Skip to main content
SpringerLink
Log in

Numerical Analysis and Theoretical Prediction of Axial Crushing Characteristics of Mixed Thin-walled Tubes with Dual-variable Attribute

  • Published:
International Journal of Automotive Technology Aims and scope Submit manuscript

Abstract

Thin-walled structures with varying thickness (single variable attribute) had been proven to be able improve energy absorption characteristics. In order to further study the energy absorption characteristics of thin-walled structures whose material properties changed as the thickness changing, a novel type of mixed thin-walled tube with axially-varying thickness and material were proposed in this paper. The finite element (FE) model was validated under axial quasi-static loading firstly, and seven groups simulation models of thin-walled tubular structure were established. The simulation results showed that the dual-variable attribute tubes can ensure high energy absorption and reduce the initial peak crushing force effectively in the crushing process. Furthermore, the maximum crushing force efficiency of steel-aluminum mixed tube can reach 2.77, while the aluminum mixed tube increased the crushing force efficiency to 1.24. Subsequently, a analytical model for dual-variable attribute tube was established and the theoretical mean crushing force calculation formula can be derived. The simulation and theoretical results were wirelessly close, except that the error of SUT5 was about 11 %. Therefore, the theoretical prediction results were in good agreement with the simulation results, and the theoretical prediction method can provide some reference for the design of double variable tube.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abramowicz, W. (2003). Thin-walled structures as impact energy absorbers. Thin-Walled Structures 41, 2–3, 91–107.

    Article  Google Scholar 

  • Abramowicz, W. and Jones, N. (1984). Dynamic axial crushing of circular tubes. Int. J. Impact Engineering 2, 3, 263–281.

    Article  Google Scholar 

  • Abramowicz, W. and Jones, N. (1997). Transition from initial global bending to progressive buckling of tubes loaded statically and dynamically. Int. J. Impact Engineering 19, 5–6, 415–137.

    Article  Google Scholar 

  • Ahmad, Z. and Thambiratnam, D. P. (2009). Dynamic computer simulation and energy absorption of foam-filled conical tubes under axial impact loading. Computers & Structures 87, 3–4, 186–197.

    Article  Google Scholar 

  • Airoldi, A. and Janszen, G. (2005). A design solution for a crashworthy landing gear with a new triggering mechanism for the plastic collapse of metallic tubes. Aerospace Science and Technology 9, 5, 445–455.

    Article  MATH  Google Scholar 

  • Andrews, K. R. F., England, G. L. and Ghani, E. (1983). Classification of the axial collapse of cylindrical tubes under quasi-static loading. Int. J. Mechanical Sciences 25, 9–10, 687–696.

    Article  Google Scholar 

  • Baroutaji, A., Sajjia, M. and Olabi, A. G. (2017). On the crashworthiness performance of thin-walled energy absorbers: Recent advances and future developments. Thin-Walled Structures, 118, 137–163.

    Article  Google Scholar 

  • Chen, B. C., Zou, M., Liu, G. M., Song, J. F. and Wang, H. X. (2018). Experimental study on energy absorption of bionic tubes inspired by bamboo structures under axial crushing. Int. J. Impact Engineering, 115, 48–57.

    Article  Google Scholar 

  • Chen, W. and Wierzbicki, T. (2001). Relative merits of single-cell, multi-cell and foam-filled thin-walled structures in energy absorption. Thin-Walled Structures 39, 4, 287–306.

    Article  Google Scholar 

  • Fang, J., Sun, G., Qiu, N., Kim, N. H. and Li, Q. (2017). On design optimization for structural crashworthiness and its state of the art. Structural and Multidisciplinary Optimization 55, 3, 1091–1119.

    Article  MathSciNet  Google Scholar 

  • Guan, W., Gao, G., Li, J. and Yu, Y. (2018). Crushing analysis and multi-objective optimization of a cutting aluminium tube absorber for railway vehicles under quasistatic loading. Thin-Walled Structures, 123, 395–408.

    Article  Google Scholar 

  • Hong, W., Fan, H, Xia, Z., Jin, F., Zhou, Q. and Fang, D. (2014). Axial crushing behaviors of multi-cell tubes with triangular lattices. Int. J. Impact Engineering, 63, 106–117.

    Article  Google Scholar 

  • Hong, W., Jin, F., Zhou, J., Xia, Z., Xu, Y., Yang, L., Zheng, Q. and Fan, H. (2013). Quasi-static axial compression of triangular steel tubes. Thin-Walled Structures, 62, 10–17.

