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

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