Analytical Solution for the Reissner–Sagoci Problem of a Piezoelectric Half-Space

Abstract

In this paper, a transversely isotropic piezoelectric half-space with the isotropy axis parallel to the z-axis is considered under rotation on a rigid circular disk bonded to the surface of the piezoelectric medium. This is a type of Reissner–Sagoci mixed boundary value problem. By utilizing the Hankel transform, the mixed boundary value problem is simplified into solving a pair of dual integral equations. Full-field analytical expressions for displacement, stresses, and electric displacement inside the half-space are obtained. The shear stresses and electric displacement on the surface are found to be singular at the edge of the rigid circular disk, and the stress intensity factors and electric displacement intensity factor are defined. Numerical results show that material properties and geometric size have significant effects on displacement, shear stresses, and electric displacement.