Effective modeling and nonlinear shell analysis of thin membranes exhibiting structural wrinkling

Thin solar sail membranes of very large span are being envisioned for near-term space missions. One major design issue that is inherent to these very flexible structures is the formation of wrinkling patterns. Structural wrinkles may deteriorate a solar sail's performance and, in certain cases, structural integrity. A geometrically nonlinear, updated Lagrangian shell formulation is employed using the ABAQUS finite element code to simulate the formation of wrinkled deformations in thin-film membranes. The restrictive assumptions of true membranes as defined by tension field theory are not invoked. Two effective modeling strategies are introduced to facilitate convergent solutions of wrinkled equilibrium states. They include 1) the application of small, pseudorandom, out-of-plane geometric imperfections that ensure initiation of the requisite membrane-to-bending coupling in a geometrically nonlinear analysis and 2) the truncation of corner regions, where concentrated loads are prescribed, to improve load transfer, mesh quality, and kinematics and to reduce severe concentration of membrane stresses. The corner truncation necessitates replacing the concentrated force with a statically equivalent distributed traction. Several numerical studies are carried out, and the results are compared with recent experimental data. Good agreement is observed between the numerical simulations and experimental data.