Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
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IssuesArchive of Issues2021-2pp.263-270

Archive of Issues

Total articles in the database: 4932
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Radaev Yu.N., "Representation of Displacements in a Spatial Harmonic Problem of the Theory of Elasticity Using Two Screw Vectors," Mech. Solids. 56 (2), 263-270 (2021)
Year 2021 Volume 56 Number 2 Pages 263-270
DOI 10.3103/S0025654421020114
Title Representation of Displacements in a Spatial Harmonic Problem of the Theory of Elasticity Using Two Screw Vectors
Author(s) Radaev Yu.N. (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, radayev@ipmnet.ru, y.radayev@gmail.com)
Abstract Differential equations for potentials are considered that ensure the fulfillment of the basic vector differential equation of the linear theory of elasticity in the case of a harmonic dependence of the displacement field on time. An alternative scheme for splitting the vector differential equation of the linear theory of elasticity into unrelated equations is developed. It is based on the concept of a gamma vector that satisfies a screw equation. As a result, the problem of finding the vortex component of the displacement field is reduced to the sequential solution of unrelated screw first-order partial differential equations. A theorem on the completeness of the representation of the displacement field using two screw vortex vector fields is formulated and proved.
Keywords elasticity theory, displacement vector, scalar potential, vector potential, gamma vector, vortex vector, screw equation, completeness of representation
Received 04 December 2019Revised 19 March 2020Accepted 22 May 2020
Link to Fulltext https://link.springer.com/article/10.3103/S0025654421020114
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