Advertisement

Frontiers of Structural and Civil Engineering

, Volume 10, Issue 4, pp 394–408 | Cite as

Design concepts of an aircraft wing: composite and morphing airfoil with auxetic structures

  • P. R. Budarapu
  • Sudhir Sastry Y B
  • R. Natarajan
Research Article

Abstract

This paper is categorized into two parts. (1) A frame work to design the aircraft wing structure and (2) analysis of a morphing airfoil with auxetic structure. The developed design frame work in the first part is used to arrive at the sizes of the various components of an aircraft wing structure. The strength based design is adopted, where the design loads are extracted from the aerodynamic loads. The aerodynamic loads acting on a wing structure are converted to equivalent distributed loads, which are further converted point loads to arrive at the shear forces, bending and twisting moments along the wing span. Based on the estimated shear forces, bending and twisting moments, the strength based design is employed to estimate the sizes of various sections of a composite wing structure. A three dimensional numerical model of the composite wing structure has been developed and analyzed for the extreme load conditions. Glass fiber reinforced plastic material is used in the numerical analysis. The estimated natural frequencies are observed to be in the acceptable limits. Furthermore, the discussed design principles in the first part are extended to the design of a morphing airfoil with auxetic structure. The advantages of the morphing airfoil with auxetic structure are (i) larger displacement with limited straining of the components and (ii) unique deformation characteristics, which produce a theoretical in-plane Poisson’s ratio of–1. Aluminum Alloy AL6061-T651 is considered in the design of all the structural elements. The compliance characteristics of the airfoil are investigated through a numerical model. The numerical results are observed to be in close agreement with the experimental results in the literature.

