Initial Stress Field Determination of Membranes Using Optimization Technique

A two level approach is presented for shape design of membrane structures supported by frames. The stress ratio in each cutting sheet is considered as independent design variable and is optimized to minimize the deviation of the internal shape from the desired distribution. Then the displacements and compliance for the given loads are calculated parametrically with respect to the stress level, and the optimal value of the stress level is found. Various shape can be realized by considering the stress ratio of each cutting pattern as independent design variables. This way. aesthetically efficient membranes may be designed through modification of the internal shape while also reducing the deformation against design loads. Optimal stresses are found for HP-type membranes with various rises and curvatures.