Geodesic
Numerical solution of Saint-Venant's problem about torsion of a shaft with two-connected domain section by the method of conformal mapping
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2011), pp. 25-37 Cet article a éte moissonné depuis la source Math-Net.Ru

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A numerical method for solving the Saint-Venant problem about torsion of a shaft with an arbitrary two-connected section domain was developed. This method is based on preliminary building of a conformal mapping of this domain onto a circle ring followed by the solution of the reduced boundary Dirichlet problem. The testing of this method with employment of computer programs demonstrates its sufficiently high efficiency and precision.
Mots-clés : Saint-Venant problem
Keywords: shaft torsion, Dirichlet boundary problem, harmonic function, two-connect domain, conformal mapping, numerical method, computer program. 
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     title = {Numerical solution of {Saint-Venant's} problem about torsion of a~shaft with two-connected domain section by the method of conformal mapping},
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V. V. Sobolev; A. A. Molchanov. Numerical solution of Saint-Venant's problem about torsion of a shaft with two-connected domain section by the method of conformal mapping. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2011), pp. 25-37. http://geodesic.mathdoc.fr/item/VTGU_2011_2_a3/

[1] Greenhill A. G., Quart. J. Math., 16 (1879), 227

[2] Mac Donald H. M., Proc. Cambrige Phil. Soc., 8 (1893), 62

[3] Bredt R., Zeitschr. d. Ver. d. Ing., 40 (1903), 785

[4] Prandtl L., Jahresb. d. Deutschen Math. und Mech. Vereinig, 13 (1904), 31 | Zbl

[5] Gekkeler I. V., Statika uprugogo tela, L.–M., 1934, 287 pp.

[6] Arutyunyan N. Kh., Abramyan B. L., Kruchenie uprugikh tel, M., 1963, 688 pp. | Zbl

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

[8] Hasegawa H., Akiyama H., Takahashi S., “Torsion of an elastic thick walled cylinder with a semicircular notch”, Nihon kikai gakkai ronbunshu. A N Trans. Jap. Soc. Mech. Eng. A, 64:619 (1998), 656–660 | DOI

[9] Wang C. Y., “Torsion of tubes of arbitrary shape”, Int. J. Solids and Struct., 35:7–8 (1998), 719–731 | DOI

[10] Jabmolnski T. F., Andreaus U., “Torsion of a saint-venant cylinder with a non-simply connected cross-section”, Eng. Trans., 47:1 (1999), 77–91

[11] Morassi A., “Torsion of thin tubes with multicell cross-section”, Meccanica, 34:2 (1999), 115–132 | DOI | MR | Zbl

[12] Lavrentev M. A., Shabat B. V., Metody teorii funktsii kompleksnogo peremennogo, M., 1965, 716 pp. | MR

[13] Goluzin G. M., “O konformnom otobrazhenii dvusvyaznykh oblastei, ogranichennykh pryamolineinymi i krugovymi mnogougolnikami”, Konformnye otobrazheniya odnosvyaznykh i mnogosvyaznykh oblastei, M.–L., 1937, 90–97

[14] Aleksandrov I. A., “Kruchenie uprugogo sterzhnya s kratno-krugovoi oblastyu poperechnogo secheniya”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2010, no. 4(12), 56–63

[15] Kantorovich L. V., Krylov V. I., Priblizhënnye metody vysshego analiza, M.–L., 1962, 708 pp. | MR

[16] Filchakov P. F., Chislennye i graficheskie metody matematiki, Kiev, 1970, 800 pp. | MR

[17] Brebbiya K., Telles Zh., Vroubel L., Metody granichnykh elementov, M., 1987, 524 pp. | MR

[18] Sobolev V. V., Ischenko N. V., Programma chislennogo postroeniya konformnogo otobrazheniya ogranichennoi dvusvyaznoi oblasti na krugovoe koltso i obratnogo otobrazheniya, Zaregistrir. GOF AP RF (VNTITs), No 50200100349, RGASKhM, Rostov n/D, 2001, 26 pp.

[19] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, M., 1966, 628 pp. | MR | Zbl

[20] Koppenfels V., Shtalman F., Praktika konformnykh otobrazhenii, M., 1963, 406 pp. | Zbl

[21] Villat H., Lecons sur l' hydrodynamique, Paris, 1929, 291 pp.

[22] Sobol I. M., Chislennye metody Monte-Karlo, M., 1973, 64 pp. | MR

[23] I. A. Birger, Ya. G. Panovko (red.), Prochnost. Ustoichivost. Kolebaniya, Spravochnik v 3 t., v. 1, M., 1968, 831 pp.