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On a Method for Solving Boundary Value Problems of the Dynamical Theory of Elasticity in a Quarter Plane

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Abstract—

In the paper, using the coordinate block element method, 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 for the first time and is expanded in terms of solutions of boundary value problems for the Helmholtz equation. In the earlier paper of the authors, the solution was constructed by an integro-differential method. Exact solutions of vector boundary value problems using scalar ones in nonclassical domains make it possible to simplify the solutions of boundary value problems in media of complex rheology and to get information on some processes and phenomena in mechanics and physics that was previously overlooked when other approaches were used.

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Funding

Selected fragments of this study were carried out as a part of the implementation of the State Assignment for 2021 by the Ministry of Science and Higher of the Russian Federation, project no. FZEN-2020-0020) and of the Southern Science Center, Russian Academy of Sciences, project no. 00-20-13 (state registration number 01201354241), and were supported by the Russian Foundation for Basic Research, project nos. 19-41-230003, 19-41-230004, 19-48-230014, and 18-05-80008.

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Authors and Affiliations

  1. Southern Scientific Center, Russian Academy of Sciences, 344006, Rostov-on-Don, Russia

    V. A. Babeshko & O. V. Evdokimova

  2. Kuban State University, 350040, Krasnodar, Russia

    V. A. Babeshko & O. M. Babeshko

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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Corresponding authors

Correspondence to V. A. Babeshko, O. V. Evdokimova or O. M. Babeshko.

Additional information

Translated by I. Tselishcheva

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Babeshko, V.A., Evdokimova, O.V. & Babeshko, O.M. On a Method for Solving Boundary Value Problems of the Dynamical Theory of Elasticity in a Quarter Plane. Mech. Solids 56, 1373–1378 (2021). https://doi.org/10.3103/S0025654421070037

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