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The Block-Element Method in Expansion of the Solutions of Complex Boundary-Value Problems in Mechanics

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Abstract

An exact solution in the first quadrant of a plane boundary-value problem of the second kind for the dynamic Lamé elasticity equations is constructed, probably for the first time, and is expanded in terms of solutions of boundary-value problems for the Helmholtz equation. These solutions are presented in the form of packed block elements.

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REFERENCES

  1. V. A. Babeshko, O. V. Evdokimova, and O. M. Babeshko, Ecol. Bull. Res. Centers Black Sea Econ. Cooper. 2, 37 (2016). https://doi.org/10.31429/vestnik-13-1-2-37-80

    Article  Google Scholar 

  2. V. A. Babeshko, O. V. Evdokimova, and O. M. Babeshko, Acta Mech. 229, 2163 (2018).https://doi.org/10.1007/s00707-017-2092-0

  3. V. A. Babeshko, O. V. Evdokimova, and O. M. Babeshko, Acta Mech. (2018). https://doi.org/10.1007/s00707-018-2255-7

  4. V. A. Babeshko, O. V. Evdokimova, and O. M. Babeshko, Dokl. Phys. 64, 102 (2019). https://doi.org/10.1134/S1028335819030042

    Article  ADS  Google Scholar 

  5. I. M. Gelfand, Z. A. Minlos, and Z. Ya. Shapiro, Representations of the Rotation and Lorentz Groups and Their Applications (Fizmatlit, Moscow, 1958; Dover, New York, 2018).

  6. A. F. Ulitko, The Method of Eigenvector Functions in Spatial Problems of Elasticity Theory (Naukova Dumka, Kiev, 1979) [in Russian].

    Google Scholar 

  7. V. T. Grinchenko and V. V. Meleshko, Harmonic Vibrations and Waves in Elastic Bodies (Naukova Dumka, Kiev, 1981) [in Russian].

    MATH  Google Scholar 

  8. W. Nowacki, Theory of Elasticity (PWN, Warszawa, 1970) [in Polish].

    MATH  Google Scholar 

  9. W. Nowacki, Dynamic Problems of Thermoelasticity (Springer, Netherlands, 1975).

    MATH  Google Scholar 

  10. W. Nowacki, Electromagnetic Effects in Solids (PWN, Warszawa, 1983) [in Polish].

    Google Scholar 

  11. V. A. Babeshko, O. V. Evdokimova, and O. M. Babeshko, Dokl. Phys. 65, 183 (2020). https://doi.org/10.1134/S102833582007006X

    Article  Google Scholar 

  12. V. M. Babich, Mat. Sb. 65, 577 (1964).

    Google Scholar 

  13. V. M. Babich and V. S. Buldyrev, Asymptotic Methods in the Problem of Short Wave Diffraction (Nauka, Moscow, 1972) [in Russian].

    Google Scholar 

  14. I. V. Mukhina, Prikl. Mat. Mekh. 36, 667 (1972).

    Google Scholar 

  15. L. M. Brekhovskikh, Waves in Layered Media (Nauka, Moscow, 1973; Academic, New York, 1980).

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Funding

Parts of this study were carried out within the framework of the implementation of a State Assignment of the Ministry of Education and Science of the Russian Federation for 2020, project no. FZEN-2020-0020, for the Southern Science Center, Russian Academy of Sciences, project no. 00-20-13, state registration no. 01201354241, and were supported by the Russian Foundation for Basic Research, project nos. 19-41-230003, 19-41-230004, 19-48-230014, 18-08-00465, 18-01-00384, and 18-05-80008.

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Authors and Affiliations

  1. Federal Southern Research Center, Russian Academy of Sciences, 334006, Rostov-on-Don, Russia

    V. A. Babeshko & O. V. Evdokimova

  2. Kuban State University, 350040, Krasnodar, Russia

    V. A. Babeshko, O. M. Babeshko & V. S. Evdokimov

Authors
  1. V. A. Babeshko
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  2. O. V. Evdokimova
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  3. O. M. Babeshko
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  4. V. S. Evdokimov
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Correspondence to V. A. Babeshko.

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Translated by V. Bukhanov

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Babeshko, V.A., Evdokimova, O.V., Babeshko, O.M. et al. The Block-Element Method in Expansion of the Solutions of Complex Boundary-Value Problems in Mechanics. Dokl. Phys. 65, 431–435 (2020). https://doi.org/10.1134/S1028335820120022

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  • DOI: https://doi.org/10.1134/S1028335820120022

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