Large Deflections of Viscoelastic Rings

A method for the determination of finite deflections and associated moments in a circular ring of a linearly viscoelastic material is presented. The analysis is restricted to small strains. The problem consists of the successive solution of a nonlinear integro-differential equation and a linear integral equation. The numerical solution is carried out with none of the convergence difficulties encountered previously for large loads in the solution for the finite deflections of a viscoelastic cantilever by iteration. In addition to the exact formulation, an approximate method is adapted for use on a statically indeterminate ease, and is shown, for the problem treated here, to be a generalization of the elastic-viscoelastic analogy for the case of small deflections. Examples are given illustrating the range where the approximation is useful.