Electroelastic analysis for a piezoelectric layer with surface electrodes

An electroelastic analysis of a transverse isotropic piezoelectric layer with surface electrodes is made. The piezoelectric layer is infinite long along the poling direction, and the top surface is perfectly bonded to a rigid electrode. The problem is solved via the conformal mapping technique for two cases of elastic boundary conditions on the bottom surface with two spaced electrodes, and the distribution of the electrostatic field in the entire piezoelectric layer is determined in an explicit analytic form, respectively. It is found that for the bottom surface electrodes with vanishing stiffness, the induced strain is singular, but no stress. Instead, for the bottom electrodes with stiffness as infinity, the induced stress is singular, but no strain.