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Hermitian splines as basis functions of the finite-element method for plotting stress trajectories

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We propose a finite-element approach with the use of Hermitian splines for reducing the problem of plotting of stress trajectories for finding two potential functions that satisfy conditions of interpolation of first derivatives at nodes of a regular mesh. The efficiency of this approach is demonstrated on test problems, and features of computational relations are determined.

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References

  1. A. George and J. W.-H. Liu, Computer Solutions of Large Sparse Positive Definite Systems, Prentice-Hall, Englewood Cliffs (1981).

    Google Scholar 

  2. O. C. Zienkiewicz, The Finite-Element Method in Engineering Science, McGraw-Hill, London–New York (1975).

  3. F. Pinezhaninov, Base Functions for Finite Elements with Derivatives [in Russian], (2000), http://pinega.da.ru.

  4. P. G. Ciarlet, The Finite-Element Method for Elliptic Problems, North-Holland, Amsterdam (1978).

    MATH  Google Scholar 

  5. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, McGraw-Hill, New York (1970).

    MATH  Google Scholar 

  6. A. E. Scheidegger, Principles of Geodynamics, Springer, Berlin (1982).

    Google Scholar 

  7. A. N. Galybin, “Introduction of the stress trajectories element method for stress analysis in tectonic plates,” Geophys. Res. Abstr., Vol. 9, 08179. SRef-ID: 1607-7962/gra/EGU2007-A-08179, European Geosciences Union (2007).

  8. M. Jo, M. Taguchi, and H. Suzuki, “Automatic plotting of principal stress trajectories by direction function contouring,” Trans. Jpn. Soc. Mech. Eng. A, 68, No. 667, 385–390 (2002).

    Google Scholar 

  9. G. Petrucci and G. Restivo, “Automated stress separation along stress trajectories,” Exp. Mech., 47, No. 6, 733–743 (2007).

    Article  Google Scholar 

  10. J. G. Ramsay and R. G. Lisle, “The techniques of modern structural geology,” in: Applications of Continuum Mechanics in Structural Geology, Vol. 3, Elsevier (2000), pp. 701–1061.

  11. F. Thamm, “The role of the stress trajectories as an aid in the choice of the suitable shape of load-bearing structural element of engines and structure,” Period. Polytechn., Ser. Mech. Eng., 44, No. 1, 171–183 (2000).

    Google Scholar 

  12. J. Weertman, “Stress trajectories for mode I and mode II cracks,” Int. J. Fract., 137, No. 1, 251–259 (2006).

    Article  Google Scholar 

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Authors and Affiliations

  1. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    M. V. Marchuk & M. M. Khomyak

  2. Franko Lviv National University, Lviv, Ukraine

    M. M. Khomyak

Authors
  1. M. V. Marchuk
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  2. M. M. Khomyak
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Marchuk, M.V., Khomyak, M.M. Hermitian splines as basis functions of the finite-element method for plotting stress trajectories. J Math Sci 168, 673–687 (2010). https://doi.org/10.1007/s10958-010-0018-7

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  • DOI: https://doi.org/10.1007/s10958-010-0018-7

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