Metadata (abstracts and keywords) for the articles in the journal
Pestov K.N., Guzev M.A., Luybimova O.N. Geometric structure of the Beltrami-Mitchell equations // Vestnik I. Yakovlev Chuvach State Pedagogical University. Series: Mechanics of a limit state . 2025. № 1(63). p. 100-108
Author(s):
Pestov K.N., Guzev M.A., Luybimova O.N.
Index of UDK:
531.36
DOI:
10.37972/chgpu.2025.63.1.009
Title:
Geometric structure of the Beltrami-Mitchell equations
Keywords:
Ricci tensor, Einstein tensor, Beltrami-Mitchell equations, compatibility conditions of Saint-Venant.
Abstracts:
The paper demonstrates that the classical equations of stress in elasticity theory, known as the Beltrami–Mitchell equations, can be expressed as components of the Ricci tensor when considering linear deformations. This is provided that the conditions of equilibrium, Hooke’s law, and the assumption of a Euclidean space for the material continuum are satisfied. It is proven that the divergence of the Ricci tensor is zero in this case. A relationship between the Ricci tensor and the strain tensor is derived, which is significant for describing the structural and deformational characteristics of the mechanical behavior of materials based on non-Euclidean geometries. It is demonstrated that in the elastic case, the Ricci tensor equals the Einstein tensor.
The contact details of authors:
Konstantin N. Pestov, Candidate of Physical and Mathematical Sciences; e-mail: kopestov@yandex.ru;
https://orcid.org/0009-0005-4669-3070; AuthorID: 589056
Mihail A. Guzev, Doctor of Physical and Mathematical Sciences, Professor; e-mail: guzev@iam.dvo.ru;
https://orcid.org/0000-0001-9344-154X; AuthorID: 3404
Olga N. Lyubimova, Doctor of Physical and Mathematical Sciences, Professor; e-mail: lyubimova@dvfu.ru; https://orcid.org/0000-0003-4802-7352; AuthorID: 372335
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