Multi-parametric stability investigation for thin spherical membranes filled with gas and fluid

• We have studied a spherical membrane containing a gas and a fluid.
• We discuss the parameterization of the pressure loading.
• We find symmetric expressions for the loading media terms.
• We discuss the stability properties for two loading sequences.
• We conclude that fold lines and solution surfaces are useful for describing the response.

The instability behavior of spherical membranes completely or partially filled with fluid, also with internal gas over-pressure, placed on a friction-less rigid plane was investigated. The two-parameter Mooney–Rivlin model was used for material description. A third order penalty function was used to describe the rigid support. Different problem settings were considered, and different instability responses were observed. For the partially fluid-filled membrane, a multi-parametric problem was defined and analyzed. Augmenting equations were introduced to impose control constraints on variables chosen. These equations also affect the instability analysis. A generalized eigenvalue analysis was used for the stability conclusions. Numerical simulations showed that appropriate control constraints are of essence to interpret the instability conclusions. Fold line evaluations were performed to analyze the dependence of the instability behavior on the parameters. A solution surface algorithm was utilized to analyze and visualize the mechanical responses to multi-variable loading.