Universal Shapes of Fully Fluid-Filled Submerged Membrane Containers.

Membrane structures are widely used as storage containers. The accurate estimation of shape, structural tension and internal pressure are essential for the effective and safe use of such structures. This study evaluates the statics of a fluid-filled membrane section submerged in ambient fluid. Mathematical modelling is used to formalize the problem via simultaneous non-linear ordinary differential equations with undetermined boundary conditions. A close examination of the problem confirms that the shapes of membrane sections fall into one of three types depending on cross-sectional volume. Analytic integration of the curvature results in a solution of the universal shape, which is expressed in terms of elliptic integrals. Using the methods described in this study, it is possible to estimate the characteristic parameters, shapes, pressures and tensions of membrane container sections of arbitrary sizes. [ABSTRACT FROM PUBLISHER]