Curved-creased folded (CCF) bending-active plates efficiently form complex curvilinear geometries with structural applications. Instead, this research proposes joining stacked plates along common curved creases into flat-foldable configurations. These unfold with an accordion-like one-degree-of-freedom mechanism into corrugated spatial structures. The proposed system, termed curved-crease unfolding (CCU), allows for simple 2D prefabrication, flat-packed transport, and rapid on-site deployment. Its globally double-curved and articulated structural geometry extends the design space of CCF and finds application as structure and formwork.
This research translates the fundamental geometric design principles of CCF to CCU for planar creases and demonstrates the design space for a multi-crease corrugated structure with non-zero thickness. A parametric model is implemented for the geometric construction and kinematic deployment in the COMPAS framework. Its deployment is validated by capturing the mechanical behavior with finite element simulation in the software SOFiSTiK.
The paper demonstrates the non-developability conditions for convex synclastic and concave anticlastic creases. For the special cases of planar creases, angle correlations are formulated with direct inversion from CCF using discrete differential geometry. The trigonometric correlation for the kinematic deployment is applied to the discrete mesh representation. Inclining subsequent osculating planes reveal restricted geometric applicability regarding crease planarity. The non-zero thickness is modeled with an axis-shift approach. Finally, a rule catalog for global shape control is derived based on crease profiles and plane layouts with inclinations resulting in synclastic and anticlastic multi-crease designs. These would be challenging to construct otherwise and are enabled solely based on its formation principles.
