Skip to main content
SpringerLink
Log in

Numerical analysis of 3D dynamic problems of the Cosserat elasticity theory subject to boundary symmetry conditions

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

In the framework of the Cosserat continuum model, one-dimensional solutions describing plane longitudinal waves, transverse (shear) waves with particle rotation, and torsional waves are analyzed. Boundary symmetry conditions for various types of loading are found. A parallel computational algorithm is worked out for solving 3D dynamic problems of the Cosserat elasticity theory on multiprocessor computer systems. Computations of the propagation of the stress and strain waves induced by a point impulse force in an elastic medium are performed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. A. Pal’mov, /ldMain Equations of Asymmetric Elasticity Theory,” Prikl. Mat. Mekh. 28, 401–408 (1964).

    MathSciNet  Google Scholar 

  2. V. T. Koiter, /ldCouple Stresses in the Theory of Elasticity,” Proc. Kon. Nederl. Akad. Wetensch., Ser. B, 67, 17–44 (1964).

    MATH  Google Scholar 

  3. O. V. Sadovskaya and V. M. Sadovskii, Mathematical Modeling in the Problems of Mechanics of Granular Materials (Fizmatlit, Moscow, 2008) [in Russian].

    Google Scholar 

  4. V. I. Erofeev, Wave Processes in Solid Bodies with a Microstructure (Mosk. Gos. Univ., Moscow, 1999) [in Russian].

    Google Scholar 

  5. O. V. Sadovskaya and V. M. Sadovsky, /ldNumerical Analysis of Elastic Waves Propagation in Cosserat Continuum,” Proc. VIII Int. Conf. on the Mathematical and Numerical Aspects of Wave Propagation (Waves 2007), (Univ. of Reading, England, 2007), pp. 327–329.

    Google Scholar 

  6. S. K. Godunov, Equations of Mathematical Physics (Nauka, Moscow, 1979) [in Russian].

    Google Scholar 

  7. R. D. Richtmyer, Principles of Advanced Mathematical Physics (Springer, New York, 1978–1981; Mir, Moscow, 1982).

    MATH  Google Scholar 

  8. V. M. Sadovskii, Discontinuous Solutions in the Dynamics of Elastoplastic Media (Fizmatlit, Moscow, 1997) [in Russian].

    Google Scholar 

  9. G. I. Marchuk, Splitting Methods (Nauka, Moscow, 1988) [in Russian].

    Google Scholar 

  10. A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Aspects of the Numerical Solution of Hyperbolic Systems of Equations (Fizmatlit, Moscow, 2001) [in Russian].

    Google Scholar 

  11. O. V. Sadovskaya and V. M. Sadovskii, /ldA Parallel Implementation of an Algorithm for the Calculation of Elastoplastic Waves in Granular Media,” Vychisl. Met. Programmirovanie 6(2), 86–93 (2005).

    Google Scholar 

  12. O. V. Sadovskaya and V. M. Sadovskii, /ldParallel Computations in 3D Problems of the Dynamics of Granular Media,” Vestn. Krasnoyarsk Gos. Univ., No. 1, 215–221 (2006).

Download references

Author information

Authors and Affiliations

  1. Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, 660036, Russia

    O. V. Sadovskaya

Authors
  1. O. V. Sadovskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. V. Sadovskaya.

Additional information

Original Russian Text © O.V. Sadovskaya, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2009, Vol. 49, No. 2, pp. 313–322.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sadovskaya, O.V. Numerical analysis of 3D dynamic problems of the Cosserat elasticity theory subject to boundary symmetry conditions. Comput. Math. and Math. Phys. 49, 304–313 (2009). https://doi.org/10.1134/S0965542509020109

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542509020109

Keywords

Search

Navigation