Review of the crushing response of collapsible tubular structures
Vivek PATEL, Gaurav TIWARI, Ravikumar DUMPALA
Review of the crushing response of collapsible tubular structures
Studies on determining and analyzing the crushing response of tubular structures are of significant interest, primarily due to their relation to safety. Several aspects of tubular structures, such as geometry, material, configuration, and hybrid structure, have been used as criteria for evaluation. In this review, a comprehensive analysis of the important findings of extensive research on understanding the crushing response of thin-walled tubular structures is presented. Advancements in thin-walled structures, including multi-cell tube, honeycomb and foam-filled, multi wall, and functionally graded thickness tubes, are also discussed, focusing on their energy absorption ability. An extensive review of experimentation and numerical analysis used to extract the deformation behavior of materials, such as aluminum and steel, against static and dynamic loadings are also provided. Several tube shapes, such as tubes of uniform and nonuniform (tapered) cross sections of circular, square, and rectangular shapes, have been used in different studies to identify their efficacy. Apart from geometric and loading parameters, the effects of fabrication process, heat treatment, and triggering mechanism on initiating plastic deformation, such as cutouts and grooves, on the surface of tubular structures are discussed.
monolithic structure / crashworthiness / energy absorber / static and dynamic loadings / multicellular tube structure / filled tube
[1] |
Hanssen A G, Langseth M, Hopperstad O S. Static and dynamic crushing of circular aluminium extrusions with aluminium foam filler. International Journal of Impact Engineering, 2000, 24(5): 475–507
CrossRef
Google scholar
|
[2] |
Baroutaji A, Sajjia M, Olabi A G. On the crashworthiness performance of thin-walled energy absorbers: Recent advances and future developments. Thin-Walled Structures, 2017, 118: 137–163
CrossRef
Google scholar
|
[3] |
Livermore Software Technology Corporation. LS-DYNA Keyword User’s Manual. 2007
|
[4] |
Clausen A H, Hopperstad O S, Langseth M. Sensitivity of model parameters in stretch bending of aluminium extrusions. International Journal of Mechanical Sciences, 2001, 43(2): 427–453
CrossRef
Google scholar
|
[5] |
Tarigopula V, Langseth M, Hopperstad O S,
CrossRef
Google scholar
|
[6] |
Abramowicz W, Jones N. Dynamic axial crushing of square tubes. International Journal of Impact Engineering, 1984, 2(2): 179–208
CrossRef
Google scholar
|
[7] |
Abramowicz W, Jones N. Dynamic progressive buckling of circular and square tubes. International Journal of Impact Engineering, 1986, 4(4): 243–270
CrossRef
Google scholar
|
[8] |
Alexander J. An approximate analysis of the collapse of thin cylindrical shells under axial loading. Quarterly Journal of Mechanics and Applied Mathematics, 1960, 13(1): 10–15
CrossRef
Google scholar
|
[9] |
Abramowicz W, Jones N. Dynamic axial crushing of circular tubes. International Journal of Impact Engineering, 1984, 2(3): 263–281
CrossRef
Google scholar
|
[10] |
Hong W, Jin F, Zhou J,
CrossRef
Google scholar
|
[11] |
Wierzbicki T, Abramowicz W. On the crushing mechanics of thin-walled structures. Journal of Applied Mechanics, 1983, 50(4a): 727–734
CrossRef
Google scholar
|
[12] |
Abramowicz W, Wierzbicki T. Axial crushing of multi corner sheet metal columns. Journal of Applied Mechanics, 1989, 56(1): 113–120
CrossRef
Google scholar
|
[13] |
