| Abstract: | Consider a cylindrical pipe twisted by terminal couples. For a large twist θ, the elastic-plastic stress function, Ψ (·,θ), is shown to be the positive in the interior of the pipe, an increasing function of θ and converging to the completely plastic stress function, $ bar Psi left(cdot right) $ (·), as θ→∞. A geometric procedure for constructing Ψ(·) has been developed to provide qualitative information. The main result states that $ psi left({cdot,theta} right) = bar Psi left(cdot right) $ on the cross-sectional boundary of the pipe, if θ is greater than or equal to a certain critical value, In addition, an example has been constructed to give additional insights. |
