Similarity Shapes of a Fully Liquid-Filled Membrane on an Incline

Abstract

AbstractMembranes, such as geosynthetic tubes, have been widely used in civil construction and as storage tanks. Estimation of the shape, structural tension, and internal pressure are essential for effective and safe use of these structures. Motivated by a numerical study on the case of a partially liquid-filled membrane, this study presents a novel general mathematical static analysis of a fully liquid-filled geosynthetic-tube membrane section anchored on an incline. The membrane problem can be modeled analytically as a set of simultaneous nonlinear ordinary differential equations with some undetermined boundary conditions. A close examination of possible analytical solutions for increasing the cross-sectional area of the membrane identifies that the membrane sections have four similarity (or canonical) shapes. Integration of the curvature expression results in a similarity solution of the canonical shape, expressed in terms of analytical elliptic integrals. Using the analysis method developed, the range...