Sun F, Fan H. Inward-contracted folding element for thin-walled triangular tubes. Journal of Constructional Steel Research, 2017, 130: 131–137
CrossRef
Google scholar
|
[14] |
Jones N. Energy-absorbing effectiveness factor. International Journal of Impact Engineering, 2010, 37(6): 754–765
CrossRef
Google scholar
|
[15] |
Luo X, Xu J, Zhu J,
CrossRef
Google scholar
|
[16] |
Abramowicz W, Jones N. Transition from initial global bending to progressive buckling of tubes loaded statically and dynamically. International Journal of Impact Engineering, 1997, 19(5–6): 415–437
CrossRef
Google scholar
|
[17] |
Moalem D, Sideman S. Theoretical analysis of a horizontal condenser–evaporator tube. International Journal of Heat and Mass Transfer, 1976, 19(3): 259–270
CrossRef
Google scholar
|
[18] |
Pugsley A. The large-scale crumpling of thin cylindrical columns. Quarterly Journal of Mechanics and Applied Mathematics, 1960, 13(1): 1–9
CrossRef
Google scholar
|
[19] |
Wierzbicki T, Bhat S U, Abramowicz W,
CrossRef
Google scholar
|
[20] |
Singace A A, Elsobky H, Reddy T Y. On the eccentricity factor in the progressive crushing of tubes. International Journal of Solids and Structures, 1995, 32(24): 3589–3602
CrossRef
Google scholar
|
[21] |
Gupta N, Gupta S. Effect of annealing, size and cut-outs on axial collapse behavior of circular tubes. International Journal of Mechanical Sciences, 1993, 35(7): 597–613
CrossRef
Google scholar
|
[22] |
Gupta N. Some aspects of axial collapse of cylindrical thin-walled tubes. Thin-Walled Structures, 1998, 32(1–3): 111–126
CrossRef
Google scholar
|
[23] |
Daneshi G, Hosseinipour S. Elastic–plastic theory for initial buckling load of thin-walled grooved tubes under axial compression. Journal of Materials Processing Technology, 2002, 125–126: 826–832
CrossRef
Google scholar
|
[24] |
Daneshi G, Hosseinipour S. Grooves effect on crashworthiness characteristics of thin-walled tubes under axial compression. Materials & Design, 2002, 23(7): 611–617
CrossRef
Google scholar
|
[25] |
Mokhtarnezhad F, Salehghaffari S, Tajdari M. Improving the crashworthiness characteristics of cylindrical tubes subjected to axial compression by cutting wide grooves from their outer surface. International Journal of Crashworthiness, 2009, 14(6): 601–611
CrossRef
Google scholar
|
[26] |
Karagiozova D, Jones N. Dynamic effects on buckling and energy absorption of cylindrical shells under axial impact. Thin-Walled Structures, 2001, 39(7): 583–610
CrossRef
Google scholar
|
[27] |
Wang B, Lu G. Mushrooming of circular tubes under dynamic axial loading. Thin-Walled Structures, 2002, 40(2): 167–182
CrossRef
Google scholar
|
[28] |
Tabiei A, Nilakantan G. Axial crushing of tubes as an energy dissipating mechanism for the reduction of acceleration induced injuries from mine blasts underneath infantry vehicles. International Journal of Impact Engineering, 2009, 36(5): 729–736
CrossRef
Google scholar
|
[29] |
Huang M, Tai Y, Hu H. Dynamic crushing characteristics of high strength steel cylinders with elliptical geometric discontinuities. Theoretical and Applied Fracture Mechanics, 2010, 54(1): 44–53
CrossRef
Google scholar
|
[30] |
Isaac C W, Oluwole O. Energy absorption improvement of circular tubes with externally press-fitted ring around tube surface subjected under axial and oblique impact loading. Thin-Walled Structures, 2016, 109: 352–366
CrossRef
Google scholar
|
[31] |
Vinayagar K, Kumar A S. Crashworthiness analysis of double section bi-tubular thin-walled structures. Thin-Walled Structures, 2017, 112: 184–193
CrossRef
Google scholar
|
[32] |
