LAUSR

Wrinkling, a common phenomenon found in space membrane structures, is the main factor affecting the performance, stability, and dynamic characteristics of these membrane structures. This article presents an active control method to improve the surface accuracy of membrane structures. A model of a thin rectangular membrane subjects to uniaxial uniform tensile stress is discussed. Initially, the relationship between the out-of-plane deformation of the wrinkles and the boundary conditions is built with the Föppl–Von Karman plate theory by introducing the slow varying Fourier series. Because vertical tensions perpendicular to the direction of the initial wrinkles are necessary to reduce these wrinkles, reasonable locations and magnitudes of these tensions are the key problems. The finite element method and variational principle method are used to solve this issue. Finally, a manufacturing error is added to the model as an initial defect, and the robustness of the controller is verified. Simulation results show that wrinkles are reduced quickly and effectively with the proposed method.