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On the fundamental problem for an infinite elastic plane bonded by different anisotropic materials with cracks. (English) Zbl 0862.73013

Summary: The first fundamental problem for an infinite elastic plane bonded by different anisotropic materials with cracks of arbitrary shape is discussed. The problem is reduced to a system of singular integral equations with undetermined constants, which is proved to be uniquely solvable when these constants are suitably and uniquely chosen.

MSC:

74B99 Elastic materials
74H99 Dynamical problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74R99 Fracture and damage
74E10 Anisotropy in solid mechanics
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References:

[1] Lu Jianke. Complex Variable Methods in Plane Elasticity. World Scientific, Singapore, 1995. · Zbl 0845.73002
[2] Lu Jianke. On Fundamental Problems for the Infinite Elastic Plane with Cracks.J. Wuhan Univ., 1963, 8(2): 37–49.
[3] Zheng Ke. On the Fundamental Problems in an Infinite Anisotropic Elastic Plane with Doubly-periodic Cracks.Communication on Applied Mathematics and Computation, 1993, 17(1): 14–20.
[4] Muskhelishvili N.I. Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Groningen, 1963. · Zbl 0124.17404
[5] Muskhelishvili N.I. Singular Integral Equations, 3rd. ed. Nauka, Mescow, 1968. · Zbl 0174.16202
[6] Vekua N.P. Systems of Singular Integral Equations and Some Boundary Value Problems. Noordhoff, Groningen, 1967. · Zbl 0166.09802
[7] Lekhnitskii, S.C. Anisotropic Plates. Gordon and Breach Science Publishers, New York, 1968.
[8] Litvinchuk G.S. Singular Integral Equations and Boundary Problems with Shifts. Nauka, Moscow, 1980.
[9] Lu Jianke. Boundary Value Problems for Analytic Functions. World Scientific, Singapore, 1993. · Zbl 0780.73012
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