Kinematics of deployable hyperbolic paraboloid umbrellas

Deployable 4-sided hyperbolic paraboloid (hypar) umbrellas have been demonstrated as a feasible countermeasure against coastal inundation along urban shorelines. Such structures remain upright during normal operation providing shade and shelter, but transition into a flood barrier prior to storm surge scenarios via a rotational hinge at the vertex. These deployable hypar umbrellas also exhibit the potential to serve as temporary shelters during public emergencies such as pandemics. Building upon previous studies into the performance of deployed hypars, design considerations facilitating their efficient and safe deployment are explored. This paper derives closed-form solutions parameterizing the geometry of 4-sided hypar forms, which are utilized to compute the kinematic response of such structures during the gravity-assisted deployment process. In particular, hinge damping characteristics necessary to achieve a suitable impact velocity at the end of its transition phase are developed and validated via dynamic finite element modeling assuming rigid body behavior. Furthermore, a case study is considered to demonstrate the practical feasibility of appropriate damping mechanisms for implementation within a typical umbrella system without compromise to aesthetic appeal. This research ultimately provides a theoretical basis for the design of kinetic components governing the deployment of hypar umbrellas for coastal hazard adaptation or as a general form of temporary shelter.