In the recent development of active structural systems and microelectromechanical systems, piezoelectrics are widely used as sensors and actuators. Because of the limitations of theoretical and experimental models in design applications, finite element development and analysis are proposed and presented in this paper. A new laminated quadratic C° piezoelastic triangular shell finite element is developed using the layerwise constant shear angle theory. Element and system equations are also derived. The developed piezoelastic triangular shell element is used to model 1) a piezoelectric bimorph pointer and 2) a semicircular ring shell. Finite element (triangular shell finite element) solutions are compared closely with the theoretical, experimental, and finite element (thin solid finite element) results in the bimorph pointer case. Natural frequencies and distributed control effects of the ring shell with piezoelectric actuators of various length are also studied. Finite element analyses suggested that the inherent piezoelectric effect has little effect on natural frequencies of the ring shell. Vibration control effect increases as the actuator length increases, and it starts leveling off at the seven-patch (70%) actuator. Coupling and control spillover of lower natural modes are also observed.

Piezothermoelastic effects of distributed piezoelectric sensor/actuator and structural systems are studied. Distributed controls (static and dynamic) of piezoelectric laminates subjected to a steady-state temperature field are investigated. Piezothermoelastic constitutive equations are defined, followed by three energy functionals for the displacement, electric, and temperature fields, respectively. A new 3-D piezothermoelastic thin hexahedron finite element with three internal degrees of freedom is formulated using a variational formulation which includes thermal, electric, and mechanical energies. A system equation for the piezoelectric continuum exposed to combined displacement, electric, and temperature fields is formulated. Distributed sensing and control equations of piezoelectric laminates in a temperature field are derived. Thermal influences on the sensing and control of piezoelectric PZT/steel laminates are investigated in case studies.

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Nonlinear behavior due to either material or geometrical nonlinearity can significantly influence the performance of distributed piezoelectric sensors and actuators in adaptive piezoelectric laminated structures. This paper is concerned with the mathematical modeling of a nonlinear laminated anisotropic piezoelectric structure in which geometric nonlinearity induced by large deformations is considered.A generic theory is proposed and its nonlinear thermo-electromechanical equations are derived based on the variational principle.Thermo-electromechanical couplings among the elastic, electric, and temperature fields are discussed, and nonlinear components identified. Applications of the nonlinear theory to other materials, continua, and linear cases are discussed.

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