A shape optimization approach to integrated design and nonlinear analysis of tensioned fabric membrane structures with boundary cables

In this article, a shape-optimization approach for tensioned fabric membrane structures with boundary cables is developed. Within the framework of shape optimization, an integrated design and analysis of the structure is studied. Assuming that the fabric membrane is initially flat and stress free, the ultimate goal of this study is to find an optimum shape of this fabric membrane so that the stress level on the resulting tensioned structure remains in a desired level while the shape difference between the resulting structure and the designed structure is minimized. While there are several studies on the integrated design and analysis of membrane structures, only a few of them have combined a shape optimization technique and nonlinear finite element analysis. Yet those studies simplify the interaction between the boundary cables and the fabric membrane and also do not include comprehensive nonlinear material models. This article aims to overcome the abovementioned limitations using a comprehensive nonlinear material model, including the geometrical nonlinearities, and considering an advanced nonlinear kinematical interaction between the boundary cables and the tensioned membrane. The shape of the fabric membrane and the length of the boundary cables are adjusted automatically during the optimization process. The obtained results show that a more realistic material model and interaction model between the boundary cables and the tensioned membrane can significantly affect the initial flat shape of the membrane.