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Journal of Applied and Industrial Mathematics

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01-02-2021

About Elastic Torsion around Three Axes

Authors: S. I. Senashov, I. L. Savostyanova

Published in: Journal of Applied and Industrial Mathematics | Issue 1/2021

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Abstract

We consider the equations of nonlinear elasticity assuming that the components of the deformation vector depend only on the two space coordinates each of which has the two corresponding coordinates. Some system of the three differential equations for three tangent components of the stress tensor is obtained in result of this study. This system can be used to describe the elastic torsion of a parallelepiped around the three orthogonal axes. We show that the solution of this problem, in stresses, depends on the three arbitrary functions each of which depends only on the two space variables.

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B. D. Annin, V. O. Bytev, and S. I. Senashov, Group Properties of the Equations of Elasticity and Plasticity (Nauka, Novosibirsk, 1985) [in Russian].MATH

V. Novatsky, Theory of Elasticity (Mir, Moscow, 1975) [in Russian].

S. I. Senashov, O. V. Gomonova, and A. N. Yakhno, Mathematical Issues of Two-Dimensional Equations of Elasticity (Sibir. Gos. Aerokosm. Univ., Krasnoyarsk, 2012) [in Russian].

Title: About Elastic Torsion around Three Axes
Authors: S. I. Senashov
I. L. Savostyanova
Publication date: 01-02-2021
Publisher: Pleiades Publishing
Published in: Journal of Applied and Industrial Mathematics / Issue 1/2021
Print ISSN: 1990-4789
Electronic ISSN: 1990-4797
DOI: https://doi.org/10.1134/S1990478921010129

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