A finite element model for the analysis of wrinkled membrane structures

The problem of wrinkling in membrane structures has been a field of research since the publication of the tension field theory for plane structures. Significant progress in wrinkling analysis of arbitrarily shaped membranes has been made with the development of numerical methods. In the paper we present the enhancements of a standard finite element membrane formulation which allow to depict the wrinkles within the plane of the structure. A mathematical-numerical method is derived, which describes a valid stress state by minimising the differences in the stress density function while observing the wrinkling conditions. A consistent linearization of the proposed algorithms ensures quadratic convergence behaviour.