Axisymmetric solutions for the multi-layered transversely isotropic piezoelectric medium

By introducing the precise integration algorithm (PIA) and the technique of the mixed variable formalism accounting for any number of layers, variations of components of the axisymmetric piezoelectric field including elastic displacement, vertical normal stress, electric potential and electric displacement along the axis of symmetry in the cylindrical coordinate system are explored. The piezoelectric field is induced by the vertical loadings of mechanical or electric types uniformly distributed over a circular region. With the aid of the mixed variable formulations, along with the Hankel integral transform and the corresponding matrix algebraic operations, the governing partial differential equations of equilibrium expressed in terms of displacements and electric potential are reduced to the first order ordinary differential matrix equations. As a highly accurate algorithm, the PIA is provided to evaluate the obtained ordinary differential matrix equations in the transformed domain. Both mechanical and electrical quantities in the physical domain can be acquired by taking the inversion of the Hankel integral transform. An example as benchmark is illustrated to examine the applicability and performance of the proposed technique compared with results in the literature. Numerical examples are used to demonstrate the influence of the degree of the material anisotropy and stratified parameters.