Author(s)

M S Nerantzaki & J T Katsikadelis

Abstract

Membranes subjected to ponding loads and floating on a liquid are analyzed. The initially flat membrane, which may be prestressed by edge in-plane tractions or displacements, is subjected to the weight of a liquid (e.g. rain water) filling the space created by the deflection of the membrane. Large deflections are considered, which result from nonlinear kinematic relations. The three coupled nonlinear equations in terms of the displacements governing the response of the membrane are solved using the Analog Equation Method (AEM), which reduces the problemto the solution of three uncoupled Poisson’s equations with fictitious sources. The problem is strongly nonlinear. In addition to thegeometrical nonlinearity, the ponding problem is itself nonlinear, because the ponding load and the liquid reaction are not a priori known as they depend on the produced deflection surface. Iterative schemes are developed which converge to the equilibrium state of the membrane. Example problems are presented, which illustrate the method and demonstrate its efficiency. The method has all the advantages of the pure BEM.

Keywords