Research Papers

Nonlinear Hydrostatic Restoring of Floating Platforms

[+] Author and Article Information
Mohammed Khair Al-Solihat

Department of Mechanical Engineering,
Centre for Intelligent Machines,
McGill University,
Montreal, QC H3A 2K6, Canada
e-mail: solihat@cim.mcgill.ca

Meyer Nahon

Department of Mechanical Engineering,
Centre for Intelligent Machines,
McGill University,
Montreal, QC H3A 2K6, Canada
e-mail: meyer.nahon@mcgill.ca

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 14, 2013; final manuscript received May 19, 2014; published online April 2, 2015. Assoc. Editor: Carlo L. Bottasso.

J. Comput. Nonlinear Dynam 10(4), 041005 (Jul 01, 2015) (11 pages) Paper No: CND-13-1284; doi: 10.1115/1.4027718 History: Received November 14, 2013; Revised May 19, 2014; Online April 02, 2015

This paper provides a comprehensive theoretical analysis to determine the nonlinear hydrostatic restoring loads and stiffnesses of a floating offshore platform. A new approach is developed to calculate the buoyancy forces and the corresponding moments for general 3D displacements of offshore platforms that utilize cylindrical floaters, such as barge (rectangular cylinder), spar, tension leg platform (TLP), and semisubmersible (circular cylinders) offshore platforms. The exact buoyancy force magnitude and point of action (center of buoyancy) and hydrostatic restoring moments for general fully coupled 3D displacements are derived. Exact expressions for the coupled water plane area restoring moments in pitch, roll, and yaw are derived in the body and inertial frames. The analysis is subsequently used to evaluate the hydrostatic loads and stiffness of floating cylinders that undergo large displacement, such as floating wind turbine (FWT) platforms. Moreover, it can be used to determine the equilibrium positions and orientation of free floating cylindrical bodies.

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Fig. 1

(a) Rotated floating cylinder in roll motion and (b) cylinder cross-sections. B and B′ are the centers of buoyancy before and after the rotation, respectively, SWL: still water level

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Fig. 2

Normalized water plane area: (a) moment and (b) stiffness

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Fig. 3

3-2-1 Euler angle sequence

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Fig. 4

General coupled analysis for computing the hydrostatic loads

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Fig. 5

Submerged volume in the body fixed frame

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Fig. 6

Integration region A for circular and rectangular cylinders

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Fig. 7

Normalized water plane: (a) moments Mwpx and Mwpy and (b) moment magnitude for cylinders of identical Ixx and Iyy

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Fig. 8

Normalized (a) Kwp44 and (b) Kwp45 for circular/square cylinder

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Fig. 9

Normalized (a) Kwp55 and (b) Kwp54 for circular/square cylinder

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Fig. 10

Buoyancy restoring forces and moments at zero rotation angles

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Fig. 11

Three-dimensional equilibrium of a floating rectangular cylinder subject to a vertical load




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