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Article

The Mechanical Response of Freestanding Circular Elastic Films Under Point and Pressure Loads

[+] Author and Article Information
U. Komaragiri, M. R. Begley, J. G. Simmonds

Structural and Solid Mechanics Program, Department of Civil Engineering, University of Virginia, Charlottesville, VA 22904

J. Appl. Mech 72(2), 203-212 (Mar 15, 2005) (10 pages) doi:10.1115/1.1827246 History: Received May 23, 2003; Revised June 17, 2004; Online March 15, 2005
Copyright © 2005 by ASME
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Figures

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Schematic illustration of the dimensions and variables used in the analysis of a thin circular film subjected to a point load
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Parameter space delineating between regions of plate behavior (1), linear (or pre-stretched) membrane behavior (2), and nonlinear membrane behavior (3). Note that increasing pre-stretch and load (εo and P) corresponds to decreasing α and γ, respectively.
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Load-deflection relationships for a thin film with several values of pre-stretch; the inset depicts where these cases fall in the behavior map given as Fig. 2
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Boundaries in the behavioral map determined by comparing numerical and asymptotic solutions: the shaded regions correspond to load/pre-stretch combinations for which analytical solutions have less than 10% error
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Illustration of combinations of load and pre-stretch for which asymptotic solutions are accurate: the shaded region represents the plate-to-membrane transition regime where no accurate analytical solution exists
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Illustration of combinations of load and film thickness for which asymptotic solutions are accurate: the shaded region represents the plate-to-membrane transition regime where no accurate analytical solution exists
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Illustration of combinations of load and film thickness for which small rotation assumptions are accurate: the shaded region represents combinations where small rotation membrane analytical solutions are accurate. For h/a∼0.075, there is no accurate small rotation analytical membrane result.
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Universal results for cases with several pre-stretch illustrating transition from plate to membrane behavior

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