The dynamic behavior of fractal-like tubes with Sierpinski hierarchy under axial loading

Abstract

To improve the energy absorption characteristics of regular triangular tubes, a novel thin-walled structure named as Sierpinski hierarchical triangular (SHT) tube is proposed by connecting the midpoint of each side of regular triangular tube. Finite-element (FE) model established by LSDYNA is developed to explore the mechanical behavior of SHT tube under axial loading, and the numerical models are validated by test results. Numerical simulations show that the dominant deformation mechanisms of SHT structure are in-extensional and extensional folding element. Based on Simplified Super Folding Element (SSFE) theory, mean crushing force of SHT tubes is deduced subsequently. The results show that the introduction of Sierpinski hierarchy significantly enhance energy absorption capacity. The mean crushing force of 1st, 2nd, and 3rd SHT tubes tend to increase by 70.5%, 113.2%, and 150.1% compared with the single-cell triangular (ST) tubes under the same relative density, respectively. Therefore, these studies encourage designers to introduce Sierpinski hierarchy in potential applications of thin-walled structures as energy absorption equipment.