Zarei and Kroger (2008Zarei, H.R. & Kroger, M. 2008. Optimization of the foam-filled aluminum tubes for crush box application. Thin-Walled Structures 46(2): 214-221.) |
Square columns |
Bending /Dynamic |
D-optimal |
Response surface method |
Response surface method |
Zarei and Kroger (2008Zarei, H.R. & Kroger, M. 2008. Optimization of the foam-filled aluminum tubes for crush box application. Thin-Walled Structures 46(2): 214-221.) |
Square tubes |
Axial/Dynamic |
D-optimal |
Response surface method |
Response surface method |
Hou et al. (2009Hou, S.J., Li, Q., Long, S.Y., Yang, X. & Li, W. 2009. Crashworthiness design for foam filled thin-wall structures. Materials and Design 30(6): 2024-2032.) |
squared columns |
Axial/Dynamic |
D-optimal |
Response surface method |
Weighted arithmetical average method Geometrical average method |
Sun et al. (2010Sun, G.Y., Li, G.Y., Hou, S.J., Zhou, S.W., Li, W., Li, Q. 2010. Crashworthiness design for functionally graded foam filled thin-walled structures. Material Science Engineering 527: 1911-1919.) |
squared columns |
Axial/Dynamic |
polynomial functions |
response surface method |
particle swarm optimization |
Bi et al. (2010Bi, J., Fang, H., Wang, Q. & Ren, X. 2010. Modeling and optimization of foam-filled thin-walled columns for crashworthiness designs. Finite Elements in Analysis and Design 46: 698-709.) |
Hexagonal columns |
Axial/Dynamic |
polynomial functions |
Response surface method |
Response surface method |
Hou et al. (2011Hou, S., Han, X., Sun, G., Long, S., Li, W., Yang, X. & Li, Q. 2011. Multiobjective optimization for tapered circular tubes. Thin-Walled Structures 49: 855-863.) |
Tapered circular tubes |
Axial/Dynamic |
Factorial design Latin Hypercube Sampling |
Response surface method |
Particle swarm optimization |
Qi et al. (2012Qi, C., Yang, S. & Dong, F. 2012. Crushing analysis and multiobjective crashworthiness optimization of tapered square tubes under oblique impact loading, Thin-Walled Structures 59: 103-119.) Zhang et al (2012Zhang, Y., Sun, G., Li, G., Luo, Z. & Li, Q. 2012 Optimization of foam-filled bitubal structures for crashworthiness criteria. Materials and Design 38: 99-109.) |
Tapered square tubes Double square column |
Oblique/Dynamic Axial/Dynamic |
Full factorial design D-optimal |
Response surface method Kriging |
Particle swarm optimization Genetic algorithm Non-dominated Sorting Genetic Algorithm II |
Yang and Qi (2013Yang, S. & Qi, C. 2013. Multiobjective optimization for empty and foam-filled square columns under oblique impact loading. Interna-tional Journal Impact Engineering 54: 177-191.) |
Square columns |
Oblique/Dynamic |
D-optimal |
Kriging |
Particle swarm optimization |
Yin et al. (2013Yin, H., Wen, G., Hou, S. & Qing, Q. 2013. Multiobjective crashworthiness optimization of functionally lateral graded foam-filled tubes. Materials and Design 44: 414-428) |
Square columns |
Lateral/Dynamic |
Full factorial design |
polynomial functions |
multiobjective particle swarm optimization |
Yin et al. (2014aYin, H., Wen, G., Liu, Z. & Qing, Q. 2014a. Crashworthiness optimization design for foam-filled multi-cell thin-walled structures. Thin-Walled Structures 75: 8-17.) |
tapered tube |
Axial/Dynamic |
Latin Hypercube Design |
polynomial response surface radial basis function support vector regression |
multiobjective particle swarm optimization |
Fang et al. (2014Fang, J., Gao, Y., Sun, G., Zhang, Y. & Li, Q. 2014. Crashworthiness design of foam-filled bitubal structures with uncertainty. Interna-tional Journal of Non-linear Mechanics 65: 113-124.) |
Square beam |
Lateral/Quasi- static |
Latin Hypercube sampling |
Kriging |
multiobjective particle swarm optimization |
