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Structures and Safety Reliability

Nonlinear Coupled Hydrostatics of Arctic Conical Platforms

[+] Author and Article Information
Oddgeir Dalane1

Department of Civil and Transport Engineering, Marine Civil Engineering,  Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norwayoddd@statoil.com

Finn Faye Knudsen

Department of Mathematical Science,  Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norwayfinn.faye.knudsen@math.ntnu.no

Sveinung Løset

Department of Civil and Transport Engineering, Marine Civil Engineering,  Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norwaysveinung.loset@ntnu.no

1

Corresponding author.

J. Offshore Mech. Arct. Eng 134(2), 021602 (Dec 02, 2011) (10 pages) doi:10.1115/1.4004633 History: Received November 20, 2009; Revised June 15, 2011; Published December 02, 2011; Online December 02, 2011

The increased exploration of deeper Arctic waters motivates the designs of new floating structures to operate under harsh Arctic conditions. Based on several model tests and investigations, structures with conical sections at the waterline have been shown to be a good design for waters where drifting ice is present, because the approaching ice fails in bending, which induces smaller loads than a crushing failure of ice. However, in most Arctic waters ice features are only present during part of the year and a large portion of the operation time of these structures will be in open water. Therefore, the floating structures must perform well in both conditions.Conical sections at the waterline will induce nonlinear coupling in the hydrostatic restoring forces and moments. It is important to understand how this affects the behavior in both ice and open water conditions. In order to investigate the nonlinear coupled hydrostatic restoring forces, an exact analytic expression for the metacentric height of a regular cone is presented. This is further used to develop an exact analytic expression for the hydrostatic restoring forces and moments for any body whose waterline intersects the frustum of a cone. A platform of the shallow draft-type, the platform type for which exact hydrostatics is most important, is used as a basis for the discussion and the effect of the coupled nonlinear restoring forces is illustrated by comparison to a model test performed in both open water and ice conditions.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Definition of the body modes for a floating body

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Figure 2

Definition of the parameters used in stability calculations. K is the keel position, B0 and B is the initial and the instant center of buoyancy, respectively, G is the center of gravity, and M0 and M is the initial and the instant metacenter, respectively.

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Figure 3

(a) Oblique elliptical cone, (b) oblique elliptical frustum of a cone, and (c) conical structure

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Figure 4

Illustration of the intersection of a cone with two different waterlines, shown in two planes. The crosses represent the geometrical centers of the intersected shapes, a circle and an ellipse.

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Figure 5

Dimensions of the Shallow Draft Buoy in the open water test, and the extended model in the ice test. The extended part for the ice test is marked in gray.

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Figure 6

The area below the curve gives the validity area for using exact hydrostatics for the Shallow Draft Buoy with a conical freeboard of 5 m. The validity area is also shown for an extended conical freeboard of 9 m. The bold lines mark the region where the upper cone part limits the validity area.

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Figure 7

Restoring force in heave for the linear and exact solutions. The area inside the walls indicate the valid area for the Shallow Draft Buoy, while the area outside is for a floater with an extended freeboard.

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Figure 8

Restoring moment in pitch for the linear and exact solutions. The area inside the walls indicate the valid area for the Shallow Draft Buoy, while the area outside is for a floater with an extended freeboard.

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Figure 9

Measured time series from a decay test in open water, together with the numerical simulated time series

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Figure 10

Left Measured response in heave and pitch during ridge interaction. Right: Back calculated restoring moment based on exact modeling and linear modeling.

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Figure 11

Calculated pitch response with linear hydrostatic modeling for the overturning moment applied on the Shallow Draft Buoy in the ridge test, together with the measured pitch response.

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Figure 12

The result of the factorial design analysis on the hydrostatic restoring moment for the low value of metacentric height GM0¯(-) = 8 m. The values inside the circles are the mean errors and the numbers on the lines give the factor of change.

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Figure 13

The result of the factorial design analysis on the hydrostatic restoring moment for the low value of metacentric height GM0¯(+) = 15 m. The values inside the circles are the mean errors and the numbers on the lines give the factor of change.

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Figure 14

Contour plot of the error between linear and exact pitch restoring moments for the factorial design case 5, giving the design of a SPAR-type floater. For this case the mean error errorF5¯ = 8.0%.

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Figure 15

Contour plot of the error between linear and exact pitch restoring moments for the factorial design case 12, giving the design of a shallow draft-type floater. For this case the mean error errorF5¯ = 18.2%.

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Figure 16

This figure shows the projection of the cone into a plane perpendicular to the cutting-plane and parallel to the major axis. The cutting-plane is represented by the line AB. The point M is the midpoint between A and B, and D is the intersection point between the center line and the cutting-plane. The point C is the center of mass.

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