Equilibrium problems in membrane structures with rigid boundaries
DOI:
https://doi.org/10.3989/ic.08.038Keywords:
membrane, footbridge, rigid boundary, eliptic problem, hyperbolic problemAbstract
This paper presents the equilibrium analysis of a membrane with rigid boundary. The idea of using membranes in applications such as footbridges, a new technology being developed in Spain, implies a more accurate analysis procedure. Due to the tension stresses, membrane is identifi ed to a negative gaussian curvature surface. Equilibrium is directly expressed by means of partial differential equations, in terms of the membrane shape and stress tensor. Starting from these equations, two dual approaches can be defi ned, namely direct problem and dual problem. Both problems are analyzed, studying their possible solutions in order to obtain practical results. In particular, the main analytical aspects of the direct problem are discussed, a numerical resolution procedure is proposed and, fi nally, analytical and numerical solution examples are presented.
Downloads
References
(1) Bonet J., Mahaney J., 2001. Form fi nding of membrane structures by updated reference method with minimum mesh distortion. International Journal of Solids and Structures, Vol. 38, pp. 5469 - 5480. doi:10.1016/S0020-7683(00)00382-6
(2) Brezis H., 1983. Analyse functionnelle. Théorie et applications, Masson Editeur, París.
(3) Flugge W., 1973. Stresses in Shells, 2nd ed., Springer-Verlag, New York.
(4) Gilbarg L., Trudinger N. S., 1998. Elliptic Partial Differential Equations of Second Order, Springer.
(5) Haas L.M. 1964. Disign of Thin Shells. Wiley, New York.
(6) Hörmander L, 1964 Linear Partial Differential Operators. Springer, Berlin.
(7) Hughes T.J.R., 1987. The Finite Element Method. Linear Static and Dynamic Finite Element Analysis; Mineola, New York Dover Publications.
(8) Linkwitz K., 1999. About formfi nding of double-curved structures. Engineering Structures; Vol. 21, pp. 709 - 718. doi:10.1016/S0141-0296(98)00025-X
(9) Murcia J., 2007. Tecnología de pasarelas con estructura de membrana. Informes de la Construcción; No. 507; 21 - 31.
(10) Timoshenko S., Woinowsky-Krieger S., 1959. Theory of Plates and Shells. McGraw-Hill, Inc., New York.
(11) Tüzel V.H., Erbay H.A., 2004. The dynamic response of an incompressible nonlinearly elastic membrane tube subjected to a dynamic extension. International Journal of Non-Linear Mechanics; Vol. 39, pp. 515 - 537. doi:10.1016/S0020-7462(02)00220-2
(12) Viglialoro G., 2006. Análisis matemático del equilibrio en estructuras de membrana con bordes rígidos y cables. Pasarelas: forma y pretensado. Tesis doctoral, UPC. Enlace: http://www.tesisenxarxa.net/TDX-0515107-100745/.
(13) Zienkiewicz O. C., Taylor R. L., 2000. The Finite Element Method, Butterworth Heinemann.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2009 Consejo Superior de Investigaciones Científicas (CSIC)
This work is licensed under a Creative Commons Attribution 4.0 International License.
© CSIC. Manuscripts published in both the print and online versions of this journal are the property of the Consejo Superior de Investigaciones Científicas, and quoting this source is a requirement for any partial or full reproduction.
All contents of this electronic edition, except where otherwise noted, are distributed under a Creative Commons Attribution 4.0 International (CC BY 4.0) licence. You may read the basic information and the legal text of the licence. The indication of the CC BY 4.0 licence must be expressly stated in this way when necessary.
Self-archiving in repositories, personal webpages or similar, of any version other than the final version of the work produced by the publisher, is not allowed.
