 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4810 |
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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 2019 | Revised |
19 March 2020 | Accepted |
22 May 2020 |
| Link to Fulltext |
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| << Previous article | Volume 56, Issue 2 / 2021 | Next article >> |
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