Abstract:
The classical problem of torsion of a straight rod with convex contour of the cross-section is considered in the paper. The cross-section is multiply connected domain. It is assumed that the region of plastic deformation occupies the whole outer boundary. To solve the problem the conservation laws are used. In the case when the boundary is piecewise smooth the solution is found in explicit form. Computer programs that allow one to find the elastic-plastic boundary in a rod under torsion with any precision are developed. Examples of calculation of elastic-plastic boundaries from presented analytical formulas are given. The obtained results are in good agreement in comparison with known solutions and experimental data.
Keywords:
conservation laws, exact solution, unknown boundary, torsion problem of straight rod, multiply connected cross-section.
Received: 24.05.2015 Received in revised form: 14.06.2015 Accepted: 15.07.2015
Document Type:
Article
UDC:
539.374
Language: English
Citation:
Sergey I. Senashov, Alexander V. Kondrin, Olga N. Cherepanova, “On elastoplastic torsion of a rod with multiply connected cross-section”, J. Sib. Fed. Univ. Math. Phys., 8:3 (2015), 343–351
\Bibitem{SenKonChe15}
\by Sergey~I.~Senashov, Alexander~V.~Kondrin, Olga~N.~Cherepanova
\paper On elastoplastic torsion of a rod with multiply connected cross-section
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2015
\vol 8
\issue 3
\pages 343--351
\mathnet{http://mi.mathnet.ru/jsfu437}
\crossref{https://doi.org/10.17516/1997-1397-2015-8-3-343-351}
Linking options:
https://www.mathnet.ru/eng/jsfu437
https://www.mathnet.ru/eng/jsfu/v8/i3/p343
This publication is cited in the following 7 articles:
Sergei I. Senashov, Irina L. Savostyanova, Olga N. Cherepanova, “Elasto-plastic twisting of a two-layer rod weakened by holes”, Zhurn. SFU. Ser. Matem. i fiz., 16:5 (2023), 591–597
Olga V. Gomonova, Sergey I. Senashov, Olga N. Cherepanova, “Distribution of zones of elastic and plastic deformation appearing in a layer under compression by two rigid parallel plates”, Zhurn. SFU. Ser. Matem. i fiz., 14:4 (2021), 492–496
Gomonova O.V., Senashov S.I., “Determining Elastic and Plastic Deformation Regions in a Problem of Unixaxial Tension of a Plate Weakened By Holes”, J. Appl. Mech. Tech. Phys., 62:1 (2021), 157–163
S. I. Senashov, O. V. Gomonova, I. L. Savostyanova, O. N. Cherepanova, “Symmetries and conservation laws in the theory of plasticity”, Reshetnev Readings 2018, IOP Conference Series-Materials Science and Engineering, 822, IOP Publishing Ltd, 2020, 012030
S. Senashov, I. Savostyanova, “About the limit state of deformable bodies”, 21St International Scientific Conference Reshetnev Readings-2017, IOP Conference Series-Materials Science and Engineering, 467, IOP Publishing Ltd, 2019, 012006
S. I. Senashov, O. V. Gomonova, “Construction of elastoplastic boundary in problem of tension of a plate weakened by holes”, Int. J. Non-Linear Mech., 108 (2019), 7–10
Sergei I. Senashov, Irina L. Savostyanova, Olga N. Cherepanova, “Solution of boundary value problems of plasticity with the use of conservation laws”, Zhurn. SFU. Ser. Matem. i fiz., 11:3 (2018), 356–363
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