 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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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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|
| Received |
07 August 2006 |
| Link to Fulltext |
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