Shape optimization for cable reinforced tension fabric membrane structures

Albeit tension fabric membrane structures are used now worldwide, there are few design guidance and limited analysis methodologies [1], [2]. At this moment, design of these structures is highly dependent on the experience and empirical knowledge of designers [1], [3]. However, the edge of experience can be reached because tension fabric membrane structures behave severely nonlinear due to material nonlinearity, large displacements (geometrical nonlinearity). In addition, the nonlinearity is also from the interaction between the membrane and the pre-stressed cables. These nonlinearities render difficulties in design and analysis of tension membrane structures and demand a dedicated structural analysis and design methodology. This article describes a shape optimization of cable reinforced fabric membrane structures. In the framework of the shape optimization, an integrated design and analysis of the structure is presented. The target of the optimization is to find optimum cutting patterns such that differences between the resulted structure and the design one are minimized with respect to stress distributions. In each iteration of the optimization, a nonlinear finite element analysis of the structure is performed. In this analysis, material and geometrical nonlinearities are considered. Moreover, the nonlinear interaction of the reinforced cables and the fabric membrane is also taken into simulations. Because the optimization problem is highly nonlinear, the genetic algorithm is opted to solve it. It is shown from the obtained results that the nonlinear material model and the interaction between the cables and the membrane affect significantly to the optimum cutting