Topological method in the problem of estimating the concentration of stresses in the faults of lithospheric plates

Authors

  • Babeshko O.M. Kuban State University, Krasnodar, Российская Федерация

UDC

539.3

Abstract

A static boundary about the interaction of lithospheric plates, contacting at a fault and locating on a deformable foundation is considered. The problem is reduced to the research and solution of the system of Wiener-Hopf functional equations, the exact solution of which is obtained recently. The boundary value problem was reduced to functional equations transformed to pseudo differential equations applying the topological method. The factorization of the matrix-functions were made and the exterior forms were used to calculate the Lere residue. The solving of the Wiener and Hopf equations were performed and the asymptotic behavior of the solutions were received. As a result of researches, it is shown that unlimited stress concentration occurs under certain conditions of the interaction nature between the ends of lithospheric plates to each other and the external environment in the fault zone.

Keywords:

localization, stress-strain state, factorization, topology, boundary-value problems, differential equations, exterior forms

Acknowledgement

Отдельные фрагменты работы выполнены при поддержке грантов РФФИ (14-08-00404, \mbox{13-01-12003-м}, 13-01-96502, 13-01-96505, 13-01-96508, 13-01-96509, 15-01-01379, 15-08-01377), гранта Президента РФ НШ-1245.2014.1, Программ Президиума РАН № 3 и № 43.

Author Info

Olga M. Babeshko

д-р физ.-мат. наук, главный научный сотрудник Научно-исследовательского центра прогнозирования и предупреждения геоэкологических и техногенных катастроф Кубанского государственного университета

e-mail: babeshko49@mail.ru

References

  1. Babeshko V.A., Evdokimova O.V., Babeshko O.M. Topologicheskie metody v teorii skrytykh defektov i nekotorye anomalii [Topological methods in the theory of hidden defects and some anomalies]. Doklady Akademii nauk [Reports of Academy of Sciences], 2014, vol. 457, no. 6. S. 650-655. (In Russian)
  2. Babeshko V.A., Evdokimova O.V., Babeshko O.M. O raznotipnykh pokrytiyakh s defektami v staticheskikh zadachakh seysmologii i nanomaterialakh [About different types of coatings with defects in static problems of seismology and nanomaterials]. Doklady Akademii nauk [Reports of Academy of Sciences], 2014, vol. 459, no. 6, pp. 41-45. (In Russian)
  3. Babeshko V.A., Pavlova A.V., Ratner S.V., Vil'yams R. K resheniyu zadachi o vibratsii uprugogo tela, soderzhashchego sistemu vnutrennikh polostey treshchin [To solve the problem of vibration of an elastic body containing internal cavities cracks]. Doklady Akademii nauk [Reports of Academy of Sciences], 2002, vol. 382, no. 5, pp. 625-628. (In Russian)
  4. Babeshko V.A., Babeshko O.M. Metod faktorizatsii v kraevykh zadachakh v neogranichennykh oblastyakh [Method of factorization in boundary value problems in unbounded domains]. Doklady Akademii nauk [Reports of Academy of Sciences], 2003, vol. 392, no. 6, pp. 767-770. (In Russian)
  5. Babeshko V.A., Babeshko O.M. Formuly faktorizatsii nekotorykh meromorfnykh matrits-funktsiy [Formula some factorization of meromorphic matrix functions]. Doklady Akademii nauk [Reports of Academy of Sciences], 2004, vol. 399, no. 1, pp. 163-167. (In Russian)
  6. Babeshko V.A., Babeshko O.M. Metod faktorizatsii resheniya nekotorykh kraevykh zadach [Method of factorization of the solution of some boundary value problems]. Doklady Akademii nauk [Reports of Academy of Sciences], 2003, vol. 389, no. 2, pp. 184-188. (In Russian)
  7. Babeshko V.A., Evdokimova O.V., Babeshko O.M. Ob avtomorfizme i psevdodifferentsial'nykh uravneniyakh v metode blochnogo elementa [About the automorphism and pseudo-differential equations in method block element]. Doklady Akademii nauk [Reports of Academy of Sciences], 2011, vol. 438, no. 5, pp. 623-625. (In Russian)
  8. Babeshko V.A., Babeshko O.M., Evdokimova O.V. K probleme issledovaniya materialov s pokrytiyami [The problem of research of materials with coatings]. Doklady Akademii nauk [Reports of Academy of Sciences], 2006, vol. 410, no. 1, pp. 49-52. (In Russian)
  9. Babeshko V.A., Babeshko O.M., Evdokimova O.V. K probleme otsenki sostoyaniya materialov s pokrytiyami [The problem of assessing the condition of coated materials]. Doklady Akademii nauk [Reports of Academy of Sciences], 2006, vol. 409, no. 4, pp. 481-485. (In Russian)
  10. Babeshko V.A. Belyankova T.I., Kalinchuk V.V. Metod fiktivnogo pogloshcheniya v zadachakh teorii uprugosti dlya neodnorodnogo poluprostranstva [The method of fictitious absorption in the problems of elasticity theory for nonhomogeneous half-space]. Prikladnaya matematika i mekhanika [Applied mathematics and mechanics], 2002, vol. 66, Iss. 2, pp. 276-284.
  11. Vorovich I.I., Babeshko V.A. Dinamicheskie smeshannye zadachi teorii uprugosti dlya neklassicheskikh oblastey [Dynamic mixed problems of elasticity theory for nonclassical domains]. Moscow, Nauka Publ., 1979, 320 p. (In Russian)
  12. Babeshko V.A. O sistemakh integral'nykh uravneniy dinamicheskikh kontaktnykh zadach [About the systems of integral equations of dynamic contact problems]. Doklady Akademii nauk SSSR [Reports of the USSR Academy of Sciences], 1975, vol. 220, no. 6, pp. 1293-1296. (In Russian)
  13. Babeshko V.A. Staticheskie i dinamicheskie kontaktnye zadachi so stsepleniem [Static and dynamic contact problems with adhesion]. Prikladnaya matematika i mekhanika [Applied mathematics and mechanics], 1975, vol. 39, iss. 3, pp. 505-512. (In Russian)
  14. Babeshko V.A. Faktorizatsiya odnogo klassa matrits-funktsiy i ee prilozheniya [Factorization of a class of matrix functions and its applications]. Doklady Akademii nauk SSSR [Reports of the USSR Academy of Sciences], 1975, vol. 223, no. 5, pp. 1094-1097. (In Russian)
  15. Babeshko V.A., Evdokimova O.V., Babeshko O.M., Grishenko D.V. Localization in mechanics and nature. Proc. of the XLI Summer School-Conference "Advanced problems in mechanics", St. Petersburg, June 30 - July 5, 2014, pp. 209-216.
  16. Babeshko V.A., Evdokimova O.V., Babeshko O.M. Ob odnoy faktorizatsionnoy zadache Gil'berta-Vinera i metode blochnogo elementa [About one factorization problem of Hilbert-Wiener method and block element]. Doklady Akademii nauk [Reports of Academy of Sciences], 2014, vol. 459, no. 5, pp. 557-561. (In Russian)

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Issue

2015. No. 2

Pages

14-21

Submitted

2015-05-31

Published

2015-06-25

How to Cite

Babeshko O.M. Topological method in the problem of estimating the concentration of stresses in the faults of lithospheric plates. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2015, no. 2, pp. 14-21. (In Russian)

Copyright (c) 2015 Babeshko O.M.

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