Abstract
This paper presents the quasi-static free inversion behavior of a new conical tube absorber. The absorber is composed of a multi-component conical tube with a spherical end cap and varying lengths and diameters. When this structure undergoes an axial load, each tube component freely inverts inside the next component like a telescope. Finite element (FE) models were made using ABAQUS explicit code to simulate the deformation and energy absorption of multi-component conical tubes. To verify the accuracy of the FE models, they were validated with experimental tests. As a general framework for a design optimization study, structural parameters such as wall thickness, cap radius, and edge length of the absorber affect the initial peak load and specific energy absorption. To achieve the optimal design for the multi-component conical tube, mathematical models were developed using the response surface method, and the multi-objective optimization procedure was applied to find the optimal values for the design variables. The results of the multi-objective optimization demonstrated improvements in both objective functions compared to existing designs. Specifically, by increasing the cap radius and decreasing the edge length, the initial peak load was reduced, while increasing the wall thickness the specific energy absorption was enhanced.
Similar content being viewed by others
Data availability
No data from elsewhere is associated with this manuscript.
References
Ketata, H., Essouli, I., Masmoudi, M., and Krichen, A. "Effects of Die Parameters on External Inversion of Thin-Walled Tube," International Conference on Innovative Materials, Manufacturing, and Advanced Technologies. Springer, 2022, pp. 50–59.
Guist, L., and Marble, D. P. "Prediction of the inversion load of a circular tube." 1966.
Ahmad, Z., Thambiratnam, D.: Crushing response of foam-filled conical tubes under quasi-static axial loading. Mater. Des. 30(7), 2393–2403 (2009). https://doi.org/10.1016/j.matdes.2008.10.017
Ahn, S.H., Jung, H.S., Kim, J.S., Son, S.W.: Crashworthiness analysis and shape design optimization of corrugated tubes for railway application. Int. J. Crashworth. (2022). https://doi.org/10.1080/13588265.2022.2083748
Albak, E.İ, Solmaz, E., Yıldız, A.R., Öztürk, F.: Multiobjective crashworthiness optimization of graphene type multi-cell tubes under various loading conditions. J. Braz. Soc. Mech. Sci. Eng. 43(5), 1–19 (2021). https://doi.org/10.1007/s40430-021-02979-6
Alves, L.M., Vilaça, P., Martins, P.A.: Nosing of thin-walled hollow spheres using a die: experimental and theoretical investigation. Int. J. Mech. Mater. Des. 3(4), 337–346 (2006)
Asanjarani, A., Mahdian, A., Dibajian, S.: Comparative analysis of energy absorption behavior of tapered and grooved thin-walled tubes with the various geometry of the cross section. Mech. Adv. Mater. Struct. 27(8), 633–644 (2020). https://doi.org/10.1080/15376494.2018.1488311
Azarakhsh, S., Rezvani, M.J., Maghsoudpour, A.: Experimental and numerical study of telescopic conical energy absorber under inversion process. Mech. Based Des. Struct. Machines (2023). https://doi.org/10.1080/15397734.2023.2200807
Chahardoli, S., Shabanzadeh, M., Marashi, S.M.: Introducing a new mechanism for energy absorption through simultaneous inversion-folding process. Int. J. Crashworth. 27(1), 92–106 (2022). https://doi.org/10.1080/13588265.2020.1774481
Ghamarian, A., Zarei, H.: Crashworthiness investigation of conical and cylindrical end-capped tubes under quasi-static crash loading. Int. J. Crashworth. 17(1), 19–28 (2012). https://doi.org/10.1080/13588265.2011.623025
Guan, W., Gao, G., Yu, Y., Zhuo, T.: Crashworthiness analysis and multi-objective optimization of expanding circular tube energy absorbers with cylindrical anti-clamber under eccentric loading for subway vehicles. Struct. Multidiscip. Optim. 61(4), 1711–1729 (2020). https://doi.org/10.1007/s00158-019-02427-z
Guler, M.A., Cerit, M.E., Bayram, B., Gerceker, B., Karakaya, E.: The effect of geometrical parameters on the energy absorption characteristics of thin-walled structures under axial impact loading. Int. J. Crashworth. 15(4), 377–390 (2010). https://doi.org/10.1080/13588260903488750
Gupta, P.: A study on inversion of metallic thin-walled conical shells. Int. J. Crashworth. 16(6), 607–619 (2011). https://doi.org/10.1080/13588265.2011.606997
Gupta, P.: Numerical investigation of process parameters on external inversion of thin-walled tubes. J. Mater. Eng. Perform. 23(8), 2905–2917 (2014). https://doi.org/10.1007/s11665-014-1041-5
Jafarian, N., Rezvani, M.J.: Crushing behavior of multi-component conical tubes as energy absorber: a comparative analysis between end-capped and non-capped conical tubes. Eng. Struct. 178, 128–135 (2019). https://doi.org/10.1016/j.engstruct.2018.09.092
Jiang, H., Ren, Y., Zheng, J.: Gradient-degraded material-induced trigger to improve crashworthiness of composite tubes in a controlled manner. J. Reinf. Plast. Compos. 39(1–2), 60–77 (2020). https://doi.org/10.1177/0731684419872004
Kathiresan, M.: Influence of shape, size and location of cutouts on crashworthiness performance of aluminium conical frusta under quasi-static axial compression. Thin-Walled Struct. 154, 106793 (2020). https://doi.org/10.1016/j.tws.2020.106793
Liu, Y., Qiu, X., Yu, T.: A theoretical model of the inversion tube over a conical die. Thin-Walled Struct. 127, 31–39 (2018). https://doi.org/10.1016/j.tws.2018.01.035
Luo, Y., Huang, Z., Zhang, X.: FEM analysis of external inversion and energy absorbing characteristics of inverted tubes. J. Mater. Process. Technol. 187, 279–282 (2007). https://doi.org/10.1016/j.jmatprotec.2006.11.125
Lu, G., and Yu, T. Energy absorption of structures and materials: Elsevier, 2003.
