Recent research development of energy-absorption structure and application for railway vehicles

Abstract

As the application of energy-absorption structure reaches an unprecedented scale in both academia and industry, a reflection upon the state-of-the-art developments in the crashworthiness design and structural optimization, becomes vital for successfully shaping the future energy-absorption structure. Physical impacting test and numerical simulation are the main methods to study the crashworthiness of railway vehicles at present. The end collision deformation area of the train can generally be divided into two kinds of structural design forms: integral absorbing structure design form and specific energy absorbing structure design form, and different energy-absorption structures introduced in this article can be equipped on different railway vehicles, so as to meet the balance of crashworthiness and economy. In pursuit of improving the capacity of energy dissipation in energy-absorption structures, studies are increasingly investigating multistage energy absorption systems, searching breakthrough when the energy dissipation capacity of the energy-absorption structure reaches its limit. In order to minimize injuries, a self-protective posture for occupants is also studied. Despite the abundance of energy-absorption structure research methods to-date, the problems of analysis and prediction during impact are still scarce, which is constituting one of many key challenges for the future.

Keywords

railway vehicle / energy-absorption structure / crashworthiness

References

[1] MarsolekJ, ReimerdesH G. Energy absorption of metallic cylindrical shells with induced non-axisymmetric folding patterns [J]. International Journal of Impact Engineering, 2004, 30: 1209-1223

[2] European Committee for Standardization. EN 12663: 2007. Railway applications: Structural requirements of railway vehicle bodies [S]. London (UK): British Standard Published.

[3] European Committee for Standardization. EN 15227:2008. Railway applications: Crashworthiness requirements for railway vehicle bodies [S]. London (UK): British Standard Published.

[4] European Railway AgencyTechnical specification for interoperability [S], 2002, EU, Railway Interoperability and Safety Committee

[5] British Standards Institution. Railway group standard GM/RT2100. Structural requirements for railway vehicles [S]. London (UK): RSSB.

[6] Federal Railroad Administration. Improving railroad safety and rail passenger technology through targeted research demonstrations: 1992–1997 [R]. 1999.

[7] MAYVILLE R A, STRINGFELLOW R G, RANCATORE R J. LOcomotive crashworthiness research. Final report. Volume 5: cab car crashworthiness report [R]. 1996.

[8] SEVERSON K J, PARENT D P, TYRELL D C. Two-car impact test of crash-energy management passenger rail cars: Analysis of occupant protection measurements [C]// ASME 2004 International Mechanical Engineering Congress and Exposition. New York, 2004: 87–96.

[9] STRANG J, HYNES R, PEACOCK T. Development of crash energy management specification for passenger rail equipment [J]. Transp Res Record, 2007: 76–83. DOI: https://doi.org/10.1109/RRCON.2006.215303.

[10] TYRELL D. Liquefied natural gas tender crashworthiness research [C]// 2015 Joint Rail Conference. New York: 2015: V001T02A015.

[11] HaN S, LuG. A review of recent research on bio-inspired structures and materials for energy absorption applications [J]. Composites Part B: Engineering, 2020, 181(8): 107496

[12] ChambeJ E, BouvetC, DorivalO, FerreroJ. Energy absorption capacity of composite thin-wall circular tubes under axial crushing with different trigger initiations [J]. Journal of Composite Materials, 2019, 9: 0021998319877221

[13] YalcinM M, GenelK. On the axial deformation characteristic of PVC foam-filled circular aluminium tube: Effect of radially-graded foam filling [J]. Thin-Walled Structures, 2019, 14411106335

[14] TianK, ZhangY, YangF, ZhaoQ, FanH L. Enhancing energy absorption of circular tubes under oblique loads through introducing grooves of non-uniform depths [J]. International Journal of Mechanical Sciences, 2020, 1661105239

[15] IsaacC W. Crushing response of circular thin-walled tube with non-propagating crack subjected to dynamic oblique impact loading [J]. International Journal of Protective Structures, 2020, 11341-68

[16] AlaviN A, ParsapourM. Comparative analysis of energy absorption capacity of simple and multi-cell thin-walled tubes with triangular, square, hexagonal and octagonal sections [J]. Thin-Walled Structures, 2014, 74(1): 155-165

[17] HongW, LaiC, FanH. Frusta structure designing to improve quasi-static axial crushing performances of triangular tubes [J]. International Journal of Steel Structures, 2016, 16(1): 257-266

