On the explicit formulations of circular tube, bar and shell of cylindrically piezoelectric material under pressuring loading

Two-dimensional problems of anisotropic cylindrical piezoelectric tube, bar and shell in a cylindrical coordinate system are studied in detail. The equilibrium equations and the constitutive equations of an inhomogeneous linear piezoelectric material in a compact form in a cylindrical coordinate system are deduced by using matrix notations. For the two-dimensional deformation, the result resembles the Stroh eight formalism in the rectangular coordinate system. After doing so, the constitutive coefficients referred to the cylindrical coordinate system are chosen to be constants. Only in this way, could the problems subjected to a uniform normal stress at their inner and outer surfaces be studied, respectively. Then the explicit solutions of such problems are obtained. It is found that the material parameters of piezoelectric material influence the formations of the solutions significantly.