Axisymmetric elasticity solution for an undrained saturated poro-piezoelastic thick disk

In this paper, a circular thick plate made of poroelastic piezoelectric ceramic is studied. The porosities of the plate vary through the thickness and axisymmetric behavior of a piezoelectric disk exhibiting hexagonal material symmetry of class 6 mm. Additionally, external mechanical loads which are in axi-symmetric general form act on the plate. The material properties of the plate vary exponentially as functions of the $z$ variable in cylindrical coordinates. Based on an elasticity solution in terms of radial and axial displacements $(u, w)$, the governing partial differential equations are derived and solved analytically; mechanical stresses and electric displacements are then calculated. Finally an example which illustrates the application of the derived formulas is presented.