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Isogeometric blended shells for dynamic analysis: simulating aircraft takeoff and the resulting fatigue damage on the horizontal stabilizer

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Abstract

Aircraft horizontal stabilizers are prone to fatigue damage induced by the flow separation from aircraft wings and the subsequent impingement on the stabilizer structure in its wake, which is known as a buffet event. In this work, the previously developed isogeometric blended shell approach is reformulated in a dynamic analysis setting for the simulation of aircraft takeoff using varying pitch angles. The proposed Kirchhoff–Love (KL) and continuum shell blending allows the critical structural components of the aircraft horizontal stabilizer to be modeled using continuum shells to obtain high-fidelity 3D stresses, whereas the less critical components are modeled using computationally efficient KL thin shells. The imposed aerodynamic loads are generated from a hybrid immersogeometric and boundary-fitted computational fluid dynamics (CFD) analysis to accurately record the dynamic excitation on the stabilizer external surface. Specifically, the entire aircraft except for the wings and stabilizers is immersed into a non-boundary-fitted fluid domain based on the immersogeometric analysis (IMGA) concept for computational savings, whereas the mesh surrounding the aircraft wing and stabilizers is boundary-fitted to accurately compute the aerodynamic loads on the stabilizer. The obtained time histories of the loads are then applied to dynamic blended shell analysis of the horizontal stabilizer, and the high-fidelity stress response is evaluated for subsequent fatigue assessment. A simple frequency-domain fatigue analysis is then carried out to evaluate the buffet-induced fatigue damage of the stabilizer. The results from both the steady-state and dynamic nonlinear blended shell analyses of a representative horizontal stabilizer demonstrate the numerical accuracy and computational efficiency of the proposed approach.

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References

  1. Liu N, Cui X, Xiao J, Lua J, Phan N (2020) A simplified continuum damage mechanics based modeling strategy for cumulative fatigue damage assessment of metallic bolted joints. Int J Fatigue 131:105302

    Article  Google Scholar 

  2. Liu N, Xiao J, Cui X, Liu P, Lua J (2019) A continuum damage mechanics (CDM) modeling approach for prediction of fatigue failure of metallic bolted joints. In: AIAA Scitech 2019 Forum, AIAA 2019-0237

  3. Kiendl J, Bletzinger K-U, Linhard J, Wüchner R (2009) Isogeometric shell analysis with Kirchhoff–Love elements. Comput Methods Appl Mech Eng 198:3902–3914

    Article  MathSciNet  MATH  Google Scholar 

  4. Kiendl J, Hsu M-C, Wu MCH, Reali A (2015) Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials. Comput Methods Appl Mech Eng 291:280–303

    Article  MathSciNet  MATH  Google Scholar 

  5. Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195

    Article  MathSciNet  MATH  Google Scholar 

  6. Liu N, Jeffers AE (2018) A geometrically exact isogeometric Kirchhoff plate: feature-preserving automatic meshing and C 1 rational triangular Bézier spline discretizations. Int J Numer Meth Eng 115(3):395–409

    Article  Google Scholar 

  7. Herrema AJ, Kiendl J, Hsu M-C (2019) A framework for isogeometric-analysis-based optimization of wind turbine blade structures. Wind Energy 22:153–170

    Article  Google Scholar 

  8. Liu N, Jeffers AE (2019) Feature-preserving rational Bézier triangles for isogeometric analysis of higher-order gradient damage models. Comput Methods Appl Mech Eng 357:112585

    Article  MATH  Google Scholar 

  9. Liu N , Jeffers AE (2018) Rational Bézier triangles for the analysis of isogeometric higher-order gradient damage models. In: 13th World congress on computational mechanics (WCCM XIII) and 2nd Pan American congress on computational mechanics (PANACM II), New York City, NY, USA

  10. Liu N (2018) Non-uniform rational B-splines and rational Bezier triangles for isogeometric analysis of structural applications. Ph.D. thesis, University of Michigan

