On Elastic Geodesic Grids and Their Planar to Spatial Deployment

摘要

We propose a novel type of planar–to–spatial deployable structures thatwe call elastic geodesic grids. Our approach aims at the approximation offreeform surfaces with spatial grids of bent lamellas which can be deployedfrom a planar configuration using a simple kinematic mechanism. Such elasticstructures are easy–to–fabricate and easy–to–deploy and approximateshapes which combine physics and aesthetics. We propose a solution basedon networks of geodesic curves on target surfaces and we introduce a set ofconditions and assumptions which can be closely met in practice. Our formulationallows for a purely geometric approach which avoids the necessity ofnumerical shape optimization by building on top of theoretical insights fromdifferential geometry.We propose a solution for the design, computation, andphysical simulation of elastic geodesic grids, and present several fabricatedsmall-scale examples with varying complexity. Moreover, we provide anempirical proof of our method by comparing the results to laser-scans of thefabricated models. Our method is intended as a form-finding tool for elasticgridshells in architecture and other creative disciplines and should give thedesigner an easy-to-handle way for the exploration of such structures.