Crushing behavior of multi-cell tubes with a novel pattern of design for their cross-section under multiple crushing angles

References

• M. M. Sofi, A review on energy absorption of multi cell thin walled structure, J Adv Rev Sci Res., vol. 16, pp. 18–24, 2015.
   Google Scholar
• P. Hosseini-Tehrani, and A. Nankali, Study on characteristics of a crashworthy high-speed train nose, Int. J. Crashworthiness, vol. 15, pp. 161–173, 2010. DOI: 10.1080/13588260903094418.
   Web of Science ®Google Scholar
• A. A. Nia, and J. H. Hamedani, Comparative analysis of energy absorption and deformations of thin walled tubes with various section geometries, Thin-Walled Struct., vol. 48, pp. 946–954, 2010.
   Web of Science ®Google Scholar
• S. Guillow, G. Lu, and R. Grzebieta, Quasi-static axial compression of thin-walled circular aluminium tubes, Int. J. Mech. Sci., vol. 43, pp. 2103–2123, 2001. DOI: 10.1016/S0020-7403(01)00031-5.
   Web of Science ®Google Scholar
• W. Abramowicz, and N. Jones, Dynamic progressive buckling of circular and square tubes, Int. J. Impact Eng., vol. 4, pp. 243–270, 1986. DOI: 10.1016/0734-743X(86)90017-5.
   Google Scholar
• P. Hosseini-Tehrani, and S. Pirmohammad, Collapse study of thin-walled polygonal section columns subjected to oblique loads, Proc. Inst. Mech. Eng., vol. 221, pp. 801–810, 2007. DOI: 10.1243/09544070JAUTO482.
   PubMed Web of Science ®Google Scholar
• P. Hosseini-Tehrani, and S. Pirmohammad, Collapse study of a pair thin-walled prismatic column subjected to oblique loads, Proc. Inst. Mech. Eng., vol. 2011, 267–279, 2011.
   Google Scholar
• G. Sun, T. Pang, J. Fang, G. Li, and Q. Li, Parameterization of criss-cross configurations for multiobjective crashworthiness optimization, Int. J. Mech. Sci., vol. 124, pp. 145–157, 2017. DOI: 10.1016/j.ijmecsci.2017.02.027.
   Web of Science ®Google Scholar
• A. Eyvazian, M. K. Habibi, A. M. Hamouda, and R. Hedayati, Axial crushing behavior and energy absorption efficiency of corrugated tubes, Mater. Des. (1980-2015), vol. 54, pp. 1028–1038, 2014. DOI: 10.1016/j.matdes.2013.09.031.
   Web of Science ®Google Scholar
• A. Eyvazian, T. Tran, and A. M. Hamouda, Experimental and theoretical studies on axially crushed corrugated metal tubes, Int. J. Non. Linear Mech., vol. 101, pp. 86–94, 2018. DOI: 10.1016/j.ijnonlinmec.2018.02.009.
   Web of Science ®Google Scholar
• A. Baykasoğlu, and C. Baykasoğlu, Multiple objective crashworthiness optimization of circular tubes with functionally graded thickness via artificial neural networks and genetic algorithms, Proc. Inst. Mech. Eng. vol. 231, pp. 2005–2016, 2017. DOI: 10.1177/0954406215627181.
   Web of Science ®Google Scholar
• E. Çetin, and C. Baykasoğlu, Energy absorption of thin-walled tubes enhanced by lattice structures, Int. J. Mech. Sci., vol. 157, pp. 471–484, 2019. DOI: 10.1016/j.ijmecsci.2019.04.049.
   Web of Science ®Google Scholar
• C. Baykasoğlu, A. Baykasoğlu, and M. Tunay Çetin, A comparative study on crashworthiness of thin-walled tubes with functionally graded thickness under oblique impact loadings, Int. J. Crashworthiness, vol. 24, pp. 453–471, 2019. DOI: 10.1080/13588265.2018.1478775.
   Web of Science ®Google Scholar
• H. Kavi, A. K. Toksoy, and M. Guden, Predicting energy absorption in a foam-filled thin-walled aluminum tube based on experimentally determined strengthening coefficient, Mater. Des., vol. 27, pp. 263–269, 2006. DOI: 10.1016/j.matdes.2004.10.024.
   Web of Science ®Google Scholar
• M. Seitzberger, F. G. Rammerstorfer, R. Gradinger, H. P. Degischer, M. Blaimschein, and C. Walch, Experimental studies on the quasi-static axial crushing of steel columns filled with aluminium foam, Int. J. Solids Struct., vol. 37, pp. 4125–4147, 2000. DOI: 10.1016/S0020-7683(99)00136-5.
