A new computational method for wrinkling analysis of gossamer space structures

A new Modified Displacement Component (MDC) method is proposed to accurately predict wrinkling characteristics in the membrane by eliminating the singularity of the displacement solution. In MDC method, a singular displacement component is primarily obtained at the wrinkling point by introducing the first-order characteristic vector multiplied by a positive intermediate parameter in the singular stiffness matrix. The non-singularity displacement solution is then obtained by modifying the singular displacement component based on three equality relationships at the wrinkling point. Where, the accurate introduction and the timely removal of the critical wrinkling mode are two key steps. In our simulation, we use a direct perturbed method to accurately consider these two key steps. In the direct perturbed method, some small, quantitative, out-of-plane forces are applied onto the membrane surface directly based on the first wrinkling mode, and then removed immediately after wrinkling starts. Several effective strategies are then used to advance the convergence. A wrinkling test using photogrammetry is used to verify the validity of our method. In addition, we also studied the secondary wrinkling characteristics occurred in the post-wrinkling phase in the end. The secondary wrinkling characteristics are the basic explanations of the wrinkling expansion and evolution in the post-wrinkling phase.