    Article  Google Scholar 

  • Hou, S., Li, Q., Long, S., Yang, X. and Li, W. (2007). Design optimization of regular hexagonal thin-walled columns with crashworthiness criteria. Finite Elements in Analysis and Design 43, 6–7, 555–565.

    Article  Google Scholar 

  • Huang, X. and Lu, G. (2003). Axisymmetric progressive crushing of circular tubes. Int. J. Crashworthiness 8, 1, 87–95.

    Article  Google Scholar 

  • Hussein, R. D., Ruan, D., Lu, G. and Sbarski, I. (2016). Axial crushing behaviour of honeycomb-filled square carbon fibre reinforced plastic (CFRP) tubes. Composite Structures, 140, 166–179.

    Article  Google Scholar 

  • Jin, X., Wang, Z., Ning, J., Xiao, G., Liu, E. and Shu, X. (2016). Dynamic response of sandwich structures with graded auxetic honeycomb cores under blast loading. Composites Part B: Engineering, 106, 206–217.

    Article  Google Scholar 

  • Li, J., Gao, G., Dong, H., Xie, S. and Guan, W. (2016a). Study on the energy absorption of the expanding—Splitting circular tube by experimental investigations and numerical simulations. Thin-Walled Structures, 103, 105–114.

    Article  Google Scholar 

  • Li, S., Li, X., Wang, Z., Wu, G., Lu, G. and Zhao, L. (2016b). Finite element analysis of sandwich panels with stepwise graded aluminum honeycomb cores under blast loading. Composites Part A: Applied Science and Manufacturing, 80, 1–12.

    Article  Google Scholar 

  • Li, Z., Duan, L., Chen, T. and Hu, Z. (2018). Crashworthiness analysis and multi-objective design optimization of a novel lotus root filled tube (LFT). Structural and Multidisciplinary Optimization 57, 2, 865–875.

    Article  Google Scholar 

  • Meguid, S. A., Yang, F. and Hou, P. (2016). Crush behaviour of foam-filled thin-walled conical frusta: Analytical, numerical and experimental studies. Acta Mechanica 227, 12, 3391–3406.

    Article  MathSciNet  Google Scholar 

  • Nia, A. A. and Hamedani, J. H. (2010). Comparative analysis of energy absorption and deformations of thin walled tubes with various section geometries. Thin-Walled Structures 48, 12, 946–954.

    Article  Google Scholar 

  • Nian, Y., Wan, S., Li, X., Su, Q. and Li, M. (2019). How does bio-inspired graded honeycomb filler affect energy absorption characteristics?. Thin-Walled Structures, 144, 106269.

    Article  Google Scholar 

  • Oftadeh, R., Haghpanah, B., Papadopoulos, J., Hamouda, A. M. S., Nayeb-Hashemi, H. and Vaziri, A. (2014). Mechanics of anisotropic hierarchical honeycombs. Int. J. Mechanical Sciences, 81, 126–136.

    Article  Google Scholar 

  • Pang, T., Li, Y., Kang, H., Sun, G., Fang, J. and Li, Q. (2017). On functionally-graded crashworthy shape of conical structures for multiple load cases. J. Mechanical Science and Technology 31, 6, 2861–2873.

    Article  Google Scholar 

  • Pang, T., Zheng, G., Fang, J., Ruan, D. and Sun, G. (2019). Energy absorption mechanism of axially-varying thickness (AVT) multicell thin-walled structures under out-of-plane loading. Engineering Structures, 196, 109130.

    Article  Google Scholar 

  • Qi, C., Sun, Y., Hu, H. T., Wang, D. Z., Cao, G. J. and Yang, S. (2016). On design of hybrid material double-hat thin-walled beams under lateral impact. Int. J. Mechanical Sciences, 118, 21–35.

    Article  Google Scholar 

  • Reuter, C., Sauerland, K. H. and Tröster, T. (2017). Experimental and numerical crushing analysis of circular CFRP tubes under axial impact loading. Composite Structures, 174, 33–44.

    Article  Google Scholar 

  • Shahi, V. J. and Marzbanrad, J. (2012). Analytical and experimental studies on quasi-static axial crush behavior of thin-walled tailor-made aluminum tubes. Thin-Walled Structures, 60, 24–37.

    Article  Google Scholar 

  • Song, X., Sun, G. and Li, Q. (2016). Sensitivity analysis and reliability based design optimization for high-strength steel tailor welded thin-walled structures under crashworthiness. Thin-Walled Structures, 109, 132–142.

