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H.A. Mang:
"On Bounding Properties of Eigenvalues from Linear Initial FE Stability Analyses of Thin, Elastic Shells with Respect to Stability Limits from Geometrically Nonlinear Prebuckling Analyses";
International Journal for Numerical Methods in Engineering, 31 (1991), 1087 - 1111.

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 possess bounding properties with respect to corresponding stability limits from geometrically non-linear stabiltiy analyses. A 'linear initial stability analysis' by the FEM represents 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 eigenvalue from mode 2 will be shown to exist. The existence of these properties is important from the standpoint of engineering practice.