  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.
