X-Shells

Abstract

We present X-shells , a new class of deployable structures formed by an ensemble of elastically deforming beams coupled through rotational joints. An X-shell can be assembled conveniently in a flat configuration from standard elastic beam elements and then deployed through force actuation into the desired 3D target state. During deployment, the coupling imposed by the joints will force the beams to twist and buckle out of plane to maintain a state of static equilibrium. This complex interaction of discrete joints and continuously deforming beams allows interesting 3D forms to emerge. Simulating X-shells is challenging, however, due to unstable equilibria at the onset of beam buckling. We propose an optimization-based simulation framework building on a discrete rod model that robustly handles such difficult scenarios by analyzing and appropriately modifying the elastic energy Hessian. This real-time simulation method forms the basis of a computational design tool for X-shells that enables interactive design space exploration by varying and optimizing design parameters to achieve a specific design intent. We jointly optimize the assembly state and the deployed configuration to ensure the geometric and structural integrity of the deployable X-shell. Once a design is finalized, we also optimize for a sparse distribution of actuation forces to efficiently deploy it from its flat assembly state to its 3D target state. We demonstrate the effectiveness of our design approach with a number of design studies that highlight the richness of the X-shell design space, enabling new forms not possible with existing approaches. We validate our computational model with several physical prototypes that show excellent agreement with the optimized digital models.

On elastic geodesic grids and their planar to spatial deployment

“…While this ensures easy fabrication, at the same time it poses a limitation on the design space. As shown by Panetta et al [2019], the shape-space of similar grid structures can be controlled by changing the profile of cross sections. However, when using more complicated cross sections, parts of them may buckle during deployment.…”

“…Recently [Panetta et al 2019] introduced an interactive approach for finding deployable grid structures. Their method requires the user to create an initial grid design by iterating between layout editing and grid simulation steps.…”

“…Our approach is intended as a form-finding tool for 2d-3d elastically deployable gridshell structures. Although we only validated our approach with small scale models, [Panetta et al 2019] examined the deployment of structures that use a similar deployment mechanism, but are bigger in size. Investigating how our approach can be adapted to the challenges of large scale architecture is an interesting engineering problem and a potential topic for future work.…”

Design and Fabrication of Elastic Geodesic Grid Structures

“…A lot of research is currently being carried out on gridshell-structures that can be deployed. They can be classified based on their deployment mechanism: inscribed in a grid that is deployed Panetta et al 2019;Pillwein et al 2020;Soriano et al 2019] or by other external mechanisms like inflatable air cushions [Quinn and Gengnagel 2018]. We are interested in the first case.…”

“…To create an X-Shell [Panetta et al 2019], a planar grid layout is designed and actuated with a physical simulator. The grid curves of the planar layout do not have to be straight.…”