It is possible to accurately predict the large deformation behavior of the circular film by representing the ETFE film as an elasto-plastic model and solving the equilibrium equation between the internal pressure and the film tension assuming that the film surface is spherical. The circular air cushion receiving applied pressure can limit the unknown values of the displacement to two vertical displacements at the center of the upper and lower membrane, assuming that the curved surface shape is a sphere. It is possible to express in a simple form the equilibrium condition formula strictly based on Boyle-Charles’ law considering the pressure, volume, amount of air, temperature parameters, wrinkle and elastoplasticity of the air cushion. The validity of these is verified by comparison with the pressure experiment of circular air cushion.
When a positive applied pressure of the same magnitude as the initial internal pressure acts on the constant pressure type air cushion, the membrane tension becomes zero and the stiffness is lost. Since the internal pressure of the closed type air cushion changes in the direction of canceling the applied pressure w, the displacement and stress change of the closed type with respect to the same additional pressure is smaller than that of the constant pressure type. When the initial rise ratio h1/L ≥ 0.1, wrinkle does not occur until the absolute value of the applied pressure reaches about twice the initial internal pressure p1. When one of the upper and lower membranes wrinkles due to the applied pressure, the wrinkled membrane is in an unstable state that causes rigid body displacement, but the stiffness of the air contained in the air cushion (pneumatic stiffness) is maintained. Therefore, the decrease in stiffness of the entire air cushion is slight and maintains a stable state. When the film yield by the applied pressure, the stiffness of the air cushion is reduced, but it retains sufficient load bearing capacity. The smaller the initial rise ratio h1/L and the higher the initial internal pressure p1, the more difficult it is for the closed type air cushion to wrinkle when a positive pressure is applied to the upper membrane side. However, when the initial rise ratio h1/L is small, the initial tension σ1 becomes high, and the inferior membrane tends to yield.
For closed type air cushion that receives negative pressure on the upper membrane side, the upper membrane is less likely to yield when the initial rise ratio h1/L is large and the initial internal pressure p1 is small. The geometric stiffness effect due to the initial internal pressure p1 is smaller than the effect of curvature, and an excessive p1 often leads to an increase in stress σi and is disadvantageous. While the atmospheric pressure Pe and temperature Ti change slowly over time, the amount of air ni inside the air cushion may change significantly in a short time due to the movement of air through the air duct.
The behavior of the air-moving type air cushion changes depending on the magnitude of resistance to the movement of air. When the resistance is large, it shows characteristics close to the closed type, and when the resistance is small, it shows characteristics close to the constant pressure type.