   Web of Science ®Google Scholar
• S. Pirmohammad, and S. Ahmadi-Saravani, Crashworthiness performance of stiffened foam-filled tapered structures under axial and oblique dynamic loads, Latin Am. J. Solids Struct., vol. 15, pp. 1–21, 2018. DOI: 10.1590/1679-78254596.
   Web of Science ®Google Scholar
• S. Pirmohammad, S. Ahmadi-Saravani, and J. Zakavi, Crashworthiness optimization design of foam-filled tapered decagonal structures subjected to axial and oblique impacts, J Central South Univ., vol. 26, pp. 2729–2745, 2019. DOI: 10.1007/s11771-019-4209-1.
   Web of Science ®Google Scholar
• W. Chen, and T. Wierzbicki, Relative merits of single-cell, multi-cell and foam-filled thin-walled structures in energy absorption, Thin-Walled Struct., vol. 39, pp. 287–306, 2001. DOI: 10.1016/S0263-8231(01)00006-4.
   Web of Science ®Google Scholar
• H. Yin, G. Wen, S. Hou, and K. Chen, Crushing analysis and multiobjective crashworthiness optimization of honeycomb-filled single and bitubular polygonal tubes, Mater. Des., vol. 32, pp. 4449–4460, 2011. DOI: 10.1016/j.matdes.2011.03.060.
   Web of Science ®Google Scholar
• A. Baroutaji, A. Arjunan, A. Niknejad, T. N. Tran, and A. G. Olabi, Application of cellular material in crashworthiness applications: an overview, Reference Module in Materials Science and Materials Engineering, 2019. DOI: 10.1016/B978-0-12-803581-8.09268-7.
   Google Scholar
• S. Yang, and C. Qi, Multiobjective optimization for empty and foam-filled square columns under oblique impact loading, Int. J. Impact Eng., vol. 54, pp. 177–191, 2013. DOI: 10.1016/j.ijimpeng.2012.11.009.
   Web of Science ®Google Scholar
• A. Baroutaji, A. Arjunan, J. Robinson, M. Ramadan, M. A. Abdelkareem, and A. G. Olabi, Metamaterial for crashworthiness applications, 2021. DOI: 10.1016/B978-0-12-815732-9.00092-9.
   Google Scholar
• X. Zhang, H. Zhang, and Z. Wen, Axial crushing of tapered circular tubes with graded thickness, Int. J. Mech. Sci., vol. 92, pp. 12–23, 2015. DOI: 10.1016/j.ijmecsci.2014.11.022.
   Web of Science ®Google Scholar
• P. Hosseini-Tehrani, S. Pirmohammad, and M. Golmohammadi, Study on the collapse of tapered tubes subjected to oblique loads, Proc. Inst. Mech. Eng., vol. 222, pp. 2025–2039, 2008. DOI: 10.1243/09544070JAUTO912.
   Web of Science ®Google Scholar
• C. Qi, and S. Yang, Crashworthiness and lightweight optimisation of thin-walled conical tubes subjected to an oblique impact, Int. J. Crashworthiness, vol. 19, pp. 334–351, 2014. DOI: 10.1080/13588265.2014.893788.
   Web of Science ®Google Scholar
• A. Baroutaji, A. Arjunan, M. Stanford, J. Robinson, and A. G. Olabi, Deformation and energy absorption of additively manufactured functionally graded thickness thin-walled circular tubes under lateral crushing, Eng. Struct., vol. 226, pp. 111324, 2021. DOI: 10.1016/j.engstruct.2020.111324.
   Web of Science ®Google Scholar
• H. Nikkhah, A. Baroutaji, and A. G. Olabi, Crashworthiness design and optimisation of windowed tubes under axial impact loading, Thin-Walled Struct., vol. 142, pp. 132–148, 2019. DOI: 10.1016/j.tws.2019.04.052.
   Web of Science ®Google Scholar
• J. Song, and F. Guo, A comparative study on the windowed and multi-cell square tubes under axial and oblique loading, Thin-Walled Struct., vol. 66, pp. 9–14, 2013. DOI: 10.1016/j.tws.2013.02.002.
   Web of Science ®Google Scholar
• S. Pirmohammad, and S. Esmaeili-Marzdashti, Multi-objective crashworthiness optimization of square and octagonal bitubal structures including different hole shapes, Thin-Walled Struct., vol. 139, pp. 126–138, 2019. DOI: 10.1016/j.tws.2019.03.004.
