SRI performed experiments and analyses on impulsively loaded thin cylindrical aluminum shells. The cosine distributed external impulsive loads drive the shell inward producing compressive circumferential stresses and pulse buckling on the loaded side of the shell. These buckles produce strain concentrations that govern the eventual fracture of the structure. Thus the buckling response needs to be correctly modeled to predict failure.

Predicting the buckling response of thin shells is difficult because most finite element models do not include the physical characteristics of the problem that initiate instabilities. A methodology was developed to accurately predict the buckling response of the thin shell structures by incorporating either the measured imperfections in the structure and loading, or accurate statistical approximations to the imperfections. A cross section of a dynamically pulse buckled thin cylindrical shell and the calculated response are shown in Figure 1. In the calculation, we used the measured imperfections in the cylinder shape to initiate the buckling. The buckling response can clearly seen on the loaded (front) side of the cylinder and is accurately reproduced in the calculation.

These modeling techniques, developed for analysis of pulse buckling of thin aerospace shell structures, have been used in other structural applications. These include analysis of crash energy management structures for vehicles, static axial collapse of cylinders, and dynamic buckling of thick shells. One example application for thick shells is the buckling that occurs in explosively formed penetrators (EFPs) as shown in Figure 2. Understanding and modeling the processes that lead to dynamic plastic buckling in EFP liners allows the designer to control the buckling process to gain enhanced aerostability.

Figure 1 Thin Shell Buckling Impulsive Loading on a Thin Aluminum Cylinder.

Figure 2 EFP Formation Explosively Formed Penetrator (EFP): Analysis with Dynamic Buckling of the Liner.

	S.W. Kirkpatrick and B.S. Holmes, "Effect of Initial Imperfections on Dynamic Buckling of Shells," J. Engineering Mechanics, Vol. 115, No. 5, pp. 1075-1093, May, 1989.
	Florence, A.L., Gefken, P.R., and Kirkpatrick, S.W., "Dynamic Plastic Buckling of Copper Cylindrical Shells," Int. J. Solids and Structures, Vol. 27, No. 1, pp. 89-103, 1991.