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Crashworthiness analysis and multi-objective optimization of expanding circular tube energy absorbers with cylindrical anti-clamber under eccentric loading for subway vehicles

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Abstract

This paper presents an investigation of the crashworthiness of expanding circular tube energy absorbers with a cylindrical anti-clamber under eccentric loading for subway vehicles. A finite-element model of energy absorbers is created and validated by two quasi-static experiments, and the strain rate sensitivity is evaluated using standard coefficients of the Cowper-Symonds constitutive model. A parametric study is performed using the validated finite-element models. It is found that the eccentric collision of two energy absorbers has a significant effect on their crashworthiness and leads to a decrease in the specific energy absorption (SEA) and an increase in the peak crushing force (PCF). The structural parameters of the energy absorber, including the wall thickness t, conical angle α, and punch radius rp, have a significant effect on its crashworthiness under different eccentric distances. Sobol sensitivity analysis is employed to analyze the effects of the design parameters (t, α, and rp) on the objective responses (EA and PCF). The results show that the design variables t and α have a greater effect on the sensitivity of the EA and PCF functions for the eccentric distance of h = 0 and 40 mm. The interaction between punch angle α and punch radius rp has significant effect on EA. To improve the crashworthiness of the expanding circular tubes, a multi-objective optimization is applied to achieve the maximum EA and minimum PCF values, and weight factors are introduced to investigate the crashworthiness optimization under single-eccentric loading and multiple-eccentric loading. The optimization solutions of the expanding circular tubes under different single-eccentric loadings have considerable implications. For multiple-eccentric loading, the results show that the crashworthiness of the expanding circular tube energy absorber can be better balanced.

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References

  • Abedi MM, Niknejad A, Liaghat GH, Nejad MZ (2012) Theoretical and experimental study on empty and foam-filled columns with square and rectangular cross section under axial compression. Int J Mech Sci 65(1):134–146

    Article  Google Scholar 

  • Almeida BPP, Alves ML, Rosa PAR, Brito AG, Martins PAF (2006) Expansion and reduction of thin-walled tubes using a die: Experimental and theoretical investigation. Int J Mach Tools Manuf 46(12–13):1643–1652

    Article  Google Scholar 

  • Choi WM, Kim JS, Jung HS, Kwon TS (2011) Study on rupture of tube type crash energy absorber using finite element method. World Acad Sci Eng Technol 76:595–607

    Google Scholar 

  • Choi WM, Kim JS, Jung HS, Kwon TS (2012) Influence of impact velocity on energy absorption characteristics and friction coefficient of expansion tube. Int J Crashworthiness 17(6):1–9

    Article  Google Scholar 

  • Daxner T, Rammerstorfer FG, Fischer FD (2005) Instability phenomena during the conical expansion of circular cylindrical shells. Comput Method Appl Mech 194(21–24):2591–2603

    Article  MATH  Google Scholar 

  • Djamaluddin F, Abdullah S, Ariffin AK, Nopiah ZM (2016) Finite element analysis and crashworthiness optimization of foam-filled double circular under oblique loading. Lat Am J Solids Stru 13(11):2176–2189

    Article  Google Scholar 

  • Gao Q, Wang LM, Wang YL, Wang CZ (2016) Crushing analysis and multiobjective crashworthiness optimization of foam-filled ellipse tubes under oblique impact loading. Thin-Walled Struct 100:105–112

    Article  Google Scholar 

  • Gao GJ, Guan WY, Li J, Dong HP, Zou X, Chen W (2017) Experimental investigation of an active–passive integration energy absorber for railway vehicles. Thin-Walled Struct 117:89–97

    Article  Google Scholar 

  • GB/T 228.1-2010 (2010) Metallic materials-tensile testing – part 1: method of test at room temperature. Standardization Administration of the People's Republic of China

  • Guan WY, Gao GJ, Li J, Yu Y (2018) Crushing analysis and multi-objective optimization of a cutting aluminium tube absorber for railway vehicles under quasi-static loading. Thin-Walled Struct 123:395–408

    Article  Google Scholar 

  • Hallquist JO (2007) LS-DYNA keyword user’s manual. Livermore Software Technology Corporation. 970:299–800.