[18] GoyalS, AnandC S, SharmaS K, SharmaR. Crashworthiness analysis of foam filled star shape polygon of thin-walled structure [J]. Thin-Walled Structures, 2019, 144(11): 106312

[19] LiuW Y, LinZ Q, WangN L, DengX. Dynamic performances of thin-walled tubes with star-shaped cross section under axial impact [J]. Thin-Walled Structures, 2016, 100325-37

[20] TiwariG, IqbalM A, GuptaP K. Energy absorption characteristics of thin aluminium plate against hemispherical nosed projectile impact [J]. Thin-Walled Structures, 2018, 126246-257

[21] DaoT D, HaN S, GooN S, YuW R. Design, fabrication, and bending test of shape memory polymer composite hinges for space deployable structures [J]. Journal of Intelligent Material Systems and Structures, 2018, 29(8): 1560-1574

[22] LiuJ, ZhengB, ZhangK, YangB, YuX. Ballistic performance and energy absorption characteristics of thin nickel-based alloy plates at elevated temperatures [J]. International Journal of Impact Engineering, 2019, 126: 160-171

[23] YahayaM A, RuanD, LuG, DarguschM S. Response of aluminium honeycomb sandwich panels subjected to foam projectile impact-An experimental study [J]. International Journal of Impact Engineering, 2015, 75: 100-109

[24] Alantalia, AliaR A, Umerr, CantwellW J. Energy absorption in aluminium honeycomb cores reinforced with carbon fibre reinforced plastic tubes [J]. Journal of Sandwich Structures & Materials, 2019, 21(11): 2801-2815

[25] KangH G, KimJ K. Damage mitigation of a steel column subjected to automobile collision using a honeycomb panel [J]. Journal of Performance of Constructed, 2020, 34(1): 04019107

[26] ZhouH, GuoR, BaoK, WeiH Y, LiuR. Energy absorption investigation of square CFRP honeycomb reinforced by PMI foam fillers under quasi-static compressive load [J]. Steel and Composite Structures, 2019, 3312837-847

[27] KaderM A, HazellP J, BrownA D, TahtaliM, AhmedS, EscobedoJ P, SaadatfarM. Novel design of closed-cell foam structures for property enhancement [J]. Additive Manufacturing, 2020, 31(1): 100976

[28] WangY-h, ZhaiX-m. Numerical study and multi-objective optimization of an energy absorbing connector with curved plate and aluminum foam [J]. International Journal of Steel Structures, 2020, 201287-299

[29] GaoG-j. The energy distribution of a train impact process based on the active-passive energy-absorption method [J]. Transportation Safety and Environment, 2019, 1(1): 54-67

[30] GaoG J, GuanW Y, LiJ, DongH P, ZouX, ChenW. Experimental investigation of an active-passive integration energy absorber for railway vehicles [J]. Thin-Walled Structures, 2017, 117: 89-97

[31] AlexanderJ M. An approximate analysis of the collapse of thin cylindrical shells under axial load [J]. Quarterly Journal of Mechanics and Applied Mathematics, 1960, 13(1): 5-10

[32] AbramowiczW, JonesN. Dynamic axial crushing of square tubes [J]. International Journal of Impact Engineering, 1984, 2(2): 179-208

[33] HuangX, LuG, YuT X. Energy absorption in splitting square metal tubes [J]. Thin-Walled Structures, 2002, 40: 153-165

[34] MarzbanradJ, MehdikhanloM, SaeediP A. An energy absorption comparison of square, circular and elliptic steel and aluminum tubes under impact loading [J]. Turkish Journal of Engineering and Environmental Sciences, 2010, 33: 159-166

[35] AlaviN A, ParsapourM. An investigation on the energy absorption characteristics of multi-cell square tubes [J]. Thin-Walled Structures, 2013, 68: 26-34

[36] SongJ, ChenY, LuG-x. Axial crushing of thin-walled structures with origami patterns [J]. Thin-Walled Structures, 2012, 54: 65-71

[37] MarzbanradJ, RezaE M. Multi-objective optimization of aluminum hollow tubes for vehicle crash energy absorption using a genetic algorithm and neural networks [J]. Thin-Walled Structures, 2011, 49: 1605-1615

[38] MarzbanradJ, AbdollahpoorA, MashadiB. Effects of the triggering of circular aluminum tubes on crashworthiness [J]. International Journal of Crashworthiness, 2009, 14(6): 1605-1615

[39] GaoG-j, DongH-p, TianH-q. Collision performance of square tubes with diaphragms [J]. Thin-Walled Structures, 2014, 80: 167-177

