Analytic Analysis of Liquid-Filled Membrane Container Resting on Horizontal Foundation with Given Cross-Sectional Volume Choi, Yoon-Rak;
In this paper, a liquid-filled long membrane container resting on a horizontal foundation is considered. All of the quantities are normalized to obtain similarity solutions. A system of nonlinear ordinary differential equations with undetermined boundary conditions is solved analytically. The integration of the curvature gives the solutions, which are expressed in terms of the elliptic integrals. A method for finding the shape and characteristic values is proposed for a given cross-sectional volume. The validity of these solutions is confirmed, and some results are shown for characteristic values and shapes.
Long membrane container;Analytic approach;Elliptic integral;Similarity solution;Sectional volume;
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