International Journal of Aeronautical and Space Sciences

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
권호 표지
DOI QR코드

DOI QR Code

Static Aeroelastic Response of Wing-Structures Accounting for In-Plane Cross-Section Deformation

  • Varello, Alberto (Department of Mechanical and Aerospace Engineering, Politecnico di Torino) ;
  • Lamberti, Alessandro (Department of Mechanical and Aerospace Engineering, Politecnico di Torino) ;
  • Carrera, Erasmo (Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Faculty of Science, King Abdulaziz University)
  • Received : 2013.10.21
  • Accepted : 2013.12.12
  • Published : 2013.12.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, the aeroelastic static response of flexible wings with arbitrary cross-section geometry via a coupled CUF-XFLR5 approach is presented. Refined structural one-dimensional (1D) models, with a variable order of expansion for the displacement field, are developed on the basis of the Carrera Unified Formulation (CUF), taking into account cross-sectional deformability. A three-dimensional (3D) Panel Method is employed for the aerodynamic analysis, providing more accuracy with respect to the Vortex Lattice Method (VLM). A straight wing with an airfoil cross-section is modeled as a clamped beam, by means of the finite element method (FEM). Numerical results present the variation of wing aerodynamic parameters, and the equilibrium aeroelastic response is evaluated in terms of displacements and in-plane cross-section deformation. Aeroelastic coupled analyses are based on an iterative procedure, as well as a linear coupling approach for different free stream velocities. A convergent trend of displacements and aerodynamic coefficients is achieved as the structural model accuracy increases. Comparisons with 3D finite element solutions prove that an accurate description of the in-plane cross-section deformation is provided by the proposed 1D CUF model, through a significant reduction in computational cost.

