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Translated from Mekhanika Kompozitnykh Materialov, Vol. 55, No. 1, pp. 19-42, January-February, 2019.
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.
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F. Erdogan, “Stress distribution in bonded dissimilar materials containing circular or ring-shaped cavities,” Trans ASME. Ser. E. J. Appl. Mech., 32, No. 4, 829-836 (1964). CrossRef
V. I. Mossakovskii and M. T. Rybka, “Generalization of the Griffith-Sneddon criterion for the case of a nonhomogeneous body,” J. Appl. Math. and Mech., 28, No. 6, 1061-1069 (1964). CrossRef
J. R. Willis, “The penny-shaped crack on an interface,” Quart J. Mech. and Appl. Math., 25, No. 3, 367-385 (1972). CrossRef
G. Ya. Popov, “About concentration of elastic stresses near thin delaminated inclusion,” Modern Problems of Mechanics and Aviation, 156-162 (1980).
V. N. Hakobyan and L. L. Dashtoyan, “An axisymmetric problem for a compound space weakened by a semi-infinite ring-shaped crack,” Izv. NAN RA, Mechanics, 59, No. 1, 3-10 (2006).
V. N. Hakobyan, “Stresses near an absolutely rigid penny-shaped inclusion in a piecewise homogeneous space,” Proc. of Int. Conf. “Topical Problems of the Mechanics of Continuous Media,” devoted to the 95th anniversary of birth of N. Kh. Arutyunyan, Yerevan, 45-51 (2007).
V. N. Hakobyan, S. E. Mirzoyan, and L. L. Dashtoyan, “Axisymmetric mixed problem for a compound space with a penny-shaped crack,” Bulletin of MGTU named by N. E. Bauman. Series Natural Sci., No. 3, 31-46 (2015).
V. N. Hakobyan, Mixed Boundary-Value Problems on the Interaction of Continuous Deformable Bodies with Stress Concentrators of Various Types [in Russian], Izd. Gitutyun NAN RA, Yerevan (2014).
S. M. Mkhitaryan, L. A. Shekyan, S. V. Verlinski, D. Aidun, and P. Marzocca, “Stationary theory of heat-conductivity for an axi-symmetrical piecehomogeneous space with circular inclusion,” J. Thermal Stresses, 35, No. 5, 424-447 (2012). CrossRef
G. Ya. Popov, Selected Works [in Russian], Vol. 1, Izd. Tipogr. “VBV” (2007).
G. Ya. Popov, Selected Works [in Russian], Vol. 2, Izd. “VBV” (2007).
V. N. Hakobyan, “Axisymmetric stress state of piecewise-homogeneous layered space with parallel penny-shaped cracks,” Proc. of XVIII Int. Conf. “Modern Problems of Mechanics of Continuous Media,” Rostov-on-Don, Vol. 1, 35-39 (2016).
B. Korenev, H. J. Glaeske, E. Moiseev, and M. Saigo, Bessel Functions and Their Applications, CRC Press, London, (2002).
F. D. Gakhov, Boundary-Value Problems [in Russian], Nauka, Moscow (1977).
A. A. Amirjanyan and A. V. Sahakyan, “Mechanical quadrature method as applied to singular integral equations with logarithmic singularity on the right-hand side,” Comput. Math. and Math. Phys., 57, No. 8, 1285-1293 (2017). CrossRef
I. S. Gradshtein, and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Fizmatgiz, Moscow (1962).
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marychev, Integrals and Series [in Russian], Nauka, Moscow (1981).
M. K. Kassir and A. M. Bregman, “The stress-intensity factor for a penny-shaped crack between two dissimilar materials,” Trans ASME. Ser. E. J. Appl. Mech., 39, No. 1, 308-310 (1972). CrossRef
- Discontinuous Solutions of Axisymmetric Elasticity Theory for a Piecewise Homogeneous Layered Space with Periodical Interfacial Disk-Shape Defects
V. N. Hakobyan
L. V. Hakobyan
L. L. Dashtoyan
- Springer US
in-adhesives, MKVS, Hellmich GmbH/© Hellmich GmbH, Zühlke/© Zühlke