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Fig. 3. Cross sectional shapes for a = 0.4 :
(a) State B, beta= 0, alpha = 0.2783
(b) State C, beta = -0.2846, alpha= 0.1515
(c) State D, beta= -0.3994, alpha = 0.0810
(d) State G, beta= -0.2846, alpha= 0.02770
(e) State E, beta= -0.3994, alpha= 0.00929.
Dotted line indicates ground level.
beta=pressure; alpha=tension
The curve beta vs. alpha is shown in the next image. The positions of the States B,C,D,G.E on that curve are shown in the next image.
This and the next image are from:
C.Y. Wang (Departments of Mathematics and Mechanical Engineering, Michigan State University, East Lansing, MI, 48824, USA),
“Inflating and deflating an underwater cylindrical membrane structure”, European Journal of Mechanics - A/Solids, Vol. 85, Article 104127, January-February 2021, https://doi.org/10.1016/j.euromechsol.2020.104127
ABSTRACT: The submerged air-inflated membrane cylinder is studied through perturbation and numerical integration. The problem depends on the distance between the anchors and a parameter which quantifies the pressure difference. Partial similarity and full similarity solutions are found. The results show nonlinear phenomena such as instability, snap through and hysteresis, especially during the deflation process.
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