Influence of spherical triggers on axial collapse of tapered tubes

References

• Kılıçaslan C. Numerical crushing analysis of aluminum foam-filled corrugated single- and double-circular tubes subjected to axial impact loading. Thin-Walled Struct. 2015;96:82–94.
   Web of Science ®Google Scholar
• Gao Q, Wang L, Wang Y, et al. Optimization of foam-filled double ellipse tubes under multiple loading cases. Adv Eng Softw. 2016;99:27–35.
   Web of Science ®Google Scholar
• Yin H, Fang H, Xiao Y, et al. Multi-objective robust optimization of foam-filled tapered multi-cell thin-walled structures. Struct Multidisc Optim. 2015;52(6):1051–1067.
   Web of Science ®Google Scholar
• Song X, Sun G, Li G, et al. Crashworthiness optimization of foam-filled tapered thin-walled structure using multiple surrogate models. Struct Multidisc Optim. 2013;47(2):221–231.
   Web of Science ®Google Scholar
• Sun H, Ge C, Gao Q, et al. Crashworthiness of sandwich cylinder filled with double-arrowed auxetic structures under axial impact loading. Int J Crashworthiness. 2022;27(5):1383–1392.
   Web of Science ®Google Scholar
• Deng X, Liu W. Experimental and numerical investigation of a novel sandwich sinusoidal lateral corrugated tubular structure under axial compression. Int J Mech Sci. 2019;151:274–287.
   Web of Science ®Google Scholar
• Su P-B, Han B, Yang M, et al. Axial compressive collapse of ultralight corrugated sandwich cylindrical shells. Mater Des. 2018;160:325–337.
   Web of Science ®Google Scholar
• Qiu N, Gao Y, Fang J, et al. Topological design of multi-cell hexagonal tubes under axial and lateral loading cases using a modified particle swarm algorithm. Appl Math Modell. 2018;53:567–583.
   Web of Science ®Google Scholar
• Qiu N, Gao Y, Fang J, et al. Crashworthiness analysis and design of multi-cell hexagonal columns under multiple loading cases. Finite Elem Anal Des. 2015;104:89–101.
   Web of Science ®Google Scholar
• Fang J, Gao Y, Sun G, et al. On design of multi-cell tubes under axial and oblique impact loads. Thin-Walled Struct. 2015;95:115–126.
   Web of Science ®Google Scholar
• Tran TN, Baroutaji A, Estrada Q, et al. Crashworthiness analysis and optimization of standard and windowed multi-cell hexagonal tubes. Struct Multidisc Optim. 2021;63(5):2191–2209.
   Web of Science ®Google Scholar
• Abdullahi HS, Gao S. A two-stage approach to the optimization design of multi-cell square tubal structures. Struct Multidisc Optim. 2021;63(2):897–913.
   Web of Science ®Google Scholar
• Fang J, Gao Y, Sun G, et al. Dynamic crashing behavior of new extrudable multi-cell tubes with a functionally graded thickness. Int J Mech Sci. 2015;103:63–73.
   Web of Science ®Google Scholar
• Qiu N, Zhang J, Yuan F, et al. Mechanical performance of triply periodic minimal surface structures with a novel hybrid gradient fabricated by selective laser melting. Eng Struct. 2022;263:114377.
   Web of Science ®Google Scholar
• Fang J, Sun G, Qiu N, et al. On design optimization for structural crashworthiness and its state of the art. Struct Multidisc Optim. 2017;55(3):1091–1119.
   Web of Science ®Google Scholar
• Ha NS, Lu G, Xiang X. High energy absorption efficiency of thin-walled conical corrugation tubes mimicking coconut tree configuration. Int J Mech Sci. 2018;148:409–421.
   Web of Science ®Google Scholar
• Wu S, Li G, Sun G, et al. Crashworthiness analysis and optimization of sinusoidal corrugation tube. Thin-Walled Struct. 2016;105:121–134.
   Web of Science ®Google Scholar
• Li Y, You Z. Origami concave tubes for energy absorption. Int J Solids Struct. 2019;169:21–40.
   Web of Science ®Google Scholar
• Yao S, Zhu H, Liu M, et al. Energy absorption of origami tubes with polygonal cross-sections. Thin-Walled Struct. 2020;157:107013.
   Web of Science ®Google Scholar
• Ma J, Hou D, Chen Y, et al. Quasi-static axial crushing of thin-walled tubes with a kite-shape rigid origami pattern: numerical simulation. Thin-Walled Struct. 2016;100:38–47.
   Web of Science ®Google Scholar
• Ming S, Song Z, Li T, et al. The energy absorption of thin-walled tubes designed by origami approach applied to the ends. Mater Des. 2020;192:108725.
