Application of the topological optimization method for the structural synthesis of a stiffeners in a kink zone of a high aspect ratio wing

DOI: 10.34759/trd-2023-129-04


Balunov K. A.1*, Solyaev Y. O.2**, Golubkin K. S.***

1. Central Aerohydrodynamic Institute named after N.E. Zhukovsky (TsAGI), Zhukovsky, Moscow region, Russia
2. Institute of Applied Mechanics of Russian Academy of Science, IPRIM RAS, 7, Leningradskiy Prospekt, Moscow, 125040, Russia



The article considers an approach to the reinforced thin-walled structures design based on the topological optimization method application for models of variable thickness shells. The authors regard the problem of the optimal structural scheme selection of stiffeners in the kink zone of a high aspect ratio wing. The authors regard the problem on the structure-force scheme selection in the fracture zone of the high-aspect-ratio wing. The article contains the optimization problem formulation and computational results for the three variants of the wingtip sweep angle with the specified loading in the form of distributed aerodynamic pressure and concentrated forces at the points of the wing mechanization elements fixing. Numerical modeling is being performed with the models of Mindlin-Reissner type shells, which thickness is being determined by the values of the additional node variable, being introduced in the topological optimization problem. Optimal thicknesses distribution along the model elements at the specified limitations on the structure weight and stiffening fins height is being defined by the results of the optimization problem solution with the goal function in the form of the total energy of deformations, occurring in the solution. The solution regularization is being ensured by the minimum size selection of the finite element mesh elements. The article demonstrates that the applied technique and topological optimization results may be employed for optimal framing set configuration of reinforced thin-walled structures with enhanced weight effectiveness.


structural scheme, stiffeners geometry, topology optimization, design, reinforced panels, variable thickness shell models, wing kink zone