Chen D, Ozaki S. Numerical study of axially crushed cylindrical tubes with corrugated surface. Thin-Walled Structures, 2009, 47(11): 1387–1396
CrossRef
Google scholar
|
[33] |
Eyvazian A, Habibi M K, Hamouda A M,
CrossRef
Google scholar
|
[34] |
Salehghaffari S, Tajdari M, Panahi M,
CrossRef
Google scholar
|
[35] |
Nia A A, Khodabakhsh H. The effect of radial distance of concentric thin-walled tubes on their energy absorption capability under axial dynamic and quasi-static loading. Thin-Walled Structures, 2015, 93: 188–197
CrossRef
Google scholar
|
[36] |
Ghamarian A, Abadi M T. Axial crushing analysis of end-capped circular tubes. Thin-Walled Structures, 2011, 49(6): 743–752
CrossRef
Google scholar
|
[37] |
Kumar A P, Mohamed M N, Jusuf A,
CrossRef
Google scholar
|
[38] |
Airoldi A, Janszen G. A design solution for a crashworthy landing gear with a new triggering mechanism for the plastic collapse of metallic tubes. Aerospace Science and Technology, 2005, 9(5): 445–455
CrossRef
Google scholar
|
[39] |
Zhang X, Tian Q, Yu T. Axial crushing of circular tubes with buckling initiators. Thin-Walled Structures, 2009, 47(6–7): 788–797
CrossRef
Google scholar
|
[40] |
Liu Y, Day M L. Bending collapse of thin-walled circular tubes and computational application. Thin-Walled Structures, 2008, 46(4): 442–450
CrossRef
Google scholar
|
[41] |
Zhan Z, Hu W, Meng Q,
CrossRef
Google scholar
|
[42] |
Galib D A, Limam A. Experimental and numerical investigation of static and dynamic axial crushing of circular aluminium tubes. Thin-Walled Structures, 2004, 42(8): 1103–1137
CrossRef
Google scholar
|
[43] |
Yamashita M, Kenmotsu H, Hattori T. Dynamic axial compression of aluminium hollow tubes with hat cross-section and buckling initiator using inertia force during impact. Thin-Walled Structures, 2012, 50(1): 37–44
CrossRef
Google scholar
|
[44] |
Lu G, Ong L, Wang B,
CrossRef
Google scholar
|
[45] |
Huang X, Lu G, Yu T X. Energy absorption in splitting square metal tubes. Thin-Walled Structures, 2002, 40(2): 153–165
CrossRef
Google scholar
|
[46] |
Han D, Park S. Collapse behavior of square thin-walled columns subjected to oblique loads. Thin-Walled Structures, 1999, 35(3): 167–184
CrossRef
Google scholar
|
[47] |
DiPaolo B, Monteiro P, Gronsky R. Quasi-static axial crush response of a thin-wall, stainless steel box component. International Journal of Solids and Structures, 2004, 41(14): 3707–3733
CrossRef
Google scholar
|
[48] |
Xu F, Sun G, Li G,
CrossRef
Google scholar
|
[49] |
Otubushin A. Detailed validation of a non-linear finite element code using dynamic axial crushing of a square tube. International Journal of Impact Engineering, 1998, 21(5): 349–368
CrossRef
Google scholar
|
[50] |
Rusinek A, Zaera R, Forquin P,
CrossRef
Google scholar
|
[51] |
Gümrük R, Karadeniz S. A numerical study of the influence of bump type triggers on the axial crushing of top hat thin-walled sections. Thin-Walled Structures, 2008, 46(10): 1094–1106
CrossRef
Google scholar
|
[52] |
Zhang X, Huh H. Energy absorption of longitudinally grooved square tubes under axial compression. Thin-Walled Structures, 2009, 47(12): 1469–1477
CrossRef
Google scholar
|
[53] |
Langseth M, Hopperstad O. Static and dynamic axial crushing of square thin-walled aluminium extrusions. International Journal of Impact Engineering, 1996, 18(7–8): 949–968
CrossRef
Google scholar
|
[54] |
Langseth M, Hopperstad O, Berstad T. Crashworthiness of aluminium extrusions: Validation of numerical simulation, effect of mass ratio and impact velocity. International Journal of Impact Engineering, 1999, 22(9–10): 829–854
