Geodesic
Lagrange variational principle in the micropolar elasticity theory for non-isothermal processes
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2023), pp. 64-68
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, the Ritz method and piecewise polynomial serendipity shape functions are used to obtain a stiffness matrix and a system of linear algebraic equations in the micropolar theory of elasticity for anisotropic, isotropic and centrally symmetric material in case of a non isothermal process. 
@article{VMUMM_2023_4_a11,
     author = {A. V. Romanov},
     title = {Lagrange variational principle in the micropolar elasticity theory for non-isothermal processes},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {64--68},
     year = {2023},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2023_4_a11/}
}
TY  - JOUR
AU  - A. V. Romanov
TI  - Lagrange variational principle in the micropolar elasticity theory for non-isothermal processes
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2023
SP  - 64
EP  - 68
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2023_4_a11/
LA  - ru
ID  - VMUMM_2023_4_a11
ER  - 
%0 Journal Article
%A A. V. Romanov
%T Lagrange variational principle in the micropolar elasticity theory for non-isothermal processes
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2023
%P 64-68
%N 4
%U http://geodesic.mathdoc.fr/item/VMUMM_2023_4_a11/
%G ru
%F VMUMM_2023_4_a11
A. V. Romanov. Lagrange variational principle in the micropolar elasticity theory for non-isothermal processes. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2023), pp. 64-68. http://geodesic.mathdoc.fr/item/VMUMM_2023_4_a11/

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

[2] Syarle F., Metod konechnykh elementov dlya ellipticheskikh zadach, Mir, M., 1980 | 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 Conf. (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 mekh.-mat. f-ta 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, Germany | 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. Germany, 34:2 (2022) | DOI | MR

[10] Nikabadze M.U., “Topics on tensor calculus with applications to mechanics”, J. Math. Sci, 225 (2017), 1–194 | DOI | MR | Zbl

[11] Zienkiewicz O. C., Taylor R. L., Zhu J.Z., The Finite Element Method: Its Basis and Fundamentals, 7th ed., Butterworth-Heinemann, Oxford, 2013 | MR | Zbl

[12] Romanov A.V., “O variatsionnom printsipe Lagranzha mikropolyarnoi teorii uprugosti v sluchae transversalno-izotropnoi sredy”, Vestn. Mosk. un-ta. Matem. Mekhan., 2022, no. 4, 35–39

[13] Romanov A.V., “O variatsionnom printsipe Lagranzha mikropolyarnoi teorii uprugosti v sluchae ortotropnoi sredy”, Vestn. Mosk. un-ta. Matem. Mekhan., 2023, no. 1, 68–72 | DOI | MR