  11. Johnson EL, Hsu M-C (2020) Isogeometric analysis of ice accretion on wind turbine blades. Comput Mech 66:311–322

    Article  MathSciNet  MATH  Google Scholar 

  12. Johnson EL, Laurence DW, Xu F, Crisp CE, Mir A, Burkhart HM, Lee C-H, Hsu M-C (2021) Parameterization, geometric modeling, and isogeometric analysis of tricuspid valves. Comput Methods Appl Mech Eng 384:113960

    Article  MathSciNet  MATH  Google Scholar 

  13. Takizawa K, Tezduyar TE, Otoguro Y, Terahara T, Kuraishi T, Hattori H (2017) Turbocharger flow computations with the space-time isogeometric analysis (ST-IGA). Comput Fluids 142:15–20

    Article  MathSciNet  MATH  Google Scholar 

  14. Takizawa K, Tezduyar TE, Terahara T (2016) Ram-air parachute structural and fluid mechanics computations with the space-time isogeometric analysis (ST-IGA). Comput Fluids 141:191–200

    Article  MathSciNet  MATH  Google Scholar 

  15. Takizawa K, Tezduyar TE, Sasaki T (2017) Aorta modeling with the element-based zero-stress state and isogeometric discretization. Comput Mech 59:265–280

    Article  MathSciNet  Google Scholar 

  16. Takizawa K, Tezduyar TE, Terahara T, Sasaki T (2017) Heart valve flow computation with the integrated space-time VMS, slip interface, topology change and isogeometric discretization methods. Comput Fluids 158:176–188

    Article  MathSciNet  MATH  Google Scholar 

  17. Liu N, Jeffers AE (2017) Isogeometric analysis of laminated composite and functionally graded sandwich plates based on a layerwise displacement theory. Compos Struct 176:143–153

    Article  Google Scholar 

  18. Liu N, Jeffers AE (2018) Adaptive isogeometric analysis in structural frames using a layer-based discretization to model spread of plasticity. Comput Struct 196:1–11

    Article  Google Scholar 

  19. Liu N, Beata PA, Jeffers AE (2019) A mixed isogeometric analysis and control volume approach for heat transfer analysis of nonuniformly heated plates. Numer Heat Transf Part B Fundam 75(6):347–362

    Article  Google Scholar 

  20. Benson DJ, Bazilevs Y, Hsu M-C, Hughes TJR (2011) A large deformation, rotation-free, isogeometric shell. Comput Methods Appl Mech Eng 200:1367–1378

    Article  MathSciNet  MATH  Google Scholar 

  21. Takizawa K, Tezduyar TE, Sasaki T (2019) Isogeometric hyperelastic shell analysis with out-of-plane deformation mapping. Comput Mech 63:681–700

    Article  MathSciNet  MATH  Google Scholar 

  22. Liu N, Ren X, Lua J (2020) An isogeometric continuum shell element for modeling the nonlinear response of functionally graded material structures. Compos Struct 237:111893

    Article  Google Scholar 

  23. Liu N, Hsu M-C, Lua J, Phan N (2022) A large deformation isogeometric continuum shell formulation incorporating finite strain elastoplasticity. Comput Mech. https://doi.org/10.1007/s00466-022-02193-8

    Article  Google Scholar 

  24. Hosseini S, Remmers JJC, Verhoosel CV, De Borst R (2014) An isogeometric continuum shell element for non-linear analysis. Comput Methods Appl Mech Eng 271:1–22

    Article  MathSciNet  MATH  Google Scholar 

  25. Guo Y, Ruess M (2015) A layerwise isogeometric approach for nurbs-derived laminate composite shells. Compos Struct 124:300–309

    Article  Google Scholar 

  26. Leonetti L, Liguori F, Magisano D, Garcea G (2018) An efficient isogeometric solid-shell formulation for geometrically nonlinear analysis of elastic shells. Comput Methods Appl Mech Eng 331:159–183

    Article  MathSciNet  MATH  Google Scholar 

  27. Herrema AJ, Johnson EL, Proserpio D, Wu MCH, Kiendl J, Hsu M-C (2019) Penalty coupling of non-matching isogeometric Kirchhoff–Love shell patches with application to composite wind turbine blades. Comput Methods Appl Mech Eng 346:810–840