CrossRef
Google scholar
|
[55] |
Jensen Ø, Langseth M, Hopperstad O. Experimental investigations on the behavior of short to long square aluminium tubes subjected to axial loading. International Journal of Impact Engineering, 2004, 30(8–9): 973–1003
CrossRef
Google scholar
|
[56] |
Stronge W, Yu T, Johnson W. Long stroke energy dissipation in splitting tubes. International Journal of Mechanical Sciences, 1983, 25(9–10): 637–647
CrossRef
Google scholar
|
[57] |
Reyes A, Langseth M, Hopperstad O S. Square aluminium tubes subjected to oblique loading. International Journal of Impact Engineering, 2003, 28(10): 1077–1106
CrossRef
Google scholar
|
[58] |
Nia A A, Fallah Nejad K, Badnava H,
CrossRef
Google scholar
|
[59] |
Zhang X, Cheng G, You Z,
CrossRef
Google scholar
|
[60] |
Arnold B, Altenhof W. Experimental observations on the crush characteristics of AA6061 T4 and T6 structural square tubes with and without circular discontinuities. International Journal of Crashworthiness, 2004, 9(1): 73–87
CrossRef
Google scholar
|
[61] |
Cheng Q, Altenhof W, Li L. Experimental investigations on the crush behavior of AA6061-T6 aluminium square tubes with different types of through-hole discontinuities. Thin-Walled Structures, 2006, 44(4): 441–454
CrossRef
Google scholar
|
[62] |
Zhang X, Zhang H. Crush resistance of square tubes with various thickness configurations. International Journal of Mechanical Sciences, 2016, 107: 58–68
CrossRef
Google scholar
|
[63] |
Fyllingen Ø, Hopperstad O, Langseth M. Stochastic simulations of square aluminium tubes subjected to axial loading. International Journal of Impact Engineering, 2007, 34(10): 1619–1636
CrossRef
Google scholar
|
[64] |
Mamalis A, Johnson W. The quasi-static crumpling of thin-walled circular cylinders and frusta under axial compression. International Journal of Mechanical Sciences, 1983, 25(9–10): 713–732
CrossRef
Google scholar
|
[65] |
Mamalis A, Manolakos D, Saigal S,
CrossRef
Google scholar
|
[66] |
Reid S, Reddy T. Static and dynamic crushing of tapered sheet metal tubes of rectangular cross-section. International Journal of Mechanical Sciences, 1986, 28(9): 623–637
CrossRef
Google scholar
|
[67] |
Nagel G, Thambiratnam D. Computer simulation and energy absorption of tapered thin-walled rectangular tubes. Thin-Walled Structures, 2005, 43(8): 1225–1242
CrossRef
Google scholar
|
[68] |
El-Sobky H, Singace A, Petsios M. Mode of collapse and energy absorption characteristics of constrained frusta under axial impact loading. International Journal of Mechanical Sciences, 2001, 43(3): 743–757
CrossRef
Google scholar
|
[69] |
Alghamdi A, Aljawi A, Abu-Mansour T N. Modes of axial collapse of unconstrained capped frusta. International Journal of Mechanical Sciences, 2002, 44(6): 1145–1161
CrossRef
Google scholar
|
[70] |
Alghamdi A. Folding-crumpling of thin-walled aluminium frusta. International Journal of Crashworthiness, 2002, 7(1): 67–78
CrossRef
Google scholar
|
[71] |
Gupta N, Prasad G E, Gupta S. Plastic collapse of metallic conical frusta of large semi-apical angles. International Journal of Crashworthiness, 1997, 2(4): 349–366
CrossRef
Google scholar
|
[72] |
Prasad G E, Gupta N. An experimental study of deformation modes of domes and large-angled frusta at different rates of compression. International Journal of Impact Engineering, 2005, 32(1–4): 400–415
CrossRef
Google scholar
|
[73] |
Niknejad A, Tavassolimanesh A. Axial compression of the empty capped-end frusta during the inversion progress. Materials & Design, 2013, 49: 65–75
CrossRef
Google scholar
|
[74] |
