On the equilibrium of piezoelectric bodies of revolution

By means of the three-dimensional general solution in displacement functions (weighted harmonic functions) for piezoelectric materials, the general solution of stress components and electric displacements expressed by the displacement functions is derived by use of the constitutive relation and the equilibrium equations. Based on this general solution, a series of problems is solved by the trial-and-error method, including circular plate (or cylinder), annular plate (or hollow cylinder), cone and hollow cone. These problems are circular plates and cylinders under uniform radial or axial tension and electric displacements as well as pure bending, simply-supported circular plates subjected to uniformly distributed loads, rotating disks and circular shafts, cones or hollow cones subjected to concentrated forces plus charge and concentrated force couple at their apex, etc. Analytical solutions to various problems are obtained. When the cone apex angle 2a equals p, the solutions for the cases of concentrated forces plus point charges and torsion reduce to the simple and practical solutions of the half-space problem