[40] TanaskovićJ, LučaninV M D. Experimental research of characteristics of modified tube absorbers of kinetic collision energy of passenger coaches [J]. Experimental Techniques, 2014, 38(3): 37-44

[41] GibsonL J, AshbyM F, SchajerG S. The mechanics of two-dimensional cellular materials [J]. Proceedings of the Royal Society A: Mathematical and Physical Sciences, 1982, 382(1782): 25-42

[42] PapkaS D, KyriakidesS. In-plane compressive response and crushing of honeycomb [J]. Journal of the Mechanics and Physics of Solids, 1994, 42(10): 1499-1532

[43] SunD-q, ZhangW-h, WeiY-b. Mean out-of-plane dynamic plateau stresses of hexagonal honeycomb cores under impact loadings [J]. Composite Structures, 2010, 92(11): 2609-2621

[44] ReidS R, PengC. Dynamic uniaxial crushing of wood [J]. International Journal of Impact Engineering, 1997, 19(56): 531-570

[45] RuanD, LuG. In-plane dynamic crushing of honeycombs—A finite element study [J]. International Journal of Impact Engineering, 2003, 28(2): 161-182

[46] MasoudH K, HamidS A, HosseinA, MahmoudS. Bitubular square tubes with different arrangements under quasi-static axial compression loading [J]. Materials and Design, 2013, 51: 1095-1103

[47] AktayL, ToksoyA, GudenM. Quasi-static axial crushing of extruded polystyrene foam-filled thin-walled aluminum tubes: Experimental and numerical analysis [J]. Materials and Design, 2006, 27(9): 556-565

[48] GhamarianA, ZareiHR, AbadiM T. Experimental and numerical crashworthiness investigation of empty and foam-filled end-capped conical tubes [J]. Thin-Walled Structures, 2011, 49(10): 1312-1319

[49] YinH-f, WenG-l, LiuZ-b, QingQ-x. Crashworthiness optimization design for foam-filled multi-cell thin-walled structures [J]. Thin-Walled Structures, 2014, 75: 8-17

[50] WANG X, ZHENG Z. Impact resistance and energy absorption of functionally graded cellular structures [J]. Applied Mechanics and Materials, 2011: 73–78. DOI: https://doi.org/10.4028/www.scientific.net/AMM.69.73.

[51] SinghI, MishraB, BhattacharyaS. XFEM simulation of cracks, holes and inclusions in functionally graded materials [J]. International Journal of Mechanics and Materials in Design, 2011, 7(3): 199-218

[52] JonesN, JouriW S. A study of plate tearing for ship collision and grounding damage [J]. Journal of Ship Research, 1994, 31(4): 00654361

[53] ZhengZ M, CerzbickiT. A theoretical study of steady-state wedge cutting through metal plates [J]. Int J Fracture, 1996, 783445-66

[54] LuG, CalladineC R. On the cutting of a plate by a wedge [J]. International Journal of Mechanical Sciences, 1990, 32(4): 293-313

[55] ChengQ, AltenhofW. Load/displacement and energy absorption performance of AA6061T6 tubes under cutting deformation mode [J]. International Journal of Crashworthiness, 2005, 1(1): 1-13

[56] ShunY J, AltenhofW, LiZ B. A parametric study on extrusion geometry and blade quantity during axial cutting deformation of circular AA6061-T6 extrusions under impact and quasi-static loading [J]. International Journal of Impact Engineering, 2012, 49: 165-178

[57] ShunY J, AltenhofW. An analytical model on the steady-state deformation of circular tubes under an axial cutting deformation mode [J]. International Journal of Solids and Structures, 2011, 48(2): 269-279

[58] ShunY J, MajumderA, AltenhofW. Axial cutting of AA6061-T6 circular extrusions under impact using single-and dual-cutter configurations [J]. International Journal of Impact Engineering, 2010, 37(6): 735-753

[59] ShunY J, AltenhofW, TanyaK. An experimental investigation into the cutting deformation mode of AA6061-T6 round extrusions [J]. Thin-Walled Structures, 2006, 44: 773-786

[60] DongH P, GaoG J, ChenX X, GuanW Y, ZouX. Crushing analysis of splitting-Bending steel plate energy absorber under axial loading [J]. International Journal of Mechanical Sciences, 2016, 110: 217-228

[61] BING A. Collision avoidance and accident survivability, Volume l: Collision threat [R]. US Department of Transportation, 1993.

