Multi-objective optimization of a tapered elliptical tube under oblique impact loading

Abstract

All types of thin-walled tube with different configurations were studied to determine their crashworthiness performances. A novel single-cell tapered elliptical tube is proposed in this paper. First, the crashworthiness performance of the single-cell tapered elliptical tube subjected to different oblique impacts was compared with those of other tubes with different configurations (straight, tapered, and multi-cell tapered) and different cross-sections (square, rectangular, and circular). It can be found that the single-cell tapered elliptical tube shows a better crashworthiness performance at multiple loading angles by comparing the specific energy absorption values and minimizing the peak crushing force. Second, to simplify the optimization process, the radial basis function model combined with the design-of-experiments method was utilized. Third, to determine the ideal radial rate f, the taper angle θ and the thickness t of the wall of the single-cell tapered elliptical tube, this paper adopted the non-dominated sorting genetic algorithm II to maximize the specific energy absorption and to minimize the peak crushing force. When determining the effect of the uncertainty in the loading angle, two different weighting-factor cases (case 1 and case 2) can be considered. In both cases, the optimized single-cell tapered elliptical tube has a better crashworthiness performance than tubes with other different cross-sections do. The design has a great influence on the optimization results. In comparison with the original single-cell tapered elliptical tube, in case 1, the composite specific energy absorption index under multiple oblique loading of the optimal tube increases by 12.81% and the peak crushing force at 0° decreases by 16.66% and, in case 2, the specific energy absorption index under multiple oblique loading increases by 11.8% and the peak crushing force at 0° decreases by 12.83%.