Crashworthiness analysis and multiobjective robust optimization of two-stage variable thickness expansion tube under impact loading

Improving the crashworthiness performance of the expansion tube of the coupler system using the limited deformation space at the vehicle end is of vital significance for the collision safety of trains. Nevertheless, an optimal design could become less meaningful or even unacceptable when some uncertainties are present. To address the issue, this paper firstly proposes a two-stage variable thickness expansion tube for the coupler system and investigates its crashworthiness performance through the impact test and finite element (FE) simulation. Associated with the verified FE model, parametric studies are performed to evaluate the effects of design variables on specific energy absorption ( SEA ), maximum crushing force ( F max ) and crushing force efficiency ( CFE ). The results show that variation in thickness ( t_1 , t_2 ) of different stages for the expansion tube has a significant effect on CFE , but they have no obvious effects on the SEA. Meanwhile, r_in and α have a significant effect on SEA , while they have a smaller effect on CFE. Furthermore, a multiobjective robust optimization process is developed to address the effects of parametric uncertainties of the expansion tube on design optimization, which comprises a sampling approach, surrogate model, six-sigma-based robust design, the non-dominated sorting genetic algorithm II, Monte Carlo verification and technique for order preference by similarity to ideal solution. It is found that the reliability of constraints ( F max , F m ) of multiobjective robust optimization is increased from 87.0 to 94.4