Towards Neutrally Stable Compliant Shells

Abstract

Elastic neutral stability involves elastic deformation without stiffness or loads. It is a remarkable appearance, since the deformation of materials is normally associated with an increase of potential energy and a resulting opposing reaction force or moment. Neutrally stable mechanisms can be used to overcome unnecessary actuation which makes them an interesting topic for the aerospace industry, space exploration and the development of wearable assistive devices. This last group benefits from the use of spatially-curved thin-walled elastic structures, called compliant shell mechanisms. A literature review aims to give an overview of occurrences of elastic neutral stability and aims to find methods for creating neutrally stable compliant shell mechanisms. Single element mechanisms are herein further emphasized and a division between the application of pre-stress and the application of geometrical boundary conditions is proposed. So far, all neutrally stable (shell) mechanisms require either of the two conditions to be imposed. A new type of compliant shell structure, featuring a neutrally stable deformation mode without requiring one of the aforementioned conditions, is presented. The structure is composed of two initially flat compliant facets that are connected via a curved crease. It can be reconfigured into a second zero-energy state without apparent effort via propagation of a transition region. Both the structure’s local width and the local crease curvature turn out to be effective parameters for tuning the behavior regarding stability during transition. This structure shows potential for combining geometric simplicity with complex and highly tune-able behavior. However, its discontinuity obstructs physical realization. Therefore, a monolithic variant of this structure is investigated. The transition of a double-curved distributed compliant shell towards its second equilibrium configuration forms the basis of this investigation. A varying material thickness profile, described by an ideal set of design parameters, is obtained using an optimization procedure. Numerical analysis of the resulting optimized shell structure predicts a significant region of near-constant energy and associated near-zero loads within this unique deformation mode. Prototypes are manufactured using a 3D-printing process and demonstrate the validity of the modelled results by featuring a continuous equilibrium within a significant range of motion. These results lay the foundation for compliant beam elements with an internal statically balanced bending degree of freedom. Finally, a different deformation mode, involving crease actuation of the same type of structure, is examined. Curved creases are characterized by the coupled facet deformation upon actuation. The forces exerted by the facets can be used to oppose the effects of crease stiffness during actuation to achieve an overall stiffness decrease. An analytical approach, based on a combination of a pseudo-rigid-body model (PRBM) and plate theory, predicts the potential for constant-force actuation around its second stable, or ‘inverted’ state. The accuracy of the model is validated by numerical simulations. However, due to prototype inaccuracies, the experimental results do not feature the desired constant force behavior. Nevertheless, a stiffness decrease, or ‘softening’ is experienced, verifying the concept and marking a first step towards statically balanced curved creases.