Mathematical Modeling of Displacement of Rigid Elliptical Disk in Piezoelectric Space Along Symmetry Axis of Material

The stress distribution that occurs under the displacement of a rigid thin elliptical disk along the symmetry axis of the material of an electroelastic transversely isotropic space is examined using a rigorous mathematical model that takes into account the coupling of force and electric fields in piezoelectric bodies. The exact solution of the three-dimensional electroelasticity problem is obtained based on the representation of the solution of static electroelasticity equations for a transversely isotropic body in terms of harmonic functions and applying the harmonic potential of a special type. From the obtained analytical solution, the expressions as partial cases follow to evaluate the stress state of a transversely isotropic space in displacing the rigid elliptical disk as well as formulas for determining the stress state in an electroelastic space in displacing the circular rigid disk. Numerical investigations are carried out and the influence of the coupling of force and electric fields on the stress distribution under the rigid elliptical disk (during its displacement along the symmetry axis of the material of the piezoelectric space) is studied.