Design optimization of cable-membrane structures for form-finding and stiffness maximization

Membrane structures are light weight and have a unique characteristic that their surfaces can be curved optionally. On the other hand, the stiffness of membrane structures can be significantly improved by cables. However, cable-membrane structures have mechanical characteristics of that they can maintain their shape only with in-plane tensile stress, so it is important to design their optimal shapes. In the present work, we propose a free-form optimization method for designing cable-membrane structures for form-finding and stiffness maximization. The proposed free-form optimization method is a kind of non-parametric optimization method based on the H1 gradient method. In the form-finding problem, to find the minimum surface areas of membrane structures with specified arbitrary boundaries, the area minimization problem is formulated as a distributed-parameter shape optimization problem considering total length of cables as a constraint condition. Then, we perform shape optimization of cable-membrane structures in the stiffness maximization problem under the constraint conditions of total length of cables, membrane area, and membrane perimeter. The numerical results show the effectiveness of the proposed optimization method, and confirm that the optimal shape of the cable-membrane structures can be designed better than membrane structures without cables and has higher stiffness.