Chahardoli S, Nia A A. Experimental and numerical investigations on collapse properties of capped-end frusta tubes with circular triggers under axial quasi-static loading. International Journal of Mechanical Sciences, 2017, 134: 545–561
CrossRef
Google scholar
|
[75] |
Mamalis A, Johnson W, Viegelahn G. The crumpling of steel thin-walled tubes and frusta under axial compression at elevated strain-rates: Some experimental results. International Journal of Mechanical Sciences, 1984, 26(11–12): 537–547
CrossRef
Google scholar
|
[76] |
Nagel G, Thambiratnam D. A numerical study on the impact response and energy absorption of tapered thin-walled tubes. International Journal of Mechanical Sciences, 2004, 46(2): 201–216
CrossRef
Google scholar
|
[77] |
Nagel G, Thambiratnam D. Dynamic simulation and energy absorption of tapered tubes under impact loading. International Journal of Crashworthiness, 2004, 9(4): 389–399
CrossRef
Google scholar
|
[78] |
Nagel G M, Thambiratnam D P. Dynamic simulation and energy absorption of tapered thin-walled tubes under oblique impact loading. International Journal of Impact Engineering, 2006, 32(10): 1595–1620
CrossRef
Google scholar
|
[79] |
Taştan A, Acar E, Güler M,
CrossRef
Google scholar
|
[80] |
Mamalis A, Robinson M, Manolakos D,
CrossRef
Google scholar
|
[81] |
Shin K C, Lee J J, Kim K H,
CrossRef
Google scholar
|
[82] |
Ramakrishna S, Hull D. Energy absorption capability of epoxy composite tubes with knitted carbon fibre fabric reinforcement. Composites Science and Technology, 1993, 49(4): 349–356
CrossRef
Google scholar
|
[83] |
Solaimurugan S, Velmurugan R. Influence of fibre orientation and stacking sequence on petalling of glass/polyester composite cylindrical shells under axial compression. International Journal of Solids and Structures, 2007, 44(21): 6999–7020
CrossRef
Google scholar
|
[84] |
Kim J S, Yoon H J, Shin K B. A study on crushing behaviors of composite circular tubes with different reinforcing fibers. International Journal of Impact Engineering, 2011, 38(4): 198–207
CrossRef
Google scholar
|
[85] |
Hamada H, Ramakrishna S, Satoh H. Crushing mechanism of carbon fibre/PEEK composite tubes. Composites, 1995, 26(11): 749–755
CrossRef
Google scholar
|
[86] |
Song H W, Wan Z M, Xie Z M,
CrossRef
Google scholar
|
[87] |
Mirzaei M, Shakeri M, Sadighi M,
CrossRef
Google scholar
|
[88] |
Mahdi E, Sultan H, Hamouda A,
CrossRef
Google scholar
|
[89] |
Thuis H, Metz V. The influence of trigger configurations and laminate lay-up on the failure mode of composite crush cylinders. Composite Structures, 1994, 28(2): 131–137
CrossRef
Google scholar
|
[90] |
Siromani D, Henderson G, Mikita D,
CrossRef
Google scholar
|
[91] |
Huang J, Wang X. Numerical and experimental investigations on the axial crushing response of composite tubes. Composite Structures, 2009, 91(2): 222–228
CrossRef
Google scholar
|
[92] |
Chiu L N, Falzon B G, Ruan D,
CrossRef
Google scholar
|
[93] |
Mahdi E, Mokhtar A, Asari N,
CrossRef
Google scholar
|
[94] |
Abdewi E F, Sulaiman S, Hamouda A,
CrossRef
Google scholar
|
[95] |
Abdewi E F, Sulaiman S, Hamouda A,
CrossRef
Google scholar
|
[96] |
Mamalis A, Manolakos D, Demosthenous G,
CrossRef
Google scholar
|
[97] |
Mamalis A G, Manolakos D, Ioannidis M,
CrossRef
Google scholar
|
[98] |
Mamalis A, Manolakos D, Ioannidis M,
CrossRef
Google scholar
|
[99] |
Mamalis A, Manolakos D, Ioannidis M,
CrossRef
Google scholar
|
[100] |
Zarei H, Kröger M, Albertsen H. An experimental and numerical crashworthiness investigation of thermoplastic composite crash boxes. Composite Structures, 2008, 85(3): 245–257
