Stability of Torsionally Soft, Deployable Structures Supporting Prestressed Membranes

A torsionally soft rectangular frame supporting an internal prestressed membrane undergoes stable torsional buckling when the prestress reaches a critical value. Estimates of the critical prestress vary significantly, depending on how the membrane’s load on the structure is modeled. This sensitivity of the critical prestress value is highlighted by reviewing classical results on the buckling of cantilever rods under different prestress loading geometries. With this background, a numerical study of a novel deployable structure supporting an internal membrane was carried out, considering four different ways of modeling the membrane with increasing fidelity. It is shown that the critical prestress increases by a factor of four when the loads on the structure are changed from fixed-direction to follower loads, and only models that include the membrane predict the correct stiffness of the structure in the postbuckling regime.