Theoretical and Numerical Solution of Deflection of the Circular Ring under a Concentrated Force

Abstract

A circular ring is often used in the engineering. There are many applications in the tunnels, subways, and down hole. The purpose of this paper is to obtain the theoretical and numerical solution of the deflection of the circular ring under action of a concentrated force. Adopting the method of numerical analysis and Castigliano’s theory, the max deflection and the 4th equivalent stress of ring are developed. The results of the research indicate that the deflection of ring is the linear function of the concentrated force which is in accord with the elasticity body assumptions, that is Hook’s law. The theoretical solution of the deflection of ring is almost the same as the numerical one of the ring. So it is feasible that the numerical model of the ring is used to analyze the deflection of the eccentric ring.