Finite displacements of annular elastic membranes

Abstract

Axisymmetric deformations of annular membranes subjected to normal surface loads and radial edge loads or displacements are considered within the Föppl nonlinear membrane theory. When the inner edger=a is free of radial traction, the solution of the annular membrane problem is shown to reduce to the solution for the circular membrane (a=0). For nonvanishing traction atr=a, the problem is reduced to a circular pseudo-membrane problem. For both cases, existence and uniqueness of tensile solutions of the annular membrane problem are proved, including a rigorous derivation of a stress concentration factor originally found by Schwerin by formal methods.