On finite displacements of curved annular elastic membranes without wrinkling

Abstract

Axisymmetric deformations of curved annular elastic membranes subjected to vertical surface loads and radial edge loads or displacements are considered within Reissner’s finite-rotation theory of thin shells of revolution, assuming linear stress-strain relations. The principal stresses in the membrane are determined by the solutions of a nonlinear second-order ODE, dependent on a geodesic variable. Analytical methods are used in order to determine the range of those boundary data for which the solutions of the differential equation are wrinkle-free in the sense that both the radial and the circumferential stress components are nonnegative everywhere.