Approximated Solutions for Axisymmetric Wrinkled Inflated Membranes

Abstract

The axisymmetric inflation problem for a wrinkled membrane is solved by means of a simple nonlinear ordinary differential equation. The solution is illustrated in full details. Both the free and constrained cases are addressed, in the limit case where the membrane is fully wrinkled. In the constrained inflation problem, no slippage is allowed between the membrane and the constraining surfaces. It is shown that an actual membrane can in no way reach the fully wrinkled configuration during free inflation, regardless of the membrane's initial configuration and constituent material. The fully wrinkled solution is compared to some finite element results obtained by means of an expressly developed iterative–incremental procedure. When the values of the inflating pressure and length of the meridian lie within a suitable applicability range, the fully wrinkled solution may represent a reasonable approximation of the actual solution. A comparison with some numerical and experimental results available in the literature is illustrated.