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Research Papers: Design and Analysis

Shakedown of Thick Cylinders With Radial Openings Under Thermomechanical Loadings

[+] Author and Article Information
X. T. Zheng

Key Laboratory of Pressure Systems and Safety, MOE, School of Mechanical Engineering,  East China University of Science and Technology, 130 Meilong Street, P.O. Box 402, Shanghai 200237, P. R. China

F. Z. Xuan

Key Laboratory of Pressure Systems and Safety, MOE, School of Mechanical Engineering,  East China University of Science and Technology, 130 Meilong Street, P.O. Box 402, Shanghai 200237, P. R. Chinafzxuan@ecust.edu.cn

J. Pressure Vessel Technol 134(1), 011205 (Dec 02, 2011) (7 pages) doi:10.1115/1.4004567 History: Received May 14, 2010; Revised May 17, 2011; Published December 02, 2011; Online December 02, 2011

Shakedown and ratcheting behaviors of thick-walled cylindrical vessels with radial openings subjected to cyclic thermomechanical loadings are investigated by the inelastic finite element analysis. Different shakedown and ratcheting responses are described in the modified Bree diagram considering the influences of various opening radius ratios ri/Ri, thickness ratios Ro/Ri as well as different axial stress states. Then, two simplified shakedown assessment methods of perforated cylinders are discussed. The results indicate that elastic/plasticity shakedown boundary reduces significantly owing to the presence of a radial opening while varies slightly with the opening radius, which can be defined as 1.2 approximately in the modified Bree diagram for conservative elastic/plasticity shakedown evaluation. Moreover, shakedown/ratcheting boundary decreases significantly with increasing the opening radius or decreasing the axial stress. Finally, comparing with the calculated results, the two simplified methods are verified to be accurate and intuitive to estimate the shakedown behaviors of perforated cylinders under various thickness and opening radius conditions.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 2

Finite element model

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Figure 4

Modified Bree interaction diagram of thick cylinders with radial opening (Ro /Ri  = 1.5, ri /Ri  = 1/10)

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Figure 5

Modified Bree interaction diagram of thick cylinders with radial opening (Ro /Ri  = 1.5, ri /Ri  = 1/5)

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Figure 6

Modified Bree interaction diagram of thick cylinders with radial opening (Ro /Ri  = 1.5, ri /Ri  = 3/10)

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Figure 7

Modified Bree interaction diagram of thick cylinders with radial opening (Ro /Ri  = 1.5, ri /Ri  = 2/5)

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Figure 8

Modified Bree interaction diagram for sidehole cylinders

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Figure 9

Modified Bree interaction diagram of thick cylinders with radial opening (a) (Ro /Ri  = 1.25, ri /Ri  = 1/10); (b) (Ro /Ri  = 2, ri /Ri  = 1/10)

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Figure 10

Modified Bree interaction diagram for sidehole cylinders considering different relative thicknesses

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Figure 11

Modified Bree interaction diagram of the cylinder with a side hole under axial compressive ends for −0.5 σs (Ro/Ri=1.5, ri/Ri=1/10)

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Figure 12

Modified Bree interaction diagram of perforated cylinders under different end conditions

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Figure 13

Effect of the opening radius on the shakedown region under axial compressive ends

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Figure 14

Shakedown evaluation diagram of sidehole cylinders with different opening radii

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Figure 15

Shakedown estimation diagram of perforated cylinders with various opening radii and thicknesses

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