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Research Papers: Fluid-Structure Interaction

Elliptical Deformation of a Floating Roof Pontoon Due to Radial Second Mode of Sloshing (Effect of the Geometry of Pontoon Cross-Section on the Hoop Membrane Stress)

[+] Author and Article Information
M. Utsumi

Machine Element Department, Technical Research Laboratory, IHI Corporation, 1 Shinnakaharacho, Isogo-ku, Yokohama, Kanagawa Prefecture 235-8501, Japan

K. Ishida

Environment and Plants Operations, IHI Corporation, 1-1 Toyosu 3-chome, Koto-ku, Tokyo 135-8710, Japan

J. Pressure Vessel Technol 133(5), 051302 (Jul 14, 2011) (10 pages) doi:10.1115/1.4003462 History: Received March 23, 2010; Revised December 20, 2010; Published July 14, 2011; Online July 14, 2011

The radial second mode of sloshing in a circular cylindrical oil storage tank induces an out-of-plane deformation of the floating roof deck. The radial contraction of the deck due to this out-of-plane deformation contains modal components with circumferential wave numbers 0 and 2, thereby causing an elliptical deformation of the pontoon, which encloses the deck. In a previous paper, the stress caused by this elliptical deformation was analyzed by regarding the radial contraction of the deck as an enforced displacement of the whole pontoon. This paper presents an improved method for this stress analysis by considering the radial contraction of the deck as an enforced displacement of the joint between the deck and the pontoon. First, the effectiveness of the previous method in estimating the hoop membrane stress at the joint with the deck is confirmed by comparing the results obtained from the previous and improved method. Next, the improved method is used to predict also the other stress components in each portion of the pontoon. Numerical results reveal that the bending stresses are magnified locally near the joint with the deck and that the hoop membrane stress in the outer portion of the pontoon sensitively depends on the geometry of the cross-section of the pontoon. It is found that the hoop membrane stress near the joint between the outer rim and the top (or bottom) of the pontoon can be significantly reduced by increasing the slope of the top (or bottom) of the pontoon.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Computational model

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Figure 2

Global displacement components (u¯,v¯,w¯) and local displacement components (u,v,w) of shell element ij

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Figure 3

Geometry of floating roof used for numerical example

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Figure 4

Shapes of some modes considered in the analysis: (a) the free surface modes Jm(λmnr) and (b) the floating roof ’s vertical displacement modes in air Fmp(r), which are obtained from U¯mp(s) in Eq. 3 by transforming the local coordinate s into the global coordinate r

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Figure 6

Visualization of elliptical deformation of pontoon at the joint with the deck (t=31 s at which radial contraction of deck reaches local maximum in Fig. 5)

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Figure 8

Hoop stress in each portion of pontoon (thick line, membrane stress; thin line, bending stress; φ=0 deg and t=31 s at which contraction of deck reaches local maximum in Fig. 5)

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Figure 11

Pontoon deformation due to radial contraction of the deck (φ=0 deg and t=31 s): (a) cos 0φ-mode and (b) cos 2φ-mode

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Figure 5

Radial contraction and out-of-plane deformation of deck due to radial second mode of sloshing with circumferential wave number 1. (a) Radial contraction at φ=0 deg. (b) Out-of-plane deformation at r=18.9 m and φ=0 deg.

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Figure 7

Hoop membrane stress arising in inner rim at joint between deck and pontoon (thick line, present analysis; thin line, previous analysis (21)). (a) Time variation (φ=0 deg). (b) Circumferential variation (t=31 s).

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Figure 9

Meridional bending stress in each portion of pontoon (φ=0 deg and t=31 s at which contraction of deck reaches local maximum in Fig. 5)

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Figure 10

Positions at which stress values are evaluated

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