Axisymmetric Stresses and Displacements in Thick-Walled Elastic Torus

Problems of toroidal membranes and shells under pressure have received a great deal of attention in recent years, with stress, vibration, and stability analyses being performed by many researchers. However, relatively few articles have appeared concerning similar analyses for the thick-walled elastic torus. Kornecki used the method of perturbation to solve for the stresses in a thick-walled torus, loaded by internal and external pressures. Kornecki worked with two equations of elasticity that pertain to this axisymmetric problem, written in terms of stresses; simultaneously, then, four compatibility equations were necessarily solved in obtaining a third approximate solution by perturbing on the ratio of the torus' two radii. In this note, the writers present results of an analysis of an extension of this problem in which displacements as well as stresses are examined. The solution is obtained by solving the basic equation of linear elasticity by the use of finite differences.