Stable Transition of Bistable Composite Plates

Integrating a smart material in a flexible or bendable structure can create a morphing or adaptive structure that can transform its elastic body to perform functional tasks, such as shape control in aircraft wings. This transition process has to be smooth during the flight to prevent undesirable turbulence flow on aerodynamic surfaces. Precise control of this morphing movement is essentially depended on correlation between physical behavior of the structure and mathematic schemes that implement in the control systems. However, conventional procedures rely heavily on numerical calculation which requires some time to compute characteristic parameters to accurately predict morphing structural behaviors and hence, somewhat inapplicable in actual applications. To remedy these problematic issues, we purpose to construct a close-form predictive analytical model of a cross-ply laminated carbon-fiber reinforced rectangular plate bonded with piezoelectric actuators. Due to possibility to search for the close-form solution in such nonlinear structural systems, the proposed mathematical model allows us to solve the equations of state in a simple manner. Uniform curvatures of the plate configuration are adopted to capture the effect of geometrical nonlinearities and to construct stability diagrams using the Lagrangian and Hamiltonian method. Curvatures of the composite plates are treated as dependent variables of equilibrium pathways in the stability diagram, whereas the independent variables are piezoelectric inelastic strains, which are directly related to the shape morphing actuation. Conveniently, non-linear elastic strains, stretching-bending coupling stiffness components and inelastic strains can be distinctly isolated from the system of differential equations. The system can then be interpreted as basic mechanical deformations which firmly support physical compatibility of our model. This model will be validated by experiments and finite element computations to show the evidences of realistic physical behaviors. Finally, the proposed study will establish perspective for future application in various areas of shape control in morphing structures.