Analysis of Wrinkle Patterns in Prestressed Membrane Structures

Structural wrinkling is a common phenomenon found in thin membranes when subjected to di erent loading and boundary conditions. There are plans for increased use of prestressed membrane structures in space missions, for example the Next Generation Space Telescope solar shield and some Space Based Radar systems. These structures are often partially wrinkled and the formation of wrinkles drastically alters load paths and structural sti ness within the membrane. A better understanding of the e ects of wrinkles on the structural performance and stability of these structures is essential and desirable. This dissertation presents two di erent approaches, both applying a commercial non-linear nite element code (ABAQUS) to analyse and predict the wrinkle patterns and its associated wrinkle parameters. These nite element models are based on observations made in two preliminary experiments. The rst approach used the commonly available membrane element incorporating no-compression material behaviour to simulate the wrinkling condition in a two-dimensional manner. A simple analytical solution was developed and implemented in a Matlab script to predict the out-of-plane deformation of membrane structures. The second approach used shell elements in a buckling prediction analysis to give the initial imperfection that, once introduced in the structure, would induce the formation of wrinkles. This analysis predicted the nal wrinkle shapes in addition to an estimate of the out-of-plane deformation of the membrane. Compressive principal stresses were allowed to develop in this model. This study showed that the nite element analysis can provide good estimates of the wrinkling behaviour in a membrane subjected to tension and shear with free or clamped boundary conditions. The results from the analysis displayed good agreement with those observed in the experiments. An analytical wrinkle model was proposed, based on the assumption that a membrane is able to resist a small compressive stress once it has wrinkled. This model was developed for the case of a long membrane subjected to pure shear and clamped at the upper and bottom edges, by using the static equilibrium equation of the membrane in the deformed con guration. This solution was then