Zheng et al. (2014Zheng, G., Wu, S., Sun, G., Li, G. & Li, Q. 2014. Crushing analysis of foam-filled single and bitubal polygonal thin-walled tubes. Inter-national Journal of Mechanical Sciences 87: 226-240.) |
bitubal polygonal tubes |
Axial/Dynamic |
Latin Hypercube sampling |
response surface radial basis function Kriging |
Non-dominated Sorting Genetic Algorithm II |
Li et al. (2014Li, G., Zhang, Z., Sun, G., Xu, F. & Huang, X. 2014. Crushing analysis and multiobjective optimization for functionally graded foam- filled tubes under multiple load cases. International Journal of Mechanical Sciences 89: 439-452) |
Square columns |
Oblique/Dynamic |
Full factorial design |
radial basis function |
Non-dominated Sorting Genetic Algorithm II |
Zhang et al. (2014Zhang, Y., Sun, G., Xu, X., Li, G. & Li, Q. 2014. Multiobjective crashworthiness optimization of hollow and conical tubes for multiple load cases. Thin-Walled Structures 82: 331-342.) |
conical tube |
Oblique/Dynamic |
D-optimal |
Kriging model |
multiobjective particle swarm optimization |
Li et al. (2015Li, F., Sun, G., Huang, X., Rong, J. & Li, Q. 2015. Multiobjective robust optimization for crashworthiness design of foam filled thin-walled structures with random and interval uncertainties. Engineering Structures 88: 111-124 .) |
Square columns |
Lateral/Dynamic |
Latin Hypercube Sampling |
Kriging model |
Non-dominated Sorting Genetic Algorithm II |
Hou et al. (2015Hou, S., Liu, T., Zhang, Z., Han, X & Li, Q. 2015. How does negative Poisson’s ratio of foam filler affect crashworthiness? Materials and Design 82: 247-259) |
Square tube Circular tube Conical tube |
Axial/Dynamic |
full factorial design |
Response Surface Method |
Sequential quadratic programming Non-dominated Sorting Genetic Algorithm II |
Djamaluddin et al. (2015aDjamaluddin, F, Abdullah, S, Ariffin, AK, Nopiah, Z.M. 2015a. Optimization of foam-filled double circular tubes under axial and oblique impact loading conditions. Thin Walled Structure. 87:1-11.) |
Double circular tube |
Axial and Oblique/Dynamic |
D-optimal |
radial basis function |
Non-dominated Sorting Genetic Algorithm II |
Djamaluddin et al. (2015bDjamaluddin, F, Abdullah, S, Ariffin, AK, Nopiah, Z.M. 2015b. Multi objective optimization of foam-filled tubular circular tubes for quasi static and dynamic responses Latin American Journal of Solids and Structures . 12:1126-1143) |
Double circular tube |
Axial/Quasi-static and Dynamic |
D-optimal |
radial basis function |
Non-dominated Sorting Genetic Algorithm II |
Gao et al. (2016aGao, Q., Wang, L., Wang, Y. & Wang, C. 2016a. Crushing analysis and multiobjective crashworthiness optimization of foam-filled ellipse tubes under oblique impact loading. Thin-Walled Structures 100: 105-112.) |
Double ellipse tube |
Axial and Oblique/Dynamic |
D-optimal |
Kriging |
multiobjective particle swarm Optimization |
Gao et al. (2016bGao, Q., Wang, L., Wang, Y., Wang, C. & Zhang, Z. 2016b. Optimization of foam-filled double ellipse tubes under multiple loading cases. Advances in Engineering Software 99: 27-35) |
ellipse tubes |
Oblique/Dynamic |
D-optimal |
Quartic polynomial functions |
Non-dominated Sorting Genetic Algorithm II |
Yin et al. (2017Yin, H., Chen, C., Huc, T. & Wen, G. 2017. Optimisation for bending crashworthiness of functionally graded foam-filled cellular structure. International Journal of Crashworthiness 34: 212-227.) |
Tapered multi cell tube |
Bending and Quasi static |
Full Factorial |
radial basis function |
Non-dominated Sorting Genetic Algorithm II |
Ying et al. (2017Ying, L., Dai, M., Zhang, S., Ma, H. & Hu, P. 2017. Multiobjective crashworthiness optimization of thin-walled structures with functionally graded strength under oblique impact loading. Thin-Walled Structures 117: 165-177.) |
Tapered tube |
Oblique/Dynamic |
Full Factorial |
radial basis function |
Non-dominated Sorting Genetic Algorithm II |