    Article  MathSciNet  MATH  Google Scholar 

  28. Kiendl J, Bazilevs Y, Hsu M-C, Wüchner R, Bletzinger K-U (2010) The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches. Comput Methods Appl Mech Eng 199:2403–2416

    Article  MathSciNet  MATH  Google Scholar 

  29. Goyal A, Simeon B (2017) On penalty-free formulations for multipatch isogeometric Kirchhoff–Love shells. Math Comput Simul 136:78–103

    Article  MathSciNet  MATH  Google Scholar 

  30. Leonetti L, Liguori FS, Magisano D, Kiendl J, Reali A, Garcea G (2020) A robust penalty coupling of non-matching isogeometric Kirchhoff–Love shell patches in large deformations. Comput Methods Appl Mech Eng 371:113289

    Article  MathSciNet  MATH  Google Scholar 

  31. Liu N, Johnson EL, Rajanna MR, Lua J, Phan N, Hsu M-C (2021) Blended isogeometric Kirchhoff–Love and continuum shells. Comput Methods Appl Mech Eng 385:114005

    Article  MathSciNet  MATH  Google Scholar 

  32. Liu N, Lua J, Rajanna MR, Johnson EL, Hsu MC, Phan ND (2022) Buffet-induced structural response prediction of aircraft horizontal stabilizers based on immersogeometric analysis and an isogeometric blended shell approach. In: AIAA SCITECH 2022 forum, p 0852

  33. Bazilevs Y, Hsu M-C, Kiendl J, Wüchner R, Bletzinger K-U (2011) 3D simulation of wind turbine rotors at full scale. Part II: fluid–structure interaction modeling with composite blades. Int J Numer Methods Fluids 65:236–253

    Article  MATH  Google Scholar 

  34. Bazilevs Y, Hsu M-C, Scott MA (2012) Isogeometric fluid–structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines. Comput Methods Appl Mech Eng 249–252:28–41

    Article  MathSciNet  MATH  Google Scholar 

  35. Hsu M-C, Bazilevs Y (2012) Fluid–structure interaction modeling of wind turbines: simulating the full machine. Comput Mech 50:821–833

    Article  MATH  Google Scholar 

  36. Korobenko A, Hsu M-C, Akkerman I, Tippmann J, Bazilevs Y (2013) Structural mechanics modeling and FSI simulation of wind turbines. Math Models Methods Appl Sci 23(2):249–272

    Article  MathSciNet  MATH  Google Scholar 

  37. Bazilevs Y, Korobenko A, Deng X, Yan J (2014) Novel structural modeling and mesh moving techniques for advanced fluid–structure interaction simulation of wind turbines. Int J Numer Meth Eng 102(3–4):766–783

    MathSciNet  MATH  Google Scholar 

  38. Yan J, Korobenko A, Deng X, Bazilevs Y (2016) Computational free-surface fluid–structure interaction with application to floating offshore wind turbines. Comput Fluids 141:155–174

    Article  MathSciNet  MATH  Google Scholar 

  39. Korobenko A, Yan J, Gohari SMI, Sarkar S, Bazilevs Y (2017) FSI simulation of two back-to-back wind turbines in atmospheric boundary layer flow. Comput Fluids 158:167–175

    Article  MathSciNet  MATH  Google Scholar 

  40. Bazilevs Y, Yan J, Deng X, Korobenko A (2018) Computer modeling of wind turbines: 2. Free-surface FSI and fatigue-damage. Arch Comput Methods Eng 26:1101–1115

    Article  MathSciNet  Google Scholar 

  41. Hsu M-C, Kamensky D, Bazilevs Y, Sacks MS, Hughes TJR (2014) Fluid–structure interaction analysis of bioprosthetic heart valves: significance of arterial wall deformation. Comput Mech 54(4):1055–1071

    Article  MathSciNet  MATH  Google Scholar 

  42. Kamensky D, Hsu M-C, Schillinger D, Evans JA, Aggarwal A, Bazilevs Y, Sacks MS, Hughes TJR (2015) An immersogeometric variational framework for fluid–structure interaction: application to bioprosthetic heart valves. Comput Methods Appl Mech Eng 284:1005–1053