   Web of Science ®Google Scholar
• Yang K, Xu S, Shen J, et al. Energy absorption of thin-walled tubes with pre-folded origami patterns: numerical simulation and experimental verification. Thin-Walled Struct. 2016;103:33–44.
   Web of Science ®Google Scholar
• Daneshi GH, Hosseinipour SJ. Grooves effect on crashworthiness characteristics of thin-walled tubes under axial compression. Mater Des. 2002;23(7):611–617.
   Web of Science ®Google Scholar
• Hosseinipour SJ, Daneshi GH. Energy absorbtion and mean crushing load of thin-walled grooved tubes under axial compression. Thin-Walled Struct. 2003;41(1):31–46.
   Web of Science ®Google Scholar
• Salehghaffari S, Tajdari M, Panahi M, et al. Attempts to improve energy absorption characteristics of circular metal tubes subjected to axial loading. Thin-Walled Struct. 2010;48(6):379–390.
   Web of Science ®Google Scholar
• Darvizeh A, Meshkinzar A, Alitavoli M, et al. Low velocity impact of empty and foam filled circumferentially grooved thick-walled circular tubes. Thin-Walled Struct. 2017;110:97–105.
   Web of Science ®Google Scholar
• Alavi Nia A, Rahpeima R, Chahardoli S, et al. Evaluation of the effect of inner and outer transverse and longitudinal grooves on energy absorption characteristics of cylindrical thin-walled tubes under quasi-static axial load. Int J Crashworthiness. 2019;24(1):1–12.
   Web of Science ®Google Scholar
• Asanjarani A, Mahdian A, Dibajian SH. Comparative analysis of energy absorption behavior of tapered and grooved thin-walled tubes with the various geometry of the cross section. Mech Adv Mater Struct. 2020;27(8):633–644.
   Web of Science ®Google Scholar
• Rezvani MJ, Damghani NM. Analytical model for energy absorption and plastic collapse of thin-walled grooved frusta tubes. Mech Adv Mater Struct. 2015;22(5):338–348.
   Web of Science ®Google Scholar
• Mahmoodi A, Shojaeefard MH, Saeidi Googarchin H. Theoretical development and numerical investigation on energy absorption behavior of tapered multi-cell tubes. Thin-Walled Struct. 2016;102:98–110.
   Web of Science ®Google Scholar
• Nagel GM, Thambiratnam DP. Computer simulation and energy absorption of tapered thin-walled rectangular tubes. Thin-Walled Struct. 2005;43(8):1225–1242.
   Web of Science ®Google Scholar
• Jia Z, Yu Y, Hou S, et al. Biomimetic architected materials with improved dynamic performance. J Mech Phys Solids. 2019;125:178–197.
   Web of Science ®Google Scholar
• Fang J, Sun G, Qiu N, et al. On hierarchical honeycombs under out-of-plane crushing. Int J Solids Struct. 2018;135:1–13.
   Web of Science ®Google Scholar
• Zhang L, Bai Z, Bai F. Crashworthiness design for bio-inspired multi-cell tubes with quadrilateral, hexagonal and octagonal sections. Thin-Walled Struct. 2018;122:42–51.
   Web of Science ®Google Scholar
• Zhang L, Zhong Y, Tan W, et al. Crushing characteristics of bionic thin-walled tubes inspired by bamboo and beetle forewing. Mech Adv Mater Struct. 2022;29(14):2024–2039.
   Web of Science ®Google Scholar
• Fu J, Liu Q, Liufu K, et al. Design of bionic-bamboo thin-walled structures for energy absorption. Thin-Walled Struct. 2019;135:400–413.
   Web of Science ®Google Scholar
• Ma W, Xie S, Li Z. Mechanical performance of bio-inspired corrugated tubes with varying vertex configurations. Int J Mech Sci. 2020;172:105399.
   Web of Science ®Google Scholar
• Xiao Y, Yin H, Fang H, et al. Crashworthiness design of horsetail-bionic thin-walled structures under axial dynamic loading. Int J Mech Mater Des. 2016;12(4):563–576.
   Web of Science ®Google Scholar
• Hu D, Wang Y, Song B, et al. Energy-absorption characteristics of a bionic honeycomb tubular nested structure inspired by bamboo under axial crushing. Composites, Part B. 2019;162:21–32.
   Web of Science ®Google Scholar
• Chen BC, Zou M, Liu GM, et al. Experimental study on energy absorption of bionic tubes inspired by bamboo structures under axial crushing. Int J Impact Eng. 2018;115:48–57.
   Web of Science ®Google Scholar
• Dolzyk G, Jung S, Ufodike CO. Crashworthiness of circular tubes with rhombus star grooving pattern. Mater Today Commun. 2021;29:102899.
   Web of Science ®Google Scholar
• Lian X-G, Lu L-X, Pan L. Investigation of energy absorption characteristics of circular paper tubes under axial impact loading. Int J Impact Eng. 2022;165:104210.
