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

This paper investigates the large deformations of an extended fluid-filled 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 different geometries, and initial axial forces and the influence of the axial force and the fluid volume were investigated. An apparatus was developed to support vertically the extended cylindrical membrane while it is filled 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 differential equilibrium equations for this specific problem and material were derived and solved by the shooting method. When the extended membrane was filled 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.

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