Nonlinear Sloshing Analysis by Regularized Boundary Integral Method
Publication: Journal of Engineering Mechanics
Volume 143, Issue 8
Abstract
A new boundary integral method (BIM) is employed in this paper to study the two-dimensional (2D) and the three-dimensional (3D) nonlinear sloshing problems. Applying the subtracting and adding-back technique by regularized boundary integral method, the integrals of singularity and near-singularity in the boundary integral equation (BIE) can be removed and replaced appropriately by the alternative terms, respectively. In contrast to boundary element method (BEM), BIM is simpler and more straightforward. Therefore, BIM can not only provide an accurate prediction of the nonlinear free surface oscillation but also demonstrate the excellent efficiency of numerical calculation. Several small-scaled model tests on a shaking table, including harmonic and earthquake excitations, are carried out to verify the numerical methods. An artificial damping coefficient is introduced to simulate the energy dissipation of liquid motion. By comparison of the experimental and numerical results, BIM will be more reliable, efficient, and practical for nonlinear sloshing simulation.
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Acknowledgments
The authors sincerely appreciate the financial support sponsored by both the National Taiwan University and the National Science Council of the Republic of China.
References
Abramson, H. N. (1966). “The dynamic behavior of liquids in moving containers with application to space vehicle technology.”, NASA, Washington, DC.
Anderson, D. A., Tannehill, J. C., and Pletcher, R. H. (1984). Computational fluid mechanics and heat transfer, McGraw-Hill, New York.
Brebbia, C. A., and Dominguez, J. (1992). Boundary elements, McGraw-Hill, New York.
Cao, Y., Schultz, W. W., and Beck, R. F. (1991). “Three-dimension desingularized boundary integral methods for potential problems.” Int. J. Numer. Methods Fluids, 12(8), 785–803.
CEN (European Committee for Standardization). (1998). “Design provisions of earthquake resistance of structures. Part 4: Silos, tanks and pipelines.” Eurocode 8, Brussels, Belgium.
Chaiseri, P., Fujino, Y., Pacheco, B. M., and Sun, L. M. (1989). “Interaction of tuned liquid damper (TLD) and structure-theory, experimental verification and application.” Struct. Eng./Earthquake Eng., 6, 273–282.
Chen, Y. H., Hwang, W. S., and Ko, C. H. (2000). “Numerical simulation of the three-dimensional sloshing problem by boundary element method.” J. Chin. Inst. Eng., 23(3), 321–330.
Chen, Y. H., Hwang, W. S., and Ko, C. H. (2007). “Sloshing behaviors of rectangular and cylindrical liquid tanks subjected to harmonic and seismic excitations.” Earthquake Eng. Struct. Dyn., 36(12), 1701–1717.
Chen, Y. H., Hwang, W. S., Wang, J. P., and Ko, C. H. (2011). “Application of TLD to Taipei 101 for vibrational control.” J. Chin. Inst. Civ. Hydraul. Eng., 23(3), 275–286 (in Chinese).
Chern, M. J., Borthwich, A. G. L., and Eatock Taylor, R. (1999). “A pseudo-spectral sigma-transformation model of 2D nonlinear waves.” J. Fluids Struct., 13(5), 607–630.
Currie, I. G. (2003). Fundamental mechanics of fluids, CRC Press, New York.
Davis, P. J., and Robinnowitz, P. (1984). Method of numerical integration, Academic Press, Cambridge, MA.
Faltinsen, O. M. (1974). “A nonlinear theory of sloshing in rectangular tanks.” J. Ship Res., 18(4), 224–241.
Faltinsen, O. M., and Timokha, A. N. (2009). Sloshing, Cambridge University Press, New York.
Hall, J. F. (1995). “Northridge Earthquake of January 17, 1994, reconnaissance report.” Earthquake Engineering Research Institute, Oakland, CA.
Han, P. S., and Olson, M. S. (1987). “An adaptive boundary element method.” Int. J. Numer. Methods Eng., 24(6), 1187–1202.
Hwang, W. S. (2000). “A boundary node method for airfoils based on dirichlet condition.” Comput. Methods Appl. Mech. Eng., 190(13), 1679–1688.
Hwang, W. S. (2013). “A regularized boundary integral method in potential theory.” Comput. Methods Appl. Mech. Eng., 259, 123–129.
Hwang, W. S., Hung, L. P., and Ko, C. H. (2002). “Non-singular boundary integral formulations for plane interior potential problems.” Int. J. Numer. Methods Eng., 53(7), 1751–1762.
