Mechanics of Composite Materials

, Volume 54, Issue 6, pp 719–732 | Cite as

A Class of 3D Problems for Layered Plates

  • L. A. AghalovyanEmail author
  • V. V. Tagvoryan

A class of 3D problems of elasticity theory for a layered package of orthotropic plates, which, in particular, models the behavior of the lithospheric plates of Earth during the preearthquake stage, is considered. The case of separation between some layers of the package is explored. Using the asymptotic method for solving singularly perturbed differential equations, a solution of the internal 3D problem is found. The cases where the solution becomes mathematically exact are indicated, and exact solutions for a four-layer package of plates are given.


layered plate incomplete contact separation nonclassical problem asymptotic solution 


  1. 1.
    T. Rikitake, Earthquake Prediction, Elsevier, Amsterdam (1976).Google Scholar
  2. 2.
    K. Kasahara, Earthquake Mechanics, Cambridge Univers. Press, Cambridge (1981).Google Scholar
  3. 3.
    H. Le Pichon, J. Franchetean, and J. Bonnin, Plate Tectonics, Elsevier (1973).Google Scholar
  4. 4.
    J. N. Brun, “Physics of strong movements caused by earthquakes,” in: Seismic Risk and Engineering Solutions [Russian translation], Nedra, Moscow (1981).Google Scholar
  5. 5.
    Ts. Lomnits and S. K. Singh, “Earthquakes and Their Forecast,” in: Seismic Risk and Engineering Solutions [Russian translation], Nedra, Moscow (1981).Google Scholar
  6. 6.
    B. Gutenberg and C. F. Richter, “Earthquake magnitude, intensity, energy and acceleration,” Bulletin of the Seismological Soc. Am., 46, No. 2, 105−145 (1956).Google Scholar
  7. 7.
    H. F. Reid, “The elastic rebound theory of earthquakes,” Univ. of California Publications. Bulletin of the department of geological sci., 6 (1911).Google Scholar
  8. 8.
    V. A. Babeshko, O. M. Babeshko, and O. V. Evdokimova, “On the stress monitoring problem for parallel gallery regions,” Izv. RAN, Mekh. Tverd. Tela, No. 5, 6-14 (2016).Google Scholar
  9. 9.
    V. A. Babeshko, O. M. Babeshko, O. V. Evdokimova, et al., “Monitoring of parallel galleries in the region of horizontal motion of lithospheric plates,” Izv. RAN, Mekh. Tverd. Tela, No. 4, 42-49 (2017).Google Scholar
  10. 10.
    D. L. Wells and K. I. Coppersmith, “New empirical relationship among magnitude, rupture length, rupture width, rupture area, and surface displacement,” Bulletin of the Seismological Soc. Am., 84, No. 4, 974-1002 (1994).Google Scholar
  11. 11.
    F. Pollitz, “Coseismic deformation from earthquake faulting on a layered spherical earth,” Geophysical J. Int., 125, No. 1, 1-14 (1996).CrossRefGoogle Scholar
  12. 12.
    I. A. Sdel’nikova and G. M. Steblov, “Stress-strain state of the Japan subduction zone according to satellite geodesy data,” Modern Methods for Processing and Interpreting Seismological Data, Proc. XII Int. Seismological School, Obninsk, FITS EGS RAN, 315-319 (2017).Google Scholar
  13. 13.
    L. A. Aghalovyan, “On one class of three-dimensional problems of elasticity theory for plates,” Proc. A. Razmadze Mathematical Institute of Georgia, 155, 3-10 (2011).Google Scholar
  14. 14.
    L. A. Aghalovyan, R. S. Gevorkyan, and L. G. Gulgazaryan, “On the definition of stress-strain states of Earth’s lithospheric plates based on GPS data,” Dokl. NAN RA, 112, No. 3, 264-272 (2012).Google Scholar
  15. 15.
    L. A. Aghalovyan, Asymptotic Theory of Anisotropic Plates and Shells, World Scientific, Singapore−London (2015).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Mechanics of the National Academy of SciencesErevanRepublic of Armenia

Personalised recommendations