Geodesic
Numerical modeling of strong nonlinear deformation problems in Euler coordinates
Matematičeskoe modelirovanie, Tome 20 (2008) no. 3, pp. 17-28 
M. S. Agapov; E. B. Kuznetsov; V. I. Shalashilin. Numerical modeling of strong nonlinear deformation problems in Euler coordinates. Matematičeskoe modelirovanie, Tome 20 (2008) no. 3, pp. 17-28. http://geodesic.mathdoc.fr/item/MM_2008_20_3_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Numerical solution of problem of strong nonlinear deformation using method of solution continuation with respect to a parameter is considered. Euler's coordinates are used. Numerical results demonstrate efficiency of the approach.

[1] Novozhilov V. V., Teoriya uprugosti, Sudpromgiz, L., 1958, 370 pp.

[2] Shalashilin V. I., Kuznetsov E. B., Metod ppodolzheniya pesheniya po papametpu i nailuchshaya parametrizatsiya v prikladnoi matematike i mekhanike, Editorial URSS, M., 1999, 222 pp. | MR

[3] Shalashilin V. I., Kuznetsov E. B., Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics, Kluwer Academic Publishers, Dordrecht–Boston–London, 2003, 236 pp. | MR | Zbl

[4] Sedov L. I., Mekhanika sploshnoi sredy, T. 1, Nauka, M., 1970, 492 pp. | MR

[5] Ilyushin A. A., Mekhanika sploshnoi sredy, Izd-vo mosk. un-ta, M., 1971, 247 pp.

[6] Goldenblat I. I., Nelineinye problemy teorii uprugosti, Nauka, M., 1969, 336 pp. | MR

[7] Lure A. I., Nelineinaya teoriya uprugosti, Nauka, M., 1980, 512 pp. | MR

[8] Danilin A. N., Shalashilin V. I., “O parametrizatsii nelineinykh uravnenii deformirovaniya tverdogo tela”, Izv. RAN. Mekhan. tverdogo tela, 2000, no. 1, 82–92

[9] Paimushin V. N., Shalashilin V. I., “Neprotivorechivyi variant teorii deformatsii sploshnykh sred v kvadratichnom priblizhenii”, DAN, 396:4 (2004), 492–495 | MR

[10] Kalitkin N. N., Chislennye metody, Nauka, M., 1978, 512 pp. | MR