    Article  Google Scholar 

  • Sun, G., Pang, T., Xu, C., Zheng, G. and Song, J. (2017). Energy absorption mechanics for variable thickness thin-walled structures. Thin-Walled Structures, 118, 214–228.

    Article  Google Scholar 

  • Sun, G., Pang, T., Zheng, G., Song, J. and Li, Q. (2016). On energy absorption of functionally graded tubes under transverse loading. Int. J. Mechanical Sciences, 115, 465–480.

    Article  Google Scholar 

  • Sun, G., Zhang, J., Li, S., Fang, J., Wang, E. and Li, Q. (2019). Dynamic response of sandwich panel with hierarchical honeycomb cores subject to blast loading. Thin-Walled Structures, 142, 499–515.

    Article  Google Scholar 

  • Tarlochan, F., Samer, F., Hamouda, A. M. S., Ramesh, S. and Khalid, 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.

    Article  Google Scholar 

  • Wang, Z., Li, Z., Shi, C. and Zhou, W. (2019). Mechanical performance of vertex-based hierarchical vs square thin-walled multi-cell structure. Thin-Walled Structures, 134, 102–110.

    Article  Google Scholar 

  • Wierzbicki, T., Bhat, S. U., Abramowicz, W. and Brodkin, D. (1992). Alexander revisited—A two folding elements model of progressive crushing of tubes. Int. J. Solids and Structures 29, 24, 3269–3288.

    Article  Google Scholar 

  • Wu, S., Sun, G., Wu, X., Li, G. and Li, Q. (2017). Crashworthiness analysis and optimization of fourier varying section tubes. Int. J. Non-Linear Mechanics, 92, 41–58.

    Article  Google Scholar 

  • Wu, S., Zheng, G., Sun, G., Liu, Q., Li, G. and Li, Q. (2016). On design of multi-cell thin-wall structures for crashworthiness. Int. J. Impact Engineering, 88, 102–117.

    Article  Google Scholar 

  • Xiang, J. and Du, J. (2017). Energy absorption characteristics of bio-inspired honeycomb structure under axial impact loading. Materials Science and Engineering: A, 696, 283–289.

    Article  Google Scholar 

  • Xu, F. (2015). Enhancing material efficiency of energy absorbers through graded thickness structures. Thin-Walled Structures, 97, 250–265.

    Article  Google Scholar 

  • Xu, F., Tian, X. and Li, G. (2015). Experimental study on crashworthiness of functionally graded thickness thin-walled tubular structures. Experimental Mechanics 55, 7, 1339–1352.

    Article  Google Scholar 

  • Xu, F., Zhang, S. and Wu, K. (2019). Dynamic crashing behavior of thin-walled conical tubular structures with nonlinearly-graded diameters. Proc. Institution of Mechanical Engineers, Part C: J. Mechanical Engineering Science 233, 7, 2456–2466.

    Google Scholar 

  • Xu, X., Zhang, Y., Wang, J., Jiang, F. and Wang, C. H. (2018). Crashworthiness design of novel hierarchical hexagonal columns. Composite Structures, 194, 36–48.

    Article  Google Scholar 

  • Yin, H., Wen, G., Fang, H., Qing, Q., Kong, X., Xiao, J. and Liu, Z. (2014). Multiobjective crashworthiness optimization design of functionally graded foam-filled tapered tube based on dynamic ensemble metamodel. Materials & Design, 55, 747–757.

    Article  Google Scholar 

  • Yin, H., Wen, G., Hou, S. and Qing, Q. (2013). Multiobjective crashworthiness optimization of functionally lateral graded foam-filled tubes. Materials & Design, 44, 414–428.

    Article  Google Scholar 

  • Yin, H., Xiao, Y., Wen, G., Qing, Q. and Wu, X. (2015). Crushing analysis and multi-objective optimization design for bionic thin-walled structure. Materials & Design, 87, 825–834.

    Article  Google Scholar 

  • Ying, L., Zhao, X., Dai, M., Zhang, S. and Hu, P. (2016). Crashworthiness design of quenched boron steel thin-walled structures with functionally graded strength. Int. J. Impact Engineering, 95, 72–88.

    Article  Google Scholar 

  • Yu, Y., Gao, G., Dong, H., Guan, W. and Li, J. (2018). A numerical study on the energy absorption of a bending-straightening energy absorber with large stroke. Thin-Walled Structures, 122, 30–41.

