Geodesic
Application of the reduced and selective integration method in micro-polar elasticity problems
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2024), pp. 65-69 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 shape functions of brick family “linear” element are used to obtain reduced and selective integration techniques in a form of the tensor-block stiffness matrices to prevent the locking effect for nearly incompressible, isotropic and centrally symmetric material of the micropolar theory of elasticity. 
@article{VMUMM_2024_1_a7,
     author = {A. V. Romanov},
     title = {Application of the reduced and selective integration method in micro-polar elasticity problems},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {65--69},
     year = {2024},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2024_1_a7/}
}
TY  - JOUR
AU  - A. V. Romanov
TI  - Application of the reduced and selective integration method in micro-polar elasticity problems
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2024
SP  - 65
EP  - 69
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2024_1_a7/
LA  - ru
ID  - VMUMM_2024_1_a7
ER  - 
%0 Journal Article
%A A. V. Romanov
%T Application of the reduced and selective integration method in micro-polar elasticity problems
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2024
%P 65-69
%N 1
%U http://geodesic.mathdoc.fr/item/VMUMM_2024_1_a7/
%G ru
%F VMUMM_2024_1_a7
A. V. Romanov. Application of the reduced and selective integration method in micro-polar elasticity problems. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2024), pp. 65-69. http://geodesic.mathdoc.fr/item/VMUMM_2024_1_a7/

[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] 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/

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

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

[8] 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

[9] 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

[10] 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

[11] Romanov A.V., “O variatsionnom printsipe Lagranzha mikropolyarnoi teorii uprugosti pri neizotermicheskikh protsessakh”, Vestn. Mosk. un-ta. Matem. Mekhan., 2023, no. 4, 64–68 | DOI

[12] Hughes T. J. R., Cohen M., Haroun M., “Reduced and selective integration techniques in the finite element analysis of plates”, Nuclear Engineering and Design, 46 (1978), 203–222 | DOI

[13] Lakes R.S., “Experimental methods for study of Cosserat elastic solids and other generalized continua”, Continuum models for materials with micro-structure, ed. H. Muhlhaus, J. Wiley, N.Y., 1995, 1–22

[14] Lakes R.S., “Experimental microelasticity of two porous solids”, Int. J. Solids and Struct., 22:1 (1986), 55–63 | DOI

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