Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Deterministic versus reliability-based topology optimization of aeronautical structures

  • 564 Accesses

  • 7 Citations

Abstract

Aircraft design is a challenging process which is constantly looking for developing new and lighter structural components. The application of topology optimization techniques is growing widespread in the aeronautical industry as it has proven to be highly useful for saving important weight amounts in recent aircraft designs. The objective of this research is to obtain optimal and novel aeronautical architectures through topology optimization while considering uncertainty in loads and material properties. For this, a methodology that combines the Sequential Optimization and Reliability Assessment (SORA) with external optimization software has been developed in order to perform Reliability-Based Topology Optimization (RBTO). The methodology is then compared against the classical way of obtaining novel architectures in aeronautical industry, which lie in the application of Deterministic Topology Optimization (DTO) considering partial safety factors in some data influencing the structural responses. The comparison draws weight savings of up to 3 % in the examples proposed when applying RBTO which could be highly significant in an aircraft structure. Moreover it has been proven that when performing a RBTO approach the layout of the final design can be different depending on the safety level required, which may influence the next phases of aircraft design process.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

References

  1. Altair Optistruct User Manual (2013) Version 12, Altair Engineering Inc

  2. Aoues Y, Chateauneuf A (2010) Benchmark study of numerical methods for reliability-based design optimization. Struct Multidiscip Optim 41(2):277–294. doi:10.1007/s00158-009-0412-2

  3. Buchanan S (2007) Development of a wingbox rib for a passenger jet aircraft using design optimization and constrained to traditional design and manufacture requirements. Altair Engineering CAE Technology Conference, Michigan

  4. Choi SK, Grandhi RV, Canfield RA (2007) Reliability-based structural design. Springer, London

  5. Du X, Chen W (2004) Sequential optimization and reliability assessment method for efficient probabilistic design. J Mech Des Trans ASME 126(2):225–233. doi:10.1115/1.1666890

  6. Dunning P, Kim A, Mullineux G (2011) Introducing loading uncertainty in topology optimization. AIAA J 49(4):760–768. doi:10.2514/1.J050670

  7. Enevoldsen I, Sørensen JD (1994) Reliability-based optimization in structural engineering. Struct Saf 15(3):169–196. doi:10.1016/0167-4730(94)90039-6

  8. Grihon S, Krog L, Tucker A, Hertel K (2004) A380 weight savings using numerical structural optimization. 20th AAAF colloquium on material for aerospace applications, Paris, France; 763–766

  9. Hernandez S, Diaz J, Baldomir A, Cid M, López C (2013) Comparison of reliability based structural optimization methodologies in the design of aircraft structures. Safety, reliability, risk and life-cycle performance of structures and infrastructures—Proceedings of the 11th International Conference on Structural Safety and Reliability, ICCOSSAR 2013. New York, NY, 4943–4949

  10. James KA, Kennedy GJ, Martins JRRA (2014) Concurrent aerostructural topology optimization of a wing box. Comput Struct 134:1–17. doi:10.1016/j.compstruc.2013.12.007

  11. Jung HS, Cho S (2004) Reliability-based topology optimization of geometrically nonlinear structures with loading and material uncertainties. Finite Elem Anal Des 43(3):311–331. doi:10.1016/j.finel.2004.06.002

  12. Kang Z, Luo Y (2009) Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models. Comput Methods Appl Mech Eng 198(41–44):3228–3238. doi:10.1016/j.cma.2009.06.001

  13. Kang JN, Kim CI, Wang SM (2004) Reliability-based topology optimization for electromagnetic systems. COMPEL - Int J Comput Math Electric Electron Eng 23(3):715–723. doi:10.1108/03321640410540647

  14. Karadeniz H, Togan V, Vrouwenvelder T (2009) An integrated reliability-based design optimization of offshore towers. Reliab Eng Syst Saf 94:1510–1516. doi:10.1016/j.ress.2009.02.008

  15. Kaushik S (2007) Reliability-based multiobjective optimization for automotive crashworthiness and occupant safety. Struct Multidiscip Optim 33(3):255–268. doi:10.1007/s00158-006-0050-x

  16. Kharmanda G, Olhoff N, Mohamed A, Lemaire M (2004) Reliability based topology optimization. Struct Multidiscip Optim 26(5):295–307. doi:10.1007/s00158-003-0322-7

  17. Kim C, Wang S, Bae K-R, Moon H, Choi KK (2006) Reliability based topology optimization with uncertainties. J Mech Sci Technol 20(4):494–504. doi:10.1007/BF02916480

  18. Kim C, Wang S, Hwang I, Lee J. (2007) Application of reliability based topology optimization for microelectromechanical systems. AIAA J 45(12) 2926–2934. doi: 10.25114/1.28508

