Instability of hyper-elastic balloon-shaped space membranes under pressure loads

This paper discusses the evaluation of quasi-static equilibrium solutions for inflatable space membrane structures. A Mooney–Rivlin hyper-elastic material model, with variable constitutive constants, is considered. A compressible weightless medium is used to introduce within the membrane a one-parametric over-pressure loading compared to an ambient pressure. Analytical instability results are shown for a spherical and derived for a cylindrical case. These are compared to numerical simulations based on a flat linearly interpolated triangular space membrane element. Path-following procedures are used to find generalized equilibrium paths, with different parameterizations. Numerical examples show that the methods developed can give information on the stability of the membranes, but that the medium and means for introducing the internal pressure are of importance for the interpretation of stability.