Optimisation and validation of full and half foam filled double circular tube under multiple load cases

References

• Sun GY, Li GY, Stone M, et al. Application two-stage multi-fidelity optimization procedure for honeycomb-type. Comput Mat Sci. 2010;49:500–511.
   Web of Science ®Google Scholar
• Li G, Zhang Z, Sun G, et al. Crushing analysis and multiobjective optimization for functionally graded foam-filled tubes under multiple load cases. Int J Mech Sci. 2014;89:439–452.
   Web of Science ®Google Scholar
• Baroutaji A, Gilchrist MD, Smyth D, et al. Crush analysis and multi-objective optimization design for circular tube under quasi-static lateral loading. Thin Walled Struct. 2015;86:121–131.
   Web of Science ®Google Scholar
• Li ZB, Yu JL, Guo LW. Deformation and energy absorption of aluminum foam-filled tubes subjected to oblique loading. Int J Mech Sci. 2012;54:48–56.
   Web of Science ®Google Scholar
• Guo LW, Yu JL. Bending behavior of aluminum foam-filled double cylindrical tubes. Acta Mech. 2011;222:233–244.
   Web of Science ®Google Scholar
• Li ZB, Zheng Z, Yua J, et al. Crashworthiness of foam-filled thin-walled circular tubes under dynamic bending, Mater Des. 2013;52:1058–1064.
   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
• Qi C, Yang S, Dong F. Crushing analysis and multiobjective crashworthiness optimization of tapered square tubes under oblique impact loading, Thin Walled Struct. 2012;59:103–119.
   Web of Science ®Google Scholar
• Tarlochan F, Samer F, Hamouda AMS, et al. Design of thin wall structures for energy absorption applications: enhancement of crashworthiness due to axial and oblique impact forces. Thin Walled Struct. 2013;71:7–17.
   Web of Science ®Google Scholar
• Li F, Sun G, Huang X, et al. Multiobjective robust optimization for crashworthiness design of foam filled thin-walled structures with random and interval uncertainties. Eng Struct. 2015;88:111–124.
   Web of Science ®Google Scholar
• Alavi Nia A. Fallah Nejad, Kh, Badnava, H, et al. Effects of buckling initiators on mechanical behavior of thin-walled square tubes subjected to oblique loading. Thin Walled Struct. 2012;59:87–96.
   Web of Science ®Google Scholar
• Fang J, Gao Y, Sun G, et al. Crashworthiness design of foam-filled bitubal structures with uncertainty. Int J Non Linear Mech 2014;65:113–124.
   Google Scholar
• Bi J, Fang H, Wang Q, et al. Modeling and optimization of foam-filled thin-walled columns for crashworthiness designs. Finite Elem Anal Des. 2010;46:698–709.
   Web of Science ®Google Scholar
• Song J, Guo F. A comparative study on the windowed and multi-cell square tubes under axial and oblique loading. Thin Walled Struct. 2013;66:9–14.
   Web of Science ®Google Scholar
• Hou S, Li Q, Long S, et al. Crashworthiness design for foam filled thin-wall structures. Mater Des. 2009;30(6):2024–2032.
   Web of Science ®Google Scholar
• Zhang X, Zhang H, Wang Z. Bending collapse of square tubes with variable thickness. Int J Mech Sci. 2016;106:107–116.
   Web of Science ®Google Scholar
• Yang S, Qi C. Multiobjective optimization for empty and foam-filled square columns under oblique impact loading. Int J Impact Eng. 2013;54:177–191.
   Web of Science ®Google Scholar
• Gao Q, Wang L, Wang Y, et al. Crushing analysis and multiobjective crashworthiness optimization of foam-filled ellipse tubes under oblique impact loading. Thin Walled Struct. 2016;100:105–112.
   Web of Science ®Google Scholar
• Chen Y, Bai Z, Zhang L, et al. Crashworthiness analysis of octagonal multi-cell tube with functionally graded thickness under multiple loading angles. Thin Walled Struct. 2017;110:133–139.
   Web of Science ®Google Scholar
• Weibull W. A statistical function of wide applicability. J Appl Mech. 1951;18:293–307.
   Web of Science ®Google Scholar
• Swolfs Y, Morton H, Scott AE, et al. Synchrotron radiation computed tomography for experimental validation of a tensile strength model for unidirectional fibre-reinforced composites. Compos Part A. 2015;77:106–113.
   Web of Science ®Google Scholar
• Catangiu A, Ungureanu DN, Despa V. Data scattering in strength measurement of steels and glass/epoxy composite. Sci Bull Valahia Univ Mater Mech. 2017;15:11–16.
   Google Scholar
• Barbero E, Fernandez-Saez J, Navarro C. Statistical analysis of the mechanical properties of composite materials. Compos Part B Eng. 2000;31:375–381.
   Web of Science ®Google Scholar
• Huang Y, Talreja R. Statistical analysis of oblique crack evolution in composite laminates. Compos Part B Eng. 2014;65:34–39.