    Article  MathSciNet  MATH  Google Scholar 

  43. Hsu M-C, Kamensky D, Xu F, Kiendl J, Wang C, Wu MCH, Mineroff J, Reali A, Bazilevs Y, Sacks MS (2015) Dynamic and fluid–structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models. Comput Mech 55:1211–1225

    Article  MATH  Google Scholar 

  44. Xu F, Morganti S, Zakerzadeh R, Kamensky D, Auricchio F, Reali A, Hughes TJR, Sacks MS, Hsu M-C (2018) A framework for designing patient-specific bioprosthetic heart valves using immersogeometric fluid-structure interaction analysis. Int J Numer Methods Biomed Eng 34:e2938

    Article  MathSciNet  Google Scholar 

  45. Wu MCH, Zakerzadeh R, Kamensky D, Kiendl J, Sacks MS, Hsu M-C (2018) An anisotropic constitutive model for immersogeometric fluid–structure interaction analysis of bioprosthetic heart valves. J Biomech 74:23–31

    Article  Google Scholar 

  46. Balu A, Nallagonda S, Xu F, Krishnamurthy A, Hsu M-C, Sarkar S (2019) A deep learning framework for design and analysis of surgical bioprosthetic heart valves. Sci Rep 9:18560

    Article  Google Scholar 

  47. Xu F, Johnson EL, Wang C, Jafari A, Yang C-H, Sacks MS, Krishnamurthy A, Hsu M-C (2021) Computational investigation of left ventricular hemodynamics following bioprosthetic aortic and mitral valve replacement. Mech Res Commun 112:103604

    Article  Google Scholar 

  48. Kamensky D (2021) Open-source immersogeometric analysis of fluid–structure interaction using FEniCS and tIGAr. Comput Math Appl 81:634–648

    Article  MathSciNet  MATH  Google Scholar 

  49. Xu F, Bazilevs Y, Hsu M-C (2019) Immersogeometric analysis of compressible flows with application to aerodynamic simulation of rotorcraft. Math Models Methods Appl Sci 29:905–938

    Article  MathSciNet  MATH  Google Scholar 

  50. Tezduyar TE, Aliabadi SK, Behr M, Mittal S (1994) Massively parallel finite element simulation of compressible and incompressible flows. Comput Methods Appl Mech Eng 119:157–177

    Article  MATH  Google Scholar 

  51. Tezduyar T, Aliabadi S, Behr M, Johnson A, Kalro V, Litke M (1996) Flow simulation and high performance computing. Comput Mech 18:397–412

    Article  MATH  Google Scholar 

  52. Xu F, Schillinger D, Kamensky D, Varduhn V, Wang C, Hsu M-C (2016) The tetrahedral finite cell method for fluids: immersogeometric analysis of turbulent flow around complex geometries. Comput Fluids 141:135–154

    Article  MathSciNet  MATH  Google Scholar 

  53. Hsu M-C, Wang C, Xu F, Herrema AJ, Krishnamurthy A (2016) Direct immersogeometric fluid flow analysis using B-rep CAD models. Comput Aided Geom Des 43:143–158

    Article  MathSciNet  MATH  Google Scholar 

  54. Wang C, Xu F, Hsu M-C, Krishnamurthy A (2017) Rapid B-rep model preprocessing for immersogeometric analysis using analytic surfaces. Comput Aided Geom Des 52–53:190–204

    Article  MathSciNet  MATH  Google Scholar 

  55. Zhu Q, Xu F, Xu S, Hsu M-C, Yan J (2020) An immersogeometric formulation for free-surface flows with application to marine engineering problems. Comput Methods Appl Mech Eng 361:112748

  56. Saurabh K, Gao B, Fernando M, Xu S, Khanwale MA, Khara B, Hsu M-C, Krishnamurthy A, Sundar H, Ganapathysubramanian B (2021) Industrial scale large Eddy simulations with adaptive octree meshes using immersogeometric analysis. Comput Math Appl 97:28–44

