Large‐Strain Analysis of Reinforced Membranes
Publication: Journal of Engineering Mechanics
Volume 119, Issue 12
Abstract
A theoretical formulation is developed for large‐strain analysis of reinforced, multilayer membranes that contain nonlinear, viscoelastic materials and are subjected to unidirectional, in‐plane loading. Regularity conditions, satisfied by the displacement fields of interest, allow the problem to be formulated in terms of a single, in‐plane component of the displacement field, even when strains are large. The theory is implemented in a finite‐element software package called REMA (reinforced membrane analysis), designed to run on a personal computer. An explicit stiffness matrix is used. The software is designed to investigate a wide range of membrane behaviors and to model the sequential stages of reinforcement and matrix subcomponent failure. Here, it is used to predict the load‐deflection behavior and sequence of subcomponent failures produced by typical in situ loading of a reinforced roofing membrane. The predictions are compared with corresponding laboratory tests.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Alfrey, T. (1948). Mechanical behavior of high polymers. Interscience Pub., New York, N.Y.
2.
Belytschko, T., and Ong, S‐J. (1984). “Hourglass control in linear and nonlinear problems.” Comp. Methods in Appl. Mech. and Engrg., 43, 251–276.
3.
Bonafont, R. L. (1985). “Review of advances in mathematical models for structural behavior of bituminous and similar membrane systems.” Proc. 1985 Int. Symp. on Roofing and Technol. National Roofing Contractors Association, Rosemont, Ill., 49–53.
4.
Brodland, G. W., and Burnett, E. F. P. (1993). “Mechanics and failure of multilayer, reinforced membranes.” ASCE J. Mat. in Civ. Engrg., 5(3), 293–307.
5.
Brodland, G. W., and Cohen, H. (1987). “Deflection and snapping of spherical caps.” Int. J. Solids Struct., 23(10), 1341–1356.
6.
Brodland, G. W., Dell, M. J., Burnett, E. F. P., and Gailey, C. (1991). “Finite element modelling of reinforced bitumen membranes.” 3rd Int. Symp. on Roofing Technol., Montreal, Canada, 21–25.
7.
Chen, D‐K., and Xu, Z‐D. (1985). “Restrained and non‐restrained deformation of viscoelastic bodies.” 2nd Int. Symp. on Roofing Technol., National Roofing Contractors Association, Rosemont, Ill., 54–61.
8.
Dell, M. J. (1990). “Behavioural characteristics of fully adhered modified bitumen roof membranes when subjected to in‐plane loads,” M.Sc. thesis, Univ. of Waterloo, Waterloo, Ontario, Canada.
9.
Dell, M. J., Burnett, E. F. P., Blackmore, P. W., and Woiceshyn, M. D. (1991). “In‐plane testing of fully‐adhered modified bitumen roof membranes.” 3rd Int. Symp. on Roofing Technol. Montreal, Canada, 445–452.
10.
Dhatt, G., and Touzot, G. (1984). The finite element method displayed, Translated by G. Cantin, John Wiley, Chichester, England.
11.
Malvern, L. E. (1969). Introduction to the mechanics of a continuous medium. Prentice‐Hall, Englewood Cliffs, N.J.
12.
Marijs, P. D., and Bonafont, R. L. (1970). “Mechanical behavior of bituminous waterproofing membrane systems.” J. Appl. Chem., 20, 11–20.
13.
McHenry, D. (1943). “A new aspect of creep in concrete and its application to design.” Proc. Am. Soc. Test. Mat., 43, 1069–1085.
14.
Metzger, D. R., and Dubey, R. N. (1987). “Corotational rates in constitutive modeling of elastic‐plastic deformation.” Int. J. Plasticity, 4, 341–368.
15.
Pommersheim, J. M. (1988). “An overview of modeling.” Int. Symp. Proc., Mathematical Modeling of Roof Systems, U.S. Dept. of Energy, Oak Ridge Nat. Lab., Oak Ridge, Tenn., 3–14.
16.
Pommersheim, J. M., Mathey, R. G., and Clifton, J. R. (1983). “Mechanical performance model for roofing membranes.” J. Struct. Engrg., ASCE, 109(6), 1431–1449.
17.
Rudin, A. (1982). The elements of polymer science and engineering. Academic Press, Orlando, Fla.
18.
Zienkiewicz, O. C. (1977). The finite element method. McGraw‐Hill, London, England.
Information & Authors
Information
Published In
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Jun 23, 1993
Published online: Dec 1, 1993
Published in print: Dec 1993
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.