Dynamic analysis of membrane systems undergoing overall motions, large deformations and wrinkles via thin shell elements of ANCF

A computational approach is proposed for the dynamic analysis of complicated membrane systems, such as parachutes and solar sails, which undergo overall motions, large deformations, as well as wrinkles owing to the small membrane resistance to the compressive stress therein. Based on previous studies, a thin shell element of gradient deficient Absolute Nodal Coordinate Formulation (ANCF) is proposed first. Then, the strain energy of the above shell element is derived by using the definition of the Green-Lagrange strain tensor in continuum mechanics. The computationally efficient formulations of elastic forces and their Jacobian for the above shell element are also derived via the skills of tensor analysis. Afterwards, a membrane element of ANCF is proposed by integrating the criterion of wrinkle/slack into the above shell element. To deal with the small compressive stiffness for the membrane element, the Stiffness Reduction Model (SRM) is introduced to the membrane elements. Finally, four case studies including both statics and dynamics of different membrane systems are given to validate the proposed approach. The final example of the spinning deployment of a solar sail shows the efficacy of the proposed approach in the dynamic analysis of complicated membrane system undergoing an overall motion, large deformations and wrinkles.