SYMMETRIC DEFORMATION OF A RADIALLYCONSTRAINED THIN CIRCULAR RING UNDER INERTIA LOADING

This paper presents a derivation of the equations governing the elastic deformation of a thin circular ring which is acted upon by inertia loading along a direction in the plane of the ring. The ring is constrained such that no radial outward displacements are permitted. The resulting system of nonlinear equations are reduced to a convenient form which enables the application of a systematic iterative scheme for its solution. Analysis of a ring of a thickness-radius ratio of 0.01 is made. The snap-buckling behavior of the ring is indicated by a load-deflection curve. The paper also provides a simple linear analysis which is applicable to the calculation of the initial portion of the load-deflection curve.