[62] TYRELL D. A train-to-train impact test of crash energy management passenger rail equipment [C]// Proceedings of Joint Rail Conference. Pueblo, Colorado, 2005. DOI: https://doi.org/10.1109/RRCON.2005.186063.

[63] VANLNGEN-DUNN C. Single passenger rail car impact test volume 11: Summary of occupant protection program [R]. US Department of Transportation, 2000.

[64] KIRKPATRICK S W. Development and validation of high fidelity vehicle crash simulation models [J]. SAE Technical Papers, 2000: 2000-01-0627. DOI: https://doi.org/10.4271/2000-01-0627.

[65] KirkpatrickS W, SchroederM, SimonsJ W. Evaluation of passenger rail vehicle crashworthiness [J]. International Journal of Crashworthiness, 2001, 6(1): 95-106

[66] RayM H, HiranmayeeK, KirkpatrickS W. Performance validation of two finite element models of a side impact dummy [J]. International Journal of Crashworthiness, 1999, 4(3): 287-304

[67] SimonsJ W, KirkpatrickS W. High-speed passenger train crashworthiness and occupant survivability [J]. International Journal of Crashworthiness, 1999, 4(2): 121-132

[68] TyrellD, SeversonK P A. Train-to-train impact test: Analysis of structural measurements [C]. ASME 2002 International Mechanical Engineering Congress and Exposition, 2002, New York, American Society of Mechanical Engineers, 109115

[69] MARTINEZ E, TYRELL D. Rail car impact tests with steel coil: car crush [C]// Proceeding of the 2003 IEEE/ASME Joint Rail Conference. 2003: 63–72. DOI: https://doi.org/10.1109/RRCON.2003.1204651.

[70] JACOBSEN K, TYRELL D. Rail car impact tests with steel coil: collision dynamics [C]// Proceeding of the 2002 IEEE/ASME Joint Rail Conference. 2003: 73–82. DOI: https://doi.org/10.1109/RRCON.2003.1204652.

[71] MAYVILLE R A, JOHNSON K N, STRINGFELLOW R G, TYRELL D. The development of a rail passenger coach car crush zone [C]// Proceeding of the 2003 IEEE/ASME Joint Rail Conference. 2003: 55–61. DOI: https://doi.org/10.1109/RRCON.2003.1204650.

[72] ScholesA, LewisJ H. Development of crashworthiness for railway vehicle structures [J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 1993, 207(1): 1-16

[73] SCHOLES A. Passenger vehicle design loads and structural crashworthiness [C]// IMechE Conference on Railway Vehicle Body Structures. London: 1985: 147–154. DOI: https://doi.org/10.1243/PIME_PROC_1987_201_177_02.

[74] GaoG, WangS. Crashworthiness of passenger rail vehicles: A review [J]. International Journal of Crashworthiness, 2019, 24(6): 664-676

[75] LuZ, LiB, YangC, ZhaoH, XuP, YaoS, PengY, ZhangD. Numerical and experimental study on the design strategy of a new collapse zone structure for railway vehicles [J]. International Journal of Crashworthiness, 2017, 22(5): 488-502

[76] XieS, LiangX, ZhouH. Design and analysis of a composite energy-absorbing structure for use on railway vehicles [J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2016, 230(3): 825-839

[77] ZhangH, PengY, HouL, TianG, LiZ. A hybrid multi-objective optimization approach for energy-absorbing structures in train collisions [J]. Information Sciences, 2019, 481: 491-506

[78] LiR, XuP, PengY. Scaled tests and numerical simulations of rail vehicle collisions for various train sets [J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2016, 230: 1590-1600

[79] YuY, GaoG, GuanW. Scale similitude rules with acceleration consistency for trains collision [J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2018, 232(10): 2466-2480

[80] XuP, LuS, YanK. Energy absorption design study of subway vehicles based on a scaled equivalent model test [J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2019, 233(1): 3-15

[81] LuS, XuP, YanK. A force/stiffness equivalence method for the scaled modelling of a high-speed train head car [J]. Thin-Walled Structures, 2019, 137: 129-142

[82] LewisJ H, RasaiahW G, ScholesA. Validation of measures to improve rail vehicle crashworthiness [J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 1996, 210(2): 73-85

[83] KhalkhaliA, MostafapourM, TabatabaieS M, AnsariB. Multi-objective crashworthiness optimization of perforated square tubes using modified NSGAII and MOPSO [J]. Structural and Multidisciplinary Optimization, Structural and Multidisciplinary Optimization, 2016, 54(1): 45-61

