Necking limits of conoid membrane structures with variable stress ratio

Form finding of conoid membrane structures separated by two coaxial circular rings is investigated for different values of fixed stress ratios between meridianal and circumferential stress. Of primary interest is the maximum separation of the rings as a function of stress ratio to achieve a stable equilibrium solution and the corresponding radius at the mid-plane between the rings, termed the necking radius. A rapidly converging computer program was developed to determine these limits quickly for a wide range of stress ratios. Asymptotic limits for the necking radius and separation distance were determined as the stress ratio approaches infinity.

► A membrane structure spanning the space between circular rings is studied.
► The maximum separation allowable is determined for various stress ratios.
► The corresponding necking at the mid-plane is also determined.
► Limiting dependence on stress ratio found for maximum separation.
► Limits on necking for large stress ratios were determined.