Inflation of an Axisymmetric Membrane: Stress Analysis

An analysis of the stresses and deformations of an inflated axisymmetric membrane was obtained. Large deformations of Mooney material were assumed. The development of the governing differential equations is an extension of the Adkins-Rivlin equations. The extension is for a general form of undeformed profiles with symmetry of revolution. The equations obtained, when reduced identically to the special cases treated in the literature of flat, spherical, and half-ellipsoid undeformed shapes, are fully compatible. A family of axisymmetric ellipsoid curves were used as an example of undeformed shapes for numerical demonstration. A fourth-order Runge-Kutta method was applied to integrate the equations. The results show relations between the nondimensional parameters governing the deformed membrane, such as pressure, membrane height, undeformed profiles, stresses, and deformations. An analysis of a very large deformation was carried out. It was found that in this case the membrane surface approaches a spherical shape except near the support, regardless of its undeformed profile.