Abstract
The behavior of a Mooney-Rivlin membrane under fluid pressure and large deformations is studied. This kind of deformation dependent load turns out to be conservative due to the existence of a corresponding potential. An originally plane and horizontal membrane strip at the bottom of a liquid container is investigated for various loading conditions including constant pressure and dead weight of the membrane. For a certain range of fixed fluid levels there exist several equilibrium positions, stable ones and unstable ones. The discussion includes the so called puddle problem which is characterized by a partial loading of the membrane the final boundaries of the fluid being unknown. In this case the variational problem is an isoperimetric one with varying limits of one integral of the potential energy. Numerical results are obtained using finite elements. The circular membrane has been treated in an analogous manner but is not discussed here for brevity.
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