SHAPE DESIGN OF MEMBRANE STRUCTURE USING GEOMETRIC INVARIANTS OF DISCRETE SURFACE

The target surfaces of the frame supported membrane structures are generated by using the Gaussian and mean curvatures. The surface is discretized into a triangular mesh, and the Gaussian and mean curvatures are defined at the interior vertices of the surface based on the formulations of discrete differential geometry. The minimal surface with zero mean curvature, which is equivalent to the uniform stressed surface, is often used as the target surface because uniform stress distribution is desirable. However, while the membrane structure is generated by connecting planar membrane sheets; i.e. cutting patterns, the minimal surface cannot be developed to a plane without out-of-plane deformation. In this respect, the developable surface with zero Gaussian curvature may be desirable; however, it cannot realize uniform stress distribution. Therefore, in this study, the curved surface with a geometric property intermediate between those of developable and minimal surfaces is generated and used as the target surface of a membrane structure.