Keywords

References

  1. Fung, Y.C., An Introduction to the Theory of Aeroelasticity, Dover Publications, 2008.
  2. Patil, M.J., Hodges D.H., and Cesnik C.E.S., "Nonlinear aeroelasticity and flight dynamics of high-altitude longendurance aircraft", Journal of Aircraft, Vol. 38, No. 1, 2001, pp. 88-94. https://doi.org/10.2514/2.2738
  3. Sulaeman, E., Kapania, R., and Haftka, R.T., "Parametric studies of flutter speed in a strut-braced wing", Proceeding of the 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA Paper 2002-1487, Denver, CO, April 2002
  4. Hodges, D.H., and Pierce, G.A., Introduction to Structural Dynamics and Aeroelasticity, Cambridge University Press, 2002.
  5. Sofla, A.Y.N., Meguid, S.A., Tan, K.T., and Yeo, W.K., "Shape morphing of aircraft wing: status and challenges", Materials & Design, Vol. 31, No. 3, 2010, pp.1284-1292. https://doi.org/10.1016/j.matdes.2009.09.011
  6. Gamboa, P., Vale, J., Lau, F.J.P., and Suleman, A., "Optimization of a morphing wing based on coupled aerodynamic and structural constraints", AIAA Journal, Vol. 47, No. 9, 2009, pp. 2087-2104. https://doi.org/10.2514/1.39016
  7. Suleman, A., and Costa. A.P., "Adaptive control of an aeroelastic flight vehicle using piezoelectric actuators", Computers & Structures, Vol. 82, No. 17-19, 2004, pp. 1303-1314. https://doi.org/10.1016/j.compstruc.2004.03.027
  8. Kota, S., Hetrick, J.A., Osborn, R., Paul, D., Pendleton, E., Flick, P., and Tilmann, C., "Design and application of compliant mechanisms for morphing aircraft structures", Proceedings of the SPIE Vol. 5054, Smart Structures and Materials 2003: Industrial and Commercial Applications of Smart Structures Technologies, San Diego, CA, 12 August 2003.
  9. Diaconu, C.G., Weaver, P.M., and Mattioni, F., "Concepts for morphing airfoil sections using bi-stable laminated composite structures", Thin-Walled Structures, Vol. 46, No. 6, 2008, pp. 689-701. https://doi.org/10.1016/j.tws.2007.11.002
  10. Lim, S.M., Lee, S., Park, H.C., Yoon, K.J. and Goo, N.S., "Design and demonstration of a biomimetic wing section using a lightweight piezo-composite actuator (LIPCA)", Smart Materials and Structures, Vol. 14, No. 4, 2005, pp. 496-503. https://doi.org/10.1088/0964-1726/14/4/006
  11. Elzey, D.M., Sofla, A.Y.N., and Wadley, H.N.G., "A shape memory-based multifunctional structural actuator panel", International Journal of Solids and Structures, Vol. 42, No. 7, 2005, pp. 1943-1955. https://doi.org/10.1016/j.ijsolstr.2004.05.034
  12. Bhardwaj, M.K., "Aeroelastic analysis of modern complex wings using ENSAERO and NASTRAN", Technical Report NASA 19980235582, 1995.
  13. Dowell, E.H., and Hall, K.C., "Modeling of fluidstructure interaction", Annual Review of Fluid Mechanics, Vol. 33, 2001, pp. 445-490. https://doi.org/10.1146/annurev.fluid.33.1.445
  14. Henshaw, M.J. de C. et al., "Non-linear aeroelastic prediction for aircraft applications", Progress in Aerospace Sciences, Vol. 43, No. 4-6, 2007, pp. 65-137. https://doi.org/10.1016/j.paerosci.2007.05.002
  15. Katz, J., and Plotkin, A., Low-Speed Aerodynamics, Cambridge University Press, 2001.
  16. Wang, Y., Wan, Z., and Yang, C., "Application of highorder panel method in static aeroelastic analysis of aircraft", Procedia Engineering, Vol. 31, 2012, pp. 136-144.
  17. Yang, C., Zhang, B.C., Wan, Z.Q., and Wang, Y.K., "A method for static aeroelastic analysis based on the highorder panel method and modal method", Science China Technological Sciences, Vol. 54, No. 3, 2011, pp. 741-748. https://doi.org/10.1007/s11431-010-4253-4
  18. Newman, J.C. III, Newman, P.A., Taylor, A.C. III, and Hou, G.J.W., "Efficient nonlinear static aeroelastic wing analysis", Computers & Fluids, Vol. 28, No. 4, 1999, pp. 615-628. https://doi.org/10.1016/S0045-7930(98)00047-4
  19. Bathe, K.J., Finite Element Procedures, Prentice Hall, Upper Saddle River, New Jersey, 1996.
  20. Kapania, K., and Raciti, S, "Recent advances in analysis of laminated beams and plates, part II: Vibrations and wave propagation", AIAA Journal, Vol. 27, No. 7, 1989, pp. 935-946. https://doi.org/10.2514/3.59909
  21. El Fatmi, R., "Non-uniform warping including the effects of torsion and shear forces. Part I: A general beam theory", International Journal of Solids and Structures, Vol. 44, No. 18-19, 2007, pp. 5912-5929. https://doi.org/10.1016/j.ijsolstr.2007.02.006
