Curved annular elastic membranes under partially vanishing surface load (Q1272429)

The authors examine a nonlinear elastic membrane theory with special emphasis on axisymmetric deformations of curved annular membranes subjected to a partially vanishing vertical surface load and with prescribed radial stresses on the edges. The nonlinear finite-rotation theory by Reissner is employed, assuming linear stress-strain relations. This leads to a single second-order ordinary differential equation which governs the principal stresses in the membrane. Analysis previously developed for determination of boundary data which correspond to nonnegative radial and circumferential stress components is extended to the case where parts of the membrane adjacent to the inner edge remain unloaded. The curved membrane is shown to flaten out on such parts which seem up to now not to be observed.