures. Int J Numer Methods Eng 62(14):2009–2027

    Article  MATH  Google Scholar 

  • Stolpe M, Stidsen T (2006) A hierarchical method for discrete structural topology design problems with local stress and displacement constraints. Int J Numer Methods Eng 69(5):1060–1084

    Article  MathSciNet  Google Scholar 

  • Torres G (2002) Aerodynamics of low aspect ratio wings at low Reynolds numbers with applications to micro air vehicle design. Ph.D. Dissertation, Department of Aerospace and Mechanical Engineering, University of Notre Dame, South Bend, IN

  • Wang S, Tai K, Wang M (2006) An enhanced genetic algorithm for structural topology optimization. Int J Numer Methods Eng 65(1):18–44

    Article  MATH  Google Scholar 

  • Zuo K, Chen L, Zhang Y, Yang J (2007) Study of key algorithms in topology optimization. Int J Adv Manuf Technol 32(7):787–796

    Article  Google Scholar 

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Correspondence to Bret Stanford.

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Stanford, B., Ifju, P. Aeroelastic topology optimization of membrane structures for micro air vehicles. Struct Multidisc Optim 38, 301–316 (2009). https://doi.org/10.1007/s00158-008-0292-x

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  • DOI: https://doi.org/10.1007/s00158-008-0292-x

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