On the elastic snapping of structural elements

Abstract

A bistable structural component possesses more than one stable equilibrium configuration. In terms of the strain energy stored in bending, this can be thought of as a system with not only an initial equilibrium configuration represented by an isolated minimum, but also a remote minimum that might be accessed given a sufficient disturbance. Whether the system is able to stay in this new position, or revert back to the initial state when the disturbance is removed is an important practical issue. This distinction is largely determined by geometry. Continuous elastic structures of the type produced using a 3D-printer are necessarily of relatively high-order in a dimensional sense, and most previous studies have used nonlinear finite element analysis to determine parameter sensitivity. However, there is a role to be played by discrete low-order models in which the same type of essential qualitative behavior can be captured, but where the parameter dependency (in this case whether a system stays in its inverted, snapped, configuration, or not) can be assessed more directly than numerical simulation. This short note develops a discrete model specifically designed to address this issue, and presents the outcomes of some tests on 3D-printed elements.