Abstract
The title problem is formulated variationally. Especially membranes being totally or partly under hydrostatic loading are considered and it is assumed that either the liquid volume or the liquid level is constant during the deformation. The most general case is characterized by an isoperimetric variational problem and free boundaries of the loaded (wetted) surface. Particularly we analyse membrane strips, membranes of revolution, and arbitrary spatial membranes consisting of piecewise plane ones. Numerous numerical results are reported and discussed with respect to the stability of equilibrium. Contact problems are addressed also.
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