Theoretical prediction and optimization of multi-cell hexagonal tubes under axial crashing

• Theoretical predictions of mean crushing force for multi-cell tube were derived.
• MOPSO was performed based on analytical prediction and numerical surrogate model.
• Crashworthiness was compared of four multi-cell hexagonal configurational tubes.

In this paper, the analytical formulas of mean crashing force for four different hexagonal tubes with multiple cells were first derived based on the Simplified Super Folding Element (SSFE) theory through several typical constituent elements: corner element, three-panel angular element I and three-panel angular element II. The numerical simulations of hexagonal multi-cell configurations were then correlated with the derived analytical solutions. Finally, both analytical formulas and finite element analysis (FEA) based surrogate models were employed to optimize the cross-sectional dimensions of the hexagonal tubes. From the optimization results, web-to-web (W2W) is the most efficient configuration in improving the crashing behavior, while corner-to-corner (C2C) is the worst of these four configurations. Importantly, the Pareto fronts obtained from the analytical formulas agree well with those from the FEA based surrogate models. As a result, analytical formulas could be recommended in crashworthiness optimization for the sake of computational efficiency.