Structural and Multidisciplinary Optimization

, Volume 57, Issue 4, pp 1793–1807 | Cite as

Crashworthiness optimisation of a composite energy-absorbing structure for railway vehicles

INDUSTRIAL APPLICATION

Abstract

By coupling thin-walled metal and aluminium honeycomb structures, a composite energy-absorbing structure with a high strength to weight ratio was designed. The validity of equivalent models of the thin-walled metal structure and the aluminium honeycomb was separately verified by carrying out trolley impact and quasi-static compression tests. The polynomial response surface models (PRSMs) of specific energy absorption (SEA) and initial peak force (F ip) during a collision were respectively established based on an orthogonal experimental design (OED) and the polynomial response surface method. The precisions of the three PRSMs were, in descending order, quartic, cubic, and quadratic PRSM (PRSM-4 > PRSM-3 > PRSM-2) as found by error analysis. The three PRSMs were separately optimised by using single-objective particle swarm optimisation (SOPSO) and the optimal values of SEA and F ip within the design range obtained from the PRSM-4 were respectively 33.5224 kJ/kg and 231.6860 kN among these PRSMs. The relative errors between the above optimal results of the PRSM-4, and the results obtained by numerical simulation, were 0 and −0.67%, respectively. Moreover, a Pareto front of double optimisation objective SEA and F ip was obtained after being optimised by multi-objective particle swarm optimisation (MOPSO), and SEA max was 33.0936 kJ/kg (the maximum SEA) and \( {F}_{{\mathrm{ip}}_{\mathrm{min}}} \) was 232.3510 kN (the minimum F ip) as separately obtained by using the PRSM-4. The errors between the above results and those (SEA = 33.5224 kJ/kg and F ip = 233.2406 kN) obtained through numerical simulation were separately 1.28% and −0.38%, which also indicates that the optimisation result is reliable.

Keywords

Composite energy-absorbing structure Polynomial response surface method Particle swarm optimisation Experiment Numerical simulation 

Notes

Acknowledgements

This research was undertaken at the Key Laboratory for Traffic Safety on Track of the Ministry of Education, Central South University, China. The authors gratefully acknowledge the support from the National Natural Science Foundation of China (Grant nos. 51775558, 51405516) and the support from the Shenghua Yu-ying Talents Program of the Central South University (Principle Investigator: Prof. Suchao Xie).

