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Research Papers

Approximated Solutions for Axisymmetric Wrinkled Inflated Membranes

[+] Author and Article Information
Riccardo Barsotti

Assistant Professor
Department of Civil and Industrial Engineering,
University of Pisa,
Largo Lazzarino 2,
Pisa 56122, Italy
e-mail: riccardo.barsotti@unipi.it

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 7, 2015; final manuscript received August 3, 2015; published online August 25, 2015. Assoc. Editor: Kyung-Suk Kim.

J. Appl. Mech 82(11), 111007 (Aug 25, 2015) (8 pages) Paper No: JAM-15-1231; doi: 10.1115/1.4031243 History: Received May 07, 2015; Revised August 03, 2015

The axisymmetric inflation problem for a wrinkled membrane is solved by means of a simple nonlinear ordinary differential equation. The solution is illustrated in full details. Both the free and constrained cases are addressed, in the limit case where the membrane is fully wrinkled. In the constrained inflation problem, no slippage is allowed between the membrane and the constraining surfaces. It is shown that an actual membrane can in no way reach the fully wrinkled configuration during free inflation, regardless of the membrane's initial configuration and constituent material. The fully wrinkled solution is compared to some finite element results obtained by means of an expressly developed iterative–incremental procedure. When the values of the inflating pressure and length of the meridian lie within a suitable applicability range, the fully wrinkled solution may represent a reasonable approximation of the actual solution. A comparison with some numerical and experimental results available in the literature is illustrated.

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Copyright © 2015 by ASME
Topics: Membranes
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Figures

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Fig. 1

Experimental example of an inflated wrinkled membrane: the square airbag

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Fig. 2

The inflation of an axisymmetric membrane

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Fig. 3

Inflation of a membrane constrained between two rigid parallel planes: scheme of the meridian section

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Fig. 4

Inflation of a membrane constrained between two rigid parallel planes: inflated shapes of one-quarter of the meridian for different values of the dimensionless contact length a0

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Fig. 5

Inflation of a membrane constrained between two rigid parallel planes: internal tension Nr per unit pressure along one-quarter of the meridian for different values of the contact length

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Fig. 6

Diagram of xl, the left bound of the x range in which the natural width condition is fulfilled for a0 = 0.1, 0.5, 1, and 2

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Fig. 7

FE analysis of the inflation of a membrane constrained between two rigid parallel planes: symbols and notation

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Fig. 8

FE inflated shape of one-quarter of the membrane for a/R=2/3 (E = 80 GPa, ν = 0.3, R = 1500 mm, t = 1 mm, p = 0.35 N/mm2, kc=10−3)

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Fig. 10

Extension of taut region: comparison between the fully wrinkled solution and FE results for the two cases in which kc = 0.001 and kc = 0.01, respectively.

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Fig. 9

Comparison between FEM results and fully wrinkled solution: dimensionless distance between rigid planes (top) and dimensionless width of the membrane (bottom)

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Fig. 12

Contact force F versus semidistance between planes h (fully wrinkled solution)

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Fig. 11

Traction along the meridian: comparison between the fully wrinkled solution and FE results for a/R=0.091 (a) and a/R=0.50 (b)

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