Multiparameter actuation for shape control of bistable composite plates

This paper studies the stable equilibrium shapes of free multilayered orthotropic plates loaded by inelastic deformations induced by thermal and piezoelectric effects. Starting with a Von Kلrmلn plate kinematics and an energetic formulation, a discrete intrinsic nonlinear model in terms of curvatures only is deduced. The model has 3 degrees of freedom, namely the components of the symmetric curvature tensor, which is supposed to be uniform in space. Despite of this rough assumption, the analytical results about the equilibrium shapes and their stability show a good agreement with the finite element simulations performed with a commercial code. Literature results about the bistable behavior of isotropic plates under a single-parameter loading are extended to the orthotropic case with two loading parameters. In light of a global stability analysis and a phase portrait as a function of the inelastic curvatures, we study possible actuation techniques for controlling the transition of the plate between its two stable configurations. We show that with a suitable two-parameter actuation, it is possible to get a controlled quasi-static transition, avoiding any instability phenomenon. Numerical simulations on a realistic case study support the technological feasibility of the proposed actuation technique when using active piezoelectric layers to control the inelastic curvature.