The exact solution of coupled thermoelectroelastic behavior of piezoelectric laminates

Exact solutions for static analysis of thermoelectroelastic laminated plates are presented. In this analysis, a new concise procedure for the analytical solution of composite laminated plates with piezoelectric layers is developed. A simple eigenvalue formula in real number form is directly developed from the basic coupled piezoelectric differential equations and the difficulty of treating imaginary eigenvalues is avoided. The solution is defined in the trigonometric series and can be applied to thin and thick plates. Numerical studies are conducted on a five-layer piezoelectric plate and the complexity of stresses and deformations under combined loading is illustrated. The results presented here could be used as a benchmark for assessing any numerical solution by approximate approaches such as the finite element method while also providing useful physical insight into the behavior of piezoelectric plates in thermal environment.