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

Abstract

A simple iterative method is presented for cutting pattern optimization of frame-supported and pneumatic membrane structures for minimizing the variation of stresses from the target values. The plane cutting sheet is generated by minimizing the error from the shape obtained by reducing the target stress from the desired curved shape of surface. The equilibrium shape is obtained using an energy approach to minimize of total strain energy under forced deformation at the boundary nodes. The external work done by the pressure is also incorporated for analysis of pneumatic membrane structures. An approximate method is also proposed to derive a discretized form for analysis of an ethylene tetrafluoroethylene (ETFE) film, where elasto-plastic behavior under monotonic loading condition is modeled as a nonlinear elastic material under monotonic loading condition. The proposed method is applied to examples of a frame-supported polyvinyl chloride membrane structure and an air pressured square ETFE film.