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Free‐boundary values in an elastic‐plastic torsion problem
Author(s) -
Ting Tsuan Wu,
Hsiao C. G.
Publication year - 1989
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670110603
Subject(s) - torsion (gastropod) , twist , mathematics , bar (unit) , function (biology) , boundary (topology) , boundary value problem , mathematical analysis , combinatorics , geometry , physics , meteorology , biology , medicine , surgery , evolutionary biology
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, \documentclass{article}\pagestyle{empty}\begin{document}$ \bar \Psi \left(\cdot \right) $\end{document} (·), as θ→∞. A geometric procedure for constructing Ψ(·) has been developed to provide qualitative information. The main result states that \documentclass{article}\pagestyle{empty}\begin{document}$ \psi \left({\cdot,\theta} \right) = \bar \Psi \left(\cdot \right) $\end{document} 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.