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New Method for the Solution of Dynamic Problems of the Theory of Elasticity and Fracture Mechanics

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Materials Science Aims and scope

Abstract

We propose a new approach to the solution of dynamic problems of the theory of elasticity and fracture mechanics based on the application of the finite-difference method only with respect to time. In this case, the equations of motion are split into homogeneous and inhomogeneous systems of differential equations for the determination of displacements at time nodes. For trivial initial conditions, only the homogeneous system of differential equations is preserved (of the same type as in the dynamic problem in Laplace transforms). Its efficient solution can be obtained by the methods of boundary integral equations or boundary elements.

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REFERENCES

  1. Y. M. Chen, “Numerical computation of dynamic stress intensity factors by a Lagrangian finite-difference method (the hemp code),” Eng. Fract. Mech., 7, No. 4, 653–660 (1975)

    Google Scholar 

  2. Y. M. Chen and M. L. Wilkins, “Stress analysis of crack problems with a three-dimensional, time dependent computer program,” Int. J. Fract., 12, No. 4, 607–617 (1976).

    Google Scholar 

  3. Y. M. Chen and M. L. Wilkins, “Numerical analysis of dynamic crack problems,” in: G. C. Sih (editor), Mechanics of Fracture, Vol. 4, Elastodynamic Crack Problems, Noordhoff, Leyden (1977), pp. 295–345.

    Google Scholar 

  4. V. B. Poruchikov, Methods of the Dynamic Theory of Elasticity [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  5. J. Balas, J. Sladek, and V. Sladek, Stress Analysis by Boundary Element Method, Elsevier, Amsterdam (1989).

    Google Scholar 

  6. M. P. Savruk, Two-Dimensional Problems of Elasticity for Bodies with Cracks [in Russian], Naukova Dumka, Kiev (1981).

    Google Scholar 

  7. A. E. Andreikiv, Three-Dimensional Problems of the Theory of Cracks [in Russian], Naukova Dumka, Kiev (1982).

    Google Scholar 

  8. V. V. Panasyuk, Mechanics of Quasibrittle Fracture of Materials [in Russian], Naukova Dumka, Kiev (1991).

    Google Scholar 

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Authors and Affiliations

  1. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, Lviv

    M. P. Savruk

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  1. M. P. Savruk
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Savruk, M.P. New Method for the Solution of Dynamic Problems of the Theory of Elasticity and Fracture Mechanics. Materials Science 39, 465–471 (2003). https://doi.org/10.1023/B:MASC.0000010922.84603.8d

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  • DOI: https://doi.org/10.1023/B:MASC.0000010922.84603.8d

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