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Stress State of a Hollow Cylindrical Body with a System of Cracks Under Oscillations of Longitudinal Shear

  • Olga KyrylovaEmail author
  • Vsevolod Popov
Conference paper
Part of the Structural Integrity book series (STIN, volume 8)

Abstract

The problem of determining the stress state near the through-cracks in an infinite hollow cylinder of arbitrary cross-section under oscillations of longitudinal shear is solved. The method allows satisfying the conditions separately on the surface of cracks and on the borders of the cylinder. The solution scheme is based on the use of discontinuous solutions of equations of motion of elastic medium with jumps of displacements on the surface of defects. For this displacement are represented by the sums of discontinuous solutions, built for each defect, and an unknown characteristic function. Designed presentation enables fulfilling separately the boundary conditions on the surface of defects that leads to the set of systems of integral equations, which don’t depend from the shape of the boundaries of the body. Then the unknown coefficients of represented characteristic function are determined from the conditions on the boundaries of the body by the collocation method.

Keywords

Hollow cylinder of arbitrary cross section Harmonic oscillations Crack Stress intensity factors The system of cracks 

References

  1. 1.
    Popov, V.G.: Comparative Analysis of Diffraction Fields During the Passage of Elastic Waves Through Defects of Different Nature [in Russian]. Izv. RAN, Mekh. Tverdogo Tela. 4, 99–109 (1995)Google Scholar
  2. 2.
    Ang, D.D., Knopoff, L.: Diffraction of scalar elastic waves by a finite strip. Proc. Math. Sci. USA 51(4), 593–598 (1964)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Mykhas’kiv, V., Zhbadynskyi, I., Zhang, Ch.: Elastodynamic analysis of multiple crack problem in 3-D bi-materials by a BEM. Int. J. Num. Meth. Biomed. Eng. 26(12) 1934–1946, (2010)Google Scholar
  4. 4.
    Popov, V.G.: Interaction of plane elastic waves with systems of radial defects [in Russian]. Izv. RAN Mehanika tverdogo tela. 4, 118–129 (1999)Google Scholar
  5. 5.
    Chirino, F., Domingues, J.: Dynamic analysis of cracks using boundary element method. Eng. Fract. Mech. 34(5–6), 1051–1061 (1989)CrossRefGoogle Scholar
  6. 6.
    Bobylev, A.A., Dobrova, Y.A.: Application of the Boundary Element Method to the Calculation of Forced Vibrations of Finite-Sized Elastic Bodies with Cracks[in Russian]. Visnyk of Kharkov National University 590(1), 49–54 (2003)Google Scholar
  7. 7.
    Zhang, Ch.: A 2D hypersingular time-domain traction BEM for transient elastodynamic crack analysis. Wave Motion 35(1), 17–40 (2002)CrossRefGoogle Scholar
  8. 8.
    Popov, V.G.: Comparison of displacement fields and stresses in the diffraction of elastic shear waves at various defects: crack and thin rigid inclusion [in Russian]. Dyn. Syst. 12, 35–41 (1993)Google Scholar
  9. 9.
    Vekua, N.P.: Systems of Singular Integral Equations and Some Boundary-Value Problems [in Russian]. Nauka, Moscow (1970)Google Scholar
  10. 10.
    Belotserkovskiy, S.M., Lifanov, I. K.: Numerical Methods in Singular Integral Equations [in Russian]. Moskow, Nauka (1985)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.National University “Odesa Maritime Academy”OdesaUkraine

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