CrossRef
Google scholar
|
[101] |
Bambach M R, Elchalakani M, Zhao X L. Composite steel–CFRP SHS tubes under axial impact. Composite Structures, 2009, 87(3): 282–292
CrossRef
Google scholar
|
[102] |
Bambach M R, Jama H H, Elchalakani M. Static and dynamic axial crushing of spot-welded thin-walled composite steel–CFRP square tubes. International Journal of Impact Engineering, 2009, 36(9): 1083–1094
CrossRef
Google scholar
|
[103] |
Bambach M R, Elchalakani M. Plastic mechanism analysis of steel SHS strengthened with CFRP under large axial deformation. Thin-Walled Structures, 2007, 45(2): 159–170
CrossRef
Google scholar
|
[104] |
Bambach M. Axial capacity and crushing behavior of metal–fiber square tubes–Steel, stainless steel and aluminium with CFRP. Composites. Part B, Engineering, 2010, 41(7): 550–559
CrossRef
Google scholar
|
[105] |
Bambach M. Axial capacity and crushing of thin-walled metal, fibre–epoxy and composite metal–fibre tubes. Thin-Walled Structures, 2010, 48(6): 440–452
CrossRef
Google scholar
|
[106] |
Zheng Z, Liu Y, Yu J,
CrossRef
Google scholar
|
[107] |
Zheng Z, Yu J, Wang C,
CrossRef
Google scholar
|
[108] |
Liu Y, Schaedler T A, Chen X. Dynamic energy absorption characteristics of hollow microlattice structures. Mechanics of Materials, 2014, 77: 1–13
CrossRef
Google scholar
|
[109] |
Reid S, Reddy T, Gray M. Static and dynamic axial crushing of foam-filled sheet metal tubes. International Journal of Mechanical Sciences, 1986, 28(5): 295–322
CrossRef
Google scholar
|
[110] |
Reid S, Reddy T. Axial crushing of foam-filled tapered sheet metal tubes. International Journal of Mechanical Sciences, 1986, 28(10): 643–656
CrossRef
Google scholar
|
[111] |
Reddy T, Wall R. Axial compression of foam-filled thin-walled circular tubes. International Journal of Impact Engineering, 1988, 7(2): 151–166
CrossRef
Google scholar
|
[112] |
Seitzberger M, Rammerstorfer F G, Gradinger R,
CrossRef
Google scholar
|
[113] |
Güden M, Kavi H. Quasi-static axial compression behavior of constraint hexagonal and square-packed empty and aluminium foam-filled aluminium multi-tubes. Thin-Walled Structures, 2006, 44(7): 739–750
CrossRef
Google scholar
|
[114] |
Abramowicz W, Wierzbicki T. Axial crushing of foam-filled columns. International Journal of Mechanical Sciences, 1988, 30(3–4): 263–271
CrossRef
Google scholar
|
[115] |
Seitzberger M, Rammerstorfer F G, Degischer H P,
CrossRef
Google scholar
|
[116] |
Guillow S, Lu G, Grzebieta R. Quasi-static axial compression of thin-walled circular aluminium tubes. International Journal of Mechanical Sciences, 2001, 43(9): 2103–2123
CrossRef
Google scholar
|
[117] |
Hanssen A, Langseth M, Hopperstad O. Static crushing of square aluminium extrusions with aluminium foam filler. International Journal of Mechanical Sciences, 1999, 41(8): 967–993
CrossRef
Google scholar
|
[118] |
Hanssen A G, Langseth M, Hopperstad O S. Static and dynamic crushing of square aluminium extrusions with aluminium foam filler. International Journal of Impact Engineering, 2000, 24(4): 347–383
CrossRef
Google scholar
|
[119] |
Santosa S P, Wierzbicki T, Hanssen A G,
CrossRef
Google scholar
|
[120] |
Kavi H, Toksoy A K, Guden M. Predicting energy absorption in a foam-filled thin-walled aluminium tube based on experimentally determined strengthening coefficient. Materials & Design, 2006, 27(4): 263–269
CrossRef
Google scholar
|
[121] |
Mirfendereski L, Salimi M, Ziaei-Rad S. Parametric study and numerical analysis of empty and foam filled thin-walled tubes under static and dynamic loadings. International Journal of Mechanical Sciences, 2008, 50(6): 1042–1057
