Similarity Shapes of a Fully Liquid-Filled Membrane on an Incline
Publication: Journal of Engineering Mechanics
Volume 138, Issue 8
Abstract
Membranes, such as geosynthetic tubes, have been widely used in civil construction and as storage tanks. Estimation of the shape, structural tension, and internal pressure are essential for effective and safe use of these structures. Motivated by a numerical study on the case of a partially liquid-filled membrane, this study presents a novel general mathematical static analysis of a fully liquid-filled geosynthetic-tube membrane section anchored on an incline. The membrane problem can be modeled analytically as a set of simultaneous nonlinear ordinary differential equations with some undetermined boundary conditions. A close examination of possible analytical solutions for increasing the cross-sectional area of the membrane identifies that the membrane sections have four similarity (or canonical) shapes. Integration of the curvature expression results in a similarity solution of the canonical shape, expressed in terms of analytical elliptic integrals. Using the analysis method developed, the range of the characteristic parameters of each canonical shape and the associated pressure and tension of membrane sections of arbitrary sizes can be determined. The analytical results developed provide an efficient tool to identify the canonical shapes and transition points and are valuable in interpreting the physics.
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Acknowledgments
We acknowledge the support of both University of Ulsan and Oregon State University, at which Y.R.C. spent a sabbatical year. S.C.Y. also acknowledges support of Office of Naval Research Grant No. ONR-N00014-11-1-0094.
References
Demiray, H., and Levinson, M. (1972). “The long fluid storage bag: a contact problem for a closed membrane.” Int. J. Mech. Sci., 14(7), 431–439.IMSCAW
Frisch-Fay, R. (1962). Flexible bars, Butterworths, London.
Ghavanloo, E., and Daneshmand, F. (2009). “The equilibrium shapes of air-filled heavy membrane tubes resting on inclined planes.” Mech. Res. Commun., 36(3), 405–412.MRCOD2
Gradshteyn, I. S., and Ryzhik, I. M. (2000). Table of integrals, series, and products, 6th Ed., Academic Press, San Diego.
Koerner, R. M. (2000). “Emerging and future developments of selected geosynthetic applications.” J. Geotech. Geoenviron. Eng., 126(4), 293–306.JGGEFK
Leshchinsky, D., Leshchinsky, O., Ling, H. I., and Gilbert, P. A. (1996). “Geosynthetic tubes for confining pressurized slurry: some design aspects.” J. Geotech. Eng., 122(8), 682–690.JGENDZ
Malik, J. (2009). “Some problems connected with 2D modeling of geosynthetic tubes.” Nonlinear Anal-Real.NARWCQ, 10(2), 810–823.
Namias, V. (1985). “Load-supporting fluid-filled cylindrical membranes.” J. Appl. Mech., 52(4), 913–918.JAMCAV
Pilarczyk, K. W. (2000). Geosynthetics and geosystems in hydraulic and coastal engineering, Balkema, Rotterdam, Netherlands.
Plaut, R. H., and Suherman, S. (1998). “Two-dimensional analysis of geosynthetic tubes.” Acta Mech., 129(3–4), 207–218.AMHCAP
Restall, S. J., Jackson, L. A., Heerten, G., and Hornsey, W. P. (2002). “Case studies showing the growth and development of geotextile sand containers: an Australian perspective.” Geotext. Geomembr., 20(5), 321–342.
Shoup, T. E., and McLarnan, C. W. (1971). “On the use of the undulating elastica for the analysis of flexible link mechanisms.” J. Eng. Ind., 93(1), 263–267.JEFIA8
Szyszkowski, W., and Glockner, P. G. (1987). “On the statics of large-scale cylindrical floating membrane containers.” Int. J. Non-linear Mech., 22(4), 275–282.IJNMAG
Wang, C. Y. (2002). “Similarity shapes of an inclined, partially filled membrane container.” J. Eng. Mech.JENMDT, 128(2), 249–251.
Wang, C. Y., and Watson, L. T. (1981). “The fluid-filled cylindrical membrane container.” J. Eng. Math., 15(2), 81–88.JLEMAU
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 138 • Issue 8 • August 2012
Pages: 984 - 996
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Jun 28, 2011
Accepted: Feb 10, 2012
Published online: Feb 13, 2012
Published in print: Aug 1, 2012
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