   Web of Science ®Google Scholar
• Kim, HS, Wierzbicki T. Crush behavior of thin-walled prismatic columns under combined bending and compression. Comput Struct. 2001;79(15):1417–1432.
   Web of Science ®Google Scholar
• Zarei HR, Kroger M. Crashworthiness optimization of empty and filled aluminum crash boxes. Int J Crashworthiness. 2007;12(3):255–264.
   Web of Science ®Google Scholar
• Guo LW, Yu JL. Bending response of sandwiched double tube structures with aluminum foam core. In: Lu JWZ, Leung AYT, Iu VP, et al., editors. Proceedings of the ISCM II & EPMESC XII, Hong Kong-Macau, 2009. AIP CP1233, Part One. Melville (NY): American Institute of Physics; p. 602–607.
   Google Scholar
• Ahmad Z, Thambiratnam DP, Tan ACC. 2007 Effect of foam filling on the dynamic axial crushing of thin-walled conical tubes. 5th International Conference on Thin-walled Structures, Gold Coast, Australia, Queensland University of Technology.
   Google Scholar
• Gao Q, Wang L, Wang Y, et al. 2016. Optimization of foam-filled double ellipse tubes under multiple loading cases. Adv Eng Softw. 2010;99:27–35.
   Web of Science ®Google Scholar
• Nagel GM, Thambiratnam DP. Dynamic simulation and energy absorption of tapered thin-walled tubes under oblique impact loading. Int J Impact Eng. 2006;32(10):1595–1620.
   Web of Science ®Google Scholar
• Zheng G, Wu S, Sun G, et al. Crushing analysis of foam-filled single and bitubal polygonal thin-walled tubes. Int J Mech Sci. 2014;87:226–240.
   Web of Science ®Google Scholar
• Kleijnen JPC, Sargent RG. A methodology for the fitting and validation of metamodels in simulation. Eur J Oper Res. 2000;120(1):14–29.
   Web of Science ®Google Scholar
• Sun G, Xu F, Li G, et al. Crashing analysis and multiobjective optimization for thin-walled structures with functionally graded thickness. Int J Impact Eng. 2014;64:62–74.
   Web of Science ®Google Scholar
• Lu G, Yu T. 2003. Energy absorption of structures and materials. Cambridge (UK): Woodhead.
   Google Scholar
• Yin H, Xiao Y, Wen G, et al. Multiobjective optimization for foam-filled multi-cell thin-walled structures under lateral impact. Thin Walled Struct. 2015;94:1–12.
   Web of Science ®Google Scholar
• Reyes A, Langseth M, Hopperstad OS. Crashworthiness of aluminum extrusions subjected to oblique loading: experiments and numerical analyses. Int J Mech Sci. 2002;44:1965–1984.
   Web of Science ®Google Scholar
• Borvik T, Hopperstad OS, Reyes A, et al. Empty and foam-filled circular aluminum tubes subjected to axial and oblique quasi-static loading. Int J Crashworthines. 2003;8(5):481–494.
   Web of Science ®Google Scholar
• Reyes A, Hopperstad OS, Hanssen AG, et al. Modeling of material failure in foam-based components. Int J Impact Eng. 2004;30(7):805–834.
   Web of Science ®Google Scholar
• Selmy AL, Elsesi AR, Azab NA, et al. Interlaminar shear behavior of unidirectional glass fiber (U)/random glass fiber (R)/epoxy hybrid and nonhybrid composite laminates. Compos Part B. 2012;43:1714–1719.
   Web of Science ®Google Scholar
• Djamaluddin F, Abdullah S, Arrifin AK, et al. Modeling and optimization of aluminum foam cylindrical double tubes under axial impact. J Mech Sci. 2014;8:1383–1392.
   Google Scholar
• Djamaluddin F, Abdullah S, Ariffin AK, et al. Multi objective optimization of foam-filled tubular circular tubes for quasi-static and dynamic responses. Latin Am J Solid Struct. 2015;12:1126–1143.
   Web of Science ®Google Scholar
• Djamaluddin F, Abdullah S, Ariffin AK, et al. Non-linear finite element analysis of bitubal circular tubes for progressive and bending collapses non-linear finite element analysis of bitubal circular tubes for progressive and bending collapses. Int J Mech Sci. 2015;99:228–236.
   Web of Science ®Google Scholar
• Djamaluddin F, Abdullah S, Ariffin AK, et al. Optimization of foam-filled double circular tubes under axial and oblique impact loading conditions. Thin Walled Struct. 2015;87:1–11.
   Web of Science ®Google Scholar
• Djamaluddin F, Abdullah S, Ariffin AK, et al. Multi objective optimization of aluminum foam filled double tubes subjected to oblique impact loading for automobile bumper beam. Appl Mech Mater. 2013;663:93–97.
   Google Scholar