[84] MirzaeiM, ShakeriM, SadighiM, AkbarshahiH. Crashworthiness design for cylindrical tube using neural network and genetic algorithm [J]. Procedia Engineering, 2011, 14: 3346-3353

[85] DiasJ P, PereiramS. Optimization methods for crashworthiness design using multibody models [J]. Computers and Structures, 2004, 82(17–19): 1371-1380

[86] SunY Q, SpiryaginM, ColeC. Rail passenger vehicle crashworthiness simulations using multibody dynamics approaches [J]. Journal of Computational and Nonlinear Dynamics, 2017, 12(4): 1-11

[87] YaoS, YanK, LuS, XuP. Equivalence study involving rail vehicle collision test conditions [J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2019, 233(1): 73-89

[88] WangC, LiuR Q. Study on dynamic characteristics of train collision based on multibody dynamics [C]. IOP Conference Series: Earth and Environmental Science, 2018, 128(1): 012004

[89] SHAO H, XU P, YAO S, PENG Y, LI R, ZHAO S. Improved multibody dynamics for investigating energy dissipation in train collisions based on scaling laws [J]. Shock and Vibration, 2016: 3084052. DOI: https://doi.org/10.1155/2016/3084052.

[90] LingL, DhanasekarM, ThambiratnamD P. A passive road-rail crossing design to minimise wheel-rail contact failure risk under frontal collision of trains onto stuck trucks [J]. Engineering Failure Analysis, 2017, 806403-415

[91] LingL, DhanasekarM, ThambiratnamD P. Frontal collision of trains onto obliquely stuck road trucks at level crossings: Derailment mechanisms and simulation [J]. International Journal of Impact Engineering, 2017, 100: 154-165

[92] LingL, GuanQ, DhanasekarM, ThambiratnamD P. Dynamic simulation of train-truck collision at level crossings [J]. Vehicle System Dynamics, 2017, 55(1): 1-22

[93] LingL, DhanasekarM, ThambiratnamD P, SunY Q. Minimising lateral impact derailment potential at level crossings through guard rails [J]. International Journal of Mechanical Sciences, 2016, 113: 49-60

[94] XieS C, ZhouH, LiangX F, RenX. Contrastive analysis and crashworthiness optimization of two composite thin-walled structures [J]. Journal of Central South University, 2014, 21(11): 4386-4394

[95] ZhangH, PengY, HouL, WangD, TianG, LiZ. Multistage impact energy distribution for whole vehicles in high-speed train collisions: Modeling and solution methodology [J]. IEEE Transactions on Industrial Informatics, 2020, 16(4): 2486-2499

[96] TYRELL D C, SEVERSON K J, MAYVILLE R A, STRINGFELLOW R G, BERRY S, PERLMAN A B. Evaluation of cab car crashworthiness design modifications [C]// Proceedings of the 1997 IEEE/ASME Joint R ailroad Conference. 1997. DOI: https://doi.org/10.1109/RRCON.1997.581353.

[97] TyrellD C, SeversonK J, MarquisB J. Train crashworthiness design for occupant survivability [J]. International Mechanical Engineering Congress and Exposition, 1995, 210(30): 59-74

[98] TYRELL D C, MARTINEZ E E, WIERZBICKI T. Crashworthiness studies of locomotive wide nose short hood designs [J]. Crashworthiness, Occupant Protection and Biomechanics in Transportation S ystems, 1999, 237(45). https://www.researchgate.net/publication/254031506.

[99] TyrellD C. Rail passenger equipment accidents and the evaluation of crashworthiness strategies [J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2002, 216(2): 131-147

[100] TyrellD C. US rail equipment crashworthiness standards [J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2002, 216(F2): 123-130

[101] Gaogj, TianH Q. Train’s crashworthiness design and collision analysis [J]. Int J Crashworthiness, 2007, 12(1): 21-28

[102] XieS C, ZhouH. Impact characteristics of a composite energy absorbing bearing structure for railway vehicles [J]. Compos Part B: Eng, 2014, 67: 455-463

[103] PengY, DengW Y, XuP, YaoS G. Study on the collision performance of a composite energy-absorbing structure for subway vehicles [J]. Thin-Walled Structures, 2015, 94: 663-672

[104] XieS-c, LiH-h, YangW-l, WangN. Crashworthiness optimisation of a composite energy-absorbing structure for railway vehicles [J]. Structural and Multidisciplinar/Optimization, 2018, 57(4): 1793-1807