   Web of Science ®Google Scholar
• P. Xu, C. Yang, Y. Peng, S. Yao, J. Xing, and B. Li, Cut-out grooves optimization to improve crashworthiness of a gradual energy-absorbing structure for subway vehicles, Mater. Des., vol. 103, pp. 132–143, 2016. DOI: 10.1016/j.matdes.2016.04.059.
   Web of Science ®Google Scholar
• S. Pirmohammad, M. H. Ekbatan, and S. Esmaeili-Marzdashti, Crashworthiness of double-cell conical tubes with different cross sections subjected to dynamic axial and oblique loads, J. Central South Univ., vol. 25, pp. 632–645, 2018.
   Web of Science ®Google Scholar
• S. Pirmohammad, S. Esmaeili-Marzdashti, and A. Eyvazian, Crashworthiness design of multi-cell tapered tubes using response surface methodology, J. Comput. Appl. Res. Mech. Eng. (JCARME)., vol. 9, pp. 59–75, 2019.
   Google Scholar
• C. Qi, S. Yang, and F. Dong, Crushing analysis and multiobjective crashworthiness optimization of tapered square tubes under oblique impact loading, Thin-Walled Struct., vol. 59, pp. 103–119, 2012. DOI: 10.1016/j.tws.2012.05.008.
   Web of Science ®Google Scholar
• X. Zhang, G. Cheng, and H. Zhang, Theoretical prediction and numerical simulation of multi-cell square thin-walled structures, Thin-Walled Struct., vol. 44, pp. 1185–1191, 2006. DOI: 10.1016/j.tws.2006.09.002.
   Web of Science ®Google Scholar
• N. Qiu, Y. Gao, J. Fang, Z. Feng, G. Sun, and Q. Li, Crashworthiness analysis and design of multi-cell hexagonal columns under multiple loading cases, Finite Elem. Anal. Des., vol. 104, pp. 89–101, 2015. DOI: 10.1016/j.finel.2015.06.004.
   Web of Science ®Google Scholar
• X. Zhang, K. Leng, and H. Zhang, Axial crushing of embedded multi-cell tubes, Int. J. Mech. Sci., vol. 131, pp. 459–470, 2017. DOI: 10.1016/j.ijmecsci.2017.07.019.
   Web of Science ®Google Scholar
• A. A. Nia, and M. Parsapour, Comparative analysis of energy absorption capacity of simple and multi-cell thin-walled tubes with triangular, square, hexagonal and octagonal sections, Thin-Walled Struct., vol. 74, pp. 155–165, 2014. DOI: 10.1016/j.tws.2013.10.005.
   Web of Science ®Google Scholar
• T. Tran, Crushing and theoretical analysis of multi-cell thin-walled triangular tubes under lateral loading, Thin-Walled Struct., vol. 115, pp. 205–214, 2017. DOI: 10.1016/j.tws.2017.02.027.
   Web of Science ®Google Scholar
• A. Najafi, and M. Rais-Rohani, Mechanics of axial plastic collapse in multi-cell, multi-corner crush tubes, Thin-Walled Struct., vol. 49, pp. 1–12, 2011. DOI: 10.1016/j.tws.2010.07.002.
   Web of Science ®Google Scholar
• A. Mahmoodi, M. Shojaeefard, and H. S. Googarchin, Theoretical development and numerical investigation on energy absorption behavior of tapered multi-cell tubes, Thin-Walled Struct., vol. 102, pp. 98–110, 2016. DOI: 10.1016/j.tws.2016.01.019.
   Web of Science ®Google Scholar
• N. Qiu, Y. Gao, J. Fang, Z. Feng, G. Sun, and Q. Li, Theoretical prediction and optimization of multi-cell hexagonal tubes under axial crashing, Thin-Walled Struct., vol. 102, pp. 111–121, 2016. DOI: 10.1016/j.tws.2016.01.023.
   Web of Science ®Google Scholar
• J. Zhou, R. Qin, and B. Chen, Energy absorption properties of multi-cell thin-walled tubes with a double surface gradient, Thin-Walled Struct., vol. 145, pp. 106386, 2019. DOI: 10.1016/j.tws.2019.106386.
   Web of Science ®Google Scholar
• T. Tran, and A. Baroutaji, Crashworthiness optimal design of multi-cell triangular tubes under axial and oblique impact loading, Eng. Fail. Anal., vol. 93, pp. 241–256, 2018. DOI: 10.1016/j.engfailanal.2018.07.003.