Keywords

wing design aerodynamic loads morphing airfoil auxetic structures negative Poisson’s ratio 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Frolov V. Strength of a composite material for structural applications. Mechanics of Composite Materials, 1987, 23(2): 148–154CrossRefGoogle Scholar
  2. 2.
    Budarapu P, Narayana T, Rammohan B, Rabczuk T. Directionality of sound radiation from rectangular panels. Applied Acoustics, 2015, 89: 128–140CrossRefGoogle Scholar
  3. 3.
    Budarapu P, Rammohan B, Vijay S, Satish B, Raghunathan R. Aero-elastic analysis of stiffened composite wing structure. Journal of Vibration Engineering & Technologies, 2009, 8(3): 255–264Google Scholar
  4. 4.
    Budarapu P R, Yb S S, Javvaji B, Mahapatra D R. Vibration analysis of multi-walled carbon nanotubes embedded in elastic medium. Frontiers of Structural and Civil Engineering, 2014, 8(2): 151–159CrossRefGoogle Scholar
  5. 5.
    Benloulo I S, Sánchez-Gálvez V. A new analytical model to simulate impact onto ceramic/composite armors. International Journal of Impact Engineering, 1998, 21(6): 461–471CrossRefGoogle Scholar
  6. 6.
    Rawal S. Metal-matrix composites for space applications. Journal of the Minerals Metals & Materials Society, 2001, 53(4): 14–17CrossRefGoogle Scholar
  7. 7.
    Tucker V. Gliding birds: the effect of variable wing span. Journal of Experimental Biology, 1987, 133: 33–58Google Scholar
  8. 8.
    Weiss P. Wings of change: shape-shifting aircraft ply future skyways. Science News, 2003, 164(23): 359CrossRefGoogle Scholar
  9. 9.
    Lentink D, Mueller U, Stamhuis E, de Kat R, van Gestel W, Veldhuis L, Henningsson P, Hedenstroem A, Videler J, van Leeuwen J. How swifts control their glide performance with morphing wings. Nature, 2007, 446(7139): 1082–1085CrossRefGoogle Scholar
  10. 10.
    Parrott G. Aerodynamics of gliding flight of a black vulture coragyps atratus. Journal of Experimental Biology, 1970, 53: 363–374Google Scholar
  11. 11.
    Newman B. Soaring and gliding flight of the black vulture. Journal of Experimental Biology, 1958, 35: 280–285Google Scholar
  12. 12.
    McGowan A, Washburn A, Horta L, Bryant R. Recent results from nasas morphing project. In: Proceedings of the 9th International Symposium on Smart Structures and Materials. SPIE 4698–11, San Diego, California, 2002Google Scholar
  13. 13.
    Campanile L, Sachau D. The belt-rib concept: a structronic approach to variable camber. Journal of Intelligent Material Systems and Structures, 2000, 11(3): 215–224CrossRefGoogle Scholar
  14. 14.
    Monner H, Sachau D, Breitbach E. Design aspects of the elastic trailing edge for an adaptive wing. In: Proceedings of the Research and Technology Organization. ADP010488, Ottawa, 1999, 1–8Google Scholar
  15. 15.
    Bueter A, Ehlert U, Sachau D, Breitbach E. Design aspects of the elastic trailing edge for an adaptive wing. In: Proceeding of RTO symposium on Active Control Technology. ADP011142, Braunschweig, 2000Google Scholar
  16. 16.
    Cadogan D, Smith T, Uhelsky F, MacCusick M. Morphing airfoil wing development for compact package unmanned aerial vehicles. In: Proceedings of the 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA, California, 2004, 3205–3217Google Scholar
  17. 17.
    Bae J, Seigler T, Inman D, Lee I. Aerodynamic and aeroelastic considerations of a variable span morphing wing. In: Proceedings of the 45th AIAA/ASME/ASCE/AHS/ASC. Structural Dynamics and Materials Conference, Aircraft, 2003, 40(4): 734–740Google Scholar
  18. 18.
    Trenker M. Design concepts for adaptive airfoils with dynamic transonic flow control. Journal of Aircraft, 2003, 40(4): 734–740CrossRefGoogle Scholar
  19. 19.
    Kudva J. Overview of the darpa smart wing project. Journal of Intelligent Material Systems and Structures, 2004, 15(4): 261–267CrossRefGoogle Scholar
  20. 20.
    Spadoni A, Ruzzene M, Scarpa F. Dynamic response of chiral trusscore assemblies. Journal of Intelligent Material Systems and Structures, 2006, 17(11): 941–952CrossRefGoogle Scholar
  21. 21.
    Thai C H, Nguyen-Xuan H, Bordas S P A, Nguyen-Thanh N, Rabczuk T. Static, free vibration and buckling analysis of laminated composite reissner-mindlin plates using nurbs-based isogeometric approach. International Journal for Numerical Methods in Engineering, 2012, 91(6): 571–603MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Nguyen-Xuan H, Nguyen-Thanh N, Bordas S, Rabczuk T. Isogeometric analysis of laminated composite plates using the higher-order shear deformation theory. Mechanics of Advanced Materials and Structures, 2015, 22(6): 451–469CrossRefGoogle Scholar
  23. 23.
    Phan-Dao H, Nguyen-Xuan H, Thai-Hoang C, Nguyen-Thoi T, Rabczuk T. An edge-based smoothed finite element method for analysis of laminated composite plates. International Journal of Computational Methods, 2013, 10(1): 1340005MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Kerfriden P, Schmidt K, Rabczuk T, Bordas S. Statistical extraction of process zones and representative subspaces in fracture of random composites. International Journal for Multiscale Computational Engineering, 2013, 11(3), 253–287CrossRefGoogle Scholar
