Piezoelectric study on confocally multicoated elliptical inclusion

Within the framework of linear piezoelectricity, an effective method is developed and used to derive an analytical solution for the problem of a confocally multicoated elliptical inclusion embedded in an unbounded matrix which is subjected to arbitrary electromechanical loadings. Each layer of the composite is assumed to have different material constants, but has the same material orientation with x3 being the poling direction. The alternating technique in conjunction with the method of analytical continuation is applied to derive the general series solution of electric field and displacement field for each layer of the composite. This approach has a clear advantage in deriving the solution to the heterogeneous problem in terms of the solution to the corresponding homogeneous problem. Several specific solutions are provided in closed form, which are verified by comparison with the existing ones. Some numerical results are provided to investigate the influence of material combinations and different electromechanical loadings on the shear stress and electric field. Besides, they also show that the derived solutions are well satisfied with the boundary conditions.