Dimitris Varelis

Nonlinear coupled mechanics and initial buckling of composite plates with piezoelectric actuators and sensors

The nonlinear mechanics for piezoelectric laminates and plates is presented, including nonlinear effects due to large displacements and rotations. The mechanics is incorporated into the piezoelectric mixed-field laminate theory. Using this mechanics, a nonlinear finite-element method and an incremental solution are formulated for the nonlinear analysis of adaptive plate structures. An eight-node-plate finite element is developed. The mechanics is applied to predict the buckling of piezoelectric plates induced by combined electromechanical loading. Application cases quantify the mechanical buckling of composite beams and plates with piezoelectric sensors, the piezoelectric buckling of active beams and plates, and the feasibility of active buckling compensation.

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.

Small-amplitude free-vibration analysis of piezoelectric composite plates subject to large deflections and initial stresses

A coupled theoretical and computational framework is presented for analyzing the small amplitude-free vibrational response of composite laminated plates with piezoelectric actuators and sensors, subject to nonlinear effects due to large rotations and initial stresses. Coupled laminate mechanics incorporating nonlinear governing equations with mixed-field shear-layerwise assumptions for the piezoelectric laminate are implemented. A finite element method is formulated to yield the linearized discrete dynamic equations of a piezocomposite plate on top of its nonlinear electrostatic response, and a novel eight-node coupled nonlinear plate finite element forms the basis of numerical analyses. The natural frequencies in a beam with a piezoceramic actuator and sensor subject to in-plane mechanical loading, high enough to induce buckling and postbuckling are also experimentally characterized, and comparisons to numerical results show excellent correlation. Additional numerical evaluations quantify the active shifting of natural frequencies in adaptive beams and plates subject to high out-of-plane and in-plane electromechanical loading, and the variation of modal frequencies during buckling and postbuckling response. Finally, the possibility to detect and actively manage buckling in adaptive piezocomposite plates is illustrated.

Linearized Frequencies and Damping in Composite Laminated Beams Subject to Buckling

This paper considers the damped small-amplitude free-vibration of composite laminated strips subject to large in-plane forces and rotations. A theoretical framework is formulated for the prediction of the nonlinear damping of composite laminates subject to large Green–Lagrange axial strains and assuming a Kelvin viscoelastic solid. An extended beam finite element is developed capable of providing the nonlinear stiffness and damping matrices of the system. The linearized damped free-vibration equations associated with the deflected strip shape in the pre- and postbuckling region are presented. Numerical results quantify the strong geometric nonlinear effect of compressive in-plane loads on the modal damping and frequencies of composite strips. Measurements of the modal damping of a cross-ply glass/epoxy beam subject to buckling were also conducted and correlate well with the finite element predictions.

COUPLED FINITE ELEMENT FOR NON-LINEAR LAMINATED PIEZOELECTRIC COMPOSITE SHELLS WITH APPLICATIONS TO BUCKLING AND POSTBUCKLING BEHAVIOR

A theoretical framework for analyzing the coupled nonlinear response of shallow doubly curved adaptive piezocomposite shells, undergoing large displacements and rotations, is presented. The mechanics are formulated in cylindrical coordinates, and explicitly incorporate coupling between in-plane and flexural stiffness terms due to curvature, between the mechanical and electric field express by a mixedfield shear-layerwise shell theory. Based on the above formulation, a finite element methodology together with a Newton-Raphson based incremental-iterative technique are developed for solving the nonlinear response of piezocomposite shells under mechanical and electric loading. An eight-node isoparametric nonlinear shell element is also developed. Evaluation cases are presented for curved beams and cylindrical panels. Numerical results show the inherent capability of smart shell structures to induce large displacements, through piezoelectric actuators, and subsequently to snap from one equilibrium state to another. Finally the possibility to actively mitigate the mechanical snap-through buckling, through the use of piezoelectric actuators is quantified.