  • Huang XD, Lu GX, Yu TX (2002) Energy absorption in splitting square metal tubes. Thin-Walled Struct 40(2):153–165

    Article  Google Scholar 

  • Jiang L, Shi YL, Cui YL (2002) Effect of low strain rate on strength of Q235 & 20MnSi steel. Heat Treat Met-UK 27(7):9–12

    Google Scholar 

  • Kamran M, Xue P, Ahmed N, Zahran MS, Hanif AAG (2017) Axial crushing of uni-sectional bi-tubular inner tubes with multiple outer cross-sections. Lat Am J Solids Stru 14(12):2198–2220

    Article  Google Scholar 

  • Karrech A, Seibi A (2010) Analytical model for the expansion of tubes under tension. J Mater Process Technol 210(2):356–362

    Article  Google Scholar 

  • Kwang HA, Jin SK, Hoon H (2008) Energy absorption of expansion tube considering local buckling characteristics. Int J Mod Phys B 22(31-32):5993–5999

    Google Scholar 

  • Li J, Gao GJ, Guan WY, Wang S, Yu Y (2018) Experimental and numerical investigations on the energy absorption of shrink circular tube under quasi-static loading. Int J Mech Sci 137:284–294

    Article  Google Scholar 

  • Liu Y, Qiu XM (2016) A theoretical study of the expansion metal tubes. Int J Mech Sci 114:157–165

    Article  Google Scholar 

  • Liu B, Villavicencio R, Soares CG (2013) Experimental and numerical plastic response and failure of pre-notched transversely impacted beams. Int J Mech Sci 77:314–332

    Article  Google Scholar 

  • Lu GX, Yu TX (2003) Energy absorption of structures and materials. Woodhead Publishing Limited, Cambridge

    Book  Google Scholar 

  • Lučanin V, Tanasković J, Milković D, Golubović S (2007) Experimental research of the tube absorbers of kinetic energy during collision. FME Trans 35(4):201–204

    Google Scholar 

  • Luo M, Yang J, Liu H, Liu H, Lu GX, Yu JL (2019) Energy absorption of expansion tubes using a conical-cylindrical die: Theoretical model. Int J Mech Sci 157:207–220

  • Mohammadiha O, Ghariblu H (2016) Crush response of variable thickness distribution inversion tubes under oblique loading. Thin-Walled Struct 109:159–173

    Article  Google Scholar 

  • Moreno C, Beaumont R, Hughes DJ, Williams T, Dashwood R (2017) Quasi-static and dynamic testing of splitting, expansion and expansion-splitting hybrid tubes under oblique loading. Int J Impact Eng 100:117–130

    Article  Google Scholar 

  • Morquio A, Riera JD (2004) Size and strain rate effects in steel structures. Eng Struct 26(5):669–679

    Article  Google Scholar 

  • Niknejad A, Moeinifard M (2012) Theoretical and experimental studies of the external inversion process in the circular metal tubes. Mater Des 40:324–330

    Article  Google Scholar 

  • Qiu N, Gao Y, Fang J, Feng ZX, Sun GY, Li Q (2015) Crashworthiness analysis and design of multi-cell hexagonal columns under multiple loading cases. Finite Elem Anal Des 104:89–101

    Article  Google Scholar 

  • Shakeri M, Salehghaffari S, Mirzaeifar R (2007) Expansion of circular tubes by rigid tubes as impact energy absorbers: experimental and theoretical investigation. Int J Crashworthiness 12(5):493–501

    Article  Google Scholar 

  • Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 55(1-3):271–280

    Article  MathSciNet  MATH  Google Scholar 

  • Taghipoor H, Damghani Nouri M (n.d.) Axial crushing and transverse bending responses of sandwich structures with lattice core. J Sandw Struct Mater 1099636218761321

  • Taghipoor H, Damghani Nouri M (2018a) Experimental and numerical investigation of lattice core sandwich beams under low-velocity bending impact. J Sandw Struct Mater 2018:1099636218761315

    Google Scholar 

  • Taghipoor H, Damghani Nouri M (2018b) Experimental and numerical study on energy absorption of lattice-core sandwich beam. Steel Compos Struct 27:135–147

    Google Scholar 

  • Tran TN, Hou SJ, Han X (2014) Theoretical prediction and crashworthiness optimization of multi-cell triangular tubes. Thin-Walled Struct 2014(82):183–195

    Article  Google Scholar 

  • Wang GG, Shan S (2007) Review of metamodeling techniques in support of engineering design optimization. J Mech Des 129(4):370–380

