Finite element formulations for thermopiezoelastic laminated composite plates

Finite element formulations are presented which account for the coupled mechanical, electrical, and thermal response of piezoelectric composite plate structures. The mathematical model is based upon a high-order displacement field, a quadratic electric potential field and a linear temperature field. The dynamic governing equations are derived using the virtual work principle. These formulations in general will enable the modeling of vibration and shape control applications in solving a wide variety of coupled thermal–piezoelectric problems. Three numerical examples, including a piezoelectric bimorph, a cantilevered aluminum plate with two bonded piezoelectric patches and a clamped carbon/epoxy composite plate with an attached full piezoceramic layer, have been developed. The actual through-the-thickness electric potential distribution is captured accurately with the present quadratic distribution assumption for each piezoelectric layer. However, the nonlinear induced electric potentials of piezoelectric actuators are inferior to the directly applied linear electric potentials. The higher induced electric potential of a piezoelectric sensor in open circuit would lead to a higher induced stiffness and a higher global frequency response. Numerical results for the thermopiezoelastic behavior of a piezoelectric laminated plate have shown the significant impact of piezoelectric coupling and pyroelectric effects on the sensory response of thermal piezoelectric structures.