0
Journal of Offshore Mechanics and Arctic Engineering | Volume 134 | Issue 2 | Structures and Safety Reliability
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
Article
References
Figures
Tables
Citing Articles

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
Your Session has timed out. Please sign back in to continue.

References

1
Løset, S., Shkhinek, K., Gudmestad, O. T., Strass, P., Michalenko, E., Frederking, R., and Kärnä, T., 1999, “Comparison of The Physical Environment of Some Arctic Seas,” Cold Regions Sci. Technol., 29 , pp. 201–214.  [CrossRef]
2
Gravesen, H., Sørensen, S. L., Vølund, P., Barker, A., and Timco, G., 2005, “Ice Loading on Danish Wind Turbines: Part 2. Analyses of Dynamic Model Test Results,” Cold Regions Sci. Technol., 41 , pp. 25–47.  [CrossRef]
3
Wright, B., 2000, “Full Scale Experience with Stationkeeping Operations in Pack Ice,” PERD/CHC Report No. 25–44.
4
Dalane, O., Gudmestad, O. T., Løset, S., Amdahl, J., Fjell, K. H., and Hildèn, T. E., 2008, “Model Testing of a Surface Buoy for Arctic Conditions,” "Proceedings of the 27th International Conference on Offshore Mechanics and Arctic Engineering", Estoril, Portugal, 15–20 June.
5
Dalane, O., Aksnes, V., Løset, S., and Aarsnes, J. V., 2009, “A Moored Arctic Floater in First-Year Sea Ice Ridges,” "Proceedings of the 28th International Conference on Ocean, Offshore and Arctic Engineering", Honolulu, Hawaii, USA, 31 May–5 June.
6
Srinivasan, N., Chakrabarti, S., Sundaravadivelu, R., and Kanotra, R., 2008, “Hydrodynamics of a SPAR-type FPSO Concept for Application as a Production Platform,” "Proceedings of the 27th International Conference on Offshore Mechanics and Arctic Engineering", Estoril, Portugal, 15–20 June.
7
Chernetsov, V. A., Malyutin, A. A., and Karlinsky, A. L., 2008, “Floating Production Platform for Polar Seas Designed to Resist Iceberg Impact,” "Proceedings of the Eighteenth International Offshore and Polar Engineering Conference", Vancouver, BC, Canada, 6–11 July.
8
Bruun, P., Husvik, J., Le-Guennec, S., and Hellmann, J., 2009, “Ice Model Test of an Arctic SPAR,” "The 20th International Conference on Port and Ocean Engineering under Arctic Conditions", Luleå, Sweden, 9–12 June.
9
Murray, J., LeGuennec, S., Spencer, D., Yang, C., and Yang, W., 2009, “Model Tests on a Spar in Level Ice and Ice Ridge Conditions,” "Proceedings of the 28th International Conference on Ocean, Offshore and Arctic Engineering", Honolulu, Hawaii, USA, 31 May–5 June.
10
Cummins, W., 1962, “The Impulse Response Function and Ship Motions,” Schiffstechnik, 9 , pp. 101–109.
11
Ogilvie, T., 1964, “Recent Progress Towards the Understanding and Prediction of Ship motions,” "Fifth Symposium on Naval Hydrodynamics", Bergen, Norway, 10–12 September, pp. 3–79.
12
Newman, J. N., 1977"Marine Hydrodynamics", The MIT Press, Cambridge.
13
Faltinsen, O. M., 1990, "Sea Loads on Ships and Offshore Structures", Cambridge University Press, Cambridge, England.
14
Taghipour, R., Perez, T., and Moan, T., 2008, “Hybrid Frequency-Time Domain Models for Dynamic Response Analysis of Marine Structures,” Ocean Eng., 35 (7), pp. 685–705.  [CrossRef]
15
Perez, T., and Fossen, T. I., 2008, “Time- vs. Frequency-Domain Identification of Parametric Radiation Force Models for Marine Structures at Zero Speed,” Model. Identif. Control, 29 (1), pp. 1–19.  [CrossRef]
16
Rawson, K. J., and Tupper, E. C., 2001, "Basic Ship Theory", 5th ed., Butterworth-Heinemann, Oxford, Vol. 1 .
17
Haslum, H. A., 2000, “Simplified Methods Applied to Nonlinear Motion of Spar Platforms,” Doctoral thesis, Norwegian University of Science and Technology.
18
Edwards, C. H., and Penney, D. E., (1998) "Calculus with Analytic Geometry", 5th ed., Prentice Hall, Englewood Cliffs, NJ.
19
Taz Ul Mulk, M., and Falzarano, J., 1994, “Complete Six-Degrees-Of-Freedom Nonlinear Ship Rolling Motion,” ASME J. Offshore Mech. Arct. Eng., 116 (4), pp. 191–201.  [CrossRef]
20
Dalane, O., Knudsen, F., and Løset, S., 2009, “Nonlinear Coupled Hydrostatics of Floating Conical Platforms,” "Proceedings of the 28th International Conference on Ocean, Offshore and Arctic Engineering", Honolulu, Hawaii, USA, 31 May–5 June.
21
WAMIT, 2009. WAMIT Inc. MA, USA. Version 6.4.
22
Multisurf, 2008. Aerohydro Inc. USA. Version 6.9.
23
Perez, T., and Fossen, T. I., 2008, “A Derivation of High-Frequency Asymptotic Values of 3D Added Mass and Damping Based on Properties of the Cummins Equation,” J. Marit. Res., 5 (1), pp. 65–78.
24
Standsberg, C. T., 2006, “Shallow Draft Buoy - Feasibility Model Test,” MARINTEK Technical Report No. 580060.00.01.
25
Bonnemaire, B., Shkhinek, K., Lundamo, T., Bolshev, A., Liferov, P., and Le Guennec, S., 2009, “Dynamic Effects in the Response of Moored structure to Ice Ridge Interactions,” "Proceedings of the 20th International Conference on Port and Ocean Engineering under Arctic Conditions", Luleå, Sweden, June 9-12.
26
ISO/DIS 19906, 2008, “Petroleum and natural gas industries - Arctic offshore structures,” Geneva, Switzerland.
27
Lundamo, T., Bonnemaire, B., Jensen, A., and Gudmestad, O., 2008, “Back-Calculation of the Ice Load Applying on a Moored Vessel,” "Proceedings of the 19th IAHR International Symposium on Ice", Vancouver, Canada, 6–11 July.
28
Box, G. E. P., Hunter, J. S., and Hunter, W. G., 2005, "Statistics for Experimenters", 2nd ed., Wiley-Interscience, New Jersey.
29
Brown, T. G., and Määttänen, M., 2009, “Comparison of Kemi-I and Confederation Bridge Cone Ice Load Measurement Results,” Cold Regions Sci. Technol., 55 (1), pp. 3–13.  [CrossRef]
30
Ralston, T. D., 1977, “Ice Force Design Considerations for Conical Offshore Structures,” "Proceedings of the 4th International Conference on Port and Ocean Engineering under Arctic Conditions", 26–30 September, Vol. 2 , pp. 741–752.

