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Thin-walled structures have been used in many fields due to their superior mechanical properties. In this paper, two types of hierarchical multi-cell tubes, inspired by the self-similarity of Pinus sylvestris, are proposed to enhance structural energy absorption performance. The finite element models of the hierarchical structures are established to validate the crashworthiness performance under axial dynamic load. The theoretical model of the mean crushing force is also derived based on the simplified super folded element theory. The finite element results demonstrate that the energy absorption characteristics and deformation mode of the bionic hierarchical thin-walled tubes are further improved with the increase of hierarchical sub-structures. It can be also obtained that the energy absorption performance of corner self-similar tubes is better than edge self-similar tubes. Furthermore, multi-objective optimization of the hierarchical tubes is constructed by employing the response surface method and genetic algorithm, and the corresponding Pareto front diagram is obtained. This research provides a new idea for the crashworthiness design of thin-walled structures.
Xu et al. (Sat,) studied this question.