Form finding of deployable elastic gridshells based on nets of geodesic curves

Abstract

This thesis proposes a novel type of planar–to–spatial deployable structures called elastic geodesic grids. It aims at approximating freeform surfaces with spatial grids of bent lamellas, which can be deployed from a planar configuration using a simple kinematic mechanism. Encoded in the layout of the planar grids is the intrinsic shape of the target surface. When deployed, the grids buckle by design, approximating the curved target shape closely as grid elements bend and twist. Such elastic structures are easy–to–fabricate and easy–to–deploy and produce shapes that combine physics and aesthetics. They may serve architectural purposes like free-form envelopes, sun and rain protectors, pavilions, or equally smaller-scale applications like decorative panels, deployable furniture, baskets, lamps, etc.The thesis proposes solutions based on nets of geodesic curves on target surfaces and introduces a set of conditions and assumptions which can be closely met in practice. Target surfaces with different characteristics allow different solutions: Restricting the target surfaces to patches enclosed by convex geodesic quadrilaterals simplifies the design problem and enables solutions with high practical usability. Clearly, this approach potentially leads to big cut-offs, unacceptable for many design purposes. Conveniently, decomposing surfaces into smaller patches is an effective strategy for tackling the problem with cut-offs and curvature-related issues. But even arbitrary boundaries of patches can be considered. Dealing with non-convex boundaries requires additional procedures, as shortest connections are not necessarily geodesic curves. It is possibleto deal with surface patches of this sort, generalizing the notion of elastic geodesic grids. All these approaches are deeply connected to the inner geometry of the target surface. They involve solving optimization problems in abstract spaces, where solutions are found more easily.The form-finding of such grids is challenging. Fortunately, their shape is deeply linked to geometry. Exploiting insights from differential geometry allows to speed up form-finding by avoiding the necessity of numerical shape optimization and physical simulation at an acceptable loss of accuracy. The proposed algorithms finally ensure that the 2d grids are perfectly planar, making the resulting gridshells inexpensive, easy to fabricate, transport, assemble, and deploy. Additionally, since the structures are pre-strained, they also come with load-bearing capabilities. This thesis proposes a solution for the design, computation,and physical simulation of elastic geodesic grids. It presents several fabricated small-scale examples and a prototype of some meters in size, all with varying geometric complexity. Moreover, it provides empirical proof of the employed methods and assumptions by comparing the results to laser scans of the fabricated models. The outcome of this research is intended as a form-finding tool for elastic gridshells in architecture and other creative disciplines. It should give the designer an easy-to-handle way to explore such structures, as results can be obtained in a matter of seconds.