Review: deformation and optimisation crashworthiness method for foam filled structures

Djamaluddin, Fauzan

doi:10.1590/1679-78255702

Fauzan Djamaluddin

Departement of Mechanical Engineering, Faculty of Engineering Hasanuddin University, Gowa, South Sulawesi, Indonesia. E-mail: fauzanman_77@yahoo.com

http://orcid.org/0000-0002-7114-9254

*Corresponding author

Editor:

Marcílio Alves.

Figures (12)
Tables (1)

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Figure 1
Energy versus displacement for crashworthiness performance. Source: Tarlochan et al. (2013Tarlochan, F., Samer, F., Hamouda, A.M.S., Ramesh, S., Karam, K. 2013. Design of thin wall structures for energy absorption applications: Enhancement of crashworthiness due to axial and oblique impact forces. Thin-Walled Structures 71: 7-17.).

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Figure 2
Deformation modes of foam filled square tubes under axial loading (a) Hanssen et al. (2000Hanssen, A.G., Langseth, M. & Hopperstad, O.S. 2000. Static and dynamic crushing of square aluminium extrusions with aluminium foam filler. International Journal of Impact Engineering 24: 347-383.), (b) Santosa et al. (2000Santosa, S., Wierzbicki, T., Hanssen, A.G. & Langseth, M. 2000. Experimental and numerical studies of foam-filled sections. Interna-tional Journal of Impact Engineering. 24(5): 509-534.), (c)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.) and (d) Abedi et al. (2012Abedi, M.M., Niknejad, A., Liaghat, G.H., & Nejad, M.Z. (2012). Theoretical and experimental study on empty and foam-filled columns with square and rectangular cross section under axial compression. International Journal of Mechanical Sciences 65: 134-146.).

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Figure 3
Deformation modes of foam filled circular tubes under axial loading: (a) Borvik et al. (2003Borvik, T., Hopperstad, O.S., Reyes, A., Langseth, M., Solomos, G. & Dyngeland, T. 2003. Empty and foam-filled circular aluminium tubes subjected to axial and oblique quasi static loading. International Journal of Crashworthiness 8(5): 481-494.), (b) Toksoy and Guden (2005Toksoy, A.K. & Guden, M. 2005. The strengthening effect of polystyrene foam filling in aluminum thin-walled cylindrical tubes. Thin-Walled Structures 43(2): 333-350.), (c) Yan et al. (2007Yan, W.Y., Durif, E., Yamada, Y. & Wen, C. 2007. Crushing simulation of foam- filled aluminium tubes. Materials Transactions 48(7): 1901-1906.), (d) Ghamarian et al. (2011Ghamarian, H.R., Zarei, M.T. & Abadi. 2011. Experimental and numerical crashworthiness investigation of empty and foam‐filled end‐ capped conical tubes, Thin-Walled Structures 49: 1312‐1319.).

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Figure 4
Deformation modes of foam filled hat tubes under axial loading; (a) Wang et al. (2007Wang, Q., Fan, Z. & Gui, L. 2007. Theoretical analysis for axial crushing behaviour of aluminium foam‐filled hat sections. International Journal Mechanical Sciences 5(3): 515‐521) (b) Song et al. (2005Song, H.W., Fan, Z.H., Yu, G., Wang, Q.C. & Tobota, A. 2005. Partition energy absorption of axially crushed aluminum foam-filled hat sections. International Journal of Solids and Structures 42(9-10): 2575-2600.) (c)Altenhof, et al. (2002Altenhof, W., Harte, A.M. & Turchi, R. 2002. Experimental and numerical compressive testing of aluminium foam-filled mild steel tubular hat sections. 7th International LS-DYNA Users Conference, May, 21-24, 2002 Ontario, Canada.).

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Figure 5
Deformation modes of foam filled tapered tubes under axial loading. Source: Mirfendereski et al. 2008Mirfendereski, L., Salimi, M. & Ziaei-Rad, S. 2008. Parametric study and numerical analysis of empty and foam-filled thin-walled tubes under static and dynamic loadings. International Journal of Mechanical Sciences 50(6): 1042-1057.

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Figure 6:
Deformation modes of foam filled cone tubes under axial loading; (a) Ahmad and Thambiratnam (2009Ahmad, Z. & Thambiratnam, D.P. 2009. Dynamic computer simulation and energy absorption of foam-filled conical tubes under axial impact loading. Computers and Structures 87(3-4): 186-197.), (b)Ghamarian et al. (2011Ghamarian, H.R., Zarei, M.T. & Abadi. 2011. Experimental and numerical crashworthiness investigation of empty and foam‐filled end‐ capped conical tubes, Thin-Walled Structures 49: 1312‐1319.), Hou et al., (2013Hou, S., Zhao, S., Rena, L., Han, X. & Li, Q. 2013. Crashworthiness optimization of corrugated sandwich panels. Materials and Design 51: 1071-1084.).

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Figure 7:
Foam filled structures under oblique loading; (a) Square tube by Reyes, Langseth and Hopperstad (2003Reyes, A., Langseth, M. & Hopperstad, O.S. 2003. Square aluminum tubes subjected to oblique loading. International Journal of Im-pact Engineering 28(10): 1077-1106.), (b) Circular tube by Borvik et al., (2003Borvik, T., Hopperstad, O.S., Reyes, A., Langseth, M., Solomos, G. & Dyngeland, T. 2003. Empty and foam-filled circular aluminium tubes subjected to axial and oblique quasi static loading. International Journal of Crashworthiness 8(5): 481-494.), (c) Cone tube by Ahmad et al. (2010Ahmad, Z., Thambiratnam, D.P. & Tan, A.C.C. 2010. Dynamic energy absorption characteristics of foam-filled conical tubes under oblique impact loading. International Journal of Impact Engineering 37: 475-488).

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Figure 8:
Double tube under axial loading; (a) square tube by Seitzberger and Willminger (2001Seitzberger, M. & Willminger, S. 2001. Application of plastic collapse mechanisms for the axial crushing analysis of tubular steel struc-tures filled with aluminium foam. International Journal of Crashworthiness 6(2): 165-176.), (b) circular tube by Guo and Yu (2010Guo, L.W. & Yu, J.L. 2010. Bending response of sandwiched double tube structures with aluminum foam core. Proceedings of the ISCM II & EPMESC XII, November, 30 - December, 3, 2009, Hong Kong.).

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Figure 9:
Metamodel development process for optimisation. Source: Acar et al. (2011Acar, E., Guler, M.A., Gerçeker, B., Cerit, M.E., & Bayram, B. 2011. Multi-objective crashworthiness optimization of tapered thin-walled tubes with axisymmetric indentations. Thin-Walled Structures 49: 94-105.).

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Figure 10:
Schematic for a neuron device. Source: Ibrahim (2009Ibrahim, H. K. 2009. Design Optimzation of Vehicle Structure for Crashworthiness Improvement. PhD Thesis, Concordian University.).

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Figure 11:
Deformation modes of double foam filled tubes for (a) experiment, and (b) simulation. Source: 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.).

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Figure 12:
Deformation modes of the tapered tube under oblique load; (a) experiment and (a) simulation. Source: 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.).

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Tables 1
Optimising design of crashworthiness for foam filled thin-walled structures.

Researchers	Structures	Loading Condition	Design of Experiment	Meta model	Optimization
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

[1] *Corresponding author

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Review: deformation and optimisation crashworthiness method for foam filled structures

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