  25. 25.
    Amiri F, Anitescu C, Arroyo M, Bordas S, Rabczuk T. Xlme interpolants, a seamless bridge between xfem and enriched meshless methods. Computational Mechanics, 2014, 53(1): 45–57MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Amiri F, Millán D, Shen Y, Rabczuk T, Arroyo M. Phase-field modeling of fracture in linear thin shells. Theoretical and Applied Fracture Mechanics, 2014, 69: 102–109CrossRefGoogle Scholar
  27. 27.
    Areias P, Rabczuk T. Finite strain fracture of plates and shells with configurational forces and edge rotation. International Journal for Numerical Methods in Engineering, 2013, 94(12): 1099–1122MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Areias P, Rabczuk T, Camanho P. Initially rigid cohesive laws and fracture based on edge rotations. Computational Mechanics, 2013, 52(4): 931–947CrossRefzbMATHGoogle Scholar
  29. 29.
    Areias P, Rabczuk T, Camanho P. Finite strain fracture of 2d problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics, 2014, 72: 50–63CrossRefGoogle Scholar
  30. 30.
    Areias P, Rabczuk T, Dias-da Costa D. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 2013a, 110: 113–137CrossRefzbMATHGoogle Scholar
  31. 31.
    Belytschko T, Lu Y, Gu L. Element-free galerkin methods. International Journal for Numerical Methods in Engineering, 1994, 37(2): 229–256MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Bordas S P A, Natarajan S, Kerfriden P, Augarde C E, Mahapatra D R, Rabczuk T, Pont S D. On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM). International Journal for Numerical Methods in Engineering, 2011, 86(4–5): 637–666CrossRefzbMATHGoogle Scholar
  33. 33.
    Bordas S, Rabczuk T, Nguyen-Xuan H, Natarajan S, Bog T, Nguyen V, Do M, Nguyen-Vinh H. Strain smoothing in fem and xfem. Computers & Structures, 2010, 88(23–24): 1419–1443CrossRefGoogle Scholar
  34. 34.
    Bordas S, Rabczuk T, Zi G. Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment. Engineering Fracture Mechanics, 2008, 75(5): 943–960CrossRefGoogle Scholar
  35. 35.
    Budarapu P, Gracie R, Bordas S, Rabczuk T. An adaptive multiscale method for quasi-static crack growth. Computational Mechanics, 2014, 53(6): 1129–1148CrossRefzbMATHGoogle Scholar
  36. 36.
    Budarapu P, Gracie R, Yang S, Zhuang X, Rabczuk T. Efficient coarse graining in multiscale modeling of fracture. Theoretical and Applied Fracture Mechanics, 2014, 69: 126–143CrossRefGoogle Scholar
  37. 37.
    Budarapu P R, Javvaji B, Sutrakar V K, Roy Mahapatra D, Zi G, Rabcz. Crack propagation in graphene. Journal of Applied Physics, 2015, 118(6): 382–395CrossRefGoogle Scholar
  38. 38.
    Cai Y, Zhu H, Zhuang X. A continuous/discontinuous deformation analysis (cdda) method based on deformable blocks for fracture modelling. Frontiers of Structural & Civil Engineering, 2013, 7(4): 369–378CrossRefGoogle Scholar
  39. 39.
    Cai Y, Zhuang X, Zhu H. A generalized and efficient method for finite cover generation in the numerical manifold method. International Journal of Computational Methods, 2013, 10(5): 1350028MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Ghorashi S, Valizadeh N, Mohammadi S, Rabczuk T. T-spline based xiga for fracture analysis of orthotropic media. Computers & Structures, 2015, 147: 138–146CrossRefGoogle Scholar
  41. 41.
    Liu G, Gu Y T. A local radial point interpolation method (lrpim) for free vibration analyses of 2-d solids. Journal of Sound and Vibration, 2001, 246(1): 29–46CrossRefGoogle Scholar
  42. 42.
    Nguyen-Thanh N, Kiendl J, Nguyen-Xuan H, Wuchner R, Bletzinger K, Bazilevs Y, Rabczuk T. Rotation free isogeometric thin shell analysis using pht-splines. Computer Methods in Applied Mechanics and Engineering, 2011, 200(47–48): 3410–3424MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Rabczuk T, Areias P, Belytschko T. A meshfree thin shell method for nonlinear dynamic fracture. International Journal for Numerical Methods in Engineering, 2007, 72(5): 524–548MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Rabczuk T, Belytschko T. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343CrossRefzbMATHGoogle Scholar
  45. 45.
    Rabczuk T, Belytschko T. Application of particle methods to static fracture of reinforced concrete structures. International Journal of Fracture, 2006, 137(1–4): 19–49CrossRefzbMATHGoogle Scholar
  46. 46.
    Rabczuk T, Belytschko T. A three dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Rabczuk T, Belytschko T, Xiao S. Stable particle methods based on lagrangian kernels. Computer Methods in Applied Mechanics and Engineering, 2004, 193(12–14): 1035–1063MathSciNetCrossRefzbMATHGoogle Scholar
  48. 48.
    Rabczuk T, Bordas S, Zi G. A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics. Computational Mechanics, 2007, 40(3): 473–495CrossRefzbMATHGoogle Scholar
  49. 49.
    Rabczuk T, Gracie R, Song J, Belytschko T. Immersed particle method for fluidstructure interaction. International Journal for Numerical Methods in Engineering, 2010, 81(1): 48–71MathSciNetzbMATHGoogle Scholar
  50. 50.
