The thin film wrinkling membrane problems give rise to the increasing interests recently due to the membranes forming an important class of structures in many technological applications, such as space inflatable structures, fabric constructions, manufacture and handling of paper webs, films, textiles, metal foils and polymer sheets. The existing membrane models and theories for the problem of wrinkled membrane, due to their deficits, make solving this problem be a tough thing. My research work is focused on developing effective theory and numerical tools for dealing with wrinkling problem of large-scale and complex membrane structure systems. In this study, first a new two-variable-parameter (2-VP) membrane model is proposed, which can describe the basic three states, taut, wrinkle and slack, of wrinkled membrane in the straight form. Second, we derive the corresponding parameter varational principle (PVP) for this 2-VP model, which makes the solution processes no stresses iteration, thus avoiding the convergent and pivoting problem in traditionally numerical process. Third, using the finite element discretization to change the membrane problem into a nonlinear complementarity problem, this makes the 2-VP membrane model based on PVP can be applied to deal with wrinkled membrane structures with arbitrary shape and boundary condition. Finally by solving the nonlinear complementarity problem, we obtain the wrinkled region and pattern, the stress and strain field of the wrinkled membrane and the forming process of wrinkles. Examples are given, which prove the effectiveness of this theory by comparison with the results obtained by finite element method and experimental test.
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