Strength of Materials

, Volume 22, Issue 12, pp 1841–1847 | Cite as

Determination of deformations in zones of stress concentration using partitioning grids

  • V. I. Skripchenko
  • V. A. Khyuvenen
Scientific-Technical Section


A universal computational method of determining the strain state in zones of geometric stress risers from results obtained by the method of partitioning grids is proposed. The method is based on use of a modified quadratic element of the Lagrange family, which has intermediate nodes on the sides and inside the element that are displaced with respect to the center. The error generated in calculating extremal values of the strain components on the perimeter of a riser is investigated. It is demonstrated that it is minimal when the modified element is used. An example of the developed method is cited in determining strains in the zone of an opening in a flat plate subjected to uniaxial tension.


Stress Concentration Strain State Riser Flat Plate Develop Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    R. M. Shneiderovich, O. A. Levin, N. A. Makhutov, and M. D. Novopashin, “Methods of measuring fields of cyclic elastoplastic strains,” Zavod. Lab., No. 10, 1246–1252 (1972).Google Scholar
  2. 2.
    N. A. Novikov and K. D. Del', Experimental-Computational Methods of Investigating the Stress-Strain State from the Distortion of Partitioning Grids [in Russian], Voronezh. Politekh. Inst., Voronezh (1976), 133.Google Scholar
  3. 3.
    P. I. Polukhin, V. K. Vorontsov, A. B. Kudrin, and N. A. Chichenev, Strains and Stresses Induced during the Pressure Treatment of Metals [in Russian], Metallurgiya, Moscow (1974), 336 p.Google Scholar
  4. 4.
    A. Karimi, “Plastic flow study using microgrid technique,” Mater. Sci. Eng.,63, No. 2, 267–276 (1984).Google Scholar
  5. 5.
    G. Yagawa, S. Matsuura, and Y. Ando, “Strain measurement using point recognition picture processing,” Trans. Jap. Soc. Mech. Eng.,A49, No. 447, 1435–1443 (1983).Google Scholar
  6. 6.
    V. I. Skripchenko, Computational-experimental method of investigating the strain state of structural components in a region of stress concentration, All-Union Scientific-Technical Conference “Improving the Longevity and Reliability of Machinery and Instruments”: Theses of Papers [in Russian], Byull. Izobr., Kuibyshev (1981), pp. 349–350.Google Scholar
  7. 7.
    Yu. V. Tykvin and A. V. Lyasnikov, Experimental determination of the parameters of the stress-strain state in a zone of plastic-strain concentration, Investigations in the Field of Plasticity and the Pressure Treatment of Metals [in Russian], Byull. Izobr., Tula (1983), pp. 112–117.Google Scholar
  8. 8.
    G. Melykuti, Anwendung der finiten elements beider Verarbeitung von deformationsmessungen, Proceedings of the Third International Symposium on Deformation Measurement, Budapest (1983), pp. 433–438.Google Scholar
  9. 9.
    V. I. Skripchenko, “Use of isoparametric elements for experimental investigation of strain fields under low-cycle loading,” Probl. Prochn., No. 1, 27–31 (1986).Google Scholar
  10. 10.
    O. S. Zeinkewicz, Finite-Element Method in Engineering [Russian translation], Mir, Moscow (1975), 541 p.Google Scholar
  11. 11.
    L. Farmer and S. Conning, “Numerical smoothing of flow pattern,” Int. J. Mech. Sci.,11., No. 10, 577–597 (1979).Google Scholar
  12. 12.
    S. Mohamed and A. Shabaik, “Stress and strain distributions beyond general yield in the Charpy v-notch specimen,” J. Mech. Phys. Solids,22, No. 6, 503–518 (1977).Google Scholar
  13. 13.
    D. Segalman, D. Woyak, and R. Rowlands, “Smoothing spline-like finite-element differentiation of full-field experimental data over arbitrary geometry,” Exp. Mech.,19, No. 12, 429–437 (1979).Google Scholar
  14. 14.
    V. A. Srizhalo and V. I. Skripchenko, Low-Temperature Low-Cycle Fatigue [in Russian], Naukova Dumka, Kiev (1987), 216 p.Google Scholar
  15. 15.
    V. I. Skripchenko, “Determination of extremal deformations in zones of stress concentration in flat structural components,” Vestn. Kiev. Politekh. Inst. Mashinostr., No. 22, 57–60 (1985).Google Scholar
  16. 16.
    R. S. Barsoum, “On the use of isoparametric finite element in linear fracture mechanics,” Int. J. Numer. Meth. Eng.,10, No. 1, 25–37 (1976).Google Scholar
  17. 17.
    R. Mullen and R. Dickerson, “An isoparametric finite element with decreased sensitivity to midside node location,” Computer and Structures,17, No. 4, 611–615 (1983).Google Scholar
  18. 18.
    M. Celia and W. Gray, “Improved coordinate transformations for finite elements,” Int. J. Numer. Meth. Eng.,23, 1529–1545 (1986).Google Scholar
  19. 19.
    V. I. Skripchenko, A. L. Kaplinskii, and V. A. Khyuvenen, “Application of the method of partitioning grids to investigation of plastic deformations in a zone of stress concentration,” Probl. Prochn., No. 9, 116–119 (1983).Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • V. I. Skripchenko
    • 1
    • 2
  • V. A. Khyuvenen
    • 1
    • 2
  1. 1.Institute of Strength ProblemsAcademy of Sciences of the Ukrainian SSRKiev
  2. 2.Scientific Production Union “Vesta”USSR

Personalised recommendations