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IssuesArchive of Issues2009-5pp.691-704

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A.V. Andreev, "Method for Determining Power-Type Complex Singularities in Solutions of Singular Integral Equations with Generalized Kernels and Complex Conjugate Unknowns," Mech. Solids. 44 (5), 691-704 (2009)
Year 2009 Volume 44 Number 5 Pages 691-704
DOI 10.3103/S0025654409050069
Title Method for Determining Power-Type Complex Singularities in Solutions of Singular Integral Equations with Generalized Kernels and Complex Conjugate Unknowns
Author(s) A.V. Andreev (Elektrogorsk Research and Engineering Center for Nuclear Power Plant Safety (FSUE "EREC"), Svyatogo Konstanina 6, Electrogorsk, Moscow Region, 142530 Russia, andreev@erec.ru)
Abstract We develop a method for determining power-type complex singularities of solutions for a class of one-dimensional singular integral equations with generalized kernels and complex conjugate unknown functions. By analyzing the characteristic part of a singular integral equation, we reduce the problem of determining the solution singularity exponents at the ends of the integration interval to two independent transcendental equations for these exponents. We show that the distribution of admissible singularity exponents is of continuous character. We present numerical results for a two-dimensional elasticity problem whose mathematical statement leads to a singular integral equation of the class under study. We also reveal the drawbacks of one classical approach to the determination of stress field singularities.
Keywords singular integral equation, generalized kernel, solution singularity, complex function
References
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9.  A. V. Andreev, "Direct Numerical Method for Solving Singular Integral Equations of the First Kind with Generalized Kernels," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 126-146 (2005) [Mech. Solids (Engl. Transl.) 40 (1), 104-119 (2005)].
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Received 07 August 2006
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