Abstract
We analyze axisymmetric equilibrium deformations of a pressurized, hemispherical, isotropic elastic membrane subjected to a concentrated force at its pole. Wrinkling of the membrane is taken into account by using a relaxed energy derived from Ogden's three-term strain energy function. The special features of the theory in wrinkled regions of the membrane are used to reduce the analysis to quadratures. Existence of solutions requires that the uniaxial stress-stretch relation satisfy a certain growth condition for large stretches.
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