AZIMUTHAL SHEARING AND TRANSVERSE DEFLECTION OF AN ANNULAR ELASTIC MEMBRANE

We consider an annular membrane which has its outer rim fixed and its inner rim displaced normal to the reference plane and twisted. The res ulting deformation is assumed to be axisymmetric and a direct two-dime nsional formulation is adopted. The analysis is based on the Mooney-Ri vlin strain energy function for isotropic elastic solids. The formatio n of wrinkles is accommodated in an approximate way by introducing a r elaxed strain energy function. We first study the problem without twis t, 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 differe ntial equations and solved numerically. Using convexity conditions, we discuss the local stability of the computed deformations.