    Article  Google Scholar 

  • Zhang, D., Fei, Q., Jiang, D. and Li, Y. (2018a). Numerical and analytical investigation on crushing of fractal-like honeycombs with self-similar hierarchy. Composite Structures, 192, 289–299.

    Article  Google Scholar 

  • Zhang, D., Fei, Q., Liu, J., Jiang, D. and Li, Y. (2020). Crushing of vertex-based hierarchical honeycombs with triangular substructures. Thin-Walled Structures, 146, 106436.

    Article  Google Scholar 

  • Zhang, L., Bai, Z. and Bai, F. (2018b). Crashworthiness design for bio-inspired multi-cell tubes with quadrilateral, hexagonal and octagonal sections. Thin-Walled Structures, 122, 42–51.

    Article  Google Scholar 

  • Zhang, X. and Zhang, H. (2012). Experimental and numerical investigation on crush resistance of polygonal columns and angle elements. Thin-Walled Structures, 57, 25–36.

    Article  Google Scholar 

  • Zhang, X. and Zhang, H. (2013). Theoretical and numerical investigation on the crush resistance of rhombic and kagome honeycombs. Composite Structures, 96, 143–152.

    Article  Google Scholar 

  • Zhang, X. and Zhang, H. (2014). Axial crushing of circular multi-cell columns. Int. J. Impact Engineering, 65, 110–125.

    Article  Google Scholar 

  • Zhang, X. G., Ren, X., Jiang, W., Zhang, X. Y., Luo, C., Zhang, Y. and Xie, Y. M. (2022). A novel auxetic chiral lattice composite: Experimental and numerical study. Composite Structures, 282, 115043.

    Article  Google Scholar 

  • Zhang, X., Leng, K. and Zhang, H. (2017). Axial crushing of embedded multi-cell tubes. Int. J. Mechanical Sciences, 131, 459–470.

    Article  Google Scholar 

  • Zhang, X., Wen, Z. and Zhang, H. (2014). Axial crushing and optimal design of square tubes with graded thickness. Thin-Walled Structures, 84, 263–274.

    Article  Google Scholar 

  • Zhang, X., Zhang, H. and Wang, Z. (2016). Bending collapse of square tubes with variable thickness. Int. J. Mechanical Sciences, 106, 107–116.

    Article  Google Scholar 

  • Zhang, X., Zhang, H. and Wen, Z. (2015). Axial crushing of tapered circular tubes with graded thickness. Int. J. Mechanical Sciences, 92, 12–23.

    Article  Google Scholar 

  • Zheng, G., Pang, T., Sun, G., Wu, S. and Li, Q. (2016). Theoretical, numerical, and experimental study on laterally variable thickness (LVT) multi-cell tubes for crashworthiness. Int. J. Mechanical Sciences, 118, 283–297.

    Article  Google Scholar 

  • Zhu, G., Li, S., Sun, G., Li, G. and Li, Q. (2016). On design of graded honeycomb filler and tubal wall thickness for multiple load cases. Thin-Walled Structures, 109, 377–389.

    Article  Google Scholar 

  • Zou, M., Xu, S., Wei, C., Wang, H. and Liu, Z. (2016). A bionic method for the crashworthiness design of thin-walled structures inspired by bamboo. Thin-Walled Structures, 101, 222–230.

    Article  Google Scholar 

Download references

Acknowledgement

The support of this work by the National Natural Science Foundation of China (51975438, U1564202) is greatly appreciated. The work was also supported by the 111 Project (B17034).

Author information

Authors and Affiliations

  1. Hubei Key Laboratory of Advanced Technology of Automotive Components, Wuhan University of Technology, Wuhan, Hubei, 430070, China

    Xu Feng Xiang, Niu Xiao Qiang & Shao Tian Ru

  2. Hubei Collaborative Innovation Center for Automotive Components Technology, Wuhan University of Technology, Wuhan, Hubei, 430070, China

    Xu Feng Xiang, Niu Xiao Qiang & Shao Tian Ru

Authors
  1. Xu Feng Xiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Niu Xiao Qiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shao Tian Ru
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xu Feng Xiang.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xiang, X.F., Qiang, N.X. & Ru, S.T. Numerical Analysis and Theoretical Prediction of Axial Crushing Characteristics of Mixed Thin-walled Tubes with Dual-variable Attribute. Int.J Automot. Technol. 23, 1555–1568 (2022). https://doi.org/10.1007/s12239-022-0136-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12239-022-0136-5

Key Words

Search

Navigation