Geodesic
A variational principle of Lagrange of the micropolar theory of elasticity in the case of transversely isotropic medium
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2022), pp. 35-39 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, a variational principle of Lagrange in the micropolar theory of elasticity for transversely isotropic and centrally symmetric material is formulated. The Ritz method and piecewise polynomial serendipity shape functions are used to obtain the stiffness matrix and a system of linear algebraic equations. 
@article{VMUMM_2022_4_a4,
     author = {A. V. Romanov},
     title = {A variational principle of {Lagrange} of the micropolar theory of elasticity in the case of transversely isotropic medium},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {35--39},
     year = {2022},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2022_4_a4/}
}
TY  - JOUR
AU  - A. V. Romanov
TI  - A variational principle of Lagrange of the micropolar theory of elasticity in the case of transversely isotropic medium
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2022
SP  - 35
EP  - 39
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2022_4_a4/
LA  - ru
ID  - VMUMM_2022_4_a4
ER  - 
%0 Journal Article
%A A. V. Romanov
%T A variational principle of Lagrange of the micropolar theory of elasticity in the case of transversely isotropic medium
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2022
%P 35-39
%N 4
%U http://geodesic.mathdoc.fr/item/VMUMM_2022_4_a4/
%G ru
%F VMUMM_2022_4_a4
A. V. Romanov. A variational principle of Lagrange of the micropolar theory of elasticity in the case of transversely isotropic medium. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2022), pp. 35-39. http://geodesic.mathdoc.fr/item/VMUMM_2022_4_a4/

[1] Pobedrya B. E., Chislennye metody v teorii uprugosti i plastichnosti, Ucheb. posobie, 2-e izd., Izd-vo MGU, M., 1995 | MR

[2] Berdichevskii V. P., Variatsionnye printsipy mekhaniki sploshnoi sredy, Nauka, Glavnaya redaktsiya fiziko-matematicheskoi literatury, M., 1983 | MR

[3] Novatskii V., Teoriya uprugosti, Mir, M., 1975

[4] Eringen A. C., Microcontinuum Field Theories, v. 1, Foundation and Solids, Springer-Verlag, N.Y., 1999 | MR | Zbl

[5] Lakes R., “Cosserat micromechanics of structured media: Experimental methods”, Proc. Amer. Soc. Composites. 3rd Technical Conference (Sept. 25–29, Seatle, 1988), 505–516

[6] Nikabadze M. U., Razvitie metoda ortogonalnykh polinomov v mekhanike mikropolyarnykh i klassicheskikh uprugikh tonkikh tel, Izd-vo Popechitelskogo soveta mekhaniko-matematicheskogo fakulteta MGU im. M.V. Lomonosova, M., 2014 https://istina.msu.ru/publications/book/6738800/

[7] Nikabadze M., Ulukhanyan A., “Some variational principles in the three-dimensional micropolar theories of solids and thin solids”, Theoretical Analyses, Computations, and Experiments of Multiscale Materials, Advanced Structured Materials, 175, Switzerland, 2022, 193–251 | DOI | MR

[8] Nikabadze M., Ulukhanyan A., “On some variational principles in micropolar theories of single-layer thin bodies”, Continuum Mechanics and Thermodynamics, 2022 | DOI | MR

[9] Nikabadze M., Ulukhanyan A., “Generalized Reissner-type variational principle in the micropolar theories of multilayer thin bodies with one small size”, Continuum Mechanics and Thermodynamics, 34:2 (2022) | DOI | MR

[10] Nikabadze M. U., “Topics on tensor calculus with applications to Mechanics”, J. Math. Sci., 225:1 (2017) | DOI | MR | Zbl

[11] Streng G., Fiks Dzh., Teoriya metoda konechnykh elementov, Mir, M., 1977 | MR

[12] Zienkiewicz O. C., Taylor R. L., Fox D. D., The Finite Element Method for Solid Mechanics, 7th ed., Butterworth-Heinemann, Oxford, 2014 | MR | Zbl