Form finding of membrane structures based on nonlinear displacement analysis

This paper describes the basic theory of nonlinear displacement method for form finding of membranes. On this basis, the iteration equations for structures which use planar triangular elements as membrane elements are derived. These equations are used as governing equations for form finding of tension membranes or air-supported membranes, which provides a more simple and efficient approach than nonlinear displacement method. Form finding based on the iteration equations is compared with the surface stress density method which shows that the governing equations for the two approaches have the same form. This demonstrates that nonlinear displacement method is a generalization form of the surface stress density method and the two methods are identical inherently. Finally, a brief example is illustrated with the computer program designed by the author.