Mathematics & Physics 2015, 7(1), 343–351 УДК 539.374 On Elastoplastic Torsion of a Rod with Multiply Connected Cross-Section Sergey I. Senashov Alexander V.Kondrin Siberian State Aerospace University Krasnoyarsky Rabochy, 31, Krasnoyarsk, 660014 Russia Olga N.Cherepanova∗ Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia Received 24.05.2015, received in revised form 14.06.2015, accepted 15.07.2015 The classical problem of torsion of a straight rod with convex contour of the cross-section is considered in the paper. <...> 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. <...> All rights reserved c – 343 – Sergey I.Senashov, Alexander V.Kondrin, Olga N.Cherepanova On Elastoplastic Torsion of a Rod . <...> The rod is twisted around the axis Oz by couple of forces with the moment M. At some value of the moment M part of the rod changes to plastic state. <...> Plastic deformation begins at the outer contour L0. <...> The remaining part of the rod is in elastic state. <...> Our problem is to define the boundary between elastic and plastic zones. <...> In the case of simply connected cross-section bounded by a piecewise smooth contour the problem was solved [1]. <...> In the paper we assume that the cross-section of the rod is multiply connected domain. <...> Fig. 2 shows the contour of the cross section of the rod in the plane Oxy(z = const). <...> We assume that the plastic region fully occupies these contours. <...> Then plastic P and elastic E cross-section areas may occur and L marks dividing lines between areas (Fig. 3). <...> Most of these solutions are based on some assumptions on the form <...>