Approximate method for cutting pattern optimization of frame-supported and pneumatic membrane structures

A computationally efficient method is presented for approximate optimization of cutting pattern of frame-supported and pneumatic membrane structures. The plane cutting sheet is generated by minimizing the error from the shape obtained by reducing the stress from the desired curved shape. The equilibrium shape is obtained solving a minimization problem of total strain energy. The external work done by the pressure is also incorporated for analysis of pneumatic membrane. An approximate method is also proposed for analysis of an Ethylene TetraFluoroEthylene (ETFE) film, where elasto-plastic behavior is modeled as a nonlinear elastic material under monotonic loading condition. Efficiency of the proposed method is demonstrated through examples of a frame-supported PolyVinyl Chloride (PVC) membrane structure and an air pressured square ETFE film.