[105] XieS-c, LiH-h, YangC-x, YaoS-g. Crashworthiness optimization of a composite energy-absorbing structure for subway vehicles based on hybrid particle swarm optimization [J]. Structural and Multidisciplinary Optimization, 2018, 58(5): 2291-2308

[106] XuP, YangC, PengY. Crash performance and multi-objective optimization of a gradual energy-absorbing structure for subway vehicles [J]. International Journal of Mechanical Sciences, 2016, 107: 1-12

[107] XuP, YangC, PengY. Cut-out grooves optimization to improve crashworthiness of a gradual energy-absorbing structure for subway vehicles [J]. Materials & Design, 2016, 103: 132-143

[108] XuP, XingJ, YaoS-g. Energy distribution analysis and multi-objective optimization of a gradual energy-absorbing structure for subway vehicles [J]. Thin-Walled Structures, 2017, 115: 255-263

[109] XuP, XuK, YaoS. Parameter study and multi-objective optimization of an axisymmetric rectangular tube with diaphragms for subways [J]. Thin-Walled Structures, 2019, 136: 186-199

[110] WangS, PengY, WangT. Collision performance and multi-objective robust optimization of a combined multi-cell thin-walled structure for high speed train [J]. Thin-Walled Structures, 2019, 135: 341-355

[111] WangS-m, PengY, WangT-t, ChenX-z, HouL, ZhangH-h. The origami inspired optimization design to improve the crashworthiness of a multi-cell thin-walled structure for high speed train [J]. International Journal of Mechanical Sciences, 2019, 159: 345-358

[112] YaoS, XiaoX, XuP. The impact performance of honeycomb-filled structures under eccentric loading for subway vehicles [J]. Thin-Walled Structures, 2018, 123: 360-370

[113] YanJ, YaoS, XuP. Theoretical prediction and numerical studies of expanding circular tubes as energy absorbers [J]. International Journal of Mechanical Sciences, 2016, 105: 206-214

[114] YaoS, LiZ, YanJ. Analysis and parameters optimization of an expanding energy-absorbing structure for a rail vehicle coupler [J]. Thin-Walled Structures, 2018, 125: 129-139

[115] AlvesM L. End forming of thin-walled tubes [J]. Journal of Materials Processing Technology, 2006, 177(1–3): 183-187

[116] AlvesL M, MartinspaF. Cold expansion and reduction of thin-walled PVC tubes using a die [J]. Journal of Materials Processing Technology, 2009, 209(9): 4229-4236

[117] AlmeidaB P P, AlvesM L, RosaP A R, BritoA G, MartinsP A F. Expansion and reduction of thin-walled tubes using a die: Experimental and theoretical investigation [J]. International Journal of Machine Tools and Manufacture, 2006, 46(1213): 1643-1652

[118] LiJ, GaoG, GuanW. Experimental and numerical investigations on the energy absorption of shrink circular tube under quasi-static loading [J]. International Journal of Mechanical Sciences, 2018, 137: 284-294

[119] YaoS, LiZ, MaW. Crashworthiness analysis of a straight-tapered shrink tube [J]. International Journal of Mechanical Sciences, 2019, 157: 512-527

[120] TanaskovicJ. Experimental investigations of the shrinking-splitting tube collision energy absorber [J]. Thin-Walled Structures, 2015, 86: 142-147

[121] StrongeW J, YuT X, JohnsonW. Long stroke energy dissipation in splitting tubes [J]. International Journal of Mechanical Sciences, 1983, 25(910): 637-647

[122] YuenS C K, AltenhofW, OppermanC J. Axial splitting of circular tubes by means of blast load [J]. International Journal of Impact Engineering, 2013, 53: 17-28

[123] NiknejadA, RezaeiB, LiaghatG H. Empty circular metal tubes in the splitting process-theoretical and experimental studies [J]. Thin-Walled Structures, 2013, 72: 48-60

[124] TanaskovicJ, MilkovicD, LucaninV. Experimental investigations of the shrinking-splitting tube collision energy absorber [J]. Thin-Walled Structures, 2015, 86: 142-147

[125] LiJ, GaoG, DongH. Study on the energy absorption of the expanding-splitting circular tube by experimental investigations and numerical simulations [J]. Thin-Walled Structures, 2016, 103: 105-114

[126] LiJ, GaoG, YuY. Experimental and numerical study on splitting process of circular steel tube with enhanced crashworthiness performance [J]. Thin-Walled Structures, 2019, 145: 106406

[127] PengY, WangS, YaoS. Crashworthiness analysis and optimization of a cutting-style energy absorbing structure for subway vehicles [J]. Thin-Walled Structures, 2017, 120225-235

