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Research Papers: Design and Analysis

Buckling of Thin-Walled Long Steel Cylinders Subjected to Bending

[+] Author and Article Information
Sotiria Houliara

Department of Mechanical Engineering, University of Thessaly, Volos 38334, Greeceschoul@mie.uth.gr

Spyros A. Karamanos

Department of Mechanical Engineering, University of Thessaly, Volos 38334, Greeceskara@mie.uth.gr

J. Pressure Vessel Technol 133(1), 011201 (Dec 22, 2010) (9 pages) doi:10.1115/1.4002902 History: Received January 26, 2010; Revised September 01, 2010; Published December 22, 2010; Online December 22, 2010

The present paper investigates structural response and buckling of long unstiffened thin-walled cylindrical steel shells, subjected to bending moments, with particular emphasis on stability design. The cylinder response is characterized by cross-sectional ovalization, followed by buckling (bifurcation instability), which occurs on the compression side of the cylinder wall. Using a nonlinear finite element technique, the bifurcation moment is calculated, the post-buckling response is determined, and the imperfection sensitivity with respect to the governing buckling mode is examined. The results show that the buckling moment capacity is affected by cross-sectional ovalization. It is also shown that buckling of bent elastic long cylinders can be described quite accurately through a simple analytical model that considers the ovalized prebuckling configuration and results in very useful closed-form expressions. Using this analytical solution, the incorporation of the ovalization effects in the design of thin-walled cylinders under bending is thoroughly examined and discussed, considering the framework of the provisions of the new European Standard EN1993-1-6.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Bending of cylinders; normal stress components σv, responsible for ovalization

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Figure 2

Moment-curvature path for elastic cylinders; two-dimensional analysis

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Figure 3

Ovalization-curvature diagram for elastic cylinders; two-dimensional analysis

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Figure 4

Ovalization response of inelastic cylinders under bending loads: (a) moment-curvature path and (b) ovalization-curvature diagram; arrows (↓) denote the first yielding points

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Figure 5

Finite element analysis of elastic cylinders: (a) m−κ path and (b) detail at bifurcation point; the arrow (↓) shows the buckling point predicted by the analytical solution 7

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Figure 6

Buckling mode of an elastic cylinder under bending

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Figure 7

Numerical results of the imperfection sensitivity of elastic cylinders under bending (detail at bifurcation point)

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Figure 8

Reduction of maximum moment and its corresponding curvature in terms of imperfection amplitude

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Figure 9

Buckling of a thin-walled cylinder (r/t=50.5(32))

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Figure 10

Imperfection sensitivity in the plastic range (r/t=120 and σy=483 MPa); symbol (◆) denotes the first yielding and symbol (◼) stands for the bifurcation point as it is calculated with the employment of Hill’s comparison solid concept

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Figure 11

Localization of deformation (r/t=120 and σy=483 MPa) and finite element analysis of a three-wavelength segment: (a) entire m−κ paths and (b) detail at bifurcation

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Figure 12

(a) Finite element analysis results showing the progressive onset of inelastic localization in bent cylinders and (b) wavy pattern at the compression zone just after localization

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Figure 13

Variation of moment capacity in terms of slenderness parameter defined in Eq. 5; numerical results and reduction factor χ(λ)

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Figure 14

Ovalization of cylinder cross section; describing ovalization with Eqs. 1,2 (a represents the ovalization amplitude)

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Figure 15

(a) Tube element and (b) deformation parameters (displacements and rotations)

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