Contact of Inflated Membranes With Rigid Surfaces

The equilibrium of an inflated cylindrical membrane in contact with two rigid cylindrical surfaces is considered. The cross section of the membrane consists of two circular arcs of radius R and an arc in contact with each surface. Equations for R and the end points of the contact regions are obtained. These equations are solved numerically for a membrane squeezed between parallel planes, and graphs of the results are shown. In addition we treat the case in which the cross section has ends which are attached to two points on one of the surfaces. In this case there are two solutions for certain values of the force on the planes, one of which is unstable.