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Review Article

Mechanics of Confined Thin-Walled Cylinders Subjected to External Pressure

[+] Author and Article Information
Daniel Vasilikis

e-mail: davasili@uth.gr

Spyros A. Karamanos

e-mail: skara@mie.uth.gr
Department of Mechanical Engineering,
University of Thessaly,
Volos 38334, Greece

1Corresponding author.

Manuscript received August 21, 2012; final manuscript received March 29, 2013; published online November 26, 2013. Editor: Harry Dankowicz.

Appl. Mech. Rev 66(1), 010801 (Nov 26, 2013) (15 pages) Paper No: AMR-12-1043; doi: 10.1115/1.4024165 History: Received August 21, 2012; Revised March 29, 2013

Motivated by practical engineering applications, the present paper examines the mechanical response of thin-walled cylinders surrounded by a rigid or deformable medium, subjected to uniform external pressure. Emphasis is given to structural stability in terms of buckling, postbuckling, and imperfection sensitivity. The present investigation is computational and employs a two-dimensional model, where the cylinder and the surrounding medium are simulated with nonlinear finite elements. The behavior of cylinders made of elastic material is examined first, and a successful comparison of the numerical results is conducted with available closed-form analytical solutions for rigidly confined cylinders. Subsequently, the response of confined thin-walled steel cylinders is examined. The numerical results show an unstable postbuckling response beyond the point of maximum pressure and indicate severe imperfection sensitivity on the value of the maximum pressure. A good comparison with limited available test data is also shown. Furthermore, the effects of the deformability of the surrounding medium are examined. In particular, soil embedment conditions are examined, with direct reference to the case of buried thin-walled steel pipelines. Finally, based on the numerical results, a comparison is attempted between the present buckling problem and the problem of “shrink buckling.” The differences between those two problems of confined cylinder buckling are pinpointed, emphasizing the issue of imperfection sensitivity.

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Figures

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Fig. 1

Schematic representation of the buckling problem of an externally pressurized cylinder confined by the surrounding medium

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Fig. 2

Finite element model of cylinder-medium system

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Fig. 3

Schematic representation of a confined ring with (a) gap-type initial imperfection and (b) out-of-roundness initial imperfection

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Fig. 4

Comparison between numerical results and analytical predictions from Glock's Eq. (1) and El-Sawy and Moore Eq. (4) for the buckling pressure of rigidly confined cylinders

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Fig. 5

Structural response of rigidly confined elastic cylinders in the presence of small gaps; (a) general response and (b) initial response for very low-pressure values

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Fig. 6

Consecutive deformation shapes of a tightly fitted elastic cylinder; configuration (2) corresponds to the ultimate pressure stage

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Fig. 7

Structural response of rigidly confined elastic cylinders in the presence of small initial out-of-roundness

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Fig. 8

Buckling pressure of imperfect elastic cylinders over the buckling pressure of the corresponding perfect elastic cylinders, confined within a rigid medium; (a) effects of initial out-of-roundness and (b) effects of initial gap

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Fig. 9

Effects of small initial out-of-roundness imperfection amplitudes on the buckling pressure of imperfect elastic cylinders; FEM results and predictions from the imperfection sensitivity formula of Eq. (15)

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Fig. 10

Response of tightly fitted steel cylinders (g/R = 0), embedded in a rigid confinement medium for different values of initial out-of-roundness

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Fig. 11

Postbuckling shapes of initially “perfect” steel cylinders with elastic-plastic material; configuration (2) corresponds to the ultimate pressure stage

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Fig. 12

Effects of initial out-of-roundness and initial gap on the external pressure response of a confined steel cylinder embedded in a rigid confinement medium (E'/E = 10-1, D/t = 200)

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Fig. 13

Effects of initial out-of-roundness and initial gap (g/R) on the maximum pressure sustained by a confined steel cylinder embedded in a rigid confinement medium (E'/E = 10-1, D/t = 200)

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Fig. 14

Effects of initial out-of-roundness and D/t ratio on the maximum pressure sustained by a confined steel cylinder embedded in a rigid confinement medium (E'/E = 10-1, g/R = 0)

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Fig. 15

Variation of maximum pressure pmax steel cylinders with no imperfections (g/R = 0,δ0/R = 0), embedded in a rigid confinement medium with respect to the slenderness parameter λ defined in Eq. (18)

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Fig. 16

Variation of maximum pressure pmax steel cylinders embedded in a rigid confinement medium with respect to the slenderness parameter λ defined in Eq. (18); finite element results and predictions of Eqs. (20), (21), and (22)

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Fig. 17

Comparison between numerical results and analytical predictions from Montel's simplified Eq. (5) [17]

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Fig. 18

Structural response of perfect (g/R = 0, δ0/R = 0) steel cylinders (D/t = 200) for different values of confinement medium modulus (E'/E); pressure versus deformation equilibrium paths

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Fig. 19

Effects of initial out-of-roundness and stiffness of confinement medium (E'/E) on the maximum pressure sustained by a confined steel cylinder (g/R = 0, D/t = 200)

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Fig. 20

Comparison between elastic and steel cylinders (D/t = 200) with respect to the E'/E value for perfect cylinders (δ0/R = g/R = 0)

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Fig. 21

Structural response of perfect steel cylinders for different values of confinement medium modulus; pressure versus displacement (δ) equilibrium paths for (a) ν = 0.3 and (b) ν = 0.49

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Fig. 22

Structural response of perfect steel cylinders for different values of confinement medium modulus; pressure versus detachment (w) equilibrium paths for (a) ν = 0.3 and (b) ν = 0.49

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Fig. 23

(a) Effect of elastic-plastic medium on the structural response of confined steel cylinder, (b) distribution of equivalent plastic strain on the medium

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Fig. 24

(a) Schematic representation of test setup [42]; (b) finite element model of cylinder-medium system

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Fig. 25

Maximum acting stress for rigidly confined elastic and steel cylinders

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