Determining Ice Pressure Distribution on a Stiffened Panel Using Orthotropic Plate Inverse Theory
Publication: Journal of Structural Engineering
Volume 143, Issue 5
Abstract
Inverse algorithms are presented for calculating the variable pressure acting on a stiffened steel plate. The analytical models are formulated to calculate the quasi-static pressure caused by contact of lake ice driven primarily by thermal expansion and winds. Loading pressures are calculated using strain measurements from a stiffened plate installed on a Keweenaw Peninsula lighthouse in Lake Superior. The ice sheet was essentially stationary through the winter months. The linear relationships between pressure and strain values are obtained by both strip beam theory and orthotropic plate theory. Because the inverse solutions are not necessarily unique, multiple approaches are developed and compared. Fourier pressure terms are calculated from the strain measurements using the inverse orthotropic plate theory algorithms. Two of the approaches are applied using orthotropic plate theory to reflect the variability of the ice: the first submodel presumes the pressure acts over the entire plate; the second submodel presumes the pressure acts only within the depth of the measured ice thickness. Favorable comparisons are made of results determined from orthotropic plate theory to results from finite-element (FE) analyses. A truncated singular value expansion (TSVE) method is applied to retain the robustness of the inverse process for the second submodel. Both inverse approaches show results with satisfying accuracy and efficiency compared to the FE analysis. In addition, laboratory calibration and an examination using the recorded data from field measurements exhibit the effectiveness of the presented approach. Inverse strip beam theory and the inverse orthotropic methods are applied for the evaluations. Through the recorded winter season 2013–2014, the peak ice pressures calculated by the inverse orthotropic plate theories are in the range of 3.5 MPa for the local contact ice pressures and a maximum of 3.0 MPa for the average ice pressures over the entire plate.
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Acknowledgments
The work described in this paper was supported by the Department of Energy of the United States (DE-EF005376). An award for the first author from the Link Ocean Engineering and Instrumentation Ph.D. Fellowship Program is gratefully acknowledged. Also, the contributions of Dr. David R. Lyzenga in providing the figure of ice thickness, Prof. Jason P. McCormick for his assistance and use of the laboratory facilities, and Nitin Garg for his contribution with IFMS plate design are gratefully acknowledged. Assistance from personnel from the Great Lakes Research Center is also greatly appreciated: Dr. Guy Meadow, Michael Abbot, Jamey Anderson and Colin Tyrrell. Further assistance from Dr. Roger De Roo, Dr. Lin Van Nieuwstadt and Prof. Anthony England is gratefully acknowledged.
References
Andrews, H., and Patterson, C. (1976). “Singular value decompositions and digital image processing.” IEEE Trans. Acoust. Speech Sig. Process., 24(1), 26–53.
Andrieux, S., and Abda, A. B. (1996). “Identification of planar cracks by complete overdetermined data: Inversion formulae.” Inverse Problems, 12(5), 553–563.
Bjerkås, M. (2007). “Review of measured full scale ice forces to fixed structures.” Proc., 26th Int. Conf. on Offshore Mechanics and Arctic Engineering, ASME, New York.
Bjerkås, M., and Skiple, A. (2005). “Occurrence of continuous and intermittent crushing during ice-structure interaction.” Proc., 18th Int. Conf. of Port and Ocean Engineering under Arctic Conditions (POAC), 3, Potsdam, New York.
Bonnet, M., and Constantinescu, A. (2005). “Inverse problems in elasticity.” Inverse problems, 21(2), R1.
Boot, J. C., and Moore, D. B. (1988). “Stiffened plates subject to transverse loading.” Int. J. Solids Struct., 24(1), 89–104.
Chock, J., and Kapania, R. (2003). “Load updating for finite element models.” AIAA J., 41(9), 1667–1673.
Deb, A., and Booton, M. (1988). “Finite element models for stiffened plates under transverse loading.” Comput. Struct., 28(3), 361–372.
Dempsey, J. P., Palmer, A. C., and Sodhi, D. S. (2001). “High pressure zone formation during compressive ice failure.” Eng. Fract. Mech., 68(17), 1961–1974.
Engl, H. W., and Kügler, P. (2005). “Nonlinear inverse problems: Theoretical aspects and some industrial applications.” Multidisciplinary methods for analysis optimization and control of complex systems, Springer, Berlin, 3–47.
Ewing, R. E., Lin, T., and Lin, Y. (1999). “A mixed least-squares method for an inverse problem of a nonlinear beam equation.” Inverse Problems, 15(1), 19–32.
Frederking, R., and Schwarz, J. (1982). “Model tests of ice forces on fixed and oscillating cones.” Cold Reg. Sci. Technol., 6(1), 61–72.
Hansen, P. C. (1987). “The truncated svd as a method for regularization.” BIT Numer. Math., 27(4), 534–553.
Hansen, P. C., and O’Leary, D. P. (1993). “The use of the L-curve in the regularization of discrete ill-posed problems.” SIAM J. Sci. Comput., 14(6), 1487–1503.
