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Research Papers

Finite Inflation Analysis of Two Circumferentially Bonded Hyperelastic Circular Flat Membranes

[+] Author and Article Information
Nikhil N. Dhavale

Department of Mechanical Engineering,
Centre for Theoretical Studies,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, India
e-mail: nikhil.dhavale@gmail.com

Ganesh Tamadapu

KTH Mechanics,
Royal Institute of Technology,
Osquars Backe 18,
Stockholm SE-100 44, Sweden
e-mail: tamadapu@kth.se

Anirvan DasGupta

Professor
Department of Mechanical Engineering,
Centre for Theoretical Studies,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, India
e-mail: anir@mech.iitkgp.ernet.in

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 9, 2014; final manuscript received July 4, 2014; accepted manuscript posted July 9, 2014; published online July 21, 2014. Assoc. Editor: Taher Saif.

J. Appl. Mech 81(9), 091012 (Jul 21, 2014) (9 pages) Paper No: JAM-14-1164; doi: 10.1115/1.4027972 History: Received April 09, 2014; Revised July 04, 2014; Accepted July 09, 2014

A finite inflation analysis of two circumferentially bonded hyperelastic circular flat membranes with uniform internal pressure is presented. The governing equations of equilibrium are obtained using the variational formulation. By making a suitable change in the field variables, the problem is formulated as a set of two coupled nonlinear two point boundary value problem (TPBVP) and is solved using the shooting method. Membranes of identical and dissimilar material properties are considered in the analysis. For dissimilar membranes, asymmetric inflation, and remarkably, deflation (after an initial phase of inflation) in one of the membranes in certain cases, has been observed. The effect of inflation pressure and material properties on the geometry of inflated configuration, state of stress, and the impending wrinkling condition of the membranes are also studied. This work has relevance to tunable inflated reflectors and lenses among other applications.

FIGURES IN THIS ARTICLE
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Copyright © 2014 by ASME
Topics: Membranes , Pressure , Stress
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Figures

Grahic Jump Location
Fig. 1

Two circular flat membranes bonded at the boundary

Grahic Jump Location
Fig. 2

Variation of the principal stretches (λ1,λ˜1) (dashed lines) and (λ2,λ˜2) (solid lines) along the radial coordinate (x1) for certain inflation pressures. The point x1= 0 for the upper (lower) membrane represents the zenith (nadir). The membrane junction is at x1= 1.

Grahic Jump Location
Fig. 3

Principal stretches of the membrane between x1=0 and x1=1 for all possible inflation pressure values on the λ1-λ2 plane with zero principal stress boundaries λ2=λ1-1/2 (solid line with hollow circle as marker) and λ1=λ2-1/2 (solid line with hollow square as marker). Beyond the indicated value of the inflation pressure Pw (corresponding to point A), no impending wrinkling is observed in the membranes. For (a) α1=α2  (———), (b) α1 (———), α2 (– – – – –).

Grahic Jump Location
Fig. 4

Inflated configurations of the membranes for certain inflation pressures (as indicated by solid lines) for the upper membrane α1(y3≥0) and the lower membrane α2(y3≤0). The dotted lines represent the path followed by the material points during inflation. The membrane junction is at y3=0.

Grahic Jump Location
Fig. 5

Variation of the Gaussian curvature of the membrane along the radial coordinate x1 for three inflation pressure values

Grahic Jump Location
Fig. 6

Variation of the Cauchy stress resultants (T1,T˜1) (dashed lines) and (T2,T˜2) (solid lines) along the radial coordinate (x1) for certain inflation pressures

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