Boundary-Element Methods In Offshore Structure Analysis

[+] Author and Article Information
J. N. Newman

MIT, Cambridge, MA 02139e-mail: jnn@mit.edu

C.-H. Lee

WAMIT Inc., Chestnut Hill, MA 02467e-mail: chlee@wamit.com

J. Offshore Mech. Arct. Eng 124(2), 81-89 (Apr 11, 2002) (9 pages) doi:10.1115/1.1464561 History: Received July 01, 2001; Revised November 01, 2001; Online April 11, 2002
Copyright © 2002 by ASME
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Perspective view of the McIver toroid generated by a ring source of unit radius, with the inner waterline at r=0.2 and the outer waterline at r=2.4687. The view is from above the free surface, and the two waterlines are circular. The geometry is defined by one patch, in the first quadrant (x>0,y>0).
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Perspective view of the array of nine cylinders with spherical buoyancy caps. Only the submerged portions are shown. The top edge of each cylinder is in the plane of the free surface.
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Perspective view of the FPSO. The bow is a semi-elliptical cylinder. The stern is prismatic with a vertical transom. All transverse sections are rectangular. The upper figure shows the geometry for the higher-order method, including the patches (six on each side, bounded by dark lines) and panels (light lines, with the obscured panels hidden from view). The panels in the bow have smooth continuous curvature, although this is not clear from the plot. The lower figure shows a typical low-order panel arrangement (with obscured panels hidden from view).
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Results for the McIver toroid. The left figure shows the heave added-mass coefficient, including results from the low-order analysis with N=128, 512, 2048 panels on one quadrant of the body surface, and higher-order results with explicit geometry definition (N=100 unknowns). The latter results are converged within graphical accuracy. The right figure shows the convergence of the low- and higher-order results to the singular wavenumber J0(k)=0.IRR=1 denotes that the irregular-frequencY effects are removed.
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Exciting force (solid line), and the force on the middle element (long dashed line), for the array shown in Fig. 2. The force on a single isolated body is represented by the short dashed line, for comparison. The maximum value of the exciting force is at K=0.932, with the peak value equal to 111. All forces are in the direction parallel to the array axis, and the incident wave propagates in the same direction.
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Mean yaw moment about the mid-section of the FPSO, as a function of the period, T. the solid line is evaluated from the higher-order method using momentum analysis. the corresponding results from the low-order momentum analysis are shown by solid square symbols. The open squares (low-order) and circles (higher-order) represent the corresponding results using the pressure analysis. The moment is normalized by the product of water density, gravity, wave amplitude squared and the square of unit length.
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Schematic description of the evaluation of the influence from the source or normal dipole distribution on the panel ‘S’ to the panel ‘N’ in the near field and to the panel ‘F’ in the far field. The large gray area is the near field where the influence of ‘S’ on ‘N’ is evaluated directly by (9) and (10). The indirect evaluation between ‘S’ and ‘F’ using FFT is denoted by a dotted line. The projection of ‘S’ to the nearby grid nodes is denoted by the white outward arrows. The interpolation of the potential on ‘F’ from the potentials at the nearby grid nodes is denoted by white inward arrows.
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Perspective view of the MOB, made up of five semi-subs (lower figure) and the array of truncated cylinders corresponding to the columns of the semi-subs without the pontoons (upper figure).
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Modulus of the free-surface elevation along the centerline of the MOB configuration shown in the lower part of Fig. 8. Results are shown for five different wave periods (T). Note that different vertical scales are used for each wave period. The incident wave is traveling toward the negative x-axis. The elevation is normalized by the incident-wave amplitude.
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Modulus of the free-surface elevation along the centerline of the array of cylinders shown in the upper part of Fig. 8. Note that different vertical scales are used for each wave period. Other definitions are the same as in Fig. 9.




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