Bistable plates for morphing structures: A refined analytical approach with high-order polynomials

Abstract

a b s t r a c tThe multistability of composite thin structures has shown potential for morphing applications. The present work combines a Ritz model with path-following algorithms to study bistable plates' behaviour. Classic low-order Ritz models predict stable shapes' geometry with reasonable accuracy. However, they may fail when modelling other aspects of the elastic structural behaviour. A refined higher-order model is here presented. In order to improve the inherently poor conditioning properties of Ritz approximations of slender structures, a non-dimensional version of Classical Plate Lamination Theory with von Kármán nonlinear strains is developed and presented. In the current approach, we continue numerical solutions in parameter space, that is, we path-follow equilibrium configurations as the control parameter varies, find stable and unstable configurations and identify bifurcations. The numerics are carried out using a set of in-house MATLAB Ò routines for numerical continuation. The increased degrees of freedom within the model are shown to accurately reflect buckling loads and provide useful insight into the relative importance of different aspects of nonlinear behaviour. Finally, the complex, experimentally observed snap-through geometry is captured analytically for the first time. Results are validated against finite elements analysis throughout the course of the paper.

Thermally Driven Morphing and Snap-Through Behavior of Hybrid Laminate Shells

“…The model's overprediction of the deadband range indicates that it is overestimating the thermal loads required for snap-through. This observation is in agreement with the work of Pirrera et al 42 and Lamacchia et al, 43 who show that the constant curvature shape functions used in this work overconstrain the laminate's kinematics during snap-through transitions, compared to models with more degrees of freedom. Should such a class of laminate be implemented as an actuation device, the designer will most likely be concerned primarily with κ x rather than κ y on account of the fact that both stiffness and curvature generation capability of the laminate are maximized along the x-direction.…”

Simplified analytical model for tapered sandwich beams using variable stiffness materials

“…Note, higher order polynomials are prone to ill-conditioning and numerical instabilities, which leads to loss in results accuracy [25,26]. …”

A nonlinear spring mechanism incorporating a bistable composite plate for vibration isolation

“…The layup and dimensions were chosen to give relatively low curvature in each bistable 5 state, to prevent the plate forming 'half-snap' states during snap-through as reported in [28,31,30,32], which would cause an undesired non-smooth response.…”