   Web of Science ®Google Scholar
• Tiwary CS, Kishore S, Sarkar S, et al. Morphogenesis and mechanostabilization of complex natural and 3D printed shapes. Sci Adv. 2015;1:e1400052.
   PubMed Web of Science ®Google Scholar
• Qiu N, Gao Y, Fang J, et al. Theoretical prediction and optimization of multi-cell hexagonal tubes under axial crashing. Thin-Walled Struct. 2016;102:111–121.
   Web of Science ®Google Scholar
• Yao R-Y, Yin G-S, Hao W-Q, Zhao Z-y, et al. Axial buckling modes and crashworthiness of circular tube with external linear gradient grooves. Thin-Walled Struct. 2019;134:395–406.
   Web of Science ®Google Scholar
• Bai Y, Wierzbicki T. Application of extended Mohr–Coulomb criterion to ductile fracture. Int J Fract. 2010;161(1):1–20.
   Web of Science ®Google Scholar
• Fang J, Wu C, Rabczuk T, et al. Phase field fracture in elasto-plastic solids: abaqus implementation and case studies. Theor Appl Fract Mech. 2019;103:102252.
   Web of Science ®Google Scholar
• Fang J, Wu C, Rabczuk T, et al. Phase field fracture in elasto-plastic solids: a length-scale insensitive model for quasi-brittle materials. Comput Mech. 2020;66(4):931–961.
   Web of Science ®Google Scholar
• Fang J, Wu C, Li J, et al. Phase field fracture in elasto-plastic solids: variational formulation for multi-surface plasticity and effects of plastic yield surfaces and hardening. Int J Mech Sci. 2019;156:382–396.
   Web of Science ®Google Scholar
• Jeong SB, Yi SI, Kan CD, et al. Structural optimization of an automobile roof structure using equivalent static loads. Proc Inst Mech Eng, Part D: J Automob Eng. 2008;222(11):1985–1995.
   Google Scholar
• Yi SI, Lee JY, Park GJ. Crashworthiness design optimization using equivalent static loads. Proc Inst Mech Eng, Part D: J Automob Eng. 2011. 226:23–38.
   Google Scholar
• An X, Gao Y, Fang J, et al. Crashworthiness design for foam-filled thin-walled structures with functionally lateral graded thickness sheets. Thin-Walled Struct. 2015;91:63–71.
   Web of Science ®Google Scholar
• Yang K, Xu S, Zhou S, et al. Multi-objective optimization of multi-cell tubes with origami patterns for energy absorption. Thin-Walled Struct. 2018;123:100–113.
   Web of Science ®Google Scholar
• Gui C, Bai J, Zuo W. Simplified crashworthiness method of automotive frame for conceptual design. Thin-Walled Struct. 2018;131:324–335.
   Web of Science ®Google Scholar
• Fang J, Qiu N, An X, et al. Crashworthiness design of a steel–aluminum hybrid rail using multi-response objective-oriented sequential optimization. Adv Eng Softw. 2017;112:192–199.
   Web of Science ®Google Scholar
• Fang J, Gao Y, Sun G, et al. Multiobjective sequential optimization for a vehicle door using hybrid materials tailor-welded structure. Proc Inst Mech Eng, Part C: J Mech Eng Sci. 2016;230(17):3092–3100.
   Web of Science ®Google Scholar
• Salehghaffari S, Rais-Rohani M, Najafi A. Analysis and optimization of externally stiffened crush tubes. Thin-Walled Struct. 2011;49(3):397–408.
   Web of Science ®Google Scholar
• Sun G, Pang T, Fang J, et al. Parameterization of criss-cross configurations for multiobjective crashworthiness optimization. Int J Mech Sci. 2017;124-125:145–157.
   Web of Science ®Google Scholar
• Qiu N, Jin Z, Liu J, et al. Hybrid multi-objective robust design optimization of a truck cab considering fatigue life. Thin-Walled Struct. 2021;162:107545.
   Web of Science ®Google Scholar
• Park J-S. Optimal Latin-hypercube designs for computer experiments. J Stat Plann Inference. 1994;39(1):95–111.
   Web of Science ®Google Scholar
• Bai J, Li Y, Zuo W. Cross-sectional shape optimisation for thin-walled beam crashworthiness with stamping constraints using genetic algorithm. IJVD. 2017;73(1/2/3):76.
   Google Scholar
• Deb K, Pratap A, Agarwal S, et al. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput. 2002;6(2):182–197.
   Web of Science ®Google Scholar
• Sun G, Li G, Gong Z, et al. Multiobjective robust optimization method for drawbead design in sheet metal forming. Mater & Des. 2010;31(4):1917–1929.
   Web of Science ®Google Scholar