On elastic geodesic grids and their planar to spatial deployment

Abstract

We propose a novel type of planar-to-spatial deployable structures that we call elastic geodesic grids. Our approach aims at the approximation of freeform surfaces with spatial grids of bent lamellas which can be deployed from a planar configuration using a simple kinematic mechanism. Such elastic structures are easy-to-fabricate and easy-to-deploy and approximate shapes which combine physics and aesthetics. We propose a solution based on networks of geodesic curves on target surfaces and we introduce a set of conditions and assumptions which can be closely met in practice. Our formulation allows for a purely geometric approach which avoids the necessity of numerical shape optimization by building on top of theoretical insights from differential geometry. We propose a solution for the design, computation, and physical simulation of elastic geodesic grids, and present several fabricated small-scale examples with varying complexity. Moreover, we provide an empirical proof of our method by comparing the results to laser-scans of the fabricated models. Our method is intended as a form-finding tool for elastic gridshells in architecture and other creative disciplines and should give the designer an easy-to-handle way for the exploration of such structures.

Design and Fabrication of Elastic Geodesic Grid Structures

“…The EGG-approach of [Pillwein et al 2020] takes a design surface as input and results in a grid layout that can be deployed to approximate this surface. The layout is found geometrically and simultaneously on the design surface and in the plane.…”

“…In essence, if all geodesics on the surface patch are shorter than the value on the right hand side of Expression (1), problems with non uniqueness of shortest geodesics do not exist. The approach of [Pillwein et al 2020] is to smooth the surface, i.e. to reduce K to eliminate non unique shortest geodesics.…”

“…As proposed by [Pillwein et al 2020], supports are placed at connections on the boundary curves close to their extrema of curvature. When splitting up the surface patch into modules, a support can thus be shared by two or more grids.…”

Reduced-Order Simulation of Flexible Meta-Materials

“…Due to the advances in the digital fabrication field, such problems increasingly arise in various personal fabrication design tasks [Dumas et al 2015;Skouras et al 2014]. Of particular relevance to our work is the design of structures made out of rod-like elements [Malomo et al 2018;Panetta et al 2019;Pérez et al 2015;Pillwein et al 2020;Vekhter et al 2019;Zehnder et al 2016], which is made possible through efficient methods of simulating the deformation behavior of such elements [Bergou et al 2010[Bergou et al , 2008.…”

Generation of elastic geodesic gridshells with anisotropic cross sections

“…However, as shown by Lagally, 10 a mesh cannot be flattened in general. Pillwein et al 11 also explored the planar-to-spatial deployment of a geodesic gridshell. In their study, the continuous geodesic lines are only connected at their ends, and the inner pinned connections are not fixed on the ground.…”