References

  1. Abedrabbo N, Mayer R, Thompson A, Salisbury C, Worswick M, van Riemsdijk I (2009) Crash response of advanced high-strength steel tubes: experiment and model. Int J Impact Eng 36(8):1044–1057CrossRefGoogle Scholar
  2. Alavi Nia A, Parsapour M (2013) An investigation on the energy absorption characteristics of multi-cell square tubes. Thin-Walled Struct 68:26–34CrossRefGoogle Scholar
  3. Azaza M, Wallin F (2017) Multi objective particle swarm optimization of hybrid micro-grid system: a case study in Sweden. Energy 123:108–118CrossRefGoogle Scholar
  4. Biqiang Z, Xiaodong L, Yajun Z (2016) The structure optimization analysis of electric vehicle in small offset rear end collision. Procedia Engineering 137:103–108CrossRefGoogle Scholar
  5. Duddeck F, Hunkeler S, Lozano P, Wehrle E, Zeng D (2016) Topology optimization for crashworthiness of thin-walled structures under axial impact using hybrid cellular automata. Struct Multidiscip Optim 54:415–428CrossRefGoogle Scholar
  6. Gao GJ, Tian HQ (2007) Train's crashworthiness design and collision analysis. Int J Crashworthiness 12(1):21–28CrossRefGoogle Scholar
  7. Gibson LJ, Ashby MF (1997) Cellular solids: structure and properties. Cambridge University Press, CambridgeCrossRefMATHGoogle Scholar
  8. Hallquist JO (2006) LS-DYNA theory manual. Livermore Software Technology Corporation, CaliforniaGoogle Scholar
  9. Hong ST, Pan J, Tyan T, Prasad P (2006) Quasi-static crush behavior of aluminum honeycomb specimens under compression dominant combined loads. Int J Plast 22(1):73–109CrossRefMATHGoogle Scholar
  10. Karagoz S, Yildiz AR (2017) A comparison of recent metaheuristic algorithms for crashworthiness optimisation of vehicle thin-walled tubes considering sheet metal forming effects. Int J Veh Des 73(1/2/3):179–188CrossRefGoogle Scholar
  11. Khalkhali A, Mostafapour M, Tabatabaie SM, Ansari B (2016) Multi-objective crashworthiness optimization of perforated square tubes using modified NSGAII and MOPSO. Struct Multidiscip Optim 54(1):45–61CrossRefGoogle Scholar
  12. Kiani M, Yildiz AR (2016) A comparative study of non-traditional methods for vehicle crashworthiness and NVH optimization. Arch Comput Meth Eng 23(4):723–734MathSciNetCrossRefMATHGoogle Scholar
  13. Li J, Gao G, Dong H, Xie S, Guan W (2016a) Study on the energy absorption of the expanding–splitting circular tube by experimental investigations and numerical simulations. Thin-Walled Struct 103:105–114CrossRefGoogle Scholar
  14. Li C, Xiao Q, Tang Y, Li L (2016b) A method integrating Taguchi, RSM and MOPSO to CNC machining parameters optimization for energy saving. J Clean Prod 135:263–275CrossRefGoogle Scholar
  15. Ling L, Dhanasekar M, Thambiratnam DP (2017) Frontal collision of trains onto obliquely stuck road trucks at level crossings: derailment mechanisms and simulation. Int J Impact Eng 100:154–165CrossRefGoogle Scholar
  16. Liu Q, Xu X, Ma J, Wang J, Shi Y, Hui D (2017a) Lateral crushing and bending responses of CFRP square tube filled with aluminum honeycomb. Compos Part B 118:104–115CrossRefGoogle Scholar
  17. Liu G, Xie J, Xie S (2017b) Experimental and numerical investigations of a new U-shaped thin plate energy absorber subjected to bending and friction. Thin-Walled Struct 115:215–224CrossRefGoogle Scholar
  18. Peng Y, Deng W, Xu P, Yao S (2015) Study on the collision performance of a composite energy-absorbing structure for subway vehicles. Thin-Walled Struct 94:663–672CrossRefGoogle Scholar
  19. Perez RE, Behdinan K (2007) Particle swarm approach for structural design optimization. Comput Struct 85(19–20):1579–1588CrossRefGoogle Scholar
  20. Pholdee N, Bureerat S (2017) Hybrid real-code population-based incremental learning and differential evolution for many-objective optimisation of an automotive floor-frame. Int J Veh Des 73(1/2/3):20–53CrossRefGoogle Scholar
  21. Song X, Sun G, Li G, Gao W, Li Q (2013) Crashworthiness optimization of foam-filled tapered thin-walled structure using multiple surrogate models. Struct Multidiscip Optim 47(2):221–231MathSciNetCrossRefMATHGoogle Scholar
  22. Sun G, Li S, Liu Q, Li G, Li Q (2016) Experimental study on crashworthiness of empty/aluminum foam/honeycomb-filled CFRP tubes. Compos Struct 152:969–993CrossRefGoogle Scholar
  23. Sun G, Zhang H, Lu G, Guo J, Cui J, Li Q (2017a) An experimental and numerical study on quasi-static and dynamic crashing behaviors for tailor rolled blank (TRB) structures. Mater Des 118:175–197CrossRefGoogle Scholar
  24. Sun G, Pang T, Xu C, Zheng G, Song J (2017b) Energy absorption mechanics for variable thickness thin-walled structures. Thin-Walled Struct 118:214–228CrossRefGoogle Scholar
