Finite axisymmetric deformations of an initially stressed fluid-filled cylindrical membrane

This paper investigates the large deformations of an extended ¯uid-®lled cylindrical membrane. The static case and the behaviour of the membrane rotating at a constant angular velocity are both considered. A detailed experimental analysis was carried out involving di€erent geometries, and initial axial forces and the in¯uence of the axial force and the ¯uid volume were investigated. An apparatus was developed to support vertically the extended cylindrical membrane while it is ®lled with liquid. The membrane used in these experiments is composed of an isotropic, homogeneous and elastic rubber, which is modelled as a neo-Hookean incompressible material, described by a single elastic constant. This constant was obtained by comparing the experimental and numerical solutions for the membrane under traction. The di€erential equilibrium equations for this speci®c problem and material were derived and solved by the shooting method. When the extended membrane was ®lled with liquid, it was observed that the height of liquid increased initially as the volume of liquid inside the membrane increased until a certain critical height was reached after which it remained constant or decreased slightly with increasing volume, up to the moment when the membrane lost its stability into a non-symmetric mode. These experimental results are, as shown in the paper, in satisfactory agreement with the theory.