Effect of inflating air on the static behavior of ETFE cushions

Inflated membranes are a kind of flexible structure with the enveloping membrane supported by the inflating air. A change in the pressure of the inflating air resulting from the deformation of the enveloping membrane will induce a change in the stress state and stiffness of the enveloping membrane, and hence influence the mechanical behavior of inflated membranes. This paper studies the effect of inflating air on the static behavior of inflated membranes via the geometrically nonlinear analysis of square ETFE (ethylene-tetrafluoroethylene) cushions under a uniformly distributed load on the top membrane. Three different models are adopted in the analysis, in which the inflating air is treated respectively as the traction boundary conditions of the enveloping membrane, a kind of fluid satisfying the ideal gas equation and a potential-based fluid. The results obtained from the models are compared to investigate their accuracies and the effect of inflating air. Based on the actual variation of the internal pressure with the deformation, a new model with correct treatment of the influence of inflating air is then proposed and its validity and accuracy for different influencing parameters, e.g., initial internal pressure, membrane thickness, side length, rise-to-span ratio, etc., are further investigated. The results show that: (a) The effect of inflating air is characterized by the air-membrane interaction, and it makes the top and bottom membranes work together as a whole. (b) The inflating air has a significant influence on the mechanical behavior of a cushion with less deformation. (c) The effect of inflating air can be approximated by a linear function with respect to the ratio of its pressure to the density. (d) The proposed model of the inflating air is accurate for different influencing factors, and it can be used as an efficient approach to the effect of inflating air without any effort to deal with the fluid-structure interaction in the computation. The present research facilitates the accurate understanding of the effect of inflating air and the mechanical behavior of inflated membranes for rational design and reliable engineering application.