Dimitris A. Saravanos

Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates

Laminate and structural mechanics for the analysis of laminated composite plate structures with piezoelectric actuators and sensors are presented. The theories implement layerwise representations of displacements and electric potential, and can model both the global and local electromechanical response of smart composite laminates. Finite-element formulations are developed for the quasi-static and dynamic analysis of smart composite structures containing piezoelectric layers. Comparisons with an exact solution illustrate the accuracy, robustness and capability of the developed mechanics to capture the global and local response of thin and/or thick laminated piezoelectric plates. Additional correlations and numerical applications demonstrate the unique capabilities of the mechanics in analyzing the static and free-vibration response of composite plates with distributed piezoelectric actuators and sensors.

Mechanics and Computational Models for Laminated Piezoelectric Beams, Plates, and Shells

A considerable number of laminate theories, analytical approaches, numerical solutions and computational models have been reported for the analysis of laminates and structures with piezoelectric actuators or sensors. This article provides a review of published work in this area of mechanics. The reported laminate theories and structural mechanics are classified based on fundamental assumptions, the approximation of the through-the-thickness variation of the electromechanical state variables, the method of representation of piezoelectric layers, and their capability to model curvilinear geometries and thermal effects. The performance, advantages and limitations of the various categories of laminate theories are subsequently assessed by correlating results obtained by representative average models. The capability of each theory to model global structural response, local through-the-thickness variations of electromechanical variables, stresses, and piezoelectric laminates of high thickness is also quantified. This review article includes 103 references.

EXACT FREE-VIBRATION ANALYSIS OF LAMINATED PLATES WITH EMBEDDED PIEZOELECTRIC LAYERS

Exact solutions are developed for predicting the coupled electromechanical vibration characteristics of simply supported laminated piezoelectric plates composed of orthorhombic layers. The three‐dimensional equations of motion and the charge equation are solved using the assumptions of the linear theory of piezoelectricity. The through‐thickness distributions for the displacements and electrostatic potential are functions of eight constants for each layer of the laminate. Enforcing the continuity and surface conditions results in a linear system of equations representing the behavior of the complete laminate. The determinant of this system must be zero at a resonant frequency. The natural frequencies are found numerically by first incrementally stepping through the frequency spectrum and refining the final frequencies using bisection. Representative frequencies and mode shapes are presented for a variety of lamination schemes and aspect ratios.

Coupled Layerwise Analysis of Composite Beams with Embedded Piezoelectric Sensors and Actuators

Unified mechanics are developed with the capability to model both sensory and active composite laminates with embedded piezoelectric layers. Two discretelayer (or layerwise) formulations enable analysis of both global and local electromechanical response. The first assumes constant through-the-thickness displacement, while the second permits piecewise continuous variation. The mechanics include the contributions from elastic, piezoelectric and dielectric components. The incorporation of electric potential into the state variables permits representation of general electromechanical boundary conditions. Approximate finite element solutions for the static and freevibration analysis of beams are presented. Applications on composite beams demonstrate the capability to represent either sensory or active structures, and to model the complicated stressstrain fields, the interactions between passive/active layers and interfacial phenomena between sensors and composite plies. The capability to predict the dynamic characteristics under various electrical boundary conditions is demonstrated. Some advantages of the variable transverse displacement formulation on the freevibration response of sensory structures are also shown.

Mixed Laminate Theory and Finite Element for Smart Piezoelectric Composite Shell Structures

Mechanicsfortheanalysisoflaminatedcompositeshellswithpiezoelectricactuatorsandsensorsarepresented.A newmixedlaminatetheoryforpiezoelectricshellsisdevelopedincurvilinearcoordinatesthatcombinessingle-layer assumptions for the displacements and a layerwise representation for the electric potential. The resultant coupled governing equations for curvilinear piezoelectric laminates are described. Structural mechanics are subsequently developed and an eight-node ® nite element is formulated for the static and dynamic analysis of adaptivecomposite shell structures of general laminationscontaining piezoelectriclayers. Evaluations of themethod and comparisons with reported results were performed. Numerical results for cylindrical laminated piezoelectric composite panels with continuous piezoceramic actuators and cantilever shells with continuous or discrete piezoelectric actuators and sensors illustrate the advantages of the method and quantify the effects of curvature on the electromechanical response of piezoelectric shells.

