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A Method for the Calculation of Large Deformations in Aeroelastic Applications

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AeroStruct: Enable and Learn How to Integrate Flexibility in Design (AeroStruct 2015)

Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((NNFM,volume 138))

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Abstract

A modal-based method that calculates the geometric nonlinear effects in the regime of large deformations of wing-like structures is applied to the modeling of a highly flexible 3D wingbox of high aspect ratio. The proposed method features higher-order stiffness terms and calculates the nodal deformation field not only by normal modes but also by additional modal components. In this way, a nonlinear force-displacement relationship and a geometrically nonlinear displacement field are accounted for. Static and dynamic results for the two configurations are presented together with results from a nonlinear finite element solver. The validations highlight the capability of the method to capture the nonlinear effects and demonstrates its power to model a 3D wingbox structure made of composite shell elements with anisotropic material characteristics.

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References

  1. C.E.S. Cesnik, R. Palacios, E.Y. Reichenbach, Reexamined structural design procedures for very flexible aircraft. J. Aircr. 51(5), 1580–1591 (2014)

    Article  Google Scholar 

  2. J. Katz, A. Plotkin, Low-Speed Aerodynamics, Cambridge Aerospace Series (Cambridge University Press, Cambridge, 2001)

    Book  MATH  Google Scholar 

  3. K. Kim, A.G. Radu, X.Q. Wang, M.P. Mignolet, Nonlinear reduced order modeling of isotropic and functionally graded plates. Int. J. Non-Linear Mech. 49, 100–110 (2013)

    Article  Google Scholar 

  4. T. Klimmek, Parameterization of topology and geometry for the multidisciplinary optimization of wing structures, in Proceedings CEAS, CEAS 2009 - European Air and Space Conference (Manchester, United Kingdom, 2009), p. 2009

    Google Scholar 

  5. R.J. Kuether, M.S. Allen, Nonlinear modal substructuring of systems with geometric nonlinearities, in 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (Boston, Massachusetts, 2013)

    Google Scholar 

  6. R.J. Kuether, M.S. Allen, Substructuring with nonlinear reduced order models and interface reduction with characteristic constraint modes, in AIAA SciTech. 55th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (National Harbor, Maryland, 2014)

    Google Scholar 

  7. M.P. Mignolet, A. Przekop, S.A. Rizzi, S.M. Spottswood, A review of indirect/non-intrusive reduced order modeling of nonlinear geometric structures. J. Sound Vib. 332(10), 2437–2460 (2013)

    Article  Google Scholar 

  8. M. Ritter, C.E.S. Cesnik, W.R. KrĂĽger, An enhanced modal approach for large deformation modeling of wing-like structures, in AIAA SciTech. 56th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (Kissimmee, Florida, 2015)

    Google Scholar 

  9. D.J. Segalman, C.R. Dohrmann, Dynamics of Rotating Flexible Structures by a Method of Quadratic Modes (Sandia National Laboratories, Structural Dynamics Division, Albuquerque, New Mexico, 1990)

    Google Scholar 

  10. D.J. Segalman, C.R. Dohrmann, A method for calculating the dynamics of rotating flexible structures, part1: derivation. ASME J. Vib. Acoust. 118, 313–317 (1996)

    Article  Google Scholar 

  11. I.H. Shames, C.L. Dym, Energy and Finite Element Methods in Structural Mechanics (Hemisphere Publishing Corporation, New York, 1985)

    MATH  Google Scholar 

  12. W. Su, C.E.S. Cesnik, Strain-based analysis for geometrically nonlinear beams: a modal approach, in 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference (Honolulu, Hawaii, 2013)

    Google Scholar 

  13. L.H. van Zyl, E.H. Mathews, Quadratic mode shape components from linear finite element analysis. ASME J. Vib. Acoust. 134 (2012)

    Google Scholar 

  14. L.H. van Zyl, A.N. Sutherland, P.S. Rossouw, Parabolic mode shapes: What they are, where to get them and what to do with them (International Forum on Aeroelasticity and Structural Dynamics, Seattle, Washington, 2009)

    Google Scholar 

  15. X.Q. Wang, R.A. Perez, M.P. Mignolet, Nonlinear reduced order modeling of complex wing models, in 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (Boston, Massachusetts, 2013)

    Google Scholar 

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Acknowledgements

Parts of this work were carried out during two internships of the author at the Active Aeroelasticity and Structures Research Lab at the University of Michigan. The author would like to thank the entire team and especially Prof. Carlos Cesnik of the laboratory for their support. Furthermore, the support of the DLR Institute of Aeroelasticity and the LUFO IV Verbundvorhaben AeroStruct for this work is gratefully acknowledged.

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Correspondence to Markus Ritter .

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Ritter, M. (2018). A Method for the Calculation of Large Deformations in Aeroelastic Applications. In: Heinrich, R. (eds) AeroStruct: Enable and Learn How to Integrate Flexibility in Design. AeroStruct 2015. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 138. Springer, Cham. https://doi.org/10.1007/978-3-319-72020-3_17

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  • DOI: https://doi.org/10.1007/978-3-319-72020-3_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72019-7

  • Online ISBN: 978-3-319-72020-3

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