Magrinho, J.P., Centeno, G., Silva, M.B., Vallellano, C., Martins, P.A.F.: On the formability limits of thin-walled tube inversion using different die fillet radii. Thin-Walled Struct. 144, 106328 (2019b). https://doi.org/10.1016/j.tws.2019.106328
Magrinho, J., Centeno, G., Silva, M., Morales-Palma, D., Vallellano, C., Martins, P.: Process window of tube-end inversion: experimentation and numerical analysis. Proc. Manuf. 41, 944–951 (2019a). https://doi.org/10.1016/j.promfg.2019.10.019
Masmoudi, M., Ketata, H., Krichen, A.: External curling process of thin tubes: finite element and experimental investigation. Int. J. Adv. Manuf. Technol. 87(9), 3169–3184 (2016). https://doi.org/10.1007/s00170-016-8742-x
Mohammadiha, O., Ghariblu, H.: Multi-objective optimization of functionally graded thickness tubes under external inversion over circular dies. Int. J. Mech. Mater. Eng. 11(1), 1–14 (2016). https://doi.org/10.1186/s40712-016-0061-3
Nagel, G., Thambiratnam, D.: Dynamic simulation and energy absorption of tapered tubes under impact loading. Int. J. Crashworth. 9(4), 389–399 (2004). https://doi.org/10.1533/ijcr.2004.0298
Özbek, Ö., Bozkurt, Ö.Y., Erkliğ, A.: Development of a trigger mechanism with circular cut-outs to improve crashworthiness characteristics of glass fiber-reinforced composite pipes. J. Braz. Soc. Mech. Sci. Eng. 44(1), 1–14 (2022). https://doi.org/10.1007/s40430-021-03304-x
Patel, V., Tiwari, G., Dumpala, R.: Effect of cut-outs on the axial crushing response of cap and open-end hybrid frusta tube. Mater. Today: Proceed. 28, 2539–2546 (2020a). https://doi.org/10.1016/j.matpr.2020.05.089
Patel, V., Tiwari, G., Dumpala, R.: Crashworthiness analysis of multi-configuration thin walled co-axial frusta tube structures under quasi-static loading. Thin-Walled Structures 154, 106872 (2020b). https://doi.org/10.1016/j.tws.2020.106872
Praveen Kumar, A., Shrivaathsav, S.: Influence of forming parameters on the crash performance of capped cylindrical tubes using LS-DYNA follow-on simulations. Int. J. Interact. Des. Manuf. (ijidem) 13, 1215–1232 (2019)
Qiu, X., He, L., Gu, J., Yu, X.: A three-dimensional model of circular tube under quasi-static external free inversion. Int. J. Mech. Sci. 75, 87–93 (2013). https://doi.org/10.1016/j.ijmecsci.2013.06.009
Qiu, X.M., He, L.H., Gu, J., Yu, X.H.: An improved theoretical model of a metal tube under free external inversion. Thin-Walled Struct. 80, 32–37 (2014). https://doi.org/10.1016/j.tws.2014.02.025
Qiu, X., Yu, X., Li, Y., Yu, T.: The deformation mechanism analysis of a circular tube under free inversion. Thin-Walled Struct. 107, 49–56 (2016)
Rahi, A.: Experimental and crash-worthiness optimization of end-capped conical tubes under quasi-static and dynamic loading. Mech. Adv. Mater. Struct. 26(17), 1437–1446 (2019). https://doi.org/10.1080/15376494.2018.1432815
Razazan, M., Rezvani, M., Souzangarzadeh, H.: Evaluation of the performance of initiator on energy absorption of foam-filled rectangular tubes: experimental and numerical assessment. Exp. Tech. 42(2), 129–139 (2018). https://doi.org/10.1007/s40799-017-0206-1
Reddy, T.: Guist and Marble revisited—on the natural knuckle radius in tube inversion. Int. J. Mech. Sci. 34(10), 761–768 (1992). https://doi.org/10.1016/0020-7403(92)90040-N