CrossRef
Google scholar
|
[122] |
Ahmad Z, Thambiratnam D, Tan A. Dynamic energy absorption characteristics of foam-filled conical tubes under oblique impact loading. International Journal of Impact Engineering, 2010, 37(5): 475–488
CrossRef
Google scholar
|
[123] |
Meguid S, Attia M, Monfort A. On the crush behavior of ultralight foam-filled structures. Materials & Design, 2004, 25(3): 183–189
CrossRef
Google scholar
|
[124] |
Santosa S, Wierzbicki T. Crash behavior of box columns filled with aluminium honeycomb or foam. Computers & Structures, 1998, 68(4): 343–367
CrossRef
Google scholar
|
[125] |
Zhang Z, Liu S, Tang Z. Comparisons of honeycomb sandwich and foam-filled cylindrical columns under axial crushing loads. Thin-Walled Structures, 2011, 49(9): 1071–1079
CrossRef
Google scholar
|
[126] |
Yin H, Wen G, Hou S,
CrossRef
Google scholar
|
[127] |
Hussein R D, Ruan D, Lu G,
CrossRef
Google scholar
|
[128] |
Mamalis A, Manolakos D, Ioannidis M,
CrossRef
Google scholar
|
[129] |
Rossi A, Fawaz Z, Behdinan K. Numerical simulation of the axial collapse of thin-walled polygonal section tubes. Thin-Walled Structures, 2005, 43(10): 1646–1661
CrossRef
Google scholar
|
[130] |
Zhang X, Huh H. Crushing analysis of polygonal columns and angle elements. International Journal of Impact Engineering, 2010, 37(4): 441–451
CrossRef
Google scholar
|
[131] |
Zhang X, Cheng G, Zhang H. Theoretical prediction and numerical simulation of multi-cell square thin-walled structures. Thin-Walled Structures, 2006, 44(11): 1185–1191
CrossRef
Google scholar
|
[132] |
Tran T, Hou S, Han X,
CrossRef
Google scholar
|
[133] |
Tran T, Hou S, Han X,
CrossRef
Google scholar
|
[134] |
Zheng G, Pang T, Sun G,
CrossRef
Google scholar
|
[135] |
Zhang X, Zhang H. Energy absorption of multi-cell stub columns under axial compression. Thin-Walled Structures, 2013, 68: 156–163
CrossRef
Google scholar
|
[136] |
Tang Z, Liu S, Zhang Z. Analysis of energy absorption characteristics of cylindrical multi-cell columns. Thin-Walled Structures, 2013, 62: 75–84
CrossRef
Google scholar
|
[137] |
Yin H, Wen G, Liu Z,
CrossRef
Google scholar
|
[138] |
Hong W, Fan H, Xia Z,
CrossRef
Google scholar
|
[139] |
Tabacu S. Analysis of circular tubes with rectangular multi-cell insert under oblique impact loads. Thin-Walled Structures, 2016, 106: 129–147
CrossRef
Google scholar
|
[140] |
Chirwa E. Theoretical analysis of tapered thin-walled metal inverbucktube. International Journal of Mechanical Sciences, 1993, 35(3–4): 325–351
CrossRef
Google scholar
|
[141] |
Li G, Zhang Z, Sun G,
CrossRef
Google scholar
|
[142] |
Zhang X, Zhang H, Wen Z. Axial crushing of tapered circular tubes with graded thickness. International Journal of Mechanical Sciences, 2015, 92: 12–23
CrossRef
Google scholar
|
[143] |
Li G, Xu F, Sun G,
CrossRef
Google scholar
|
[144] |
Zhang X, Wen Z, Zhang H. Axial crushing and optimal design of square tubes with graded thickness. Thin-Walled Structures, 2014, 84: 263–274
CrossRef
Google scholar
|
[145] |
An X, Gao Y, Fang J,
CrossRef
Google scholar
|
[146] |
Gupta P. A study on mode of collapse of varying wall thickness metallic frusta subjected to axial compression. Thin-Walled Structures, 2008, 46(5): 561–571
CrossRef
Google scholar
|
[147] |
Zhang X, Zhang H. Relative merits of conical tubes with graded thickness subjected to oblique impact loads. International Journal of Mechanical Sciences, 2015, 98: 111–125
CrossRef
Google scholar
|
[148] |
