Axisymmetric elastic membranes subjected to fluid loading

We consider axisymmetric isotropic elastic membranes that areloaded by an incompressible liquid. The resulting deformationwhich contains the liquid is assumed to be axisymmetric. Weconsider undeformed plane disks of varying thickness and alsohemispherical cups. We show how the resulting deformation canbe controlled by the initial thickness variation of the disk.In all cases there is a critical loading where the membraneundergoes a very rapid change of shape, from being almost concaveto having an hourglass shape. For a hemispherical cup, the deformationproduces a wrinkled region which diminishes with increased loadingbut briefly reappears as the membrane traverses the unstableregion. The onset of instability appears to be governed by theequibiaxial deformation at the apex of the deformed container.Instability is initiated when the deformation reaches the correspondingvalue of the first bifurcation point for a spherical membrane.