| | 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: | | 12804 |
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
In English (Mech. Solids): | | 4760 |
|
<< Previous article | Volume 40, Issue 1 / 2005 | Next article >> |
A. V. Andreev, "Direct numerical method for solving singular integral equations of the first kind with generalized kernels," Mech. Solids. 40 (1), 104-119 (2005) |
Year |
2005 |
Volume |
40 |
Number |
1 |
Pages |
104-119 |
Title |
Direct numerical method for solving singular integral equations of the first kind with generalized kernels |
Author(s) |
A. V. Andreev (Moscow) |
Abstract |
The present paper is devoted to the development of methods for direct numerical
solution of a singular integral equation (SIE) of the first kind with the
Cauchy-type kernel. The case is considered in which, at the ends of the
integration interval, the solution of the SIE has power-law asymptotics,
for example, arbitrary (integrable) real-valued singularities. |
References |
1. | F. E. Erdogan, G. D. Gupta, and T. S. Cook,"The numerical
solutions of singular integral equations," in Mechanics of Fracture.
Volume 1. Methods of Analysis and Solutions of Crack Problems,
pp. 368-425, Noordhoff, Leyden, 1973. |
2. | N. I. Muskhelishvili, Singular Integral Equations [in Russian],
Nauka, Moscow, 1968. |
3. | A. I. Kalandiya, Mathematical Methods of Two-dimensional Elasticity
[in Russian], Nauka, Moscow, 1973. |
4. | M. P. Savruk, Two-dimensional Elasticity Problems for Bodies with
Cracks [in Russian], Naukova Dumka, Kiev, 1981. |
5. | R. V. Dubuchava, "Integral convolution equations with
discontinuous fore-symbols, singular integral equations with fixed
singularities, and their applications to mechanical problems," in Trudy
Tbil. Mat. In-ta AN GSSR, Vol. 60, 1979. |
6. | P. S. Theocaris and N. I. Ioakimidis, "The V-notched elastic
half-plane problem," Acta Mech., Vol. 32, No. 1-3, pp. 125-140, 1979. |
7. | M. L. Williams, "Stress singularities resulting from various
boundary conditions in angular corners of plates in extension," J. Appl.
Mech., Vol. 19, No. 4, pp. 526-528, 1952. |
8. | A. I. Kalandiya, "Comments on the singularity of elastic
solutions near corners," PMM [Applied Mathematics and Mechanics], Vol. 33, No. 1,
pp. 132-135, 1969. |
9. | A. V. Andreev, R. V. Goldstein, and Yu. V. Zhitnikov, "Asymptotic
analysis of a solution in the vicinity of a kink point of an interface
crack," PMM [Applied Mathematics and Mechanics], Vol. 63, No. 5, pp. 865-870, 1999. |
10. | C. Laurita, "Condition numbers for singular inegral equations
in weighted L2 spaces," J. Comput. and Appl. Math., Vol. 116, No. 1,
pp. 23-40, 2000. |
11. | K. Chen, "Efficient iterative solution of linear systems from
discretizing singular integral equations," Electronic Trans. on Numer.
Analysis, Vol. 2, pp. 76-91, 1994. |
12. | G. Szegö, Orthogonal Polynomials [Russian translation],
Fizmatgiz, Moscow, 1962. |
13. | W. Gautschi, "Gauss-Radau formulae for Jacobi and Lguerre
weight functions," Mathematics and Computers in Simulation, Vol. 54,
No. 4-5, pp. 403-412, 2000. |
14. | M. Kzaz, "Convergence acceleration of Jacobi-Gauss quadrature
formulae for analytic functions with poles," J. Comput. and Appl. Math.,
Vol. 57, No. 1-2, pp. 181-192, 1995. |
15. | P. Kim and S. Lee, "A piecewise linear quadrature of Cauchy
singular integrals," J. Comput. and Appl. Math., Vol. 95, No. 1-2,
pp. 101-105, 1998. |
16. | P. Kim and U. J. Choi, "A quadrature rule for weighted Cauchy
integrals," J. Comput. and Appl. Math., Vol. 126, No. 1-2, pp. 221-232,
2000. |
17. | P. S. Theocaris and N. I. Ioakimidis, "Stress intensity factors
at the tips of an antiplane shear crack terminating at a bimaterial
interface," Intern. J. Fracture., Vol. 13, No. 4, pp. 549-552, 1977. |
18. | A. V. Andreev, A Method for the Numerical Solution of a Singular
Integral Equation of the First Kind with a Generalized Cauchy-type Kernel.
Preprint No. 743 [in Russian], In-t Problem Mekhaniki RAN, Moscow, 2004. |
19. | M. M. Chawla and T. R. Ramacrihnan, "Modified Gauss-Jacobi
quadrature formulas for the numerical evaluation of Cauchy type singular
integrals," BIT, Vol. 14, No. 1, pp. 14-21, 1974. |
20. | A. V. Andreev, "Limiting equilibrium analysis of curvilinear
boundary cracks in an elastic half-plane, with the stress asymptotic
behavior being taken into account," Izv. AN. MTT [Mechanics of Solids],
No. 6, pp. 82-96, 2003. |
21. | A. F. Nikiforov and V. B. Uvarov, Special Functions of
Mathematical Physics [in Russian], Nauka, Moscow, 1984. |
22. | A. H. Stroud and D. Secrest, Gaussian Quadrature Formulas,
Prentice-Hall, New Jersey, 1966. |
23. | C. J. Lanczos, "A precision approximation of the gamma
function," SIAM J. Numer. Anal. Ser. B., Vol. 1, pp. 86-96, 1964. |
24. | Y. L. Luke, The Special Functions and their Approximations.
Volume 1, Acad. Press, New York, 1969. |
25. | I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums,
Series, and Products [in Russian], Nauka, Moscow, 1971. |
26. | D. Eliott, "Uniform asymptotic expansions of the Jacobi
polynomials and an associated function," Math. Comput., Vol. 25, No. 114,
pp. 309-315, 1971. |
27. | W. Gautchi, "Gauss quadrature approximations to hypergeometric
and confluent hypergeometric functions," J. Comput. and Appl. Math.,
Vol. 139, No. 1, pp. 173-187, 2002. |
28. | L. V. Kantorovich and V. I. Krylov, Approximate Methods of
Higher Analysis [in Russian], Fizmatgiz, Moscow, Lenigrad, 1962. |
29. | H. F. Bueckner, "On a class of singular integral equations," J.
Math. Analys. and Appl., Vol. 14, No. 3, pp. 392-426, 1996. |
30. | N. S. Bakhvalov, N. P. Zhidkov, and G. M. Kobel'kov, Numerical
Methods [in Russian], Nauka, Moscow, 1987. |
31. | V. F. Kolmogortsev, G. Ya. Popov, and M. V. Radiollo, "Internal
contact between an elastic hollow disk and an infinite plate with a
circular cut and a radial crack," Izv. AN SSSR. MTT [Mechanics of Solids],
No. 6, pp. 71-82, 1978. |
32. | A. V. Andreev, R. V. Goldstein, and Yu. V. Zhitnikov,
"Calculation of the limit equilibrium of internal and boundary cracks with
interacting surfaces in an elastic half-plane," Izv. AN. MTT [Mechanics of
Solids], No. 4, pp. 96-112, 2002. |
|
Received |
09 December 2003 |
<< Previous article | Volume 40, Issue 1 / 2005 | Next article >> |
|
If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|