Geodesic
The use of Lagrange multipliers in the triangular element of a~nonplanar shell under variable interpolation of displacements
Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 4, pp. 44-54.

Voir la notice de l'article provenant de la source Math-Net.Ru

We expose an algorithm for calculating thin arbitrary shells on usig a triangular discretization element with correction Lagrange multipliers. The rigidity matrix of the triangular element is formed using the methods for approximating displacements as scalar and vector quantities.
Keywords: shell, triangular discretization element, scalar approximation, vector approximation.
Mots-clés : Lagrange multipliers 
@article{SJIM_2017_20_4_a5,
     author = {Yu. V. Klochkov and A. P. Nikolaev and O. V. Vakhnina and T. A. Kiseleva},
     title = {The use of {Lagrange} multipliers in the triangular element of a~nonplanar shell under variable interpolation of displacements},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {44--54},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2017_20_4_a5/}
}
TY  - JOUR
AU  - Yu. V. Klochkov
AU  - A. P. Nikolaev
AU  - O. V. Vakhnina
AU  - T. A. Kiseleva
TI  - The use of Lagrange multipliers in the triangular element of a~nonplanar shell under variable interpolation of displacements
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2017
SP  - 44
EP  - 54
VL  - 20
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2017_20_4_a5/
LA  - ru
ID  - SJIM_2017_20_4_a5
ER  - 
%0 Journal Article
%A Yu. V. Klochkov
%A A. P. Nikolaev
%A O. V. Vakhnina
%A T. A. Kiseleva
%T The use of Lagrange multipliers in the triangular element of a~nonplanar shell under variable interpolation of displacements
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2017
%P 44-54
%V 20
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2017_20_4_a5/
%G ru
%F SJIM_2017_20_4_a5
Yu. V. Klochkov; A. P. Nikolaev; O. V. Vakhnina; T. A. Kiseleva. The use of Lagrange multipliers in the triangular element of a~nonplanar shell under variable interpolation of displacements. Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 4, pp. 44-54. http://geodesic.mathdoc.fr/item/SJIM_2017_20_4_a5/

[1] Novozhilov V. V., Teoriya tonkikh obolochek, Sudostroenie, L., 1962 | MR

[2] Nikolaev A. P., Klochkov Yu. V., Kiselev A. P., Gureeva N. A., Vektornaya interpolyatsiya polei peremeschenii v konechno-elementnykh raschetakh obolochek, izd. Volgograd. GAU, Volgograd, 2012

[3] Yakushev V. L., Nelineinye deformatsii i ustoichivost tonkikh obolochek, Nauka, M., 2004

[4] Timoshenko S. P., Voinovskii-Kriger S., Plastinki i obolochki, Nauka, M., 1966 | MR

[5] Galimov K. Z., Paimushin V. N., Teoriya obolochek slozhnoi geometrii, Izd-vo Kazan. gos. un-ta, Kazan, 1985 | MR

[6] Kireev I. V., Nemirovskii Yu. V., “Konservativnyi chislennyi metod resheniya lineinykh kraevykh zadach statiki uprugikh obolochek vrascheniya”, Vychisl. mekhanika sploshnykh sred, 5:1 (2012), 85–99

[7] Sedov L. I., Mekhanika sploshnoi sredy, Nauka, M., 1976 | MR

[8] Golovanov A. I., Tyuleneva O. N., Shigabutdinov A. F., Metod konechnykh elementov v statike i dinamike tonkostennykh konstruktsii, Fizmatlit, M., 2006

[9] Bate K.-Yu., Metody konechnykh elementov, Fizmatlit, M., 2010

[10] Postnov V. A., Kharkhurim I. Ya., Metod konechnykh elementov v raschetakh sudovykh konstruktsii, Sudostroenie, L., 1974

[11] Matvienko Yu. G., Chernyatin A. S., Razumovskii I. A., “Chislennyi analiz nesingulyarnykh sostavlyayuschikh trekhmernogo polya napryazhenii v vershine treschiny smeshannogo tipa”, Problemy mashinostroeniya i nadezhnosti mashin, 2013, no. 4, 40–48

[12] Savenkova M. I., Sheshenin S. V., Zakalyukina I. M., “Sravnenie rezultatov konechno-elementnogo analiza s rezultatami asimptoticheskogo metoda osredneniya v zadache uprugoplasticheskogo izgiba”, Vestnik MGSU, 2013, no. 8, 42–50

[13] Klochkov Yu. V., Nikolaev A. P., Kiselev A. P., “Osobennosti formirovaniya matritsy zhestkosti treugolnogo konechnogo elementa razmerom $54\times54$”, Izvestiya vuzov. Stroitelstvo, 1998, no. 2, 32–37

[14] Klochkov Yu. V., Nikolaev A. P., Kiseleva T. A., “Sravnenie skalyarnoi i vektornoi form metoda konechnykh elementov na primere ellipticheskogo tsilindra”, Mat. modelirovanie, 28:1 (2016), 65–77 | MR