On elastoplastic torsion of a rod with multiply connected cross-section

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.