Analytical and numerical investigation of cylindrical energy absorbers with functionally graded thickness

Authors

1 department of mechanical engineering, university of Sistan and Ba;uchestan, Zahedan, Iran

2 university of sistan and baluchestan

Abstract

In this study, the crashworthiness of cylindrical tubes with variable thickness, under axial load, is investigated. The loading is applied quasi static. Wall-Thickness changes are considered to follow the nonlinear power distribution equatiion. Firstly, by considering the elastic-perfectly plastic behavior for material, an analytical relition is extracted based on Alexander's theory. Then, in order to increase the accuracy of the results, the effects of work hardening is applied to material behavior and the formulas are rewritten. Finally, to validate the analytical results, using simulation in ABAQUS FE software, several models have been studied in different modes and the results have been compared. The results show an acceptable agreement between the analytical results and the simulation. The final result of this research is presenting two analutical relition beteen absorbed energy and mean force with mechanical properties and geometic parameters of anergy absorber. Moreover, by simplifying the drived analytical equation, we can obtain the basic equations in later researches.

Keywords


[1] Zarei H, Kröger M (2008) Optimum honeycomb filled crash absorber design. Mater Design 29(1): 193-204.
[2] Abramowicz W, Jones N (1984) Dynamic axial crushing of circular tubes. Int J Impact Eng 2(3): 263-281.
[3] Gupta N (1998) Some aspects of axial collapse of cylindrical thin-walled tubes. Thin Wall Struct 32(1-3): 111-126.
[4] Abramowicz W, Jones N (1984) Dynamic axial crushing of square tubes. Int J Impact Eng 2(2): 179-208.
[5] Al Galib D, Limam A (2004) Experimental and numerical investigation of static and dynamic axial crushing of circular aluminum tubes. Thin Wall Struct 42(8): 1103-1137.
[6] Zhang X, Tian Q, Yu T(2009) Axial crushing of circular tubes with buckling initiators. Thin wall struct 47(6-7): 788-797.
[7] Zarei H, Kröger M (2006) Multiobjective crashworthiness optimization of circular aluminum tubes. Thin wall struct 44(3): 301-308.
[8] Alexander J (1960) An approximate analysis of the collapse of thin cylindrical shells under axial loading. Q J Mech Appl Math 13(1): 10-15.
[9] Andrews K, England G, Ghani E (1983) Classification of the axial collapse of cylindrical tubes under quasi-static loading. Int J Mech Sci 25(9-10): 687-696.
[10] Wierzbicki T, Bhat SU, Abramowicz W,  Brodkin D (1992) Alexander revisited—a two folding elements model of progressive crushing of tubes. Int J Solids Struct 29(24): 3269-3288.
[11] Guillow S, Lu G, Grzebieta R (2001) Quasi-static axial compression of thin-walled circular aluminium tubes. Int J Mech Sci 43(9):2103-2123.
[12] Audi RF, Brooks RJ, Cormier JM, Smith DS, Rossi MA (2009) Modular energy absorber with ribbed wall structure, ed: Google Patents.
[13] Ralston DD, Holdren KE, Bastien KR, Gorman D, Kulkarni A (2011) Energy absorber with sidewall stabilizer ribs. ed: Google Patents.
[14] Shahravi S, Rezvani MJ, Jahan A (2019) Multi-response optimization of grooved circular tubes filled with polyurethane foam as energy absorber. Journal of Optimization in Industrial Engineering 12(1): 133-149.
[15] Nia AA, Nejad KF, Badnava H, Farhoudi H (2012) Effects of buckling initiators on mechanical behavior of thin-walled square tubes subjected to oblique loading. Thin wall struct 59: 87-96.
[16] Rezvani MJ, Jahan A (2015) Effect of initiator, design, and material on crashworthiness performance of thin-walled cylindrical tubes: A primary multi-criteria analysis in lightweight design. Thin Wall Struct 96: 169-182.
[17] Mamalis A, Manolakos D, Ioannidis M, Kostazos P, Kastanias S (2003) Numerical modelling of the axial plastic collapse of externally grooved steel thinwalled tubes. Int J Crashworthiness 8(6): 583-590.
[18] Baykasoglu C, Cetin MT (2015) Energy absorption of circular aluminium tubes with functionally graded thickness under axial impact loading. Int J Crashworthiness 20(1): 95-106.
[19] Li G, Xu F, Sun G, Li Q (2015) A comparative study on thin-walled structures with functionally graded thickness (FGT) and tapered tubes withstanding oblique impact loading. Int J Impact Eng 77: 68-83.
[20] Xu F (2015) Enhancing material efficiency of energy absorbers through graded thickness structures. Thin Wall Struct 97: 250-265.
[21] Erdin ME, Baykasoglu C, Cetin MT (2016) Quasi-static axial crushing behavior of thin-walled circular aluminum tubes with functionally graded thickness. Procedia Engineer 149: 559-565.
[22] Pang T, Kang H, Yan X, Sun G, Li Q (2017) Crashworthiness design of functionally graded structures with variable diameters. Int J Crashworthiness 22(2): 148-162.
[23] Yao S, Xing Y, Zhao K (2017) Crashworthiness analysis and multiobjective optimization for circular tubes with functionally graded thickness under multiple loading angles. Adv Mech Eng 9(4): 1687814017696660.
[24] Yin H, Dai J, Wen G, Tian W, Wu Q (2019) Multi-objective optimization design of functionally graded foam-filled graded-thickness tube under lateral impact. Int J Com Meth-sign 16(1):1850088.
[25] Baykasoğlu C, Baykasoğlu A, Tunay Çetin M (2019) A comparative study on crashworthiness of thin-walled tubes with functionally graded thickness under oblique impact loadings. Int J Crashworthiness 24(4): 453-471.
[26] Li C, Wang D (2019) Knowledge-Based Engineering–based method for containership lashing bridge optimization design and structural improvement with functionally graded thickness plates. P I Mech Eng M-J Eng 233(3):760-778.
[27] Gupta N, Abbas H (2000) Mathematical modeling of axial crushing of cylindrical tubes. Thin Wall Struct 38(4): 355-375.
[28] Hosseinipour S, Daneshi G (2003) Energy absorbtion and mean crushing load of thin-walled grooved tubes under axial compression. Thin wall struct 41(1): 31-46.
[29] Rezvani M, Nouri M D (2015) Analytical model for energy absorption and plastic collapse of thin-walled grooved frusta tubes. Mech Adv Mater Struc 22(5): 338-348.
[30] Rezvani M, Nouri MD (2017) Mathematical modelling of energy absorption in thin-walled grooved conical tubes with considering of strain hardening phenomena. Int J Struc Eng 8(4): 308-326.
[31] Chirwa E (1993) Theoretical analysis of tapered thin-walled metal inverbucktube. In J Mech Sci 35(3-4): 325-351.
[32] Rezvani M, Nouri MD (2014) Axial crumpling of aluminum frusta tubes with induced axisymmetric folding patterns. Arab J Sci Eng 39(3): 2179-2190.
[33] Ghamarian A, Zarei H (2012) Crashworthiness investigation of conical and cylindrical end-capped tubes under quasi-static crash loading. Int J Crashworthiness 17(1): 19-28.
[34] Li G, Xu F, Sun G, Li Q (2015) Crashworthiness study on functionally graded thin-walled structures. Int J Crashworthiness 20(3): 280-300.
[35] Rezvani M, Nouri MD, Rahmani H (2012)  Experimental and numerical investigation of grooves shape on the energy absorption of 6061-T6 aluminium tubes under axial compression. Int J Mater Struc Integrity 6(2-4): 151-168.