Accurate buckling equations for arbitrary and cylindrical elastic shells

Abstract

Accurate equations for the neutral equilibrium of arbitrary elastic shells are derived. These equations involve no displacement components and thus complement alternate sets of neutral equilibrium equations proposed by Koiter and Budiansky. The equations are specialized to a uniformly loaded circular cylindrical shell and reduced to a single partial differential equation. For a simply supported cylindrical shell, expressions for the buckling loads are obtained which are as simple as those predicted by the Donnell equations, yet as accurate as those predicted by the more elaborate Flügge equations. © 1969.