A Theory for the Buckling of Thin Shells

Abstract

In a series of papers written by the present author in collaboration with Th. von Karman and Louis G. Dunn, the effect of curvature of a structure on its buckling characteristics was investigated. The purpose of these investigations was to find an explanation for the discrepancy between the theory and the experiments. For the case of a thin spherical shell under external pressure and for the case of a thin cylindric shell under axial compression, equilibrium states involving large deflections are discovered which can be maintained by loads far less than the so-called buckling load calculated by the classic theory of infinitesimal deflections. I t was felt then that since some of these newly found equilibrium states closely approach the observed phenomena the shell must suddenly from the unbuckled configuration to these equilibrium states and the structures fail as a result of this sudden change. However, the reason why the shell should jump to these particular equilibrium states and not others was not explained. In the present paper a new principle involving the energy level and the geometric restraint is developed to determine this sudden change in equilibrium states. By means of this new principle the buckling load of both the spherical shell and cylindric shell can be calculated. The agreement with experiments is good.