Nonlinear Deformations of Smart Plates under Electro-Mechanical Actuations

This work presents a three-dimensional nonlinear analysis of a flexible smart thin plate consisting of a thin elastic plate and arbitrary numbers of thin piezoelectric patches distributed and bonded on the top and bottom surfaces of the plate. The patches are perfectly bonded to the elastic plate and their thicknesses are negligible compared to the thickness of the plate. Electric fields are prescribed to the piezoelectric patches, which induce axial forces and bending moments to the plate. These internal forces are determined by imposing equilibrium equations and displacement continuity conditions at the interfaces between the piezoelectric patches and elastic plate. Since the overall planar dimension of the plate is much larger than its thickness (thin plates), the deformed structure can undergo large rotations but maintain relatively small strains. Finite elements method (FEM) based on co-rotational Lagrangian description, is used for numerically determining the deformations of the active plate. Since, in practice, large deformation/displacement of the smart systems under electric actuation often requires large electric field inputs, a nonlinear electromechanical coupling constitutive model is considered for the piezoelectric material. As shown through a few examples, by varying number, location and/or size of the piezoelectric actuators or changing magnitude of the electric field inputs, it is possible to obtain desired shape configurations for the active flexible plate.