A Differential Geometry-Based Design Procedure for Self-deployable Geodesic Gridshells

The objective of this study is to propose a differential geometry-based procedure to design the arrangement of the planar grid of thin elastic rods that deploy to lay on a target surface of uniform gaussian curvature, either spherical or hyperbolic. The out-of-plane deformation of the grid is controlled by a unique degree of freedom as usual in self-deployable gridshells. The procedure is applied to design two quadrilateral units featuring a grid composed of straight elastic rods, differing in the arrangement of rods within the edge quadrilateral. These units start from a planar configuration and deform in such a way to lay on two distinct target surfaces having positive and negative Gaussian curvatures, respectively. Deployment is controlled by the distance between the opposite corners of the base quadrilateral. The procedure is finally validated by verifying the deployment process by employing Finite Element analyses and tabletop models.