Crashworthiness analysis and optimization of standard and windowed multi-cell hexagonal tubes

T. N. Tran, Ahmad Baroutaji, Quirino Estrada, Arun Arjunan, Huu Son Le, N. P. Thien*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Recently, multi-cell structures have received increased attention for crashworthiness applications due to their superior energy absorption capability. However, such structures were featured with high peak collapsing force (PCL) forming a serious safety concern, and this limited their application for vehicle structures. Accordingly, this paper proposes windowed shaped cuttings as a mechanism to reduce the high PCL of the multi-cell hexagonal tubes and systemically investigates the axial crushing of different windowed multi-cell tubes and also seeks for their optimal crashworthiness design. Three different multi-cell configurations were constructed using wall-to-wall (WTW) and corner-to-corner (CTC) connection webs. Validated finite element models were generated using explicit finite element code, LS-DYNA, and were used to run crush simulations on the studied structures. The crashworthiness responses of the multi-cell standard tubes (STs), i.e., without windows, and multi-cell windowed tubes (WTs) were determined and compared. The WTW connection type was found to be more effective for STs and less favorable for WTs. Design of experiments (DoE), response surface methodology (RSM), and multiple objective particle swarm optimization (MOPSO) tools were employed to find the optimal designs of the different STs and WTs. Furthermore, parametric analysis was conducted to uncover the effects of key geometrical parameters on the main crashworthiness responses of all studied structures. The windowed cuttings were found to be able to slightly reduce the PCL of the multi-cell tubes, but this reduction was associated with a major negative implication on their energy absorption capability. This work provides useful insights on designing effective multi-cell structures suitable for vehicle crashworthiness applications.

Original languageEnglish
Pages (from-to)2191-2209
Number of pages19
JournalStructural and Multidisciplinary Optimization
Issue number5
Early online date7 Jan 2021
Publication statusPublished - May 2021

Bibliographical note

Funding Information:
This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 107.99-2019.02.


  • Crashworthiness optimization
  • Dynamic collapsing
  • Energy absorption
  • Trigger
  • Windowed multi-cell tube


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