|
ИСТИНА |
Войти в систему Регистрация |
ИПМех РАН |
||
On Some Issues of Second Strain Tensor and Velocity Vector Gradient Theories of 3D Bodies and Thin Bodies (в печати)статья
Статья опубликована в журнале из списка RSCI Web of Science
Статья опубликована в журнале из перечня ВАКСтатья опубликована в журнале из списка Web of Science и/или Scopus
- Автор: Nikabadze Mikhail
- Журнал: Lobachevskii Journal of Mathematics
- Том: 45
- Номер: 8
- Год издания: 2024
- Издательство: Kazanskii Gosudarstvennyi Universitet/Kazan State University
- Местоположение издательства: Russian Federation
- Аннотация: The expressions for speci c energy, constitutive relations, equations of motion and equilibrium of the second strain tensor and velocity vector gradient theory for an arbitrary anisotropic bodies are given, from which corresponding relations of the second strain tensor and velocity vector gradient theory of elastic thin bodies are obtained, on the basis of which, using the method of orthogonal polynomials the corresponding relations in moments are derived. Constitutive relations for gradient bodies are written using tensor-block matrices. In addition, static boundary conditions and equations of motion and equilibrium of gradient theories are represented by dierential tensor-block matrix operators, for which, in the case of homogeneous bodies, dierential tensor-block matrix operators of cofactors are constructed, which make it possible to split the initial-boundary value problems of some gradient theories. Herewith static boundary conditions can be split only for a homogeneous body having a piecewise at boundary, i.e., for each at section of the boundary the static boundary conditions can be split. The system of equations in moments of the displacement vector of the 10th order approximation is obtained. In particular, for each moment of the displacement vector included in these systems of equations, an equation of higher order elliptic type is obtained separately, for which an analytical solution can be written using the Vekua method.
- Добавил в систему: Никабадзе Михаил Ушангиевич