    Rabczuk T, Samaniego E. Discontinuous modelling of shear bands using adaptive meshfree methods. Computer Methods in Applied Mechanics and Engineering, 2008, 197(6–8): 641–658MathSciNetCrossRefzbMATHGoogle Scholar
  51. 51.
    Rabczuk T, Zi G. A meshfree method based on the local partition of unity for cohesive cracks. Computational Mechanics, 2007, 39(6): 743–760CrossRefzbMATHGoogle Scholar
  52. 52.
    Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A geometrically nonlinear three dimensional cohesive crack method for reinforced concrete structures. Engineering Fracture Mechanics, 2008, 75(16): 4740–4758CrossRefGoogle Scholar
  53. 53.
    Rabczuk T, Zi G, Gerstenberger G, Wall W. A new crack tip element for the phantom node method with arbitrary cohesive cracks. International Journal for Numerical Methods in Engineering, 2008, 75(5): 577–599CrossRefzbMATHGoogle Scholar
  54. 54.
    Talebi H, Silani M, Bordas S, Kerfriden P, Rabczuk T. A molecular dynamics/xfem coupling by a three-dimensional extended bridging domain with applications to dynamic brittle fracture. International Journal for Multiscale Computational Engineering, 2013, 11(6): 527–541CrossRefGoogle Scholar
  55. 55.
    Talebi H, Silani M, Bordas S, Kerfriden P, Rabczuk T. A computational library for multiscale modelling of material failure. Computational Mechanics, 2014, 53(5): 1047–1071MathSciNetCrossRefzbMATHGoogle Scholar
  56. 56.
    Talebi H, Silani M, Rabczuk T. Concurrent multiscale modelling of three dimensional crack and dislocation propagation. Advances in Engineering Software, 2015, 80: 82–92CrossRefGoogle Scholar
  57. 57.
    Yang S, Budarapu P, Mahapatra D, Bordas S, Zi G, Rabczuk T. A meshless adaptive multiscale method for fracture. Computational Materials Science, 2015a, 96: 382–395CrossRefGoogle Scholar
  58. 58.
    Zhuang X, Augarde C, Mathisen K. Fracture modelling using meshless methods and level sets in 3d: framework and modelling. International Journal for Numerical Methods in Engineering, 2012, 92(11): 969–998MathSciNetCrossRefzbMATHGoogle Scholar
  59. 59.
    Zhuang X, Huang R, Zhu H, Askes H, Mathisen K. A new and simple lockingfree triangular thick plate element using independent shear degrees of freedom. Finite Elements in Analysis and Design, 2013, 75: 1–7CrossRefzbMATHGoogle Scholar
  60. 60.
    Zhuang X, Zhu H, Augarde C. An improved meshless shepard and least square method possessing the delta property and requiring no singular weight function. Computational Mechanics, 2014, 53(2): 343–357MathSciNetCrossRefzbMATHGoogle Scholar
  61. 61.
    Zi G, Chen H, Xu J, Belytschko T. The extended finite element method for dynamic fractures. Shock and Vibration, 2005, 12(1): 9–23CrossRefGoogle Scholar
  62. 62.
    Ainsworth J, Collier C, Yarrington P, Lucking R, Locke J. Airframe wingbox preliminary design and weight prediction, Society of Allied Weight Engineers, (SAWE), 2010Google Scholar
  63. 63.
    Morishima R. Analysis of composite wing structures with a morphing leading edge, Dissertation for the Doctoral Degree, 2011Google Scholar
  64. 64.
    Arunkumar K, Lohith N, Ganesha B. Effect of ribs and stringer spacings on the weight of aircraft structure for aluminum material. Journal of Applied Sciences, 2012, 12(10): 1006–1012CrossRefGoogle Scholar
  65. 65.
    Kennedy G, Martins J. A comparison of metallic and composite aircraft wings using aerostructural design optimization’, American Institute of Aeronautics and Astronautics, 2012, 1–31Google Scholar
  66. 66.
    Sudhir Sastry Y B, Budarapu P R, Krishna Y, Devaraj S. Studies on ballistic impact of the composite panels. Theoretical and Applied Fracture Mechanics, 2014, 72: 2–12CrossRefGoogle Scholar
  67. 67.
    Sudhir Y, Budarapu P, Madhavi N, Krishna Y. Buckling analysis of thin wall stiffened composite panels. Computational Materials Science, 2015a, 96B: 459–471Google Scholar
  68. 68.
    Sudhir Y, Krishna Y, Budarapu P. Parametric studies on buckling of thin walled channel beams. Computational Materials Science, 2015b, 96B: 416–424Google Scholar
  69. 69.
    Jones R. Mechanics of composite materials, Taylor and Francis, 1999Google Scholar
  70. 70.
    Reddy J. Mechanics of laminated composite plates theory and analysis, CRP press, 1997zbMATHGoogle Scholar
  71. 71.
    Prall D, Lakes R. Properties of a chiral honeycomb with a poissons ratio of–1. International Journal of Mechanical Sciences, 1997, 39 (3): 305–314CrossRefzbMATHGoogle Scholar
  72. 72.
    Spadoni A, Ruzzene M. Numerical and experimental analysis of the static compliance of chiral truss-core airfoils. Journal of Mechanics of Materials and Structures, 2007, 2(5): 965–981CrossRefGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • P. R. Budarapu
    • 1
  • Sudhir Sastry Y B
    • 2
  • R. Natarajan
    • 3
  1. 1.Department of Aerospace EngineeringIndian Institute of ScienceBangaloreIndia
  2. 2.Department of Aeronautical Engineering, College of EngineeringDefence UniversityBishoftuEthiopia
  3. 3.Department of Aeronautical EngineeringInstitute of Aeronautical EngineeringHyderabadIndia

Personalised recommendations