Mechanics of Composite Materials

, Volume 55, Issue 1, pp 13–28 | Cite as

Discontinuous Solutions of Axisymmetric Elasticity Theory for a Piecewise Homogeneous Layered Space with Periodical Interfacial Disk-Shape Defects

  • V. N. HakobyanEmail author
  • L. V. Hakobyan
  • L. L. Dashtoyan

By the method of Hankel integral transformation, discontinuous solutions of equations of the axisymmetric elasticity theory are constructed for a piecewise homogeneous uniform layered space obtained by alternately joining two heterogeneous layers of equal thickness and whose junction contains a periodic system of parallel circular disk-shaped defects. On the basis of the solutions found, as examples, the governing systems of integral equations with Weber–Sonin kernels are presented for two cases: with defects in the form of absolutely rigid disk-shape inclusions and circular cracks. Using rotation operators, the governing systems of equations, in both cases, are reduced to a singular integral equation of the second kind, which is solved by the method of mechanical quadratures. Simple formulas for determining the rigid-body displacement of inclusions and crack opening are obtained.


periodical mixed boundary-value problems disk-shape crack circular rigid inclusion 



This research was performed at a financial support by the GKN MON of Armenia Republic and FSI of Russian Federation within the framework of joint scientific projects SCS 18RF061 and RFBR 18-51-05012, respectively.


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Authors and Affiliations

  • V. N. Hakobyan
    • 1
    Email author
  • L. V. Hakobyan
    • 1
  • L. L. Dashtoyan
    • 1
  1. 1.Institute of Mechanics of the National Academy of Sciences of Republic of ArmeniaYerevanArmenia

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