Rezvani, M.J., Jahan, A.: Effect of initiator, design, and material on crashworthiness performance of thin-walled cylindrical tubes: a primary multi-criteria analysis in lightweight design. Thin-Walled Struct. 96, 169–182 (2015). https://doi.org/10.1016/j.tws.2015.07.026
Rezvani, M.J., Souzangarzadeh, H.: Effects of triggering and polyurethane foam on energy absorption of thin-walled circular tubes under the inversion process. J. Energy Storage 27, 101071 (2020). https://doi.org/10.1016/j.est.2019.101071
Rosa, P., Rodrigues, J., Martins, P.: External inversion of thin-walled tubes using a die: experimental and theoretical investigation. Int. J. Mach. Tools Manuf 43(8), 787–796 (2003). https://doi.org/10.1016/S0890-6955(03)00062-2
Rosa, P.A., Rodrigues, J.M., Martins, P.A.: Internal inversion of thin-walled tubes using a die: experimental and theoretical investigation. Int. J. Mach. Tools Manuf 44(7–8), 775–784 (2004). https://doi.org/10.1016/j.ijmachtools.2004.01.013
Rosa, P., Rodrigues, J., Martins, P.: Invert-forming of thin-walled tubes using a die. Proceed. Inst. Mech. Eng. Part b: J. Eng. Manuf. 220(1), 35–41 (2006). https://doi.org/10.1243/095440505X32580
Sadighi, A., Azimi, M.B., Asgari, M., Eyvazian, A.: Crashworthiness of hybrid composite-metal tubes with lateral corrugations in axial and oblique loadings. Int. J Crashworth. (2021). https://doi.org/10.1080/13588265.2021.2017654
Santosa, S.P., Wierzbicki, T., Hanssen, A.G., Langseth, M.: Experimental and numerical studies of foam-filled sections. Int. J. Impact Eng 24(5), 509–534 (2000). https://doi.org/10.1016/S0734-743X(99)00036-6
Sarkabiri, B., Jahan, A., Rezvani, M.J.: Crashworthiness multi-objective optimization of the thin-walled grooved conical tubes filled with polyurethane foam. J. Braz. Soc. Mech. Sci. Eng. 39(7), 2721–2734 (2017). https://doi.org/10.1007/s40430-017-0747-3
Shahi, V.J., Marzbanrad, J.: Analytical and experimental studies on quasi-static axial crush behavior of thin-walled tailor-made aluminum tubes. Thin-Walled Struct. 60, 24–37 (2012). https://doi.org/10.1016/j.tws.2012.05.015
Souzangarzadeh, H., Rezvani, M.J., Jahan, A.: Selection of optimum design for conical segmented aluminum tubes as energy absorbers: application of MULTIMOORA method. Appl. Math. Model. 51, 546–560 (2017). https://doi.org/10.1016/j.apm.2017.07.005
Tian, K., Zhang, Y., Yang, F., Zhao, Q., Fan, H.: Enhancing energy absorption of circular tubes under oblique loads through introducing grooves of non-uniform depths. Int. J. Mech. Sci. 166, 105239 (2020). https://doi.org/10.1016/j.ijmecsci.2019.105239
Yang, F., Meguid, S., Hamouda, A.: Kinematically admissible folding mechanisms for the progressive collapse of foam filled conical frusta. Int. J. Mech. Mater. Des. 14, 105–126 (2018)
Yu, X., Qiu, X., Yu, T.: Analysis of the free external inversion of circular tubes based on deformation theory. Int. J. Mech. Sci. 100, 262–268 (2015). https://doi.org/10.1016/j.ijmecsci.2015.06.017
Acknowledgements
The author(s) received no financial support for the research, authorship, and/or publication of this article.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Azarakhsh, S., Rezvani, M.J., Maghsoudpour, A. et al. Inversion performance and multi-objective optimization of multi-component conical energy absorber with a spherical cap. Int J Mech Mater Des (2024). https://doi.org/10.1007/s10999-023-09694-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10999-023-09694-1