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Both nonlinear geometric and material behaviors must be included in the model.
The cylindrical shells of this study were first examined using the finite difference energy program BOSOR5 (Bushnell, 1976) as described by Rotter (1990) and the calculations repeated using the finite element formulation NEPAS (Teng and Rotter, 1989). Both of these programs have been widely used to study the elastic-plastic collapse and buckling of shells of revolution.
The geometries studied each represent the base of a cylindrical on-ground silo or tank (Fig. 5) and it is assumed that the internal pressure is relatively uniform over the studied height. This assumption is conservative relative to the normal conditions of declining internal pressure with distance above the base, but the conservatism is not normally large, since the bending half-wavelength of the shell is small compared with the internal pressure gradient length. . . .
FROM:
Rotter, J. M. (University of Edinburgh, Edinburgh EH9 3JL, UK), “Elephant's foot buckling in pressurised cylindrical shells”, Stahlbau, Vol. 75, September 2006, pp. 742–747. doi: 10.1002/stab.200610079
ABSTRACT: Metal cylindrical bins, silos and tanks are thin shell structures subject to internal pressure from stored materials together with axial compression from the frictional drag of stored materials on the walls and horizontal loads. The governing failure mode is frequently buckling under axial compression. The internal pressure exerted by the stored fluids or solids can significantly enhance the buckling strength, but high internal pressures lead to severe local bending near the base. Local yielding then precipitates an early elastic-plastic buckling failure. This failure mode, commonly known as “elephant's foot buckling”, has received relatively little attention to date and until recently was often ignored in tank and silo design. This problem is an unusual buckling condition, because it involves very high tensile stresses in one direction, coupled with rather small compressive stresses in the orthogonal direction. Thus, although it is a buckling failure involving considerable plasticity, it occurs at low buckling stresses and under conditions that appear to be classically “slender”. The normal concatenation of “slender” with “elastic” in buckling formulations does not apply at all here. This paper describes alternative approaches to the formulation of design rules for the elastic-plastic instability and collapse of axially-loaded internally-pressurised thin cylindrical shells adjacent to the base support. The differences between the different approaches arise from different conceptual models for the manner in which an elastic-plastic slender structure instability should be treated.
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