Geodesic
About oblique impact by perfectly rigid body with plane boundary on the nonlinear elastic half-space
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 4, pp. 32-40 
O. V. Dudko; D. A. Potyanikhin. About oblique impact by perfectly rigid body with plane boundary on the nonlinear elastic half-space. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 4, pp. 32-40. http://geodesic.mathdoc.fr/item/ISU_2009_9_4_a4/
@article{ISU_2009_9_4_a4,
     author = {O. V. Dudko and D. A. Potyanikhin},
     title = {About oblique impact by perfectly rigid body with plane boundary on the nonlinear elastic half-space},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {32--40},
     year = {2009},
     volume = {9},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2009_9_4_a4/}
}
TY  - JOUR
AU  - O. V. Dudko
AU  - D. A. Potyanikhin
TI  - About oblique impact by perfectly rigid body with plane boundary on the nonlinear elastic half-space
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2009
SP  - 32
EP  - 40
VL  - 9
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ISU_2009_9_4_a4/
LA  - ru
ID  - ISU_2009_9_4_a4
ER  - 
%0 Journal Article
%A O. V. Dudko
%A D. A. Potyanikhin
%T About oblique impact by perfectly rigid body with plane boundary on the nonlinear elastic half-space
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2009
%P 32-40
%V 9
%N 4
%U http://geodesic.mathdoc.fr/item/ISU_2009_9_4_a4/
%G ru
%F ISU_2009_9_4_a4

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

In this paper the impact interaction of perfectly rigid body and nonlinear elastic solid,which have plane boundaries, are investigated. Suppose that the moving rigid body has constant velocity, resulting in self-similar formulation of the problem. Possible variants of wave combinations, arising from such interaction, are discussed. The existence condition for evolutionary shock waves and the thermodynamic discontinuities compatibility condition serve as criterions for choosing the wave pattern. The scheme for the solution of a self-similar boundary-value problem includes checking for the mentioned criterion during computations.

[1] Agapov I. E., Burenin A. A., Rezunov A. V., “O soudarenii dvukh nelineino-uprugikh tel s ploskimi granitsami”, Prikladnye zadachi mekhaniki deformiruemykh sred, Sb. nauch. tr., DVO AN SSSR, Vladivostok, 1991, 206–215

[2] Burenin A. A., Lapygin V. V., Chernyshov A. D., “K resheniyu ploskikh avtomodelnykh zadach nelineinoi dinamicheskoi teorii uprugosti”, Nelineinye volny deformatsii, Materialy mezhdunar. simpoziuma, v. 2, Tallin, 1978, 25–28

[3] Burenin A. A., Lapygin V. V., “Ob otrazhenii ploskoi prodolnoi udarnoi volny postoyannoi intensivnosti ot ploskoi zhestkoi granitsy nelineinoi uprugoi sredy”, PMTF, 1985, no. 5, 125–129

[4] Kulikovskii A. G., Sveshnikova E. I., Nelineinye volny v uprugikh sredakh, Moskovskii litsei, M., 1998, 412 pp.

[5] Chugainova A. P., “Avtomodelnaya zadacha o deistvii beguschei nagruzki na granitsu nelineino-uprugogo slaboanizotropnogo poluprostranstva”, PMM, 57:3 (1993), 102–109 | MR

[6] Baskakov V. A., Bykovtsev G. I., “Ob otrazhenii ploskopolyarizovannoi volny ot svobodnoi poverkhnosti v uprochnyayuscheisya uprugoplasticheskoi srede”, PMM, 35:1 (1971), 71–72 | MR

[7] Bykovtsev G. I., Kolokolchikov A. V., Sygurov A. V., “Avtomodelnye resheniya uravnenii dinamiki idealnogo uprugoplasticheskogo tela pri uslovii plastichnosti Treska”, PMTF, 1984, no. 6, 148–156

[8] Bykovtsev A. G., “O prelomlenii udarnykh voln chistogo sdviga v uprugoplasticheskoe poluprostranstvo”, PMM, 53:2 (1989), 309–318 | MR | Zbl

[9] Bykovtsev G. I., Ivlev D. D., Teoriya plastichnosti, Dalnauka, Vladivostok, 1998, 523 pp.

[10] Burenin A. A., Chernyshov A. D., “Udarnye volny v izotropnom uprugom prostranstve”, PMM, 42:4 (1978), 711–717 | MR | Zbl

[11] Dudko O. V., Potyanikhin D. A., “Avtomodelnaya zadacha nelineinoi dinamicheskoi teorii uprugosti o vzaimodeistvii prodolnoi udarnoi volny s zhestkoi pregradoi”, Vychisl. mekh. splosh. sred, 1:2 (2008), 27–37 | MR