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Three-dimensional finite element analysis using conventional membrane elements tends to be numerically unstable because of their lack of bending stiffness. Additionally, membrane structures are highly susceptible to localized buckling, posing further numerical difficulties. In this paper, a modified stress-strain tensor, recently proposed by the authors to account for membrane wrinkling, is applied to three-dimensional finite element analysis of membrane structures with the aim to overcome the preceding numerical difficulties. It is found through numerical investigations that the use of the modified stress-strain tensor renders the iterative solution process remarkably stable, and enables one to obtain the converged solution for those problems that are difficult to solve using conventional membrane elements.

A new modification scheme of the stress-strain tensor for wrinkled membranes is presented on the basis of the tension field theory. The scheme is applicable to finite element analysis of partly wrinkled membranes with arbitrary shapes. Derivation of the modification scheme rests on an introduction of the so-called 'wrinkle strain' and a simplification of the virtual work equation of wrinkled membranes. Because all of the modifications required to account for wrinkling are totally confined within the stress-strain relations of membranes, the scheme can be easily implemented with existing finite element codes. Furthermore, the modified stress-strain tensor automatically leads to the consistent tangent stiffness matrix, where changes in both the wrinkling direction and the amount of wrinkliness are taken into account. Three numerical examples are treated to show the accuracy and effectiveness of the proposed modification scheme.