Neutrally stable transition of a curved-crease planar shell structure

Abstract

Elastic neutral stability in compliant mechanisms is a remarkable appearance since it requires the energetic state of the structure to remain unchanged during a deformation mode. Several examples in literature require either plastic deformation or external constraints to be enforced to obtain a state of pre-stress and often require the use of anisotropic materials. This paper presents a new type of compliant shell structure featuring a neutrally stable deformation mode without requiring one of the aforementioned conditions. The shell structure is composed of two initially flat compliant facets that are connected via a curved crease. The structure can be reconfigured into a second zero-energy state via propagation of a transition region, without any apparent effort. Both the structure's local width and local crease curvature can be tuned to reach neutral stability during transition. The modelled results are verified by several prototypes that match the modelled predictions qualitatively, as well as by measurement results that show quantitative agreement. The new type of structure introduced here features neutral stability without relying on the application of pre-stress during manufacturing or externally applied boundary conditions. Moreover, it shows potential for combining geometric simplicity with complex and highly tune-able behaviour.