[128] GuanW, GaoG, LiJ. Crushing analysis and multi-objective optimization of a cutting aluminum tube absorber for railway vehicles under quasi-static loading [J]. Thin-Walled Structures, 2018, 123: 395-408

[129] WangJ, LuZ, ZhongM. Coupled thermal-structural analysis and multi-objective optimization of a cutting-type energy-absorbing structure for subway vehicles [J]. Thin-Walled Structures, 2019, 141: 360-373

[130] GhamarianA, TahayeA M. Axial crushing analysis of end-capped circular tubes [J]. Thin-Walled Structures, 2011, 49(6): 743-752

[131] ZareiH R, GhamarianA. Experimental and numerical crashworthiness investigation of empty and foam-filled thin-walled tubes with shallow spherical caps [J]. Experimental Mechanics, 2014, 54(2): 115-126

[132] GhamarianA, ZareiH R, FarsiM A, AriaeifarN. Experimental and numerical crashworthiness investigation of the empty and foam-filled conical tube with shallow spherical caps [J]. Strain, 2013, 49(3): 199-211

[133] PRAVEEN KUMAR A, JUSUF A, SANTOSA S P, DIRGANTARA T. Investigations on the influence of spherical caps in the axial impact characteristics of press-formed cylindrical tubular structures [J]. Advances in Structural Engineering, 2019. DOI: https://doi.org/10.1177/1369433218819576.

[134] PraveenK A. Experimental analysis on the axial crushing and energy absorption characteristics of novel hybrid aluminium/composite-capped cylindrical tubular structures [J]. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 2019, 233(11): 2234-2252

[135] PRAVEEN KUMAR A, SATHISH KUMAR M. Deformation characteristics of press-formed cylindrical tubes with shallow and hemispherical caps for frontal crash protective structures [J]. International Journal of Protective Structures, 2019: 1–19. DOI: https://doi.org/10.1177/2041419619830701.

[136] KumarA P, ManeiahD. Crashworthiness behaviour of capped cylindrical aluminium [J]. International Journal of Mechanical and Production, Engineering Research and Development, 2019, 9(4): 1167-1172

[137] LiuG, XieJ, XieS. Experimental and numerical investigations of a new U-shaped thin plate energy absorber subjected to bending and friction [J]. Thin-Walled Structures, 2017, 115: 215-224

[138] YuY, GaoG, DongH. A numerical study on the energy absorption of a bending-straightening energy absorber with large stroke [J]. Thin-Walled Structures, 2018, 122: 30-41

[139] ChenX, GaoG, DongH. Experimental and numerical investigations of a splitting-bending steel plate energy absorber [J]. Thin-Walled Structures, 2016, 98: 384-391

[140] SEVERSON K J, PARENT D. Train-to-train impact test of crash-energy management passenger rail equipment: Occupant experiments [R]. US Department of Transportion, 2006.

[141] OminoK, ShirotoH, SaitoA. Estimation of passenger movements against the impact in train collision [J]. Quarterly Report of RTRI, 2002, 43(2): 77-82

[142] XieS C, TianH Q. Influencing factors and sensitivity analysis of occupant impact injury in passenger compartment [J]. Traffic Inj Prev, 2013, 14: 816

[143] YangW, XieS, LiH. Design and injury analysis of the seated occupant protection posture in train collision [J]. Safety Science, 2019, 117263-275

[144] WoodD P, WalshD G. Car to car interaction in frontal collisions: A model for the behaviour of the car population and options for improved crashworthiness [J]. International Journal of Crashworthiness, 2002, 7(1): 79-96

[145] US National Administration2015 motor vehicle crashes: overview [R], 2016, Washington DC, US National Administration

[146] ZhangJ-y, WangD-q, WuL-n, LiuL-d. Conceptual design of the front-end structure of automobile considering crashworthiness: A three-stage target decomposition method [J]. International Journal of Crashworthiness, 2019, 25(2): 183-191

[147] YusofN S B, SapuanS M, SultanM T H, JawaidM, MalequeM A. Design and materials development of automotive crash box: A review [J]. Ciencia e Tecnologia dos Materiais, 2017, 29(3): 129-144

[148] DavoodiM M, SapuanS M, AidyA, AbuO N A, OshkourA A, WanA W A B. Development process of new bumper beam for passenger car: A review [J]. Materials and Design, 2012, 40: 304-313