Ibrahim, R. A. (2005). Liquid sloshing dynamics: Theory and applications, Cambridge University Press, New York.
Johnson, R. L., and Fairweather, G. (1984). “The method of fundamental solutions for problem in potential flow.” Appl. Math. Modell., 8(4), 265–270.
Komatsu, K. (1987). “Non-linear sloshing analysis of liquid in tanks with arbitrary geometries.” Int. J. Non-Linear Mech., 22(3), 193–207.
Liu, D., and Lin, P. (2008). “A numerical study of three-dimensional liquid sloshing in tanks.” J. Comput. Phys., 227(8), 3921–3939.
Liu, P. F., Hsu, H. W., and Lean, M. H. (1992). “Applications of boundary integral equation methods for two-dimensional non-linear water wave problems.” Int. J. Numer. Methods Fluids, 15(9), 1119–1141.
Manos, G. C., and Clough, R. W. (1985). “Tank damage during the May 1983 Coalinga earthquake.” J. Earthquake Eng. Struct. Dyn., 13(4), 449–466.
Miles, J. W. (1967). “Surface-wave damping in closed basins.” Proc. R. Soc. London, Ser. A, 297(1451), 459–475.
Nakayama, T., and Washizu, K. (1981). “The boundary element method applied to the analysis of two-dimensional nonlinear sloshing problems.” Int. J. Numer. Methods Eng., 17(11), 1631–1646.
Okamoto, T., and Kawahara, M. (1992). “Two-dimensional sloshing analysis by the arbitrary Lagrange-Eulerian finite element method.” Struct. Eng./Earthquake Eng., 8(4), 207–216.
Peek, R., and Jennings, P. C. (1988). “Simplified analysis of unanchored tanks.” J. Earthquake Eng. Struct. Dyn., 16(7), 1073–1085.
Silverman, S., and Abramson, H. N. (1966). “Damping of liquid motions and lateral sloshing.”, NASA, Washington, DC.
Sun, L. M., and Fujino, Y. (1994). “A semi-analytical model for tuned liquid damper (TLD) with wave breaking.” J. Fluids Struct., 8(5), 471–488.
Tait, M. J. (2008). “Modelling and preliminary design of a structure-TLD system.” Eng. Struct., 30(10), 2644–2655.
Tait, M. J., El Damatty, A. A., and Isyumov, N. (2005). “An investigation of tuned liquid dampers equipped with damping screens under 2D excitation.” Earthquake Eng. Struct. Dyn., 34(7), 719–735.
Tamura, Y., Fujii, K., Ohtsuki, T., Wakahara, T., and Kohsaka, R. (1995). “Effectiveness of tuned liquid dampers under wind excitation.” Eng. Struct., 17(9), 609–621.
Tamura, Y., Kohsaka, R., Nakamura, O., Miyashita, K., and Modi, V. J. (1996). “Wind induced responses of an airport tower efficiency of tuned liquid damper.” J. Wind Eng. Ind. Aerodyn., 65(1), 121–131.
Turnbull, M. S., Borthwick, A. G. L., and Eatock Taylor, R. (2003). “Wave-structure interaction using coupled structured-unstructured finite element meshes.” Appl. Ocean Res., 25(2), 63–77.
Veletsos, A. S. (1984). “Seismic response and design of liquid storage tanks.” Guidelines Seismic Design Oil Gas Pipeline Systems, ASCE, New York, 255–370.
Warnitchai, P., and Pinkaew, T. (1998). “Modelling of liquid sloshing in rectangular tanks with flow-dampening devices.” Eng. Struct., 20(7), 593–600.
Wu, C. H., and Chen, B. F. (2012). “Transient response of sloshing fluid in a three dimensional tank.” J. Mar. Sci. Technol., 20(1), 26–37.
Wu, G. X., and Eatock Taylor, R. (1994). “Finite element analysis of two-dimensional non-linear transient water waves.” Appl. Ocean Res., 16(6), 363–372.
Wu, N. J., Tsay, T. K., and Young, D. L. (2008). “Computation of nonlinear free-surface flows by a meshless numerical method.” J. Waterw. Port Coastal Ocean Eng., 97–103.
Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 8 • August 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Jun 30, 2016
Accepted: Dec 16, 2016
Published ahead of print: Mar 21, 2017
Published online: Mar 22, 2017
Published in print: Aug 1, 2017
Discussion open until: Aug 22, 2017
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