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NUMERICAL SOLUTION OF THE PROBLEM OF DEFORMATION OF ELASTIC SOLIDS UNDER PULSED LOADING

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Abstract

Three methods of approximation of lower non-differential terms in equations of dynamic problems of mechanics of deformable solids are studied with the use of explicit algorithms of the numerical solution based on several local approximations of each of the sought functions by linear polynomials. Additional equations based on the energy conservation law are formulated in the course of algorithm construction. The properties (dissipativity, monotonicity, and stability) of the proposed schemes are studied. Results of the numerical solution of the problem of deformation of an elastic plate with constant shear strains over the plate thickness (Timoshenko model) are presented. Results of the numerical solution of the problem of deformation of an elastic disk under pulsed loading are compared with the analytical solution of this problem.

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REFERENCES

  1. S. K. Godunov, “Difference Method of the Numerical Calculation of Discontinuous Solutions of Hydrodynamic Equations," Mat. Sb.47 (3), 271–306 (1959).

  2. S. K. Godunov, A. V. Zabrodin, N. Ya. Ivanov, et al.,Numerical Solution of Multidimensional Problems of Gas Dynamics (Nauka, Moscow, 1976) [in Russian].

  3. V. P. Kolgan, “Application of Smoothing Operators in High-Order Difference Schemes," Zh. Vych. Mat. Mat. Fiz. 18(5), 1340–1345 (1978).

  4. B. van Leer, “Towards the Ultimate Conservative Difference Scheme. 4. A New Approach to Numerical Convection," J. Comput. Phis.23 (3), 276–299 (1977).

  5. G. V. Ivanov, “Design of Schemes for Solving a Plane Dynamic Problem of the Elasticity Theory Based on Approximation by Linear Polynomials," in Dynamics of Continuous Media(Collected Scientific Papers), No. 49 (Inst. Hydrodynamics, Sib. Branch, Acad. of Sci. of the USSR, Novosibirsk, 1981), pp. 27–44.

  6. I. O. Bogulskii, “Design of a Monotonic Scheme of Solving Problems for Hyperbolic Equations," Preprint No. 26 (Comput. Center, Sib. Branch, Acad. of Sci. of the USSR, Krasnoyarsk, 1982).

  7. I. O. Bogulskii, “High-Accuracy Algorithms of Solving Multidimensional Problems of Dynamics of Solids," inMathematical Models and Numerical Methods of Mechanics of Continuous Media, Abstr. of Int. Conf., Novosibirsk, May 27–June 2, 1996, pp. 158–159.

  8. G. V. Ivanov, Yu. M. Volchkov, I. O. Bogulskii, et al.,Numerical Solution of Dynamic Problems of Elastoplastic Deformation of Solids (Sib. Univ. Izd., Novosibirsk, 2002) [in Russian].

  9. Yu. M. Volchkov, G. V. Ivanov, and V. D. Kurguzov, “Algorithm of Splitting of a Plane Problem of Dynamics of Elastic Deformation with Allowance for Brittle Fracture," in Dynamics of Continuous Media (Collected Scientific Papers), No. 61 (Inst. Hydrodynamics, Sib. Branch, Acad. of Sci. of the USSR, Novosibirsk, 1983), pp. 36–48.

  10. S. A. Anisimov and S. V. Stepanenko, “Method of the Numerical Solution of Axisymmetric Problems of Dynamics of Multilayered Thin Shells of Revolution," in Modeling in Mechanics(Collected Scientific Papers), Vol. 4, No. 4 (Comput. Center–Inst. of Theor. Appl. Mech., Sib. Branch, Acad. of Sci. of the USSR, Novosibirsk, 1990), pp. 59–64.

  11. S. A. Anisimov and I. O. Bogulskii, “Algorithm of Independent Approximation of Non-Differential Terms of the Numerical Solution of Boundary-Value Problems for Systems of Hyperbolic Equations," inDynamics of Continuous Media (Collected Scientific Papers), No. 109 (Inst. Hydrodynamics, Sib. Branch, Acad. of Sci. of the USSR, Novosibirsk, 1994), pp. 34–48.

  12. V. L. Ivanov, “Method of Approximation of Systems of Hyperbolic Equations Containing Large Parameters in Non-Differential Terms," Zh. Vych. Mat. Mat. Fiz. 27 (9), 1388–1394 (1987).

  13. N. N. Kalitkin, Numerical Methods (Nauka, Moscow, 1978) [in Russian].

  14. I. O. Bogulskii, “Asymptotic Behavior of Cylindrical Shock Waves near the Axis of Symmetry," Preprint No. 2 (Computational Center, Sib. Branch, Acad. of Sci. of the USSR, Krasnoyarsk, 1988), pp. 16–20.

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Authors and Affiliations

  1. Siberian Federal University, 660041, Krasnoyarsk, Russia

    I. O. Bogulskii

  2. Krasnoyarsk State Agrarian University, 660049, Krasnoyarsk, Russia

    I. O. Bogulskii

  3. Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Yu. M. Volchkov

  4. Novosibirsk State University, 630090, Novosibirsk, Russia

    Yu. M. Volchkov

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  1. I. O. Bogulskii
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  2. Yu. M. Volchkov
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Correspondence to Yu. M. Volchkov.

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Bogulskii, I.O., Volchkov, Y.M. NUMERICAL SOLUTION OF THE PROBLEM OF DEFORMATION OF ELASTIC SOLIDS UNDER PULSED LOADING. J Appl Mech Tech Phy 61, 611–622 (2020). https://doi.org/10.1134/S002189442004015X

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  • DOI: https://doi.org/10.1134/S002189442004015X

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