Geodesic
On some problems of reconstruction of inhomogeneous pre-stressed state in elastic solids
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 4, pp. 25-32 
A. O. Vatulyan; V. V. Dudarev. On some problems of reconstruction of inhomogeneous pre-stressed state in elastic solids. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 4, pp. 25-32. http://geodesic.mathdoc.fr/item/ISU_2009_9_4_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Presents a general approach to the problem of reconstruction of the inhomogeneous pre-stressed state in an elastic body on its amplitude-frequency response, measured in part of its border. Based on the previously defined generalized reciprocity is the ratio of the sequence of linear ill-posed problems, allowing for refinement of the procedure for pre-stress tensor component. As an example, presented a series of computational experiments on the restoration of monotone functions of the distribution of pre-stressed state the problem of bending vibrations of a rod.

[1] Chernyshev G. N., Popov A. L., Kozintsev V. M., Ponomarev I. I., Ostatochnye napryazheniya v deformiruemykh tverdykh telakh, Nauka, M., 1996, 240 pp.

[2] Vatulyan A. O., “Problemy identifikatsii neodnorodnykh svoistv tverdykh tel”, Vestn. Samar. un-ta, 54:4 (2007), 93–103 | MR

[3] Guz A. N., “Uprugie volny v szhimaemykh materialakh s nachalnymi napryazheniyami i nerazrushayuschii ultrazvukovoi metod opredeleniya dvukhsloinykh ostatochnykh napryazhenii”, Prikladnaya mekhanika, 30:1 (1994), 3–17 | MR

[4] Guz A. N., Makhort F. G., Guscha O. I., Vvedenie v akustouprugost, Nauk. dumka, Kiev, 1977, 152 pp.

[5] Nikitina N. E., Akustouprugost. Opyt prakticheskogo primeneniya, TALAM, N. Novgorod, 2005, 208 pp.

[6] Vatulyan A. O., Obratnye zadachi v mekhanike deformiruemogo tverdogo tela, Fizmatlit, M., 2007, 223 pp.

[7] Isakov V., Inverse problems for PDE, Springer-Verlag, N.Y., 2005, 284 pp. | MR | Zbl

[8] Vatulyan A. O., “K formulirovke integralnykh uravnenii v probleme identifikatsii predvaritelno napryazhennogo sostoyaniya”, Ekologicheskii vestn. nauchnykh tsentrov ChES, 2006, no. 2, 23–25

[9] Vatulyan A. O., “O variatsionnoi postanovke obratnykh koeffitsientnykh zadach dlya uprugikh tel”, Dokl. AN, 422:2 (2008), 182–184 | Zbl

[10] Bakushinskii A. B., Goncharskii A. V., Iterativnye metody resheniya nekorrektnykh zadach, Nauka, M., 1989, 128 pp. | MR

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

[12] Samarskii A. A., Vabischevich P. N., Chislennye metody resheniya obratnykh zadach matematicheskoi fiziki, Editorial URSS, M., 2004, 480 pp.

[13] Dudarev V. V., “Ob utochnennoi modeli izgibnykh kolebanii predvaritelno napryazhennoi balki”, Sovremennye problemy mekhaniki sploshnoi sredy, Tr. XII Mezhdunar. konf., v. 2, 2008, 56–59

[14] Filippov A. P., Kolebaniya deformiruemykh sistem, Mashinostroenie, M., 1970, 734 pp.