This article is cited in 2 papers

Beltrami-Mitchell equations in a non-Euclidean continuum model

M. A. Guzev^a, O. N. Lyubimova^b, K. N. Pestov<sup>c

a</sup> Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
^b Far Eastern Federal University, Vladivostok
^c Vladivostok Branch of Russian Customs Academy

Abstract: This work contains a generalization in covariant form of the classical Beltrami-Mitchell equations for the case of incompatible deformations. It is shown that in the corresponding relations an additional force appears, characterizing the internal non-Euclidean geometry of the material, the description of which is given in terms of the Ricci tensor.

Key words: Saint-Venant consistency conditions, Beltrami-Mitchell equations, non-Euclidean continuum model, Ricci tensor.

UDC: 531.36

MSC: Primary 74A05; Secondary 74B05

Received: 13.05.2024
Accepted: 18.11.2024

DOI: 10.47910/FEMJ202416