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

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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.

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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).

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Authors and Affiliations

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

    Suchao Xie, Haihong Li, Weilin Yang & Ning Wang

  2. School of Traffic & Transportation Engineering, Central South University, Changsha, 410075, China

    Suchao Xie, Haihong Li, Weilin Yang & Ning Wang

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  1. Suchao Xie
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  2. Haihong Li
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  3. Weilin Yang
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Corresponding author

Correspondence to Suchao Xie.

Appendix: The response model expressions

Appendix: The response model expressions

$$ \left\{\begin{array}{l} SEA\left({t}_1,l,{t}_2\right)=5.4293+7.2608{t}_1-2.5437l+9.0345\times 10{t}_2-9.1004\times {10}^{-1}{t}_1l+5.0924{t}_1{t}_2\\ {}\kern5.5em -1.8194\times 10{lt}_2-4.0907\times {10}^{-1}{t}_1^2+7.2215\times {10}^{-1}{l}^2-5.7708\times 10{t}_2^2\\ {}\kern0.75em {F}_{\mathrm{ip}}\left({t}_1,l,{t}_2\right)=-5.3847\times 10+2.5157\times {10}^2{t}_1-3.6879\times 10l+1.5524\times {10}^3{t}_2+1.4469\times 10{t}_1l\\ {}\kern5.5em -3.2422\times {10}^2{t}_1{t}_2-7.5797\times 10{lt}_2+8.0893\times 10{t}_1^2+1.3296{l}^2-1.5297\times {10}^3{t}_2^2\end{array}\right. $$
(25)
$$ \left\{\begin{array}{l} SEA\left({t}_1,l,{t}_2\right)=2.6899+5.1669{t}_1+2.2503\times {10}^{-1}l+1.1962\times {10}^2{t}_2+3.7983{t}_1l-4.2414{t}_1{t}_2\\ {}\kern5.5em +1.3198\times 10{lt}_2+1.7465{t}_1^2-4.4787\times 10{l}^2-5.3831\times {10}^2{t}_2^2-1.0590{t}_1^3\\ {}\kern5.5em +2.4949\times {10}^{-1}{t}_1^2l+8.6905{t}_1^2{t}_2+4.1405\times {10}^{-1}{t}_1{l}^2-9.2663{t}_1{t}_2^2-2.5470\times {10}^{-1}{l}^3\\ {}\kern5.5em +1.0197{l}^2{t}_2+2.1891\times {10}^2{lt}_2^2-6.0143\times {10}^2{t}_2^3-5.9707{t}_1{lt}_2\\ {}\kern0.5em {F}_{\mathrm{ip}}\left({t}_1,l,{t}_2\right)=5.8532\times 10+2.2143\times 10{t}_1+5.3372\times 10l+4.3323\times {10}^2{t}_2+1.9595\times {10}^2{t}_1l\\ {}\kern5.5em -7.0287\times 10{t}_1{t}_2+1.8788\times {10}^3{lt}_2+9.4917{t}_1^2-8.7496\times {10}^2{l}^2-1.8339\times {10}^2{t}_2^2\\ {}\kern5.5em -2.5422\times 10{t}_1^3+3.2528\times 10{t}_1^2l-7.1320\times {10}^2{t}_1^2{t}_2-2.5494{t}_1{l}^2+1.6717\times {10}^3{t}_1{t}_2^2\\ {}\kern5.5em -2.7446\times {l}^3+3.0245\times {10}^2{l}^2{t}_2-6.7908\times {10}^3{lt}_2^2+7.0637\times {10}^4{t}_2^3-6.0870\times 10{t}_1{lt}_2\end{array}\right. $$
