Finite element analysis of wrinkling membrane structures with large deformations

Membrane wrinkling problems are formulated using the geometrically nonlinear finite element method with convected coordinates. A membrane structure which is initially in an under-constrained state cannot resist compressive stresses and experiences out-of-plane deformation to avoid occurrence of compressive stresses. When a membrane is in the state of wrinkling, it is crucial to determine the wrinkling direction and the corresponding stress state for an analysis of the wrinkled membrane. Tensile strain energy is defined to correctly and simply evaluate the wrinkling directions based on the assumption that wrinkles are aligned to maximize tensile strain energy. This approach requires neither extra parameter nor kinematic assumption to predict wrinkle orientation. A pseudo-dynamic method is also introduced to initiate Newton–Raphson solution procedures for the analysis of under-constrained membranes. Several benchmark problems are analyzed to demonstrate the effectiveness and accuracy of the proposed formulation, and a space inflatable reflector example is also presented.