Asymptotic methods in dynamics of shells under shock loading

L. Yu. Kossovich

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 2, pp. 12-33.

Résumé

The paper deals with the asymptotic methods, developed for creating a mathematic model of non-stationary wave propagation in shells of revolution under shock impacts of tangential, bending types and shock impacts of normal type; the methods are also aimed at solving the boundary value problems for the strain-stress state (SSS) components with different values of variability and dynamicity indices. Classification of asymptotic approximations is also presented. This classification defines three different types of separation scheme of non-stationary SSS. This scheme uses the following asymptotic approximations: short-wave and low-frequency ones, boundary layers in the vicinities of the quasi-front, the dilatation and shear wave fronts, and the front of Rayleigh surface waves. The schemes of ranges of applicability of approximate theories and schemes for the longitudinal stress resultant, bending moment and transverse shear force are represented.

Bibliographie

[1] Kossovich L. Yu., Kaplunov Yu. D., “Asimptoticheskii analiz nestatsionarnykh uprugikh voln v tonkikh obolochkakh vrascheniya pri udarnykh tortsevykh vozdeistviyakh”, Izv. Sarat. un-ta. Novaya ser., 1:2 (2001), 115–128 | MR

[2] Goldenveizer A. L., Teoriya uprugikh tonkikh obolochek, Nauka, M., 1976, 512 pp. | MR

[3] Goldenveizer A. L., Lidskii V. B., Tovstik P. E., Svobodnye kolebaniya tonkikh uprugikh obolochek, Nauka, M., 1979, 384 pp. | MR

[4] Kossovich L. Yu., Nestatsionarnye zadachi teorii uprugikh tonkikh obolochek, Izd-vo Sarat. un-ta, Saratov, 1986, 176 pp.

[5] Kaplunov J. D., “On the quasi-front in two-dimensional shell theories”, C. R. Acad. Sci. Paris. Ser. 2, 313 (1991), 731–736 | Zbl

[6] Kaplunov J. D., Kossovich L. Yu., Nolde E. V., Dynamics of thin walled elastic bodies, Academic Press, San Diego, 1998 | MR | Zbl

[7] Shevtsova Yu. V., “Pogransloi v okrestnosti kvazifronta v tranvsersalno izotropnoi tsilindricheskoi obolochke”, Problemy prochnosti elementov konstruktsii pod deistviem nagruzok i rabochikh sred, Mezhvuz. nauch. sb., Izd-vo SGTU, Saratov, 2000, 114–117

[8] Bazhanova N. S., Kossovich L. Yu., Sukholovskaya M. S., “Nestatsionarnye volny v vyazkouprugikh obolochkakh: model Maksvella”, Izvestiya vuzov. Severokavkazskii region. Estestvennye nauki, 2000, no. 2, 17–24 | MR | Zbl

[9] Nigul U., “Regions of effective aplication of the methods of three-dimensional and two-dimensional analysis of transient stres waves in shells and plates”, Intern. J. Solids and Structures, 54 (1969), 607–627 | DOI

[10] Kaplunov Yu. D., Kossovich L. Yu., “Asimptoticheskaya model dlya vychisleniya dalnego polya volny Releya v sluchae uprugoi poluploskosti”, Dokl. AN, 395:4 (2004), 482–484 | MR

[11] Kaplunov J., Kossovich L., Zakharov A., “An explicit asymptotic model for the Bleustein–Gulyaev wave”, C. R. Mecanique, 332 (2004), 487–492 | DOI | Zbl

[12] Kossovich L. Yu., Kushekkaliev A. N., “Pole Releya v beskonechnom uprugom sloe”, Matematika, mekhanika: Sb. nauch. tr., 5, Izd-vo Sarat. un-ta, Saratov, 2004, 159–161

[13] Kovalev V. A., Kossovich L. Yu., Taranov O. V., “Pole Releya v zadache Lemba dlya tsilindricheskoi obolochki”, Izvestiya vuzov. Severo-Kavkazskii region. Estestvennye nauki., 2004, Spetsvypusk, 52–54

[14] Kovalev V. A., Kossovich L. Yu., Taranov O. V., “Dalnee pole volny Releya dlya uprugoi polupolosy pri deistvii tortsevoi nagruzki”, Izvestiya RAN. MTT, 2005, no. 5, 89–96 | MR

[15] Kushekkaliev A. N., “Reshenie zadach o rasprostranenii voln v transversalno-izotropnoi tsilindricheskoi obolochke pri normalnykh vozdeistviyakh”, Mekhanika deformiruemykh sred, 14, Izd-vo Sarat. un-ta, Saratov, 2002, 106–115

[16] Kushekkaliev A. N., “Volny tipa Releya v polubeskonechnoi plastine pri normalnom vozdeistvii poperechnogo tipa”, Mekhanika deformiruemykh sred, 15, Izd-vo Sarat. un-ta, Saratov, 2004, 66–73

[17] Kossovich L. Yu., Kushekkaliev A. N., “Analiz priblizhenii v zadache Lemba dlya beskonechnogo uprugogo sloya”, Izvestiya vuzov. Severo-Kavkazskii region. Estestvennye nauki, 2003, no. 2, 10–22

[18] Kossovich L. Yu., Kushekkaliev A. N., “Raschlenenie nestatsionarnogo NDS v zadache Lemba dlya beskonechnogo sloya na sostavlyayuschie s raznymi pokazatelyami izmenyaemosti”, Tr. III Vserossiiskoi konferentsii po teorii uprugosti s mezhdunarodnym uchastiem, Rostov n/D, 2003, 232–234

[19] Kovalev V. A., Taranov O. V., “Raschlenenie nestatsionarnogo NDS tsilindricheskikh obolochek pri udarnykh tortsevykh vozdeistviyakh normalnogo tipa”, Smeshannye zadachi mekhaniki deformirovannogo tela, Materialy V Ros. konf. s mezhdunarodnym uchastiem, Izd-vo Sarat. un-ta, Saratov, 2005, 191–193

[20] Kirillova I. V., “Oblasti soglasovaniya pogransloya i korotkovolnovogo vysokochastotnogo priblizheniya”, Matematicheskoe modelirovanie i upravlenie v tekhnicheskikh sistemakh, Sb. trudov, SGAU, Saratov, 1998, 3–11 | MR

[21] Novozhilov V. V., Slepyan L. I., “O printsipe Sen-Venana v dinamike sterzhnei”, PMM, 29:2 (1965), 261–281 | MR | Zbl

[22] Slepyan L. I., Nestatsionarnye uprugie volny, Sudostroenie, L., 1972, 374 pp.

[23] Gusein-Zade M. I., “Ob usloviyakh suschestvovaniya zatukhayuschikh reshenii ploskoi zadachi teorii uprugosti dlya polupolosy”, Prikl. mat. i mekh., 29:2 (1965), 393–399 | MR | Zbl

[24] Gusein-Zade M. I., “O neobkhodimykh i dostatochnykh usloviyakh suschestvovaniya zatukhayuschikh reshenii ploskoi zadachi teorii uprugosti dlya polupolosy”, Prikl. mat. i mekh., 29:4 (1965), 752–760 | MR | Zbl

[25] Kovalev V. A., Taranov O. V., “Analiz tochnogo i priblizhennogo resheniya dlya pogransloya v okrestnosti uslovnogo fronta poverkhnostnoi volny Releya v uprugoi polupolose”, Vestnik SamGU. Estestvennonauchnaya ser., 6(56) (2007), 57–60