Abstract
The general theory of highly elastic membrane structures is specialized for the case of axially symmetrical membranes, and reduced to a set of six simultaneous nonlinear differential equations. An arbitrary length constant is used to normalize the variables and constants of the system into nondimensional form. By assuming that meridional deformations are large, it is shown that analytical solutions can be obtained for a general class of axially symmetrical membranes made of neo-Hookean material. The validity of the assumption is demonstrated for values of the meridional extension ratio λ 1 greater than 2, and the theory is applied to several illustrative problems of varying degrees of complexity. Detailed numerical calculations are carried out for the inflation of a cylindrical membrane. The results prove to be in good agreement with results obtained from the general equations by numerical methods.
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