Buckling of an elastic membrane on a surface of revolution

This paper is concerned with a generalization of the following problem in nonlinear membrane theory studied by S. Lubkin [1] and C. Sensenig [2]: a membrane in the shape of an annulus is deformed by the application of a hydrostatic pressure to the outer boundary while the inner boundary remains stress free. The membrane is constrained to lie between two lubricated plates, so that no work is done at these surfaces during the deformation. The deformation is rotationally symmetric, each point on the membrane moving along a radius so that the deformed membrane is still in the shape of an annulus. What is to be determined is the stability of this deformation with respect to asymmetric disturbances satisfying the same stress conditions at the two boundaries and the same constraint imposed by the plates.