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An axial bulking mode of the thin-walled tube is proposed and investigated experimentally, for the purpose of transforming a pulse impact into a controllable impact. Two types of thin-walled circular copper tubes with different structures are designed based on the basic circular tubes (BCTs), namely, the uniform grooved tube (UGT) and the circumferential opening grooved tube (CGT). Then, the impact characteristics of a series of copper tubes are investigated experimentally. Results show that BCTs are compressed into two-fold forms during impact, where compression deformation occurs at the thin-walled section and a fold is formed at each thin-walled section. BGTs, UGTs, and CGTs show different performances in terms of transforming impact, and impact output via CGT can be controlled by modifying its structural parameters.

This paper introduces a biomimetic gradient hierarchical multicellular structure consisting of two tree-like fractal variants: one based on vertex connections (HCV) and the other based on wall connections (HCW). We investigate their mechanical behavior and deformation through numerical simulations. Our findings reveal that, irrespective of whether they have the same wall thickness or mass, second-order and third-order structures exhibit superior energy absorption capacity (EA) and crushing force efficiency (CFE) compared to first-order structures, resulting in significantly enhanced crashworthiness performance. In the case of HCV structures with identical wall thickness, the third-order structure outperforms the first-order structure by 79.73% in specific energy absorption (SEA) and by 38.51% in CFE. Similarly, for HCW structures, the third-order variant surpasses the first-order one by 45.57% in SEA and 28.39% in CFE. We also conduct a parametric study, exploring the influence of inner circle diameter, fractal coefficient, and fractal angle on the crashworthiness of biomimetic gradient hierarchical multicellular structures. We identify the optimal fractal coefficient and inner diameter distribution range for HCV when the fractal angle is 60${}^{\circ }$. Lastly, we compare these structures with traditional multicellular tubes, demonstrating that biomimetic gradient hierarchical multicellular tubes achieve up to 50.34% higher SEA and 55.13% higher CFE. The results of this study offer valuable design insights for developing lightweight and efficient energy-absorbing structures.

A symplectic system is developed for dynamic buckling of cylindrical shells subjected to the combined action of axial impact load, torsion and pressure. By introducing the dual variables, higher-order stability governing equations are transformed into the lower-order Hamiltonian canonical equations. Critical loads and buckling modes are converted to solving for the symplectic eigenvalues and eigensolutions, respectively. Analytical solutions are presented under various combinations of the in-plane and transverse boundary conditions. The results indicated that in-plane boundary conditions have a significant influence on this problem, especially for the simply supported shells. For the shell with a free impact end, buckling loads should become much lower than others. And the corresponding buckling modes appear as a "bell" shape at the free end. In addition, it is much easier to lose stability for the external pressurized shell. The effect of the shell thickness on buckling results is also discussed in detail.

Sandwich multi-cell conical tube was researched and a finite element model was build. Crashworthiness of sandwich multi-cell conical tube and ordinary conical tube, four-cell conical tube under axial impact were researched. The sandwich multi-cell conical tube deformation mode was analyzed. Energy absorption performance with different angles was studied. Specific energy absorption of sandwich multi-cell conical tube more than four cell conical tube increased by 35.79% and more than ordinary conical tube increased by 157%. Six different angles of sandwich cone tube with θ= 5°, θ=7.5°, θ=8.5°, θ=10°, θ=11° and θ=12.5°were researched. The initial peak force increased with the increasing of cone angle became smaller. Energy absorption is the best when sandwich multi-cell conical tube with θ=10°. As angle increases or decreases, specific energy absorption declines.