Ponding Instability of Inflated Imperfect Membranes

Abstract

The problem of ponding instability of inflated imperfect cylinderical membranes is considered. It is shown that the existence of a small depression which allows the start of ponding of a fluid may lead to instability and complete collapse of the inflated structure. Several cases where the initial depression is of uniform, triangular, sinusoidal or smooth sinusoidal shape are considered and the equations of limiting equilibrium are solved. The magnitudes of the critical initial depression depths for onset of collapse are obtained and their dependences on membrane and depression geometries, and internal pressure are studied. The results are presented in graphical form. The reinterpretations of the stability criteria in terms of an inflated perfectly cylindrical membrane subjected to distributed overloads are also briefly examined.