Layerwise mechanics and finite element model for laminated piezoelectric shells

A discrete-layer shell theory and associated finite element model is constructed for general laminated piezoelectric composite shells. The discrete-layer shell theory is based on linear piezoelectricity and accounts for general through-thickness variations of displacement and electrostatic potential by implementing one-dimensional piece-wise continuous Lagrange interpolation approximations over a specified number of sublayers. The formulation applies to shells of general shape and lamination. Initially, the static and dynamic behavior of a simply supported flat plate is studied to compare with available exact solutions, with excellent agreement being obtained. Static loading and free vibration of a cylindrical ring are then considered to evaluate the element and to study the fundamental behavior of active/sensory piezoelectric shells.

Generalized finite element formulation for smart multilayered thermal piezoelectric composite plates

Analytical formulations are presented which account for the coupled mechanical, electrical, and thermal response of piezoelectric composite laminates and plate structures. A robust layerwise theory is formulated with the inherent capability to explicitly model the active and sensory response of piezoelectric composite plates having general laminations in thermal environments. Finite element equations are derived and implemented for a bilinear 4-noded plate element. Applications demonstrate the capability to manage thermally induced bending and twisting deformations in symmetric and antisymmetric composite plates with piezoelectric actuators and attain thermal stability. The resultant stresses in the thermal piezoelectric composite laminates are also investigated.

Unified Micromechanics of Damping for Unidirectional and Off-Axis Fiber Composites

An integrated micromechanics methodology for the prediction of damping capacity in fiber-reinforced polymer matrix unidirectional composites has been developed. Explicit micromechanics equations based on hysteretic damping are presented relating the on-axis damping capacities to the fiber and matrix properties and fiber volume ratio. The damping capacities of unidirectional composites subjected to off-axis loading are synthesized from on-axis damping values. Predicted values correlate satisfactorily with experimental measurements. The hygro-thermal effect on the damping performance of unidirectional composites caused by temperature and moisture variations is also modeled. The damping contributions from interfacial friction between broken fibers and matrix are incorporated. Finally, the temperature rise in continuously vibrating composite plies is estimated. Application examples illustrate the significance of various parameters on the damping performance of unidirectional and off-axis fiber reinforced composites.

Mechanics of damping for fiber composite laminates including hygrothermal effects

An integrated mechanics theory was developed for the modeling of composite damping from the micromechanics to the laminate level. Simplified, design oriented equations based on hysteretic damping are presented for on-axis plies, off-axis plies, and laminates including the effect of temperature, moisture, and interply hysteretic damping. The temperature rise within vibrating composite laminates resulting from strain energy dissipation is also modeled, and their coupled hygro-thermo-mechanical response is predicted. The method correlates well with reported damping measurements. Application examples illustrate the effect of various ply, laminate, and hygro-thermal parameters on the overall damping performance of composite laminates.

Multi-objective shape and material optimization of composite structures including damping

A multiobjective optimal design methodology is developed for lightweight, low-cost composite structures of improved dynamic performance. The design objectives may include minimization of damped resonance amplitudes (or maximization of modal damping), weight, and material cost. The design vector includes micromechanics, laminate, and structural shape parameters. Constraints are imposed on static displacements, static and dynamic ply stresses, dynamic amplitudes, and natural frequencies. The effects of composite damping tailoring on the dynamics of the composite structure are incorporated. Applications on a cantilever composite beam and plate illustrate that only the proposed multiobjective formulation, as opposed to single objective functions, may simultaneously improve the objectives. The significance of composite damping in the design of advanced composite structures is also demonstrated, and the results indicate that the minimum-weight design or design methods based on undamped dynamics may fail to improve the dynamic performance near resonances. Nomenclature A = area [C],[c] = global and modal damping matrices, respectively E = normal modulus F(z) = objective functions / = frequency fd = damped frequency G = shear modulus G(z) = inequality constraints h = thickness [/£],[/:] = global and modal stiffness matrices, respectively k = volume ratio [M],[m] = global and modal mass matrices, respectively p^p = global and modal excitation force, respectively q — modal vector 5 = strength t = time U = dynamic amplitude u = displacement vector