    Article  MathSciNet  MATH  Google Scholar 

  57. Preumont A (1994) Random vibration and spectral analysis/Vibrations aléatoires et analyse spectral, vol 33. Springer, Berlin

    Book  MATH  Google Scholar 

  58. Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-\(\alpha \) method. J Appl Mech 60:371–75

    Article  MathSciNet  MATH  Google Scholar 

  59. Jansen KE, Whiting CH, Hulbert GM (2000) A generalized-\(\alpha \) method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190:305–319

    Article  MathSciNet  MATH  Google Scholar 

  60. Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid–structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37

    Article  MathSciNet  MATH  Google Scholar 

  61. Xu F, Moutsanidis G, Kamensky D, Hsu M-C, Murugan M, Ghoshal A, Bazilevs Y (2017) Compressible flows on moving domains: stabilized methods, weakly enforced essential boundary conditions, sliding interfaces, and application to gas-turbine modeling. Comput Fluids 158:201–220

    Article  MathSciNet  MATH  Google Scholar 

  62. Kozak N, Xu F, Rajanna MR, Bravo L, Murugan M, Ghoshal A, Bazilevs Y, Hsu M-C (2020) High-fidelity finite element modeling and analysis of adaptive gas turbine stator-rotor flow interaction at off-design conditions. J Mech 36:595–606

    Article  Google Scholar 

  63. Bazilevs Y, Takizawa K, Wu MCH, Kuraishi T, Avsar R, Xu Z, Tezduyar TE (2021) Gas turbine computational flow and structure analysis with isogeometric discretization and a complex-geometry mesh generation method. Comput Mech 67:57–84

    Article  MathSciNet  MATH  Google Scholar 

  64. Codoni D, Moutsanidis G, Hsu M-C, Bazilevs Y, Johansen C, Korobenko A (2021) Stabilized methods for high-speed compressible flows: toward hypersonic simulations. Comput Mech 67:785–809

    Article  MathSciNet  MATH  Google Scholar 

  65. Rajanna MR, Johnson EL, Codoni D, Korobenko A, Bazilevs Y, Liu N, Lua J, Phan ND, Hsu M-C (2022) Finite element methodology for modeling aircraft aerodynamics: development, simulation, and validation. Comput Mech. https://doi.org/10.1007/s00466-022-02178-7

    Article  MathSciNet  MATH  Google Scholar 

  66. Rajanna MR, Johnson EL, Codoni D, Korobenko A, Bazilevs Y, Liu N, Lua J, Phan ND, Hsu MC (2022) Finite element simulation and validation for aerospace applications: stabilized methods, weak Dirichlet boundary conditions, and discontinuity capturing for compressible flows. In AIAA SCITECH 2022 forum, p 1077

  67. Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Space-time finite element computation of complex fluid–structure interactions. Int J Numer Methods Fluids 64:1201-[object Object]

    Article  MATH  Google Scholar 

  68. Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8:83–130

    Article  MATH  Google Scholar 

  69. Pitoiset X, Preumont A (2000) Spectral methods for multiaxial random fatigue analysis of metallic structures. Int J Fatigue 22(7):541–550

    Article  Google Scholar 

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Acknowledgements

This work is supported by the U.S. Naval Air Systems Command (NAVAIR) under Grant No. N68335-20-C-0899. This support is gratefully acknowledged.

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Authors and Affiliations

  1. Global Engineering and Materials, Inc., Princeton, NJ, 08540, USA

    Ning Liu & Jim Lua

  2. Department of Mechanical Engineering, Iowa State University, Ames, IA, 50011, USA

    Manoj R. Rajanna & Ming-Chen Hsu

  3. Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Emily L. Johnson

  4. Structures Division, Naval Air Systems Command (NAVAIR), Patuxent River, MD, 20670, USA

    Nam Phan

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  1. Ning Liu
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Liu, N., Rajanna, M.R., Johnson, E.L. et al. Isogeometric blended shells for dynamic analysis: simulating aircraft takeoff and the resulting fatigue damage on the horizontal stabilizer. Comput Mech 70, 1013–1024 (2022). https://doi.org/10.1007/s00466-022-02189-4

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