Analytical modeling of cantilever bistable composites with slit cutouts

Abstract

Bistable composite laminates have been widely studied for morphing applications due to the large shape and stiffness change between their stable equilibrium states. However, these types of composites tend to lose their bistable behavior at low aspect ratios (length/width) when constrained in a cantilever configuration. To address this, a novel design introducing slit cutouts into cantilever laminates has been proposed, enabling bistability even in low aspect ratio geometries and significantly expanding their design space. The design of such slitted laminates requires the use of computationally intensive simulations to optimize the size and location of the slit cutouts, and to study their influence on the laminate’s behavior. In this work, we present an analytical model to predict the stable states and stiffness properties of multi-sectioned bistable laminates with slit cutouts, clamped along a single edge, from a symbolically calculated, parametric strain energy expression. A special discretization of the laminate’s geometry is utilized to account for the slit cutouts, and the Rayleigh–Ritz method using polynomial displacement shape functions is employed to approximate the two stable configurations of the laminates. The developed model is further used to predict the stiffness of the laminate’s stable states under concentrated forces and uniform pressure loads. The results from the model are validated against finite element simulations as well as experimental measurements. Finally, the utility of the analytical model in designing low aspect ratio bistable laminates is demonstrated through a parametric study. The presented model enables the efficient design and analysis of slitted bistable composites embeddable within larger compliant structures.