Theoretical analysis on the collapse of dumbbell-shaped tubes

Thin-walled round tube systems are widely used in impact protection. However, in these systems, additional installation time and cost is required to constrain the tubes and prevent their splashing under impact loadings. To address this problem, a self-locked system comprised of thin-walled dumbbell-shaped tubes was recently proposed, which can prevent lateral splash from impact loadings without the presence of any constraints on the boundary or between the tubes. This paper provides a theoretical analysis on the deformation and collapse of dumbbell-shaped tubes under quasi-static lateral loads. A plastic hinge model is developed to estimate the force-displacement relationship, deformation efficiency and specific energy absorption of the dumbbell-shaped tube, and besides, an elastic solution is derived to describe the mechanical response of the dumbbell-shaped tube at small deformation. The theoretical models are validated by both finite element method (FEM) simulation and experiments. Based on the theoretical analysis, the effects of the geometry of the dumbbell-shaped tube on energy absorption are studied, and the optimal geometry design of the tube is discussed. The relation between each geometry parameter and energy absorption properties is summarized in a table, which provides important reference for designing dumbbell-shaped tubes in practical applications.