Multi-objective cross-sectional shape and size optimization of S-rail using hybrid multi-criteria decision-making method

Abstract

This study proposes a multi-objective lightweight and crashworthiness optimization design of complex cross-sectional shape and size of S-rail employing a hybrid multi-criteria decision-making (HMCDM) method. Several S-rails with special cross-sectional shapes of the reinforcement plate are established and compared. Response surface models with different orders are established considering the complex cross-sectional shapes and sizes. The objective function chosen for the two objectives is the specific energy absorption (SEA) and the peak force (PF). Meanwhile, the metrics for the three-objective are the PF, the total mass (M), and the energy absorption (EA). Two-objective Pareto fronts are obtained by the three-objective optimization confronting. Different multi-criteria decision-making methods are used to find the trade-off optimum points from the Pareto fronts. Results indicate that the proposed HMCDM method, including the technique for order preferences by similarity to ideal solution, gray relational analysis, and entropy weight, demonstrates a good trade-off frontier solution. In the case of a slight increase in M, the EA and SEA performances of the optimal model are greatly improved compared with the S-rail without a stiffener. Compared with the initial optimization model, the M of the optimal model is reduced by 25.62%, and the performance is improved. Therefore, the design of the cross-sectional shape and size of the S-rail and hybrid method can improve the crashworthiness.