Three-dimensional transient piezothermoelasticity in functionally graded rectangular plate bonded to a piezoelectric plate

Abstract

In this study, the theoretical analysis of a three-dimensional transient piezothermoelasticity problem is developed for a functionally graded rectangular plate bonded to a piezoelectric plate due to partial heat supply. In this analysis, temperature distribution has a dependence on time, while the inertia term is ignored. Assuming the functionally graded rectangular plate has nonhomogeneous thermal and mechanical material properties in the thickness direction, the three-dimensional temperature in a transient state and three-dimensional transient thermal stresses of a simple supported plate for functionally graded material are analyzed by introducing the theory of laminated composites as a theoretical approximation. By using the solution for a functionally graded plate and the exact solution for piezoelectric plate of crystal class mm2, the theoretical analysis of three-dimensional transient piezothermoelasticity is developed for a simply supported combined plate. As an example, numerical calculations are carried out for a functionally graded rectangular plate made of zirconium oxide and titanium alloy, bonded to a piezoelectric plate of a cadmium selenide solid. Some numerical results for the temperature change, the displacement, the stress, electric potential, and electric displacement distributions in a transient state are shown in figures.