International Electrotechnical Commission. (2009). “Wind turbines-part, 3-1: Design requirement for offshore wind turbines.”, Geneva.
Joensuu, A., and Riska, K. (1989). “Contact between ice and structure.”, Laboratory of Naval Architecture and Marine Engineering, Helsinki Univ. of Technology, Espoo, Finland.
Jordaan, I. J. (2001). “Mechanics of ice-structure interaction.” Eng. Fract. Mech., 68(17), 1923–1960.
Kaiman, D. (1996). “A singularly valuable decomposition.” College Math. J., 27(1), 2–23.
Kim, L. V., Kulesh, V. A., and Tsuprik, V. G. (2015). “Methodology for experimental determination of local ice pressures on flexible hull of platforms and ships.” 25th Int. Offshore and Polar Engineering Conf., International Society of Offshore and Polar Engineers, Cupertino, CA.
Leira, B., Børsheim, L., Espeland, Ø., and Amdahl, J. (2009). “Ice-load estimation for a ship hull based on continuous response monitoring.” Proc. Inst. Mech. Eng. Part M: J. Eng. Mar. Environ., 223(4), 529–540.
Leone, G., and Soldovieri, F. (2003). “Analysis of the distorted Born approximation for subsurface reconstruction: Truncation and uncertainties effects.” IEEE Trans. Geosci. Remote Sens., 41(1), 66–74.
Li, J., and Kapania, R. K. (2007). “Load updating for nonlinear finite element models.” AIAA J., 45(7), 1444–1458.
Ma, C. K., Chang, J. M., and Lin, D. C. (2003). “Input forces estimation of beam structures by an inverse method.” J. Sound Vibr., 259(2), 387–407.
Nejati, H. (2014). “Passive remote sensing of lake ice and snow using wideband autocorrelation radiometer (WiBAR).” Ph.D. dissertation, Univ. of Michigan, Ann Arbor, MI.
Palmer, A., and Croasdale, K. (2013). Arctic offshore engineering, World Scientific, Singapore.
Palmer, A. C., Dempsey, J. P., and Masterson, D. M. (2009). “A revised ice pressure-area curve and a fracture mechanics explanation.” Cold Reg. Sci. Technol., 56(2), 73–76.
Riska, K. (1991). “Observations of the line-like nature of ship-ice contact.” Proc., 11th Int. Conf. on Port and Ocean Engineering under Arctic Conditions, 2, Memorial Univ. of Newfoundland, St. John’s, Canada, 24–28.
Riska, K., Uto, S., and Tuhkuri, J. (2002). “Pressure distribution and response of multiplate panels under ice loading.” Cold Reg. Sci. Technol., 34(3), 209–225.
Sanderson, T. J. O. (1988). Ice mechanics. Risks to offshore structures, Graham and Trotman, London.
Semnani, A., and Kamyab, M. (2008). “Truncated cosine Fourier series expansion method for solving 2-D inverse scattering problems.” Prog. Electromag. Res., 81, 73–97.
Semnani, A., and Kamyab, M. (2010). Solving inverse scattering problems using truncated cosine fourier series expansion method, INTECH, Rijeka, Croatia.
Shimpi, R. P., and Patel, H. G. (2006). “A two variable refined plate theory for orthotropic plate analysis.” Int. J. Solids Struct., 43(22), 6783–6799.
Snieder, R. (1998). “The role of nonlinearity in inverse problems.” Inverse Problems, 14(3), 387–404.
Sodhi, D. S. (1991). “Ice-structure interaction during indentation tests.” Ice-structure interaction, Springer, Berlin, 619–640.
Starkey, J. M., and Merrill, G. L. (1989). “On the ill-conditioned nature of indirect force-measurement techniques.” J. Modal Anal., 4(3), 103–108.
Tarp-Johansen, N. J., Manwell, J. F., and McGowan, J. (2006). “Application of design standards to the design of offshore wind turbines in the US.” Offshore Technology Conf., Offshore Technology Conference, Inc., Richardson, TX.
Tõns, T., Ralph, F., Ehlers, S., and Jordaan, I. J. (2015). “Probabilistic design load method for the Northern Sea Route.” 34th Int. Conf. on Ocean, Offshore and Arctic Engineering, ASME, New York.
Ventsel, E., and Krauthammer, T. (2001). “Thin plates and shells: Theory: Analysis, and applications.” Orthotropic and stiffened plates, Marcel Deckker, Inc., New York.
Wells, J., Jordaan, I., Derradji-Aouat, A., and Taylor, R. (2011). “Small-scale laboratory experiments on the indentation failure of polycrystalline ice in compression: Main results and pressure distribution.” Cold Reg. Sci. Technol., 65(3), 314–325.
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Published In
Journal of Structural Engineering
Volume 143 • Issue 5 • May 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Sep 16, 2015
Accepted: Oct 5, 2016
Published ahead of print: Jan 22, 2017
Published online: Jan 23, 2017
Published in print: May 1, 2017
Discussion open until: Jun 23, 2017
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