  1. Bendsøe M, Sigmund O Topology optimization: theory, methods, and applications, Springer, 2003, 370 p.
  2. Wang C. et al. Structural topology optimization considering both performance and manufacturability: strength, stiffness, and connectivity, Structural and Multidisciplinary Optimization, 2021, vol. 63 (3), pp. 1427-1453. DOI:10.1007/s00158-020-02769-z
  3. Ferrari F., Sigmund O. Revisiting topology optimization with buckling constraints, Structural and Multidisciplinary Optimization, 2019, vol. 59, no. 5, pp. 1401-1415. DOI:10.1007/s00158-019-02253-3
  4. Picelli R., Vicente W.M., Pavanello R., & Xie Y.M. Evolutionary topology optimization for natural frequency maximization problems considering acoustic—structure interaction, Finite Elements in Analysis and Design, 2015, vol. 106, pp. 56–64. DOI: 10.1016/j.finel.2015.07.010
  5. Yun K.-S., Youn S.-K. Microstructural topology optimization of viscoelastic materials of damped structures subjected to dynamic loads, International Journal of Solids and Structures, 2018, vol. 147, pp. 67–79. DOI: 10.1016/j.ijsolstr.2018.04.022
  6. Kambampati S., Townsend S., Kim, H.A. Aeroelastic Level Set Topology Optimization for a 3D Wing, 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2018. DOI: 10.2514/6.2018-2151
  7. Gao T., Xu P., Zhang W. Topology optimization of thermo-elastic structures with multiple materials under mass constraint, Computers & Structures, 2016, vol. 173, pp. 150-160. DOI: 10.1016/j.apm.2021.11.008
  8. Egorov I.A. Trudy MAI, 2022, no. 122. URL: DOI: 10.34759/trd-2022-122-04
  9. Sysoev O.E., Dobryshkin A.Yu., Sysoev E.O., Zhuravleva E.V. Trudy MAI, 2021, no. 117. URL: DOI: 10.34759/trd-2021-117-03
  10. Nizametdinov F.R., Sorokin F.D., Ivannikov V.V. Trudy MAI, 2019, no. 109. URL: DOI: 10.34759/trd-2019-109-2
  11. Lizin V.T., Pyatkin V.A. Proektirovanie tonkostennykh konstruktsii (Design of thin-walled structures. Tutorial), Moscow, Mashinostroenie, 2003, 448 p.
  12. Zhao X. et al. Simultaneous outline shape and size optimization for stiffeners in practical engineering structures, Acta Astronautica, 2022, vol. 191, pp. 216-226. DOI: 10.1016/j.actaastro.2021.10.003
  13. A. Dugr ́e, A. Vadean. et al. Challenges of using topology optimization for the design of pressurized stiffened panels, Structural and Multidisciplinary Optimization, 2016, vol. 53 (2), pp. 303–320. DOI:10.1007/s00158-015-1321-1
  14. M Rais-Rohani, J Lokits. Reinforcement layout and sizing optimization of composite submarine sail structures, Structural and Multidisciplinary Optimization, 2007, vol. 34(1), pp. 75–90. DOI:10.1007/s00158-006-0066-2
  15. Gamache J.F. et al. On generating stiffening layouts with density-based topology optimization considering buckling, CEAS Aeronautical Journal, 2021, vol. 12, no. 4, pp. 863-877. DOI:10.1007/s13272-021-00546-2
  16. Ma J. et al. Topology optimization of ribbed slabs and shells, Engineering Structures, 2023, vol. 277, pp. 115454. DOI:10.1016/j.engstruct.2022.115454
  17. Guy Bouchitt, Ilaria Fragal`a, Pierre Seppecher. Structural optimization of thin elastic plates: the three dimensional approach, Archive for rational mechanics and analysis, 2011, vol. 202(3), pp. 829-874. DOI:10.1007/s00205-011-0435-x
  18. Erik A Traff, Ole Sigmund, Niels Aage. Topology optimization of ultra high resolution shell structures Thin-Walled Structures, 2021, vol. 160, pp. 107349. DOI:10.1016/j.tws.2020.107349
  19. Haidong Lin, An Xu, Anil Misra, Ruohong Zhao. An ansys apdl code for topology optimization of structures with multi-constraints using the beso method with dynamic evolution rate (der-beso), Structural and Multidisciplinary Optimization, 2020, vol. 62(4), pp. 2229–2254. DOI:10.1007/s00158-020-02588-2
  20. Ivan Giorgio. Lattice shells composed of two families of curved kirchhoff rods: an archetyp-*al example, topology optimization of a cycloidal metamaterial, Continuum Mechanics and Thermodynamics, 2021, vol. 33(4), pp. 1063–1082. DOI:10.1007/s00161-020-00955-4
  21. Aage N. et al. Giga-voxe computational morphogenesis for structural design, Nature, 2017, vol. 550, no. 7674, pp. 84-86. DOI:10.1038/nature23911
  22. Lur’e K.A., Cherkaev A.V. Izvestiya RAN. Mekhanika tverdogo tela, 1976, no. 6, pp. 157-159.
  23. Julio Munoz and Pablo Pedregal. A review of an optimal design problem for a plate of variable thickness, SIAM journal on control and optimization, 2007, vol. 46(1), pp. 1-13. DOI:10.1137/050639569
  24. Keng-Tung Cheng, Niels Olhoff. An investigation concerning optimal design of solid elastic plates, International Journal of Solids and Structures, 1981, vol. 17(3), pp. 305–323. DOI:10.1016/0020-7683(81)90065-2
  25. Y. Lam, S. Santhikumar. Automated rib location and optimization for plate structures, Structural and multidisciplinary optimization, 2003, vol. 25 (1), pp. 35— 45. DOI:10.1007/s00158-002-0270-7
  26. Chzho Ie Ko, Solyaev Yu.O. Trudy MAI, 2021, no. 120. URL: DOI: 10.34759/trd-2021-120-07
  27. Vasiliev V.V., Morozov E.V. Advanced mechanics of composite materials and structures, Elsevier, 2018.
  28. Svanberg K. The method of moving asymptotes — a new method for structural optimization, International journal for numerical methods in engineering, 1987, vol. 24, no. 2, pp. 359-373. DOI:10.1002/NME.1620240207
  29. Balunov K, Chedrik V, Ishmuratov F, Karkle P. Aeroelastic optimization of wing shape and structural parameters for different aircraft configurations, 15th International Forum on Aeroelasticity and Structural Dynamics, IFASD 2015, Saint Petersburg, 2015, pp. 794-805.
  30. Balunov K, Chedrik V, Ishmuratov F. Structural design of wing tip part from aeroelasticity consideration, 17th International Forum on Aeroelasticity and Structural Dynamics, IFASD 2017, Como, Italy, 2017.

Download — informational site MAI

Copyright © 2000-2024 by MAI