Wrinkle-Reduction Law for Rectangular Membranes Under a Shear Load

Abstract

This study introduces a scaling law to explain wrinkle dissipation induced on a membrane under a shear load. Wrinkles in an isotropic rectangular membrane are fixed at the bottom edge and subjected to an in-plane shear stress at the upper edge. The wrinkle dissipation is simulated by an in-plane tension load applied at the upper edge, which is perpendicular to the shear load. A scaling law depicts that the ratio of residual wrinkles, which indicates the extent of wrinkle dissipation, is not affected by the membrane size but is uniquely determined by the ratio of the major principal strain to the in-plane shrinkage strain. This observation is verified by performing geometrical nonlinear finite element simulations using shell theory and tension-field theory. Additionally, a simplified equation is derived to directly estimate the ratio of tensile displacement to control membrane wrinkling. This equation reveals that the tensile displacement necessary to completely suppress membrane wrinkling is dependent on the Poisson ratio and the aspect ratio of the membranes. Wrinkles can be perfectly dissipated by applying a tensile displacement equivalent to 64% of the shear displacement when the Poisson ratio is 0.3 and the aspect ratio is larger than 3. The measures used in this study are effective descriptions of membrane wrinkling that can be used to design future spacefaring gossamer structures.