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

Abstract

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 variable in cylindrical coordinates. Based on an elasticity solution in terms of radial and axial displacements ( , ), 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.