Mechanics and Finite Element for the Nonlinear Response of Active Laminated Piezoelectric Composite Plates

A theoretical framework for analyzing piezoelectric composite laminates that includes nonlinear effects as a result of large displacements and rotations is presented. Nonlinear mechanics equations are incorporated into a coupled mixed-field piezoelectric laminate theory. Using the nonlinear laminate theory, a nonlinear finite element methodology and an incremental-iterative solution are formulated for the analysis of nonlinear adaptive laminated plate structures with piezoelectric actuators and sensors. An eight-node nonlinear plate finite element is also developed. The mechanics models are applied on the nonlinear active response of composite plates with piezoelectric actuators. Various application cases quantify the nonlinear active flexural response of beams and plates with piezoelectric actuators.