Comments on effective use of numerical modelling and extended classical shell buckling theory (original) (raw)
2023, Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences
2. Extended classical shell buckling theory A number of reviews [31-34] have covered some of the background and important applications of the RS extension to classical shell buckling theory. These have demonstrated that for wide ranges of shell forms and loading conditions, the lower limits to the reductions in buckling loads caused by increasing levels of geometric (and loading) imperfections are provided by RS analysis, including the treatment of the development of material failure [6,31-33]. The philosophical basis of the RS method can be formulated [34] in terms of the following lemmas: Lemma 2.1. Significant geometric nonlinearity in structural behaviour results from changes in incremental membrane energy (or equivalently membrane stiffness). Corollary 2.2. Significant nonlinearity in the buckling of shell and plate structures derives from changes in incremental membrane energy. Corollary 2.3. Nonlinearity arising from changes of incremental bending energy is practically negligible. Lemma 2.4. Loss of stiffness (or load carrying capacity) in the buckling 1 and postbuckling (see footnote 1) of shells is the result of loss of incremental membrane energy. Corollary 2.5. Loss of stiffness (or load carrying capacity) in the postbuckling of shells can only occur if the initial buckling mode (critical bifurcation mode) contains membrane energy. Corollary 2.6. Loss of stiffness (or load carrying capacity) resulting from changes of incremental bending energy in the postbuckling of shells is practically negligible.
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