On the bending of non-shallow polynomial shells of revolution

Abstract

Thin non-shallow polynomial shells of revolution have considerable potential for use as elevated open-top water-retaining structures, and as components of egg-shaped sludge digesters and other large multi-shell liquid-containment concrete structures. However, their structural behaviour as a particular class of thin shells has hardly been studied. Unlike other non-shallow shells of revolution, the slenderness parameter λ of higher-order polynomial shells of revolution generally varies quite rapidly over the edge zone of the shell, which invalidates the use of the popular Geckeler simplification in the evaluation of edge effects. In this paper, we propose, for the first time in the literature, a procedure for the determination of the effective slenderness parameter in the edge zone of such shells, making it possible to take advantage of the Geckeler approximation in the computation of the edge effect, without too much loss of accuracy. The accuracy of the approach is illustrated through consideration of the bending of a parabolic shell of revolution, for which some general parametric results are presented, and actual stresses calculated for the case of a uniformly pressurized shell with fixed edges. Provided the variation of λ does not exceed 30% over the edge zone (which is usually the case), the proposed approach is shown to yield reasonably accurate results (consistent with the errors already inherent in the Geckeler formulation), and is clearly applicable to polynomial shells of higher order.