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Numerical modeling and analysis of the stress-strain state in an anisotropic rock mass by the method of graphs

  • Geomechanics
  • Published:
Journal of Mining Science Aims and scope

Abstract

An anisotropic elastic medium is discrete-modeled in the form of an oriented graph, based on the energy conservation law in a continuous element and its discrete model. The proposed method is applied to calculate stress state of a host rock mass surrounding mine workings.

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References

  1. Kuzovkov, E.G., The Graph Model of an Elastic Medium in Cartesian Coordinates, Probl. Prochn., 1993, no. 12.

  2. Kuzovkov, E.G., Axisymmetric Graph Model of an Elastic Solid, Probl. Prochn., 1996, no. 6.

  3. Tyrymov, A.A., The Graph Model of an Elastic Medium in Polar Coordinates, Izv. vuzov. Mashinostroenie, 1999, no. 1.

  4. Trent, H., Isomorphism between Oriented Linear Graphs and Lumped Physical Systems, J. Acoustical Society of America, 1955, vol. 27, no. 3.

  5. Lekhnitsky, S.G., Teoriya uprugosti anizotropnogo tela (Theory of the Anisotropic Body Elasticity). Moscow: Nauka, 1977.

    Google Scholar 

  6. Erzhanov, Zh.S., The Model of a Rock Mass with Double-Periodic System of Physical Slots, Mekhanika deformiruemykh tel i konstruktsii (Mechanics of Deformable Bodies and Structures), Moscow: Mashinostroenie, 1975.

    Google Scholar 

  7. Nemirovskii, Yu.V. and Tyrymov, A.A., The Stressed State in an Undisturbed Rock Mass with Schistosity and Curvature of the Beds, Soviet Mining Science, 1977, vol. 13, no. 2.

  8. Chanyshev, A.I. and Efimenko, L.L., Mathematical Models of Block Media in Problems of Geomechanics. Part I: Deformation of Stratified Medium, Journal of Mining Science, 2003, vol. 39, no. 3, pp. 271–280.

    Article  Google Scholar 

  9. Evstigneev, V.A. and Kas’yanov, V.N., Tolkovyi slovar’ po teorii grafov v informatike i programmirovanii (Dictionary of the Graph Theory in Informatics and Programming), Novosibirsk: Nauka, 1999.

    Google Scholar 

  10. Svami, M. and Tkhulasiraman, K., Grafy, seti i algoritmy (Graphs, Nets and Algorithms), Moscow: Mir, 1984.

    Google Scholar 

  11. Zykov, A.A., Osnovy teorii grafov (Fundamentals of the Graph Theory), Moscow: Nauka, 1987.

    Google Scholar 

  12. Sigorskii, V.P., Matematicheskii apparat inzhenera (Engineer’s Mathematical Apparatus), Kiev: Tekhnika, 1975.

    Google Scholar 

  13. Gallagher, R., Finite Element Analysis: Fundamentals, Prentice-Hall, 1974.

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Authors and Affiliations

  1. Volgograd State Technical University, pr. Lenina 28, Volgograd, 400131, Russia

    A. A. Tyrymov

Authors
  1. A. A. Tyrymov
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Additional information

Original Russian Text © A.A. Tyrymov, 2012, published in Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, 2012, No. 5, pp. 52–66.

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Tyrymov, A.A. Numerical modeling and analysis of the stress-strain state in an anisotropic rock mass by the method of graphs. J Min Sci 48, 812–824 (2012). https://doi.org/10.1134/S1062739148050061

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  • DOI: https://doi.org/10.1134/S1062739148050061

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