(26)
$$ \left\{\begin{array}{l} SEA\left({t}_1,l,{t}_2\right)=4.2504-1.5522{t}_1+3.2558l+1.2346\times {10}^2{t}_2+9.4737{t}_1l-8.9827{t}_1{t}_2+7.0319\times 10{lt}_2\\ {}\kern5.25em +2.8337{t}_1^2-6.9972\times 10{l}^2-9.3459\times {10}^2{t}_2^2-8.5163\times {10}^{-1}{t}_1^3+3.0146\times {10}^{-1}{t}_1^2l\\ {}\kern5.25em -5.2452\times 10{t}_1^2{t}_2+4.1492\times {10}^{-1}{t}_1{l}^2-4.6929\times {10}^2{t}_1{t}_2^2-5.8993\times {10}^{-1}{l}^3-1.1569\times 10{l}^2{t}_2\\ {}\kern5.25em +4.4322\times {10}^2{lt}_2^2+6.2740\times {10}^3{t}_2^3+4.8326\times 10{t}_1{lt}_2-4.4016\times {10}^{-1}{t}_1^4+1.1376\times {10}^{-1}{t}_1^3l\\ {}\kern5.25em +1.8190\times 10{t}_1^3{t}_2+3.7226\times {10}^{-1}{t}_1^2{l}^2-1.9123\times 10{t}_1^2{lt}_2+2.6813\times 10{t}_1^2{t}_2^2-1.8282\times {10}^{-1}{t}_1{l}^3\\ {}\kern5.25em +5.2507\times {10}^2{t}_1{t}_2^3+4.1631{t}_1{l}^2{t}_2-9.2227{t}_1{lt}_2^2+6.9859\times {10}^{-2}{l}^4+8.3131\times {10}^{-1}{l}^3{t}_2\\ {}\kern5.25em -3.9784\times 10{l}^2{t}_2^2-1.0875\times {10}^2{lt}_2^3-1.6046\times {10}^4{t}_2^4\\ {}{F}_{\mathrm{ip}}\left({t}_1,l,{t}_2\right)=8.4610\times 10-2.6757\times {10}^{-1}{t}_1+5.6740\times 10l+2.3631\times {10}^2{t}_2+1.8778\times {10}^2{t}_1l-7.3304\times 10{t}_1{t}_2\\ {}\kern5em +2.1952\times {10}^3{lt}_2+1.1026\times 10{t}_1^2-1.0190\times {10}^3{l}^2+2.7347\times {10}^3{t}_2^2-1.9417\times 10{t}_1^3+3.4157\times 10{t}_1^2l\\ {}\kern5em -9.1887\times {10}^2{t}_1^2{t}_2-9.3203{t}_1{l}^2-4.9820\times {10}^3{t}_1{t}_2^2+2.3687\times {10}^{-1}{l}^3+8.8992\times 10{l}^2{t}_2-1.8435\times {10}^3{lt}_2^2\\ {}\kern5em +3.3759\times {10}^4{t}_2^3+3.6268\times {10}^2{t}_1{lt}_2+8.2217\times {10}^{-2}{t}_1^4-2.3043{t}_1^3l+9.6678\times 10{t}_1^3{t}_2+2.8059{t}_1^2{l}^2\\ {}\kern5em -1.7176\times {10}^2{t}_1^2{lt}_2+2.5972\times {10}^3{t}_1^2{t}_2^2+5.6863\times {10}^{-1}{t}_1{l}^3-1.7193\times {10}^4{t}_1{t}_2^3-5.3559\times 10{t}_1{l}^2{t}_2\\ {}\kern5em +1.6725\times {10}^3{t}_1{lt}_2^2-7.1035\times {10}^{-1}{l}^4+7.8244\times 10{l}^3{t}_2-3.1931\times {10}^3{l}^2{t}_2^2+5.7306\times {10}^4{lt}_2^3\\ {}\kern5em -3.8206\times {10}^5{t}_2^4\end{array}\right. $$
(27)

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Xie, S., Li, H., Yang, W. et al. Crashworthiness optimisation of a composite energy-absorbing structure for railway vehicles. Struct Multidisc Optim 57, 1793–1807 (2018). https://doi.org/10.1007/s00158-017-1829-7

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