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IssuesArchive of Issues2007-1pp.50-56

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I. P. Dobrovolskii, "Problem on an inhomogeneity in a linearly elastic space or half-space," Mech. Solids. 42 (1), 50-56 (2007)
Year 2007 Volume 42 Number 1 Pages 50-56
Title Problem on an inhomogeneity in a linearly elastic space or half-space
Author(s) I. P. Dobrovolskii (Shmidt Institute of Physics of the Earth, Russian Academy of Sciences, B. Gruzinskaya 10, Moscow, 123995, Russia)
Abstract For a weakly contrasting anisotropic inhomogeneity in a linearly elastic homogeneous space or half-space, using the perturbation method, we obtain an approximate solution and estimate its accuracy. In the case of inhomogeneity of arbitrary contrast, we reduce the problem to a system of integral equations. In the general case, it is easy to compose the procedure for solving this problem approximately. In the special case of a homogeneous anisotropic ellipsoidal inhomogeneity in space, the strain state inside the inhomogeneity turns out to be homogeneous, and we thus obtain the exact solution of the problem.
References
1.  A. I. Lurie, 3D Problems of Elasticity (GITTL, Moscow, 1955) [in Russian].
2.  A. I. Lurie, The Theory of Elasticity (Nauka, Moscow, 1970) [in Russian].
3.  V. Novatskii, The Theory of Elasticity (Mir, Moscow, 1975) [in Russian].
4.  J. D. Eshelby, Continual Theory of Dislocations (Inostr. Lit-ra, Moscow, 1963) [in Russian].
5.  V. D. Kupradze, T. G. Gegelia, M. O. Basheleishvili, and T. V. Burchuladze, Three-Dimensional Problems of Mathematical Theory of Elasticity and Thermal Elasticity (Nauka, Moscow, 1976) [in Russian].
6.  L. N. Sretenskii, Theory of Newtonian Potential (OGIZ-GOSTEKhIZDAT, Moscow-Leningral, 1946) [in Russian].
7.  L. D. Landau and E. M. Lifshits, Theoretical Physics. Vol. 2: Field Theory (Nauka, Moscow, 1967) [in Russian].
8.  V. A. Lomakin, Theory of Elasticity of Inhomogeneous Bodies (Izd-vo MGU, Moscow, 1976) [in Russian].
9.  T. Mura, Micromechanics of Defects in Solids (Martinus Nijhoff, 1982).
Received 28 September 2004
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