Showcase Project | Buckling Analysis of Shell Structures


Predicting the buckling response of thin shells in structural simulations is difficult because most models do not include the physical characteristics of the problem that initiate instabilities. For shell structures, the character of the buckling and load levels that lead to instability are governed by the nonuniformities or imperfections in either the structure or loading. 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. This analysis approach has been applied successfully to a variety of buckling problems.

One application is the analysis of dynamic pulse buckling of 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.

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 be seen on the loaded (front) side of the cylinder and is accurately reproduced in the calculation.

These modeling techniques have also been applied to other structural applications, including 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.


  • S.W. Kirkpatrick and B.S. Holmes, "The Effect of Initial Imperfections on Dynamic Buckling of Shells," ASCE Journal of 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," International Journal of Solids and Structures, Vol. 27, No. 1, pp. 89-103, 1991.

For inquiries or comments, please contact:

Dr. Steven Kirkpatrick
Principal Engineer

Dr. Robert T. Bocchieri
Principal Engineer

Robert MacNeill
Principal Engineer



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