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

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

References

[1] Frolov V. Strength of a composite material for structural applications. Mechanics of Composite Materials, 1987, 23(2): 148–154

[2] Budarapu P, Narayana T, Rammohan B, Rabczuk T. Directionality of sound radiation from rectangular panels. Applied Acoustics, 2015, 89: 128–140

[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): 255–264

[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): 151–159

[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): 461–471

[6] Rawal S. Metal-matrix composites for space applications. Journal of the Minerals Metals & Materials Society, 2001, 53(4): 14–17

[7] Tucker V. Gliding birds: the effect of variable wing span. Journal of Experimental Biology, 1987, 133: 33–58

[8] Weiss P. Wings of change: shape-shifting aircraft ply future skyways. Science News, 2003, 164(23): 359

[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): 1082–1085

[10] Parrott G. Aerodynamics of gliding flight of a black vulture coragyps atratus. Journal of Experimental Biology, 1970, 53: 363–374

[11] Newman B. Soaring and gliding flight of the black vulture. Journal of Experimental Biology, 1958, 35: 280–285

[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, 2002

[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): 215–224

[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, 1–8

[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, 2000

[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, 3205–3217

[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): 734–740

[18] Trenker M. Design concepts for adaptive airfoils with dynamic transonic flow control. Journal of Aircraft, 2003, 40(4): 734–740

[19] Kudva J. Overview of the darpa smart wing project. Journal of Intelligent Material Systems and Structures, 2004, 15(4): 261–267

[20] Spadoni A, Ruzzene M, Scarpa F. Dynamic response of chiral trusscore assemblies. Journal of Intelligent Material Systems and Structures, 2006, 17(11): 941–952

[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): 571–603

[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): 451–469

[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): 1340005

[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), 253–287

[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): 45–57

[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: 102–109

[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): 1099–1122

[28] Areias P, Rabczuk T, Camanho P. Initially rigid cohesive laws and fracture based on edge rotations. Computational Mechanics, 2013, 52(4): 931–947

[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: 50–63

[30] Areias P, Rabczuk T, Dias-da Costa D. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 2013a, 110: 113–137

[31] Belytschko T, Lu Y, Gu L. Element-free galerkin methods. International Journal for Numerical Methods in Engineering, 1994, 37(2): 229–256

[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): 637–666

[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): 1419–1443

[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): 943–960

[35] Budarapu P, Gracie R, Bordas S, Rabczuk T. An adaptive multiscale method for quasi-static crack growth. Computational Mechanics, 2014, 53(6): 1129–1148

[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: 126–143

[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): 382–395

[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): 369–378

[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): 1350028

[40] Ghorashi S, Valizadeh N, Mohammadi S, Rabczuk T. T-spline based xiga for fracture analysis of orthotropic media. Computers & Structures, 2015, 147: 138–146

[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): 29–46

[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): 3410–3424

[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): 524–548

[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): 2316–2343

[45] Rabczuk T, Belytschko T. Application of particle methods to static fracture of reinforced concrete structures. International Journal of Fracture, 2006, 137(1–4): 19–49

[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): 2777–2799

[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): 1035–1063

[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): 473–495

[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): 48–71

[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): 641–658

[51] Rabczuk T, Zi G. A meshfree method based on the local partition of unity for cohesive cracks. Computational Mechanics, 2007, 39(6): 743–760

[52] Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A geometrically non-linear three dimensional cohesive crack method for reinforced concrete structures. Engineering Fracture Mechanics, 2008, 75(16): 4740–4758

[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): 577–599

[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): 527–541

[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): 1047–1071

[56] Talebi H, Silani M, Rabczuk T. Concurrent multiscale modelling of three dimensional crack and dislocation propagation. Advances in Engineering Software, 2015, 80: 82–92

[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: 382–395

[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): 969–998

[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: 1–7

[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): 343–357

[61] Zi G, Chen H, Xu J, Belytschko T. The extended finite element method for dynamic fractures. Shock and Vibration, 2005, 12(1): 9–23

[62] Ainsworth J, Collier C, Yarrington P, Lucking R, Locke J. Airframe wingbox preliminary design and weight prediction, Society of Allied Weight Engineers, (SAWE), 2010

[65] Morishima R. Analysis of composite wing structures with a morphing leading edge, Dissertation for the Doctoral Degree, 2011

[66] 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): 1006–1012

[67] Kennedy G, Martins J. A comparison of metallic and composite aircraft wings using aerostructural design optimization’, American Institute of Aeronautics and Astronautics, 2012, 1–31

[68] 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: 2–12

[69] Sudhir Y, Budarapu P, Madhavi N, Krishna Y. Buckling analysis of thin wall stiffened composite panels. Computational Materials Science, 2015a, 96B: 459–471

[70] Sudhir Y, Krishna Y, Budarapu P. Parametric studies on buckling of thin walled channel beams. Computational Materials Science, 2015b, 96B: 416–424

[64] Jones R. Mechanics of composite materials, Taylor and Francis, 1999

[63] Reddy J. Mechanics of laminated composite plates theory and analysis, CRP press, 1997

[71] Prall D, Lakes R. Properties of a chiral honeycomb with a poissons ratio of −1. International Journal of Mechanical Sciences, 1997, 39(3): 305–314

[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): 965–981

Acknowledgements

Sudhir Sastry acknowledges the support of Department of Aeronautical Engineering, Institute of Aeronautical Engineering. Pattabhi Budarapu thankfully acknowledges the financial support from the IRSES.

RIGHTS & PERMISSIONS

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg