Dynamic Uplift Scenarios for Floating Ice
Publication: Journal of Cold Regions Engineering
Volume 20, Issue 2
Abstract
Three uplift scenarios in the forced dynamics of floating ice are studied. Linear, quadratic, and square-root uplift forcing functions are considered and the associated uplift displacement functions are computed numerically. In each case, the uplift forcing is known and the displacement at the point of forcing is unknown. This is the so-called “direct” problem. In essence, this study is aimed at learning more about the “indirect” or inverse problem, where the uplift displacement function is known and the forcing is unknown. A model problem, that is able to be solved in closed form for each of the three forcing functions considered, is used to verify the numerical calculations. By curve fitting the relative error between the model problem and the actual uplift problem, a general modus operandi is arrived at for deriving approximate expressions for the otherwise intractable uplift displacement. These approximate expressions satisfy the required initial conditions and are shown to be accurate.
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Acknowledgment
The writers are indebted to John Dempsey for numerous helpful discussions.
References
Abramowitz, M., and Stegun, I. A. (1974). Handbook of mathematical functions, Dover, New York.
Brown, R. (2002). “Table Curve 2D v5.01.” Automated curve fitting and equation discovery, Systat Software Inc., Richmond, Calif.
Dahlquist, G., and Björck, Å. (1974). Numerical methods, Prentice–Hall, Englewood Cliffs, N.J.
Dane, A. (1993). “Ice station X.” Popular Mechanics, 30–34, 132, November.
Dempsey, J. P., and Zhao, Z. (1993). “Elastohydrodynamic response of an ice sheet to forced sub-surface uplift.” J. Mech. Phys. Solids, 41(3), 487–506.
Dempsey, K. M., Grossman, N., and Vasileva, I. V. (2006). “Force inversion in floating plate dynamics.” Inverse Probl. Eng., 22(1), 381–397.
Dempsey, K., and Vasileva, I. (2003). “Forced dynamic uplift of floating plates.” Proc., IUTAM Symp. on Integrated Modeling of Fully Coupled Fluid Structure Interactions Using Analysis, Computations and Experiments, H. Benaroya and T. Wei, eds., Kluwer Academic, Dordrecht, The Netherlands, 391–400.
Erdélyi, A., ed. (1953). Higher transcendental functions, Vol. 2, McGraw–Hill, New York.
Haynes, F. D., Sodhi, D. S., Kato, K., and Hirayama, K. (1983). “Ice forces on model bridge piers.” CRREL Rep. No. 83-19, Hanover, N.H.
Hertz, H. (1884). “Über das Gleichgewicht schwimmender elastischer platten.” Ann. Phys. Chem., 22, 449–455.
McElwaine, J. (2001). “fresnel.m: Calculates fresnel sin and cos integrals.” MATLAB Central, ⟨http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=913&objectType=file⟩ (May 21, 2005)
Reismann, H., and Lee, Y.-C. (1968). “Dynamics of a floating ice sheet.” J. Hydronaut., 2(2), 108–111.
Sodhi, D. S. (1989). “Interaction forces during vertical penetration of floating ice sheets with cylindrical indentors.” Proc., 8th Int. Conf. on Offshore Mechanics and Arctic Engineering, N. K. Sinha, D. S. Sodhi, and J. S. Chung, eds., The Hague, The Netherlands, 377–382.
Wyman, M. (1950). “Deflections of an infinite plate.” Can. J. Res., Sect. A, 28(3), 293–302.
Zhao, Z. G., and Dempsey, J. P. (1996). “Planar forcing of floating ice sheets.” Int. J. Solids Struct., 33(1), 19–31.
Information & Authors
Information
Published In
Journal of Cold Regions Engineering
Volume 20 • Issue 2 • June 2006
Pages: 39 - 51
Copyright
© 2006 ASCE.
History
Received: Jun 14, 2005
Accepted: Aug 5, 2005
Published online: Jun 1, 2006
Published in print: Jun 2006
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