Wrinkle/slack model and finite element dynamics of membrane

Abstract

SUMMARYThis paper reviews conventional wrinkle models for anisotropic membrane and shows the relation between the models. A new wrinkle model is proposed which assumes virtual shear as well as virtual elongation of the membrane to estimate the real strain in the wrinkled region. This model coincides with the other models if the virtual shear and elongation is determined so that the strain energy is minimized. Another wrinkle/slack model is proposed for the dynamic analysis of thin isotropic membrane undergoing large overall motion with wrinkle and slack. It can take into account the residual compressive stress in the wrinkled and slack regions, i.e. the stiffness in the post-buckling state. It is shown that the proposed model is a generalization of the conventional ones. Finite element formulation of the proposed model is described. Furthermore, the energy momentum conservation framework is constructed for the proposed membrane element, which achieves the unconditionally stable time integration. The total of the proposed method enables us to compute the overall motion of thin isotropic membrane such as the deployment of folded membrane, which has been one of the most difficult problems in aerospace engineering.

Numerical model for prediction of wrinkling behavior on a thin-membrane structure

“…Therefore, Miyazaki, et al proposed methods to represent the area and intensity of the wrinkles by giving some small compressive stiffness in the wrinkle direction. One of the methods is the stiffness reduction model (SRM), which is a model to give compressive stiffness as a ratio of the tensile stiffness (Miyazaki, 2006), and another is the maximum compressive stress model (MCSM), which does not permit the compressive stress to exceed a certain value (Miyazaki and Arita, 2008). However, the methods for determining the compressive stiffness are not established, and the distribution of principal stress in slack areas is not valid (Inoue, 2009).…”

First Solar Power Sail Demonstration by IKAROS

“…18 confirm that the membrane is deployed smoothly by the deployment mechanism. The multi-particle model and the finite element method model 9) shown in Fig. 19 are used mainly to predict the deployment dynamics.…”

The theory of Cosserat points applied to the analyses of wrinkled and slack membranes

“…First, we briefly describe the conventional wrinkling theory by Roddeman et al [20] and modifications by other researchers [7,8,14]. Then we combine this with the quadrilateral Cosserat point formulation.…”

“…Similar approaches have also been developed for anisotropic [2,10] and orthotropic [19,30] membranes. Miyazaki [14] has critically reviewed many of these approaches and concluded that all the approaches are essentially the same. The last author has also proposed a model based on virtual elongation and virtual shear of the membrane to estimate the real strain in the wrinkled region.…”