  22. Schardt, R., "Extension of the engineer's theory of bending to the analysis of folded plate structures", Der Stahlbau, Vol. 35, 1966, pp. 161-171.
  23. Silvestre, N., and Camotim, D., "Second-order generalised beam theory for arbitrary orthotropic materials", Thin-Walled Structures, Vol. 40, No. 9, 2002, pp. 791-820. https://doi.org/10.1016/S0263-8231(02)00026-5
  24. Berdichevsky, V.L., Armanios, E., and Badir, A., "Theory of anisotropic thin-walled closed-cross-section beams", Composites Engineering, Vol. 2, No. 5-7, 1992, pp. 411-432. https://doi.org/10.1016/0961-9526(92)90035-5
  25. Yu, W., Volovoi, V.V., Hodges, D.H., and Hong, X., "Validation of the variational asymptotic beam sectional analysis (VABS)", AIAA Journal, Vol. 40, No. 10, 2002, pp. 2105-2113. https://doi.org/10.2514/2.1545
  26. Patil, M.J., "Aeroelastic tailoring of composite box beams", Proceedings of the 35th Aerospace Sciences Meeting and Exhibit, AIAA Paper 97-0015, Reno, NV, January 1997.
  27. Librescu, L., and Song., O., "On the static aeroelastic tailoring of composite aircraft swept wings modelled as thinwalled beam structures", Composites Engineering, Vol. 2, No. 5-7, 1992, pp. 497-512. https://doi.org/10.1016/0961-9526(92)90039-9
  28. Qin, Z., and Librescu, L., "Aeroelastic instability of aircraft wings modelled as anisotropic composite thinwalled beams in incompressible flow", Journal of Fluids and Structures, Vol. 18, No. 1, 2003, pp. 43-61. https://doi.org/10.1016/S0889-9746(03)00082-3
  29. Jeon, S.M., and Lee, I., "Aeroelastic response and stability analysis of composite rotor blades in forward flight", Composites: Part B, Vol. 32, No. 1, 2001, pp. 249-257. https://doi.org/10.1016/S1359-8368(00)00061-5
  30. Friedmann, P.P., Glaz, B., and Palacios, R., "A moderate deflection composite helicopter rotor blade model with an improved cross-sectional analysis", International Journal of Solids and Structures, Vol. 46, No. 10, 2009, pp. 2186-2200. https://doi.org/10.1016/j.ijsolstr.2008.09.017
  31. Carrera, E., Giunta, G., and Petrolo, M., Beam Structures: Classical and Advanced Theories, John Wiley & Sons, 2011.
  32. Varello, A., Carrera, E., and Demasi, L., "Vortex lattice method coupled with advanced one-dimensional structural models", Journal of Aeroelasticity and Structural Dynamics, Vol. 2, No. 2, 2011, pp. 53-78.
  33. Varello, A., Demasi, L., Carrera, E., and Giunta, G., "An improved beam formulation for aeroelastic applications", Proceedings of the 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA Paper 2010-3032, Orlando, FL, 12-15, April 2010.
  34. Carrera, E., Varello, A., and Demasi, L., "A refined structural model for static aeroelastic response and divergence of metallic and composite wings", CEAS Aeronautical Journal, Vol. 4, No. 2, 2013, pp. 175-189. https://doi.org/10.1007/s13272-013-0063-2
  35. Petrolo, M., "Flutter analysis of composite lifting surfaces by the 1D Carrera Unified Formulation and the doublet lattice method", Composite Structures, Vol. 95, 2013, pp. 539-546. https://doi.org/10.1016/j.compstruct.2012.06.021
  36. Maskew, B., "Program VSAERO theory Document: a computer program for calculating nonlinear aerodynamic characteristics of arbitrary configurations", NASA contractor report CR-4023, 1987.
  37. Oosthuizen, P.H., and Carscallen, W.E., Compressible fluid flow, McGraw-Hill, 1997.
  38. Deperrois, A., Guidelines for XFLR5 v6.03, 2011.
  39. Carrera, E., and Varello, A., "Dynamic response of thin-walled structures by variable kinematic onedimensional models", Journal of Sound and Vibration, Vol. 331, No. 24, 2012, pp. 5268-5282. https://doi.org/10.1016/j.jsv.2012.07.006

Cited by

  1. Recent developments on refined theories for beams with applications vol.2, pp.2, 2015, https://doi.org/10.1299/mer.14-00298
  2. Aerodynamic and mechanical hierarchical aeroelastic analysis of composite wings vol.23, pp.9, 2016, https://doi.org/10.1080/15376494.2015.1121561
  3. Computational investigation of variation in wing aerodynamic load under effect of aeroelastic deformations vol.32, pp.10, 2018, https://doi.org/10.1007/s12206-018-0914-1