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A Study of Elastic-Plastic Boundary Propagation in a Tube of Elastic-Perfectly Plastic Material Under Dynamic Loadings of Different Types

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Abstract

The dynamics of distribution of the border between areas of elasticity and plasticity for a hollow thick-walled cylinder under the influence of the internal pressure applied instantly is investigated in this work. Proof of the accuracy of the obtained numerical solution is provided. A more general regime loading a tube is examined.

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References

  1. I. O. Arushanyan, A. A. Kornev, and E. V. Chizhonkov, Tasks and Exercises on Numerical Methods [in Russian], Izd. Mekh.-Mat. Fak. MGU, Moscow (2006).

    Google Scholar 

  2. N. S. Bahvalov, N. P. Zhidkov, G. M. Kobelkov, Numerical Methods [in Russian], Binom, Moscow (2008).

    Google Scholar 

  3. R. P. Fedorenko, Introduction to Computing Physics, MFTI, Moscow (1994).

    Google Scholar 

  4. E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations. I: Nonstiff Problems, Springer, Berlin (1987).

    Book  MATH  Google Scholar 

  5. B. Hopkinson, “The effects of momentary stress in metals,” Proc. Roy. Soc. London, 74, 498–506 (1904).

    Article  Google Scholar 

  6. B. Hopkinson, “A method of measuring the pressure produced in the detonation of high explosives or by the impact of bullets,” Trans. Roy. Philos. Soc. Ser. A, 213, 437–456 (1914).

    Article  Google Scholar 

  7. L. M. Kachanov, Fundamentals of the Theory of Plasticity [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  8. E. V. Lomakin, “Influence of delay of fluidity on distribution of plastic area in a thick-walled tube under the influence of dynamic loading,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 168–171 (1968).

    Google Scholar 

  9. Yu. N. Rabotnov, Strength of Materials [in Russian], Fizmatlit, Moscow (1962).

    Google Scholar 

  10. Yu. N. Rabotnov, Mechanics of a Deformable Solid Body [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  11. L. I. Sedov, Mechanics of Solids [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  12. V. V. Sokolovsky, “Elastic-plastic tension of the tube which is under the influence of uniform internal and external loading,” Prikl. Mat. Mekh., 7, 74–80 (1943).

    Google Scholar 

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    P. V. Tishin

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  1. P. V. Tishin
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Correspondence to P. V. Tishin.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 21, No. 3, pp. 201–216, 2016.

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Tishin, P.V. A Study of Elastic-Plastic Boundary Propagation in a Tube of Elastic-Perfectly Plastic Material Under Dynamic Loadings of Different Types. J Math Sci 237, 473–484 (2019). https://doi.org/10.1007/s10958-019-04172-6

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  • DOI: https://doi.org/10.1007/s10958-019-04172-6

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