Figures

Grahic Jump Location
+Definition of the body modes for a floating body
View Large  |  Save Figure  |  Download Slide (.ppt)
Definition of the body modes for a floating body
Figure 1

Definition of the body modes for a floating body

Grahic Jump Location
+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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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.
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.

Grahic Jump Location
+(a) Oblique elliptical cone, (b) oblique elliptical frustum of a cone, and (c) conical structure
View Large  |  Save Figure  |  Download Slide (.ppt)
(a) Oblique elliptical cone, (b) oblique elliptical frustum of a cone, and (c) conical structure
Figure 3

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

Grahic Jump Location
+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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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.
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.

Grahic Jump Location
+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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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.
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.

Grahic Jump Location
+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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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.
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.

Grahic Jump Location
+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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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.
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.

Grahic Jump Location
+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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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.
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.

Grahic Jump Location
+Measured time series from a decay test in open water, together with the numerical simulated time series
View Large  |  Save Figure  |  Download Slide (.ppt)
Measured time series from a decay test in open water, together with the numerical simulated time series
Figure 9

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

Grahic Jump Location
+Left Measured response in heave and pitch during ridge interaction. Right: Back calculated restoring moment based on exact modeling and linear modeling.
View Large  |  Save Figure  |  Download Slide (.ppt)
Left Measured response in heave and pitch during ridge interaction. Right: Back calculated restoring moment based on exact modeling and linear modeling.
Figure 10

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

Grahic Jump Location
+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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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.
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.

Grahic Jump Location
+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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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.
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.

Grahic Jump Location
+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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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.
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.

Grahic Jump Location
+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%.
View Large  |  Save Figure  |  Download Slide (.ppt)
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%.
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%.

Grahic Jump Location
+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%.
View Large  |  Save Figure  |  Download Slide (.ppt)
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%.
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%.

Grahic Jump Location
+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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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.
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.

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Completing the Picture
Air Engines> Chapter 11
Design of Super-Precision Micro-Feed Tool Carrier Based on GMM
International Conference on Mechanical and Electrical Technology 2009 (ICMET 2009)
Later Single-Cylinder Engines
Air Engines> Chapter 3
Introduction
Hydraulic Fluids> Chapter 1
Characterization of a Perchlorate Contaminated Site
Intelligent Engineering Systems through Artificial Neural Networks Volume 18
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
This site uses cookies. By continuing to use our website, you are agreeing to our privacy policy. | Accept
Sign In