Kinematically admissible folding mechanisms for the progressive collapse of foam filled conical frusta

In this paper, the progressive collapse of foam filled conical frusta is investigated analytically using four different kinematically admissible folding mechanisms with varied straight folds. Comparisons are made between these four kinematically admissible mechanisms; specifically, pure inward folding, pure outward folding, first inward followed by outward folding, and first outward followed by inward folding. The instantaneous force as well as the mean crushing force was derived based on the principle of energy conversation, and the crushing energy was absorbed by the plastic deformation of the shell, the crushing of foam filler and the foam/shell interaction. The resulted upper bound solution of the four different mechanisms is compared with the finite element predictions of the same system. Our parametric study reveals that first outward then inward folding mechanism is generally energy favorable except for cases involving greater foam resistance, thin shell thickness, and/or large taper angle in which the pure outward folding mechanism may be preferable.