Zhang H, Zhang X. Crashworthiness performance of conical tubes with nonlinear thickness distribution. Thin-Walled Structures, 2016, 99: 35–44
CrossRef
Google scholar
|
[149] |
Fang J, Gao Y, Sun G,
CrossRef
Google scholar
|
[150] |
Sun G, Xu F, Li G,
CrossRef
Google scholar
|
[151] |
Haghi Kashani M, Shahsavari Alavijeh H, Akbarshahi H,
CrossRef
Google scholar
|
[152] |
Sharifi S, Shakeri M, Fakhari H E,
CrossRef
Google scholar
|
[153] |
Goel M D. Deformation, energy absorption and crushing behavior of single-, double- and multi-wall foam filled square and circular tubes. Thin-Walled Structures, 2015, 90: 1–11
CrossRef
Google scholar
|
[154] |
Azimi M B, Asgari M. A new bi-tubular conical–circular structure for improving crushing behavior under axial and oblique impacts. International Journal of Mechanical Sciences, 2016, 105: 253–265
CrossRef
Google scholar
|
[155] |
Nia A A, Chahardoli S. Mechanical behavior of nested multi-tubular structures under quasi-static axial load. Thin-Walled Structures, 2016, 106: 376–389
CrossRef
Google scholar
|
[156] |
Estrada Q, Szwedowicz D, Rodriguez-Mendez A,
CrossRef
Google scholar
|
[157] |
Sun F, Lai C, Fan H,
CrossRef
Google scholar
|
[158] |
Sun F, Lai C, Fan H. In-plane compression behavior and energy absorption of hierarchical triangular lattice structures. Materials & Design, 2016, 100: 280–290
CrossRef
Google scholar
|
[159] |
Luo Y, Fan H. Energy absorbing ability of rectangular self-similar multi-cell sandwich-walled tubular structures. Thin-Walled Structures, 2018, 124: 88–97
CrossRef
Google scholar
|
[160] |
Li W, Luo Y, Li M,
CrossRef
Google scholar
|
[161] |
Fan H, Luo Y, Yang F,
CrossRef
Google scholar
|
[162] |
Chen Y, Qiao C, Qiu X,
CrossRef
Google scholar
|
[163] |
Yang K, Qin Q, Zhai Z,
CrossRef
Google scholar
|
[164] |
Yang K, Chen Y, Zhang L,
CrossRef
Google scholar
|
[165] |
Baroutaji A, Gilchrist M, Olabi A G J T W S. Quasi-static, impact and energy absorption of internally nested tubes subjected to lateral loading. Thin-Walled Structures, 2016, 98: 337–350
CrossRef
Google scholar
|
[166] |
Olabi A G, Morris E, Hashmi M,
CrossRef
Google scholar
|
[167] |
Olabi A G, Morris E, Hashmi M,
CrossRef
Google scholar
|
[168] |
Wang H, Yang J, Liu H,
CrossRef
Google scholar
|
[169] |
Tarlochan F, Ramesh S. Composite sandwich structures with nested inserts for energy absorption application. Composite Structures, 2012, 94(3): 904–916
CrossRef
Google scholar
|
[170] |
Reddy T, Reid S. Axial splitting of circular metal tubes. International Journal of Mechanical Sciences, 1986, 28(2): 111–131
CrossRef
Google scholar
|
[171] |
Zhang X, Yu T. Energy absorption of pressurized thin-walled circular tubes under axial crushing. International Journal of Mechanical Sciences, 2009, 51(5): 335–349
CrossRef
Google scholar
|
[172] |
Chen W, Wierzbicki T. Relative merits of single-cell, multi-cell and foam-filled thin-walled structures in energy absorption. Thin-Walled Structures, 2001, 39(4): 287–306
CrossRef
Google scholar
|
[173] |
Ahmad Z, Thambiratnam D. Crushing response of foam-filled conical tubes under quasi-static axial loading. Materials & Design, 2009, 30(7): 2393–2403
CrossRef
Google scholar
|
[174] |
Alavi Nia A, Haddad Hamedani J. Comparative analysis of energy absorption and deformations of thin walled tubes with various section geometries. Thin-Walled Structures, 2010, 48(12): 946–954
CrossRef
Google scholar
|
[175] |
Zhang X, Cheng G. A comparative study of energy absorption characteristics of foam-filled and multicell square columns. International Journal of Impact Engineering, 2007, 34(11): 1739–1752
CrossRef
Google scholar
|
/
〈 | 〉 |