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.
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References
T. Rikitake, Earthquake Prediction, Elsevier, Amsterdam (1976).
K. Kasahara, Earthquake Mechanics, Cambridge Univers. Press, Cambridge (1981).
H. Le Pichon, J. Franchetean, and J. Bonnin, Plate Tectonics, Elsevier (1973).
J. N. Brun, “Physics of strong movements caused by earthquakes,” in: Seismic Risk and Engineering Solutions [Russian translation], Nedra, Moscow (1981).
Ts. Lomnits and S. K. Singh, “Earthquakes and Their Forecast,” in: Seismic Risk and Engineering Solutions [Russian translation], Nedra, Moscow (1981).
B. Gutenberg and C. F. Richter, “Earthquake magnitude, intensity, energy and acceleration,” Bulletin of the Seismological Soc. Am., 46, No. 2, 105−145 (1956).
H. F. Reid, “The elastic rebound theory of earthquakes,” Univ. of California Publications. Bulletin of the department of geological sci., 6 (1911).
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).
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).
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).
F. Pollitz, “Coseismic deformation from earthquake faulting on a layered spherical earth,” Geophysical J. Int., 125, No. 1, 1-14 (1996).
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).
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).
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).
L. A. Aghalovyan, Asymptotic Theory of Anisotropic Plates and Shells, World Scientific, Singapore−London (2015).
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 54, No. 6, pp. 1045-1062, November-December, 2018.
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Aghalovyan, L.A., Tagvoryan, V.V. A Class of 3D Problems for Layered Plates. Mech Compos Mater 54, 719–732 (2019). https://doi.org/10.1007/s11029-019-9778-4
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DOI: https://doi.org/10.1007/s11029-019-9778-4