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: 10.31772/2587-6066-2020-21-3-303-306
SOLVING BOUNDARY VALUE PROBLEMS OF EQUATIONS OF TWO-DIMENSIONAL ELASTICITY THEORY USING CONSERVATION LAWS
B. D. Annin, S. I. Senashov, O. V. Gomonova
Lavrentyev Institute of Hydrodynamics SB RAS; 15 Lavrentyev Prospect, Novosibirsk, 630090, Russian Federation; Reshetnev Siberian State University of Science and Technology; 31, Krasnoyarskii rabochii prospekt, Krasnoyarsk, 660037, Russian Federation
The plane problem for elasticity equations is well studied. It can be explained by its importance for applications and by the fact that the equations can be reduced to the Cauchy-Riemann system. In spite of this importance, exact solutions that would describe the stress-strain state of bodies of finite dimensions are not numerous. Conservation laws for differential equations have been appeared more than a hundred years ago, but, as a rule, they were not used to solve specific problems, but were of purely academic interest. The situation changed with the development of the technique of construction of conservation laws for arbitrary systems of differential equations, and then with the use of conservation laws to solve boundary value problems of the theory of plasticity and elastic-plasticity. In this article, new conservation laws are constructed for the equations of the plane theory of elasticity in the stationary case. These laws form an infinite series, which is closely related to the elasticity equations solving. This fact made possible to reduce solving of boundary value problems, in terms of displacements, to the calculation of contour integrals along the boundary of a domain bounded by the studying elastic body. As it follows from the proposed technique, the studied area can be multiply connected, and the considered boundary can be piecewise-smooth.
Keywords: conservation laws, boundary value problem, elasticity equations.
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Annin Boris Dmitrievich – Dr. Sc., Professor, academician of the Russian Academy of Sciences, head of Department;
Lavrentyev Institute of Hydrodynamics SB RAS.
Senashov Sergey Ivanovich – Dr. Sc., Professor, head of the Department; Reshetnev Siberian State University
of Science and Technology. E-mail: sen@sibsau.ru.
Gomonova Olga Valeryevna – Cand. Sc., associate Professor; Reshetnev Siberian State University of Science
and Technology.


  SOLVING BOUNDARY VALUE PROBLEMS OF EQUATIONS OF TWO-DIMENSIONAL ELASTICITY THEORY USING CONSERVATION LAWS