    Article  Google Scholar 

  • Xie SC, Liang XF, Zhou H, Li J (2016) Crashworthiness optimisation of the front-end structure of the lead car of a high-speed train. Struct Multidiscip O 53(2):339–347

    Article  Google Scholar 

  • Xie SC, Li HH, Yang CX, Yao SG (2018a) Crashworthiness optimisation of a composite energy-absorbing structure for subway vehicles based on hybrid particle swarm optimisation. Struct Multidiscip O 58(5):2291–2308

    Article  Google Scholar 

  • Xie SC, Li HH, Yang WL, Wang N (2018b) Crashworthiness optimisation of a composite energy-absorbing structure for railway vehicles. Struct Multidiscip O 57(4):1793–1807

    Article  Google Scholar 

  • Yan JL, Yao SG, Xu P, Peng Y, Shao H (2016) Theoretical prediction and numerical studies of expanding circular tubes as energy absorbers. Int J Mech Sci 105:206–214

    Article  Google Scholar 

  • Yang JL, Luo M, Hua YL, Lu GX (2010) Energy absorption of expansion tubes using a conical–cylindrical die: experiments and numerical simulation. Int J Mech Sci 52(5):716–725

    Article  Google Scholar 

  • Yao SG, Xiao XL, Xu P, Qu QY, Che QW (2018) The impact performance of honeycomb-filled structures under eccentric loading for subway vehicles. Thin-Walled Struct 123:360–370

    Article  Google Scholar 

  • Ying L, Dai MH, Zhang SZ, Ma HL, Hu P (2017) Multiobjective crashworthiness optimization of thin-walled structures with functionally graded strength under oblique impact loading. Thin-Walled Struct 117:165–177

    Article  Google Scholar 

Download references

Funding

The authors gratefully acknowledge financial support from the National Key R&D Program of China (2016YFB1200403), the National Natural Science Foundation of China (U1334208), the Strategic Leading Science and Technology Project of Central South University (ZLXD2017002), and the Fundamental Research Funds for the Central Universities of Central South University (2017gczd009 and 2018zzts026).

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Authors and Affiliations

  1. Key Laboratory of Traffic Safety on the Track, Central South University, Changsha, 410075, China

    Weiyuan Guan, Guangjun Gao, Yao Yu & Tianyu Zhuo

  2. Joint International Research Laboratory of Key Technology for Rail Traffic Safety Central South University, Changsha, 410075, China

    Weiyuan Guan, Guangjun Gao, Yao Yu & Tianyu Zhuo

  3. National & Local Joint Engineering Research Center of Safety Technology for Rail Traffic Vehicle, Central South University, Changsha, 410075, China

    Weiyuan Guan, Guangjun Gao, Yao Yu & Tianyu Zhuo

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  1. Weiyuan Guan
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  2. Guangjun Gao
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  3. Yao Yu
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  4. Tianyu Zhuo
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Correspondence to Guangjun Gao.

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Appendix: the quartic response model expressions

