AXISYMMETRICAL ELASTIC MEMBRANES SUBJECTED TO FLUID LOADING

We consider axisymmetric isotropic elastic membranes that are loaded b y an incompressible liquid. The resulting deformation which contains t he liquid is assumed to be axisymmetric. We consider undeformed plane disks of varying thickness and also hemispherical cups. We show how th e resulting deformation can be controlled by the initial thickness var iation of the disk. In all cases there is a critical loading where the membrane undergoes a very rapid change of shape, from being almost co ncave to having an hourglass shape. For a hemispherical cup, the defor mation produces a wrinkled region which diminishes with increased load ing but briefly reappears as the membrane traverses the unstable regio n. The onset of instability appears to be governed by the equibiaxial deformation at the apex of the deformed container. Instability is init iated when the deformation reaches the corresponding value of the firs t bifurcation point for a spherical membrane.