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IssuesArchive of Issues2022-1pp.34-48

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Tsurkis I.Ya. and Kuzmin Yu.O., "Stress State of an Elastic Plane With One or More Inclusions of Arbitrary Shape: the Case of Identical Shear Moduli," Mech. Solids. 57 (1), 34-48 (2022)
Year 2022 Volume 57 Number 1 Pages 34-48
DOI 10.3103/S0025654422010046
Title Stress State of an Elastic Plane With One or More Inclusions of Arbitrary Shape: the Case of Identical Shear Moduli
Author(s) Tsurkis I.Ya. (Sñhmidt Institute of Physics of the Earth of the Russian Academy of Sciences, Moscow, 123242 Russia, tsurkis@ifz.ru)
Kuzmin Yu.O. (Sñhmidt Institute of Physics of the Earth of the Russian Academy of Sciences, Moscow, 123242 Russia, kuzmin@ifz.ru)
Abstract A two-dimensional problem of the theory of elasticity is considered for a plane with several inclusions of arbitrary shape, the shear moduli of which coincide with the shear moduli of the plane. There are no restrictions on compression modules. A uniform stress state is set at an infinitely distant point of the plane. The method of complex potentials of Kolosov - Muskhelishvili is used. A general solution in quadratures and explicit formulas for several special cases are obtained. The stress field is investigated near the singular points of the boundaries of the inclusions (these boundaries are assumed to be piecewise smooth, consisting of a finite number of Lyapunov arcs).
Keywords shear modulus, boundary value problem of elasticity theory, Cauchy-type integral, Liouville's theorem, Plemelj's theorem
Received 07 April 2021Revised 26 April 2021Accepted 13 May 2021
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