Wrinkle/slack model and finite element dynamics of membrane

This 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