On bounding properties of eigenvalues from linear initial FE stability analyses of thin, elastic shells with respect to stability limits from geometrically non‐linear prebuckling analyses

Abstract There is consensus in the literature that the eigenvalues of smallest absolute value from linear initial stability analyses of thin, elastic shells by the finite element method (FEM) do not posses bounding properties with respect to corresponding stability limites from geometrically non‐linear stability analyses. A ‘linear initial stability analysis’ by the FEM representes the first step of an ‘accompanying linear stability analysis’ by this method. In this paper, two modes of such stability analyses of thin, elastic shells will be presented. It will be proved that, for mode 1, in contrast to mode 2, bounding properties of eigenvalues of smallest absolute value with respect to corresponding stability limits from geometrically non‐linear stability analyses, in fact, do exist. Moreover, bounding properties of such eigenvalues from mode 1 relative to corresponding eigenvalues from mode 2 will be shown to exist. The existence of these properties is important from the standpoint of engineering practice.