A quasi-exact solution for the analysis of smart multilayered simply supported shallow shell panels

A quasi-three-dimensional solution for the bending analysis of simply supported orthotropic piezoelectric shallow shell panels subjected to thermal, mechanical and electrical potential is introduced. The mechanical governing equations are derived in term of three-dimensional equilibrium relations and the classical Maxwell's equations. The trough-the-thickness temperature is modeled by the Fourier's heat conduction equation. The coupled partial differential equations are solved by Navier closed form solutions. The trough-the-thickness profile for electrical potential, temperature profile and displacements is obtained by using a quasi-exact method so-called the differential quadrature method (DQM). Chebyshev polynomials of the third kind are used as the basis functions and the grid thickness domain discretization for the DQM. The interlaminar conditions for transverse stresses, temperature and electrical potential are imposed. The correct traction conditions for transverse stresses and scalar potential function at the top and the bottom are applied. The results for cylindrical, spherical and rectangular plates are presented. The excellent obtained results are compared with layerwise and three-dimensional solutions reported in the literature.