Научная электронная библиотека ULRICH'S Periodicals Directory

Сибирский государственный университет
науки и технологий имени академика М.Ф. Решетнева

Сибирский аэрокосмический журнал
ISSN 2712-8970 (Print) ISSN 2782-5760 (on-line)

Сведения об образовательной организации

UDK 539.374 Doi: 10.31772/2587-6066-2020-21-2-201-205
ELASTIC-PLASTIC PROBLEM IN THE CASE OF INHOMOGENEOUS PLASTICITY UNDER COMPLEX SHEAR CONDITIONS
S. I. Senashov, I. L. Savostyanova, O. N. Cherepanova
Reshetnev Siberian State University of Science and Technology; 31, Krasnoyarskii rabochii prospekt, Krasnoyarsk, 660037, Russian Federation Siberian Federal University; 79, Svobodniy Av., Krasnoyarsk, 660041, Russian Federation
In this research, the authors solved a two-dimensional elastic-plastic problem of the stress state under com-plex shear conditions in the body weakened by a hole that is bounded by a piecewise smooth contour. The stress state of a complex shear occurs in a cylindrical body of infinite length under the action of loads directed along the cylinder generators and constant along the generators. At the same time, with a sufficiently large load, both elastic and plastic zones appear in the body. As in any problem of this kind, it is necessary to find a previously unknown boundary separating the elastic and plastic zones. Finding such a boundary is not an easy task, but the specificity of elastic-plastic problems of complex shear is that solving such problems is easier than solving simi-lar elastic problems. Apparently, for the first time this fact was noted by G. P. Cherepanov. A lot of research is devoted to elastic-plastic problems of complex shear in the case of homogeneous and iso-tropic plasticity. All articles that solve complex shear problems essentially use the representation of stresses and displacements in the elastic zone in a complex form. In this research, the problems of complex shear are solved using conservation laws. It is assumed that the yield strength is a function of the coordinates of the point where the stress state is being studied. It is known that the elastic properties of structural materials can be homogene-ous and isotropic, while their yield point and strength are inhomogeneous. This situation is observed, for exam-ple, in the case of neutron bombardment of structural materials. This research will examine exactly this situa-tion. The article presents conservation laws for equations describing a complex shear. It was assumed that the components of the conserved current depend on the components of the stress tensor and coordinates. The com-ponents of the stress tensor are included in them linearly. The problem of finding the components of the con-served current was reduced to the Cauchy-Riemann system. The solution of this system allowed us to reduce the calculations of the stress tensor components to a curvilinear integral along the contour of the hole and thus find the boundary between the elastic and plastic areas.
Keyword: elastic-plastic problem, inhomogeneous plasticity, complex shear, conservation laws.
References

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Senashov Sergei Ivanovich – D. Sc., Professor, Head of the Department of IES; Reshetnev Siberian State University of Science and Technology. E-mail: sen@sibsau.ru.
Savostyanova Irina Leonidovna – Cand. Sс., Associate Professor of the Department of IES, Reshetnev Siberian
State University of Science and Technology. E-mail: savostyanova@sibsau.ru.
Cherepanova Olga Nikolaevna – Cand. Sс., associate Professor, acting Director of the Institute of Mathematics
and Fundamental Informatics; Siberian Federal University. E-mail: cheronik@mail.ru. 


  ELASTIC-PLASTIC PROBLEM IN THE CASE OF INHOMOGENEOUS PLASTICITY UNDER COMPLEX SHEAR CONDITIONS