   Web of Science ®Google Scholar
• S. Pirmohammad, and S. Esmaeili-Marzdashti, Multi-objective optimization of multi-cell conical structures under dynamic loads, J. Central South Univ., vol. 26, pp. 2464–2481, 2019. DOI: 10.1007/s11771-019-4187-3.
   Web of Science ®Google Scholar
• S. Pirmohammad, and S. Esmaeili-Marzdashti, Crushing behavior of new designed multi-cell members subjected to axial and oblique quasi-static loads, Thin-Walled Struct., vol. 108, pp. 291–304, 2016. DOI: 10.1016/j.tws.2016.08.023.
   Web of Science ®Google Scholar
• S. Pirmohammad, and S. Esmaeili Marzdashti, Crashworthiness optimization of combined straight-tapered tubes using genetic algorithm and neural networks, Thin-Walled Struct., vol. 127, pp. 318–332, 2018. DOI: 10.1016/j.tws.2018.01.022.
   Web of Science ®Google Scholar
• S. Pirmohammad, and H. Nikkhah, Crashworthiness investigation of bitubal columns reinforced with several inside ribs under axial and oblique impact loads, Proc. Inst. Mech. Eng., vol. 232, pp. 367–383, 2018. DOI: 10.1177/0954407017702986.
   Web of Science ®Google Scholar
• S. Esmaeili-Marzdashti, S. Pirmohammad, and S. Esmaeili-Marzdashti, Crashworthiness analysis of s-shaped structures under axial impact loading, Latin Am. J. Solids Struct., vol. 14, pp. 743–764, 2017. DOI: 10.1590/1679-78253430.
   Web of Science ®Google Scholar
• T. Tran, S. Hou, X. Han, W. Tan, and N. T. Nguyen, Theoretical prediction and crashworthiness optimization of multi-cell triangular tubes, Thin-Walled Struct., vol. 82, pp. 183–195, 2014. DOI: 10.1016/j.tws.2014.03.019.
   Web of Science ®Google Scholar
• T. Tran, S. Hou, X. Han, N. Nguyen, and M. Chau, Theoretical prediction and crashworthiness optimization of multi-cell square tubes under oblique impact loading, Int. J. Mech. Sci., vol. 89, pp. 177–193, 2014. DOI: 10.1016/j.ijmecsci.2014.08.027.
   Web of Science ®Google Scholar
• T. Tran, S. Hou, X. Han, and M. Chau, Crushing analysis and numerical optimization of angle element structures under axial impact loading, Compos. Struct., vol. 119, pp. 422–435, 2015. DOI: 10.1016/j.compstruct.2014.09.019.
   Web of Science ®Google Scholar
• E. Acar, M. Altin, and M. A. Güler, Evaluation of various multi-cell design concepts for crashworthiness design of thin-walled aluminum tubes, Thin-Walled Struct., vol. 142, pp. 227–235, 2019. DOI: 10.1016/j.tws.2019.05.012.
   Web of Science ®Google Scholar
• Z. Li, W. Ma, L. Hou, P. Xu, and S. Yao, Crashworthiness analysis of corrugations reinforced multi-cell square tubes, Thin-Walled Struct., vol. 150, pp. 106708, 2020. DOI: 10.1016/j.tws.2020.106708.
   Web of Science ®Google Scholar
• H. Nikkhah, A. Baroutaji, Z. Kazancı, and A. Arjunan, Evaluation of crushing and energy absorption characteristics of bio-inspired nested structures, Thin-Walled Struct., vol. 148, pp. 106615, 2020. DOI: 10.1016/j.tws.2020.106615.
   Web of Science ®Google Scholar
• K. Yang, S. Xu, S. Zhou, and Y. M. Xie, Multi-objective optimization of multi-cell tubes with origami patterns for energy absorption, Thin-Walled Struct., vol. 123, pp. 100–113, 2018. DOI: 10.1016/j.tws.2017.11.005.
   Web of Science ®Google Scholar
• M. Altin, Ü. Kılınçkaya, E. Acar, and M. A. Güler, Investigation of combined effects of cross section, taper angle and cell structure on crashworthiness of multi-cell thin-walled tubes, Int. J. Crashworthiness, vol. 24, pp. 121–136, 2019. DOI: 10.1080/13588265.2017.1410338.
   Web of Science ®Google Scholar
• L. Zhang, Z. Bai, and F. Bai, Crashworthiness design for bio-inspired multi-cell tubes with quadrilateral, hexagonal and octagonal sections, Thin-Walled Struct., vol. 122, pp. 42–51, 2018. DOI: 10.1016/j.tws.2017.10.010.
