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Research Papers: Design and Analysis

Buckling of Thin Cylindrical Shells Under Locally Elevated Compressive Stresses

[+] Author and Article Information
J. Michael Rotter1

Institute for Infrastructure & Environment, University of Edinburgh, Edinburgh EH8 9YL, UKm.rotter@ed.ac.uk

Minjie Cai

 Scott Wilson Ltd, Buchanan House, 58 Port Dundas Road, Glasgow G4 0HF, UK

J. Mark F. G. Holst

 Ingenieurbüro Holst, Philosophenweg 31, 22763 Hamburg, Germany

1

Corresponding author.

J. Pressure Vessel Technol 133(1), 011204 (Dec 22, 2010) (11 pages) doi:10.1115/1.4002771 History: Received June 07, 2010; Revised September 20, 2010; Published December 22, 2010; Online December 22, 2010

Thin cylindrical shells used in engineering applications are often susceptible to failure by elastic buckling. Most experimental and theoretical research on shell buckling relates only to simple and relatively uniform stress states, but many practical load cases involve stresses that vary significantly throughout the structure. The buckling strength of an imperfect shell under relatively uniform compressive stresses is often much lower than that under locally high stresses, so the lack of information and the need for conservatism have led standards and guides to indicate that the designer should use the buckling stress for a uniform stress state even when the peak stress is rather local. However, this concept leads to the use of much thicker walls than is necessary to resist buckling, so many knowledgeable designers use very simple ideas to produce safe but unverified designs. Unfortunately, very few scientific studies of shell buckling under locally elevated compressive stresses have ever been undertaken. The most critical case is that of the cylinder in which locally high axial compressive stresses develop extending over an area that may be comparable with the characteristic size of a buckle. This paper explores the buckling strength of an elastic cylinder in which a locally high axial membrane stress state is produced far from the boundaries (which can elevate the buckling strength further) and adjacent to a serious geometric imperfection. Care is taken to ensure that the stress state is as simple as possible, with local bending and the effects of internal pressurization eliminated. The study includes explorations of different geometries, different localizations of the loading, and different imperfection amplitudes. The results show an interesting distinction between narrower and wider zones of elevated stresses. The study is a necessary precursor to the development of a complete design rule for shell buckling strength under conditions of locally varying axial compressive stress.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Unsymmetrical pressure patterns in experimental silos

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Figure 2

Causes and consequences of unsymmetrical silo wall loads (7)

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Figure 3

Typical local axial compression buckling failure far from a shell boundary (12)

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Figure 4

Cylinder geometry and loading to develop local axial compression

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Figure 5

Axial membrane stress pattern at buckling and its simple characterization

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Figure 6

The two different buckling modes

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Figure 7

Nominal membrane stress at linear bifurcation (LBA)

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Figure 8

Nominal membrane stress (LBA) varying with inverse strip width

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Figure 9

Nominal membrane stress (LBA) varying with inverse strip width dimensionless parameter

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Figure 10

Nominal membrane stress at buckling in GNA varying with characteristic inverse strip width parameter

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Figure 11

Comparison of geometrically nonlinear (GNA) buckling loads with linear bifurcation (LBA) buckling loads

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Figure 12

Load-displacement curves for imperfect cylinders with R/t=500 under local axial compression

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Figure 13

Imperfection sensitivity for narrow and wide strip loads

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Figure 14

Variation of GNIA buckling strength for imperfection amplitudes of δ/t=1.0

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Figure 15

Ratio of materially nonlinear to elastic buckling strengths (GMNIA/GNIA) for imperfection amplitudes of δ/t=1.0

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