Numerical method of stable solution of S.-Venant problem of shaft torsion
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2009), pp. 98-111 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Stable numerical method of solving S.-Venant problem about torsion of shaft with arbitrary bounded unity-connected domain section with Jordan boundary was developed. This method is based on direct solution of the boundary problem for harmonic functions in non-classical discrete statement with regularization procedure. Testing of this method with employment of computer programs demonstrates its sufficiently high efficiency and precision.
Mots-clés : S.-Venant problem
Keywords: shaft torsion, boundary problems, harmonic function, numerical method, regularization procedure, computer program.
@article{VTGU_2009_4_a9,
     author = {V. V. Sobolev},
     title = {Numerical method of stable solution of {S.-Venant} problem of shaft torsion},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {98--111},
     year = {2009},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2009_4_a9/}
}
TY  - JOUR
AU  - V. V. Sobolev
TI  - Numerical method of stable solution of S.-Venant problem of shaft torsion
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2009
SP  - 98
EP  - 111
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VTGU_2009_4_a9/
LA  - ru
ID  - VTGU_2009_4_a9
ER  - 
%0 Journal Article
%A V. V. Sobolev
%T Numerical method of stable solution of S.-Venant problem of shaft torsion
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2009
%P 98-111
%N 4
%U http://geodesic.mathdoc.fr/item/VTGU_2009_4_a9/
%G ru
%F VTGU_2009_4_a9
V. V. Sobolev. Numerical method of stable solution of S.-Venant problem of shaft torsion. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2009), pp. 98-111. http://geodesic.mathdoc.fr/item/VTGU_2009_4_a9/

[1] Timoshenko S.P., Guder Dzh., Teoriya uprugosti, Nauka, M., 1975, 576 pp.

[2] Kufarev P.P., “K voprosu o kruchenii i izgibe sterzhnei poligonalnogo secheniya”, PMM, 1:1 (1937), 43–76 | Zbl

[3] Arutyunyan N.Kh., Abramyan B.L., Kruchenie uprugikh tel, Fizmatgiz, M., 1963, 688 pp.

[4] Novatskii V., Teoriya uprugosti, Nauka, M., 1975, 872 pp.

[5] Muskhelishvili N.I., Nekotorye osnovnye zadachi matematicheskoi teorii uprugosti, Nauka, M., 1966, 708 pp. | Zbl

[6] Pozharskii D.A., “Smeshannye zadachi teorii uprugosti dlya sostavnogo ploskogo klina”, Izv. vuzov. Sev.-Kavk. region. Estestv. nauki, 2008, no. 5, 36–38

[7] Mikhlin S.G., Variatsionnye metody v matematicheskoi fizike, Nauka, M., 1970, 512 pp. | Zbl

[8] Brebbiya K., Telles Zh., Vroubel L., Metody granichnykh elementov, Mir, M., 1987, 524 pp.

[9] Krauch S., Starfild A., Metody granichnykh elementov v mekhanike tvërdogo tela, Mir, M., 1987, 328 pp.

[10] Gromadka T., Lei Ch., Kompleksnyi metod granichnykh elementov v inzhenernykh zadachakh, Mir, M., 1990, 303 pp.

[11] Walsh J.L., “Ueber die Entwickelung einer analytischen Function nach Polynomen”, Munchen. Math. Ann., 96 (1926/27), 430–436 | DOI | Zbl

[12] Tikhonov A.N., Arsenin V.Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979, 288 pp.

[13] Sobolev V.V., Ischenko N.V., Chislennoe integrirovanie. Metodicheskie ukazaniya k laboratornoi rabote s ispolzovaniem EVM, RGASKhM, Rostov n/D, 1999, 28 pp.

[14] Sobolev V.V., Programmy chislennogo resheniya zadachi Sen-Venana o kruchenii sterzhnya proizvolnogo secheniya (programmnyi kompleks dlya EVM), Zaregistrir. GOFAP (VNTITs), No 50200802492, RGASKhM, Rostov n/D, 2008, 22 pp.