  19. Krog L, Tucker A (2002) Application of topology, sizing and shape optimization methods to optimal design of aircraft components. Altair Engineering Conference

  20. Krog L, Tucker A, Kemp M, Boyd R (2004) Topology optimization of aircraft wing box ribs. 10th AIAA/ ISSMO multidisciplinary analysis and optimization conference, code 65014, volume 3, Albany, New York, 2020–2030

  21. MATLAB R2013a (2013) Documentation

  22. Maute K, Allen M (2004) Conceptual design of aeroelastic structures by topology optimization. Struct Multidiscip Optim 27(1–2):27–42. doi:10.1007/s00158-003-0362-z

  23. Maute K, Frangopol DM (2003) Reliability-based design of MEMS mechanisms by topology optimization. Comput Struct 81(8–11):813–824. doi:10.1016/S0045-7949(03)00008-7

  24. Maute K, Reich GW (2006) Integrated multidisciplinary topology optimization approach to adaptive wing design. AIAA J Aircraft 43(1):253–263. doi:10.2514/1.12802

  25. Nataf A (1962) Détermination des distributions de probabilités dont les marges sont donnés. C R Acad Sci 225:42–43

  26. Nguyen TH, Song J, Paulino GH (2011) Single-loop system reliability based topology optimization considering statistical dependence between limit states. Struct Multidiscip Optim 44(5):593–611. doi:10.1007/s00158-011-0669-0

  27. Niemann S, Kolesnikov B, Lohse-Busch H, Hühne C, Querin OM, Toropov VV, Liu D (2013) The use of topology optimization in the conceptual design of next generation lattice composite aircraft fuselage structures. Aeronaut J 117(1197):1139–1154

  28. Rackwitz R, Fiessler B (1976) Note on discrete safety checking when using non-normal stochastic models for basic variables. load project working session. MIT, Cambridge

  29. Santos IR, Rocha de FA (2013) Topology optimization of multiple load case structures. IV International Symposium on Solid Mechanics—MecSol 2013. Porto Alegre, Rio Grande do Sul, Brazil

  30. Silva M, Tortorelli DA, Norato J, Ha C, Bae HR (2010) Component and system reliability-based topology optimization using a single loop method. Struct Multidiscip Optim 41(1):87–106. doi:10.1007/s00158-009-0401-5

  31. Stanford B, Dunning P (2014) Optimal topology of aircraft rib and spar structures under aeroelastic loads. 10th AIAA Multidisciplinary Design and Optimization Specialist Conference, Code 102896. AIAA, National Harbor

  32. Stanford B, Ifju P (2009) Aeroelastic topology optimization of membrane structures for micro air vehicles. Struct Multidiscip Optim 38(3):301–316. doi:10.1007/s0158-008-0292-x

  33. Stanford B, Beran P, Kobayashi MH (2012) Aeroelastic optimization of flapping wing venation: a cellular division approach. AIAA J 50(4):938–951

  34. Tu J, Choi KK, Park YH (1999) A new study on reliability-based design optimization. J Mech Des Trans ASME 121(4):557–564. doi:10.1115/1.2829449

  35. Wang Q, Lu Z, Zhou C (2011) New topology optimization method for wing leading-edge ribs. AIAA J Aircraft 48(5):1741–1748. doi:10.2514/1.C031362

  36. Youn BD, Choi KK, Park YH (2003) Hybrid analysis method for reliability-based design optimization. J Mech Des Trans ASME 125(2):221–232. doi:10.1115/1.1561042

  37. Youn BD, Choi KK, Yang RJ, Gu L (2004) Reliability-based design optimization for crashworthiness of vehicle side impact. Struct Multidiscip Optim 26(3–4):272–283. doi:10.1007/s00158-003-0345-0

  38. Zou T, Mahadevan S (2005) Multi-objective RBDO for automotive door quality design. SAE Technical Paper, Paper 2005-01-0346, Detroit, MI. doi: 10.4271/2005-01-0346

Download references

Acknowledgments

The research leading to these results is part of the research project DPI2013-41893-R received from the Spanish Ministry of Economy. Further funding has been received from the Galician Government (including FEDER funding) with reference GRC2013-056 and from the program FPU (University teacher training program) from the Spanish Ministry of Education, Culture and Sports.

Author information

Correspondence to Carlos López.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

López, C., Baldomir, A. & Hernández, S. Deterministic versus reliability-based topology optimization of aeronautical structures. Struct Multidisc Optim 53, 907–921 (2016). https://doi.org/10.1007/s00158-015-1363-4

Download citation

Keywords

  • Uncertainty
  • Topology optimization
  • Reliability
  • Aircraft design