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.

We consider the problem of axisymmetric deformation of a pressurized toroidal membrane composed of an isotropic elastic material. In its unstressed state the torus has the form of a double-walled cylinder. This is modelled by taking the radius from the axis of symmetry to be constant throughout the membrane. Wrinkling of the membrane is taken into account in an approximate way by using a relaxed strain energy derived from Ogden's three-term strain energy function. The equilibrium equations are reduced to a first order system of ordinary differential equations and solved numerically. Multiple equilibria are found in each of the examples studied.