Archive of Mechanical Engineering

Abstract

The axial crumpling of frusta in the axisymmetric "concertina" mode is examined. A new theoretical model is developed in which the inward folding in both cylinders and frusta is addressed. The results were compared with previous relevant models as well as experimental findings. The flexibility of the model was substantiated by its capability of describing and estimating the inward folding in frusta in general as well as in cylinders as a special case. A declining trend of the eccentricity dependence with the D/t ratio was found in contrast with a previous theory which suggests total independency. ABAQUS 14-2 finite element software was employed to simulate the thin tube as a 3-D thin shell part. Numerical simulations of the process were found to, firstly, underestimate the theoretical values of inward folding in general, secondly anticipate more underestimations as the tubes become thinner and/or have larger apex angle, and finally anticipate as low as 300 apical angle frusta to revert its mode of deformation to global inversion. Nomenclature 𝐷smaller diameter of frustum ℎ 1 , ℎ 2 plastic half-wavelengths ℎ crushed length 𝑚 1 , 𝑚 2 eccentricity factor for ℎ 1 , ℎ 2 𝑀 𝑝 fully plastic bending moment per unit length