[149] AlbahashZ F, AnsariM N M. A review on rear under-ride protection devices for trucks [J]. International Journal of Crashworthiness, 2017, 22(1): 95-109

[150] WittemanW JImproved vehicle crashworthiness design by control of the energy absorption for different collision situations [D], 1999, Eindhoven, Eindhoven University

[151] BoisP D, ChouC C, FiletaB B, KingaiH F MVehicle crashworthiness and occupant protection [M], 2004, Michigan, Automotive Applications Committee, American Iron and Steel Institute

[152] HAMZA K S K. Design for crashworthiness of vehicle structures via equivalent mechanism approximations and crush mode matching [C]// Proceedings of the ASME 2004 International Mechanical Engineering Congress and Exposition. 2004: 949–960. DOI: https://doi.org/10.1115/IMECE2004-62226.

[153] MehrcamparsGMT bumper beam of Samand[M], 2003, Iran, Mehrcampars

[154] BodapativK KEvaluation of energy absorbing pliers underride guards for rear and side of large trucks [D], 2006, India, Wichita State University.

[155] XueL, YangJ. A study on the application of energy-dissipating protection device in car-to-truck rear underride [C]. Proceedings-2013 5th Conference on Measuring Technology and Mechatronics Automation, ICMTMA 2013, 2013, 8: 130-134

[156] AllianzSShipping 1912–2012, from Titanic to Costa Concordia [R], 2012, Munich, Germany, Allianz Global Corporate & Specialty

[157] CorporateaGSafety and shipping review 2017 [R], 2017, Munich, Germany, Allianz Global Corporate & Specialty

[158] MinorskyV UAn analysis of ship collision with reference to protection of nuclear power ships [R], 1958, New York, Sharp(George G.) Inc

[159] PRABOWO A R, PUTRANTO T, SOHN J M. Simulation of the behavior of a ship hull under grounding: Effect of applied element size on structural crashworthiness [J]. Journal of Marine Science and Engineering, 2019, 7 (8). DOI: https://doi.org/10.3390/jmse7080270.

[160] PrabowoA R, SohnJ M, PutrantoT. Crashworthiness performance of stiffened bottom tank structure subjected to impact loading conditions: Ship-rock interaction [J]. Curved and Layered Structures, 2019, 6(1): 245-258

[161] PrabowoA R, CahyonoS I, SohnJ M. Crashworthiness assessment of thin-walled double bottom tanker: A variety of ship grounding incidents [J]. Theoretical and Applied Mechanics Letters, 2019, 9(5): 320-327

[162] OzgucO, DasP K, BarltropN. A comparative study on the structural integrity of single and double side skin bulk carriers under collision damage [J]. Marine Structures, 2005, 18(78): 511-547

[163] HarisS, AmdahlJ. Analysis of ship-ship collision damage accounting for bow and side deformation interaction [J]. Marine Structures, 2013, 32: 18-48

[164] RioP A, MyungB D, MinS J, FauzanZ A, CaoB, HyungC J. Effects of the rebounding of a striking ship on structural crashworthiness during ship-ship collision [J]. Thin-Walled Structures, 2017, 115(2): 225-239

[165] KarenE, JacksonE L FNASA Langley research center impact dynamics research facility research survey [J]. Journal of Aircraft, 2003, 41(3): 511-522

[166] PifkoaB, WinterrJ D C. Crash simulation of composite and aluminum helicopter fuselages using a finite-element program [J]. Journal of Aircraft, 1979, 17(8): 591-597

[167] MccarthyM A, WiggenraadJ F M. Numerical investigation of a crash test of a composite helicopter subfloor structure [J]. Composite Structures, 2001, 51(4): 345-359

[168] WangZ J, ZhouH Z, KhaliulinV I, ShabalovA V. Six-ray folded configurations as the geometric basis of thin-walled elements in engineering structures [J]. Thin-Walled Structures, 2018, 130: 435-448

[169] ZHOU Hua-zhi, WANG Zhi-jin. Application of foldcore sandwich structures in helicopter subfloor energy absorption structure [C]// The International Conference on Structural, Mechanical and Materials Engineering. 2017: 1–7. DOI: https://doi.org/10.1088/1757-899X/248/1/012033.

[170] ZHOU Hua-zhi, WANG Zhi-jin. Study and optimization of helicopter subfloor energy absorption structure with foldcore sandwich structures [C]// 4th International Conference on Advanced Materials, Mechanics and Structural Engineering. 2017: 1–5. DOI: https://doi.org/10.1088/1757-899X/269/1/012022.