Abstract
The splitting of initial boundary value problems in the theories of elasticity is considered for some anisotropic media. In particular, the initial boundary value problems of the micropolar classical theory of elasticity are represented using the tensor-block matrix operators (or tensor operators). In the case of isotropic micropolar elastic media known also as isotropic or transversally isotropic classical media, we propose the tensor-block matrix operators of algebraic cofactors corresponding to the tensor-block matrix operators of the initial boundary value problems, which allows us to split these problems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. N. Vekua, Foundations of Tensor Analysis and the Theory of Covariants (Nauka, Moscow, 1978) [in Russian].
M. U. Nikabadze, “Construction of Eigentensor Columns in the Linear Micropolar Theory of Elasticity,” Vestn. Mosk. Univ., Ser. 1: Mat. Mekh., No. 1, 30–39 (2014) [Moscow Univ. Mech. Bull. 69 (1), 1–9 (2014)].
M. U. Nikabadze, The Method of Orthogonal Polynomials in the Mechanics of Micropolar and Classical Elastic Thin Bodies. I, available from VINITI, No. 135-B2014 (Moscow, 2014).
M. U. Nikabadze, The Method of Orthogonal Polynomials in the Mechanics of Micropolar and Classical Elastic Thin Bodies. II, available from VINITI, No. 136-B2014 (Moscow, 2014).
M. U. Nikabadze, Development of the Orthogonal Polynomials Method in the Mechanics of Micropolar and Classical Elastic Thin Bodies (Mosk. Gos. Univ., Moscow, 2014) [in Russian].
M. U. Nikabadze, The Method of Orthogonal Polynomials in the Mechanics of Micropolar and Classical Elastic Thin Bodies, Doctoral Dissertation in Mathematics and Physics (Moscow Aviation Inst., Moscow, 2014).
M. U. Nikabadze, “Some Aspects of Tensor Calculus with Applications to Mechanics,” in Contemporary Mathematics. Fundamental Directions (RUDN Univ., Moscow, 2015), Vol. 55, 3–194.
M. U. Nikabadze, “Topics on Tensor Calculus with Applications to Mechanics,” J. Math. Sci. 225 (1), 1–194 (2017).
A. I. Lurie, Nonlinear Theory of Elasticity (Nauka, Moscow, 1980; North-Holland, Amsterdam, 1990).
B. E. Pobedrya, Lectures on Tensor Analysis (Mosk. Gos. Univ., Moscow, 1986) [in Russian].
A. C. Eringen, Microcontinuum Field Theories. 1. Foundation and Solids (Springer, New York, 1999).
V. A. Baskakov, N. P. Bestuzheva, and N. A. Konchakova, Linear Dynamic Theory of Thermoelastic Media with Microstructure (Voronezh Univ. Press, Voronezh, 2001) [in Russian].
M. U. Nikabadze, “To the Problem of Decomposition of the Initial Boundary Value Problems in Mechanics,” J. Phys. Conf. Series 936, (2017). doi https://doi.org/10.1088/1742-6596/936/1/012
Acknowledgments
This work was supported by the Shota Rustaveli National Science Foundation (project no. DI-2016-41).
Author information
Authors and Affiliations
Corresponding author
Additional information
Russian Text © The Author(s), 2019, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2019, Vol. 74, No. 5, pp. 23–30.
About this article
Cite this article
Nikabadze, M.U. Splitting of Initial Boundary Value Problems in Anisotropic Linear Elasticity Theory. Moscow Univ. Mech. Bull. 74, 103–110 (2019). https://doi.org/10.3103/S0027133019050017
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0027133019050017