Multiobjective crashworthiness optimization of thin-walled structures with functionally graded strength under oblique impact loading

In this paper, the crashworthiness of a new introduced thin-walled structure made of hot stamping high strength steel with functionally graded strength (FGS), i.e. wall strength varying along the axial direction with a specific gradient, is investigated. The FGS columns are comprehensively studied under both axial crushing and oblique impact loading in the nonlinear FE mode LS_DYNA. The numerical simulation result shows that parameters of gradient exponent m and top strength S of FGS columns have a remarkable effect on the crashing behavior indicators such as critical load angle, energy absorption (EA) and peak crash force (PCF). To optimize the crashworthiness of the FGS columns, multi-objective optimization based on surrogate model of Radial Basis Function (RBF) and algorithm of Non-dominated Sorting Genetic Algorithm II (NSGA-II) are performed. To effectively consider the load angle uncertainty effect and obtain a more robust design, four schemes are employed to evaluate the comprehensive crashworthiness with different weight coefficient distributions. The result shows that all the Pareto fronts of FGS columns indicate considerably better crashworthiness compared to that of the counterpart uniform strength (US) columns. The consistent optimization result under different evaluation schemes not only provide guidance for the FGS column design, but also declare a good robustness for Pareto designs obtained by multi-objective optimization design (MOD) optimization. Finally, the obtained Pareto fronts of FGS columns are obviously found to consist of two parts. The first part contains the columns that possess gradient exponent ranging from 0 to 3 with top strength keeping a constant value near 480 MPa. The second part consists of the columns that possess gradient exponent keeping constants close to 0 with the top strength ranging from 700 to 950 MPa. This optimum results is different from that only obtained from pure axial crushing analyze in the previous researches and shows a better reference for engineering practice.