X-Shells: A New Class of Deployable Beam Structures
ACM Transactions on Graphics (Proceedings of SIGGRAPH), 2019
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.