On the equilibrium of piezoelectric bodies of revolution

By means of the three-dimensional general solution in displacement function s (weighted harmonic functions) for piezoelectric materials, the general so lution of stress components and electric displacements expressed by the dis placement 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 cyli nder), annular plate (or hollow cylinder), cone and hollow cone. These prob lems are circular plates and cylinders under uniform radial or axial tensio n and electric displacements as well as pure bending, simply-supported circ ular plates subjected to uniformly distributed loads, rotating disks and ci rcular shafts, cones or hollow cones subjected to concentrated forces plus charge and concentrated force couple at their apex, etc. Analytical solutio ns to various problems are obtained. When the cone apex angle 2 alpha equal s pi, 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. (C) 1999 Elsevier Science Ltd. All rights reserved.