Azimuthal shearing and transverse deflection of an annular elastic membrane

Abstract

We consider an annular membrane which has its outer rim fixed and its inner rim displaced normal to the reference plane and twisted. The resulting deformation is assumed to be axisymmetric and a direct two-dimensional formulation is adopted. The analysis is based on the Mooney-Rivlin strain energy function for isotropic elastic solids. The formation of wrinkles is accommodated in an approximate way by introducing a relaxed strain energy function. We first study the problem without twist, including a case in which wrinkling occurs, and then we investigate the full problem with twisting present. In both cases, the equations of equilibrium are reduced to a first order system of ordinary differential equations and solved numerically. Using convexity conditions, we discuss the local stability of the computed deformations.