AIAA 2002-1369 Computation of Wrinkle Amplitudes in Thin Membranes

There is an increasing number of space missions in which it is proposed to use high accuracy membrane structures and it is envisaged that some of these membranes will remain partially wrinkled in their operational configuration. Previous studies have focussed only on the stress distribution in wrinkled membranes, but for high accuracy applications the amplitude and wavelength of the wrinkles becomes important. This paper presents a non-linear finite-element simulation technique, where the membrane is modelled in ABAQUS with S4R5 shell elements, which accurately predicts the wrinkle details. For a rectangular membrane in shear it is found that the wrinkled pattern varies abruptly when the load magnitude is changed gradually. This simulation technique makes it possible to " look inside " a membrane and thus identify features of the complex behaviour of thin membranes that need to be included in simple models, which can be very useful. Introduction There is an increasing number of space missions in which it is proposed to use high accuracy membrane structures with a variety of shapes and sizes. Examples are sunshields for low-temperature telescopes, space based radars, inflatable reflector antennas and solar sails. Some of these membrane structures will remain partially wrinkled in their operational configuration, and this could potentially cause problems. For example, large wrinkles would compromise the performance of a sunshield or reflector, and could make a solar sail uncontrollable. However, wrinkles of smaller magnitude may be acceptable and, indeed, may even have beneficial effects, such as increasing the out-of-plane stiffness or the vibration damping of the membrane. This paper presents a computational study of a wrinkled membrane in shear, a problem for which several solutions and experimental results have already been published. Initially the aim of this study was to explore the accuracy and robustness of a numerical simulation in which the membrane is modelled with a fine mesh of shell elements. It was later discovered that —due to the finite length of the membrane— the number of wrinkles varies abruptly with the shear displacement and this behaviour has the effect of introducing a certain amount of hysteresis in the system. The same numerical tools were then used to study the mode-jumping instability associated with this behaviour. Apart from being an interesting example of complex post-buckling response, it is possible that in future this behaviour could be exploited, e.g. for designing membrane structures with high vibration damping. The paper begins with a …