 | | 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: | | 13205 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8140
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| In English (Mech. Solids): | | 5065 |
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| S.A. Lurie and P.A. Belov, "Generalized Cesaro Formulas in 3D and 4D Elasticity Theories," Mech. Solids. 60 (2), 883-890 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
2 |
Pages |
883-890 |
| DOI |
10.1134/S0025654425600436 |
| Title |
Generalized Cesaro Formulas in 3D and 4D Elasticity Theories |
| Author(s) |
S.A. Lurie (Institute of Applied Mechanics of Russian Academy of Sciences, Moscow, 125040 Russia; Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, salurie@mail.ru)
P.A. Belov (Institute of Applied Mechanics of Russian Academy of Sciences, Moscow, 125040 Russia, belovp@andex.ru) |
| Abstract |
Generalized Cesaro formulas are found, allowing to determine the displacement field with
an accuracy of up to quadratic polynomials through integro-differential operators from the strain tensor-deviator in 3D elasticity theory and 4D elasticity theory. It is shown that quadratures for the
pseudovector (pseudotensor in 4D elasticity) of local rotations and deformation of volume change are
determined by the strain deviator field with an accuracy of up to linear polynomials in coordinates.
Conditions for the existence of the listed quadratures are presented in the form of five (nine for 4D)
third-differential order compatibility equations with respect to the strain tensor-deviator components. |
| Keywords |
kinematic model, Cesaro formulas, compatibility equations, generalized compatibility equations, generalized Cesaro formulas |
| Received |
30 September 2024 | Revised |
10 October 2024 | Accepted |
11 October 2024 |
| Link to Fulltext |
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