  25. Sun G, Zhang H, Fang J, Li G, Li Q (2017c) Multi-objective and multi-case reliability-based design optimization for tailor rolled blank (TRB) structures. Struct Multidiscip Optim 55(5):1899–1916CrossRefGoogle Scholar
  26. Sun G, Pang T, Fang J, Li G, Li Q (2017d) Parameterization of criss-cross configurations for multiobjective crashworthiness optimization. Int J Mech Sci 124-125:145–157CrossRefGoogle Scholar
  27. Vinayagar K, Senthil Kumar A (2017) Crashworthiness analysis of double section bi-tubular thin-walled structures. Thin-Walled Struct 112:184–193CrossRefGoogle Scholar
  28. Wang Z, Tian H, Lu Z, Zhou W (2014) High-speed axial impact of aluminum honeycomb – experiments and simulations. Compos Part B 56:1–8CrossRefGoogle Scholar
  29. Wang Z, Yao S, Lu Z, Hui D, Feo L (2016) Matching effect of honeycomb-filled thin-walled square tube—experiment and simulation. Compos Struct 157:494–505CrossRefGoogle Scholar
  30. Wu S, Zheng G, Sun G, Liu Q, Li G, Li Q (2016) On design of multi-cell thin-wall structures for crashworthiness. Int J Impact Eng 88:102–117CrossRefGoogle Scholar
  31. Wu Y, Liu Q, Fu J, Li Q, Hui D (2017) Dynamic crash responses of bio-inspired aluminum honeycomb sandwich structures with CFRP panels. Compos Part B.  https://doi.org/10.1016/j.compositesb.2017.03.030
  32. Xie S, Zhou H (2014) Impact characteristics of a composite energy absorbing bearing structure for railway vehicles. Compos Part B 67:455–463CrossRefGoogle Scholar
  33. Xie S, Zhou H (2015) Analysis and optimisation of parameters influencing the out-of-plane energy absorption of an aluminium honeycomb. Thin-Walled Struct 89:169–177CrossRefGoogle Scholar
  34. Xie S, Liang X, Zhou H, Li J (2016) Crashworthiness optimisation of the front-end structure of the lead car of a high-speed train. Struct Multidiscip Optim 53(2):339–347CrossRefGoogle Scholar
  35. Xu P, Yang C, Peng Y, Yao S, Zhang D, Li B (2016a) Crash performance and multi-objective optimization of a gradual energy-absorbing structure for subway vehicles. Int J Mech Sci 107:1–12CrossRefGoogle Scholar
  36. Xu P, Yang C, Peng Y, Yao S, Xing J, Li B (2016b) Cut-out grooves optimization to improve crashworthiness of a gradual energy-absorbing structure for subway vehicles. Mater Des 103:132–143CrossRefGoogle Scholar
  37. Yildiz AR (2013) Comparison of evolutionary-based optimization algorithms for structural design optimization. Eng Appl Artif Intell 26(1):327–333CrossRefGoogle Scholar
  38. Yildiz BS (2017) A comparative investigation of eight recent population-based optimisation algorithms for mechanical and structural design problems. Int J Veh Des 73(1/2/3):208–218CrossRefGoogle Scholar
  39. Yildiz BS, Lekesiz H (2017) Fatigue-based structural optimisation of vehicle components. Int J Veh Des 73(1/2/3):54–62CrossRefGoogle Scholar
  40. Yildiz AR, Saitou K (2011) Topology synthesis of multicomponent structural assemblies in continuum domains. J Mech Des 133:1–9CrossRefGoogle Scholar
  41. Yildiz AR, Solanki KN (2012) Multi-objective optimization of vehicle crashworthiness using a new particle swarm based approach. Int J Adv Manuf Technol 59(1–4):367–376CrossRefGoogle Scholar
  42. Yildiz AR, Kurtulus E, Demirci E, Betul YS, Karagoz S (2016a) Optimization of thin-wall structures using hybrid gravitational search and Nelder-mead algorithm. Materials Testing 58(1):75–78CrossRefGoogle Scholar
  43. Yildiz BS, Lekesiz H, Yildiz AR (2016b) Structural design of vehicle components using gravitational search and charged system search algorithms. Materials Testing 58(1):79–81CrossRefGoogle Scholar
  44. Zeng D, Duddeck F (2017) Improved hybrid cellular automata for crashworthiness optimization of thin-walled structures. Struct Multidiscip Optim 56(1):101–115Google Scholar
  45. Zhang X, Jin X, Qi W, Guo Y (2008) Vehicle crash accident reconstruction based on the analysis 3D deformation of the auto-body. Adv Eng Softw 39(6):459–465CrossRefGoogle Scholar
  46. Zhong ZH (1993) Finite element procedures for contact-impact problems. Oxford University Press, Oxford, pp 96–213Google Scholar
  47. Zhu G, Wang Z, Huo X, Cheng A, Li G, Zhou C (2017) Experimental and numerical investigation into axial compressive behaviour of thin-walled structures filled with foams and composite skeleton. Int J Mech Sci 122:104–119CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Suchao Xie
    • 1
    • 2
  • Haihong Li
    • 1
    • 2
  • Weilin Yang
    • 1
    • 2
  • Ning Wang
    • 1
    • 2
  1. 1.Key Laboratory of Traffic Safety on Track, Ministry of EducationCentral South UniversityChangshaChina
  2. 2.School of Traffic & Transportation EngineeringCentral South UniversityChangshaChina

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