   Web of Science ®Google Scholar
• M. Altin, M. A. Güler, and S. K. Mert, The effect of percent foam fill ratio on the energy absorption capacity of axially compressed thin-walled multi-cell square and circular tubes, Int. J. Mech. Sci., vol. 131, pp. 368–379, 2017. DOI: 10.1016/j.ijmecsci.2017.07.003.
   Web of Science ®Google Scholar
• S. Pirmohammad, Crashworthiness performance of concentric structures with different cross-sectional shapes under multiple loading conditions, Proc. Inst. Mech. Eng., 2021. 235: 417–435.
   Google Scholar
• S. Xie, W. Yang, N. Wang, and H. Li, Crashworthiness analysis of multi-cell square tubes under axial loads, Int. J. Mech. Sci., vol. 121, pp. 106–118, 2017. DOI: 10.1016/j.ijmecsci.2016.12.005.
   Web of Science ®Google Scholar
• H. Yin, G. Wen, Z. Bai, Z. Chen, and Q. Qing, Theoretical prediction and crashworthiness optimization of multi-cell polygonal tubes, J. Sandwich Struct. Mater., vol. 22, pp. 190–219, 2020. DOI: 10.1177/1099636217737330.
   Web of Science ®Google Scholar
• H. Yin, and G. Wen, Theoretical prediction and numerical simulation of honeycomb structures with various cell specifications under axial loading, Int. J. Mech. Mater. Des., vol. 7, pp. 253–263, 2011. DOI: 10.1007/s10999-011-9163-5.
   Web of Science ®Google Scholar
• C. L. Hwang, and K. Yoon, Methods for multiple attribute decision making, Multiple Attribute Decision Making, Springer, Berlin, Heidelberg, pp. 58–191, 1981.
   Google Scholar
• K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comput., vol. 6, pp. 182–197, 2002. DOI: 10.1109/4235.996017.
   Web of Science ®Google Scholar
• X. Liao, Q. Li, X. Yang, W. Li, and W. Zhang, A two-stage multi-objective optimisation of vehicle crashworthiness under frontal impact, Int. J. Crashworthiness, vol. 13, pp. 279–288, 2008. DOI: 10.1080/13588260801933659.
   Web of Science ®Google Scholar
• J. D. Knowles, and D. W. Corne, Approximating the nondominated front using the Pareto archived evolution strategy, Evol. Comput., vol. 8, pp. 149–172, 2000. DOI: 10.1162/106365600568167.
   PubMed Web of Science ®Google Scholar
• G. Sun, G. Li, M. Stone, and Q. Li, A two-stage multi-fidelity optimization procedure for honeycomb-type cellular materials, Comput. Mater. Sci., vol. 49, pp. 500–511, 2010. DOI: 10.1016/j.commatsci.2010.05.041.
   Web of Science ®Google Scholar
• G. Zheng, T. Pang, G. Sun, S. Wu, and Q. Li, Theoretical, numerical, and experimental study on laterally variable thickness (LVT) multi-cell tubes for crashworthiness, Int. J. Mech. Sci., vol. 118, pp. 283–297, 2016. DOI: 10.1016/j.ijmecsci.2016.09.015.
   Web of Science ®Google Scholar
• N. Qiu, Y. Gao, J. Fang, G. Sun, Q. Li, and N. H. Kim, Crashworthiness optimization with uncertainty from surrogate model and numerical error, Thin-Walled Struct., vol. 129, pp. 457–472, 2018. DOI: 10.1016/j.tws.2018.05.002.
   Web of Science ®Google Scholar
• J. Wang, Y. Zhang, N. He, et al., Crashworthiness behavior of Koch fractal structures, Mater. Des., vol. 144, pp. 229–244, 2018. DOI: 10.1016/j.matdes.2018.02.035.
   Web of Science ®Google Scholar
• Z. Tang, S. Liu, and Z. Zhang, Analysis of energy absorption characteristics of cylindrical multi-cell columns, Thin-Walled Struct., vol. 62, pp. 75–84, 2013. DOI: 10.1016/j.tws.2012.05.019.
   Web of Science ®Google Scholar
• W. Liu, Z. Lin, J. He, N. Wang, and X. Deng, Crushing behavior and multi-objective optimization on the crashworthiness of sandwich structure with star-shaped tube in the center, Thin-Walled Struct., vol. 108, pp. 205–214, 2016. DOI: 10.1016/j.tws.2016.08.021.
   Web of Science ®Google Scholar