Appendix: the quartic response model expressions

$$ Case\ 1\kern0.5em \left\{\begin{array}{l} EA\left(t,\alpha, {r}_p\right)=-20821888.12+5861.45t+669.63\alpha +1918295.04{r}_p-1670.25{t}^2-33.47{\alpha}^2-66288.36{r_p}^2\\ {}\kern5.25em +0.23 t\alpha +12.83t{r}_p-1.38\alpha {r}_p+191.02{t}^3+0.79{\alpha}^3+1017.66{r_p}^3-8.06{t}^4-0.01{\alpha}^4-5.86{r_p}^4\\ {} PCF\left(t,\alpha, {r}_p\right)=-40793412.35+18026.95t+1708.27\alpha +3769382.79{r}_p-5154.69{t}^2-87.00{\alpha}^2-130658.09{r_p}^2\\ {}\kern6em +2.86 t\alpha +39.34t{r}_p-3.78\alpha {r}_p+588.89{t}^3+2.09{\alpha}^3+2011.81{r_p}^3-24.81{t}^4-0.02{\alpha}^4-11.61{r_p}^4\end{array}\right. $$
$$ Case\ 2\kern0.5em \left\{\begin{array}{l} EA\left(t,\alpha, {r}_p\right)=23422950.9-1978.3t-0.87\alpha -2129139.47{r}_p+556.41{t}^2+4.49{\alpha}^2+72552.10{r_p}^2\\ {}\kern5.25em -0.77 t\alpha +1.39t{r}_p+0.67\alpha {r}_p-64.64{t}^3-0.14{\alpha}^3-1098.27{r_p}^3-2.73{t}^4+0.0014{\alpha}^4-6.23{r_p}^4\\ {} PCF\left(t,\alpha, {r}_p\right)=-13314110.65+7931.14t+221.85\alpha +1222802.98{r}_p-2012.26{t}^2-10.62{\alpha}^2-42151.15{r_p}^2\\ {}\kern6em -0.81 t\alpha +1.89t{r}_p-0.24\alpha {r}_p+224.28{t}^3+0.24{\alpha}^3+645.68{r_p}^3-9.23{t}^4-0.0021{\alpha}^4-3.71{r_p}^4\end{array}\right. $$
$$ Case\ 3\kern0.5em \left\{\begin{array}{l} EA\left(t,\alpha, {r}_p\right)=-9727046.06+3902.51t+481.88\alpha +903372.56{r}_p-1113.97{t}^2-23.98{\alpha}^2-31473.62{r_p}^2\\ {}\kern5.25em -0.025 t\alpha +9.27t{r}_p-0.87\alpha {r}_p+127.16{t}^3+0.56{\alpha}^3+487.09{r_p}^3-5.36{t}^4+0.0047{\alpha}^4-2.83{r_p}^4\\ {} PCF\left(t,\alpha, {r}_p\right)=-33894430.10+15502.01t+1336.48\alpha +3130081.42{r}_p-4368.82{t}^2-67.90{\alpha}^2-108440.60{r_p}^2\\ {}\kern6em -1.94 t\alpha +29.98t{r}_p+2.89\alpha {r}_p+497.71{t}^3+1.63{\alpha}^3+1668.89{r_p}^3-20.91{t}^4-0.014{\alpha}^4-9.63{r_p}^4\end{array}\right. $$
$$ Case\ 4\kern0.5em \left\{\begin{array}{l} EA\left(t,\alpha, {r}_p\right)=1322834.65+1945.36t-294.51\alpha -107442.79{r}_p-557.93{t}^2-14.49{\alpha}^2-3200.46{r_p}^2-0.28 t\alpha \\ {}\kern5.25em +5.71t{r}_p+0.36\alpha {r}_p+63.31{t}^3-0.33{\alpha}^3+41.34{r_p}^3-2.67{t}^4+0.0026{\alpha}^4-0.19{r_p}^4\\ {} PCF\left(t,\alpha, {r}_p\right)=-27076712.71+12978.31t+964.63\alpha +2498144.64{r}_p-3583.14{t}^2-48.79{\alpha}^2-86473.34{r_p}^2\\ {}\kern6em -1.02 t\alpha +20.61t{r}_p-2.01\alpha {r}_p+406.55{t}^3+1.17{\alpha}^3+1329.77{r_p}^3-17.02{t}^4-0.01{\alpha}^4-7.67{r_p}^4\end{array}\right. $$
$$ Case\ 5\kern0.5em \left\{\begin{array}{l} EA\left(t,\alpha, {r}_p\right)=12368381.06-8.61t-106.60\alpha -1117880.34{r}_p-4.99{t}^2-37862.22{\alpha}^2-0.53{r_p}^2-0.53 t\alpha \\ {}\kern5.25em +2.16t{r}_p+0.16\alpha {r}_p+0.43{t}^3+0.09{\alpha}^3-569.59{r_p}^3-0.021{t}^4+0.0006{\alpha}^4-3.21{r_p}^4\\ {} PCF\left(t,\alpha, {r}_p\right)=-20160585.11+10451.95t+593.34\alpha +1857301.99{r}_p-2797.08{t}^2-29.72{\alpha}^2-64203.93{r_p}^2\\ {}\kern6em -0.11 t\alpha +11.26t{r}_p-1.12\alpha {r}_p+315.34{t}^3+0.71{\alpha}^3+986.08{r_p}^3-13.12{t}^4-0.006{\alpha}^4-5.68{r_p}^4\end{array}\right. $$

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Guan, W., Gao, G., Yu, Y. et al. Crashworthiness analysis and multi-objective optimization of expanding circular tube energy absorbers with cylindrical anti-clamber under eccentric loading for subway vehicles. Struct Multidisc Optim 61, 1711–1729 (2020). https://doi.org/10.1007/s00158-019-02427-z

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