On the use of interpolative quadratures for hypersingular integrals in fracture mechanics

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 458, Issue 2027, 2002, Pages 2721-2733

  Korsunsky, Alexander M ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Cracks; Hypersingular quadratures; Stress intensity factors

Indexed keywords

EID: 57249098748     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.2002.1001     Document Type: Article

References (20)

1. Bilby, B. A. & Eshelby, J. D. 1968 Dislocations and the theory of fracture. In Fracture (ed. H. Liebowitz), vol. 1. Academic.
2. Clements, D. L. & Ang, W. T. 1988 Stress intensity factors for the circular annulus crack. Int. J. Engng Sci. 26, 325-329.
3. Eason, G., Noble, B. & Sneddon, I. N. 1955 On certain integrals of Lipschitz-Hankel type involving products of Bessel functions. Phil. Trans. R. Soc. Lond. A 247, 529-551.
4. Erdogan, F., Gupta, G. D. & Cook, T. S. 1973 Numerical solution of singular integral equations. In Methods of Analysis and Solutions of Crack Problems (ed. G. C. Sih), pp. 368-425. Groningen: Noordhoff.
5. Hadamard, J. 1923 Lectures on Cauchy's Problem in Linear Partial Differential Equations. Yale University Press.
6. Hills, D. A., Dai, D. N., Kelly, P. A. & Korsunsky, A. M. 1995 Solution of Crack Problems: The Distributed Dislocation Technique, Solid Mechanics Series. Deventer: Kluwer.
7. Kaya, A. C. & Erdogan, F. 1987 On the solution of integral equations with strongly singular kernels. Q. Appl. Math. XLV, 105-122.
8. Korsunsky, A. M. 1994 The Solution of Axisymmetric Crack Problems in Inhomogeneous Media. DPhil thesis, University of Oxford.
9. Korsunsky, A. M. 1995 Fundamental eigenstrain solutions for axisymmetric crack problems. J. Mech. Phys. Solids 43, 1221-1241.
10. Korsunsky, A. M. 1997 Gauss-Jacobi quadratures for hypersingular integrals. In Proc. 1st UK Conf. on Boundary Integral Methods, Leeds (ed. L. Elliott, D. B. Ingham & D. Lesnic), pp. 164-177.
11. Korsunsky, A. M. 1998 Gauss-Chebyshev quadrature formulae for strongly singular integrals. Q. Appl. Math. 56, 461-472.
12. Krylov, V. I. 1962 Approximate Calculation of Integrals. New York: Macmillan.
13. Monegato, G. 1987 On the weights of certain for the numerical evaluation of Cauchy principal value integrals and their derivatives. Numer. Math. 50, 273-281.
14. Monegato, G. 1994 Numerical evaluation of hypersingular integrals. J. Comput. Appl. Math. 50, 9-31.
15. Muskhelishvili, N. I. 1953a Singular Integral Equations. Groningen: Noordhoff.
16. Muskhelishvili, N. I. 1953b Some Basic Problems of the Mathematical Theory of Elasticity. Groningen: Noordhoff.
17. Schwab, C. & Wendland, W. L. 1992 On numerical cubatures of singular surface integrals in boundary element methods. Numer. Math. 62, 343-369.
18. Stroud, A. H. & Secrest, D. 1966 Gaussian Quadrature Formulas. New York: Macmillan.
19. Szegö, G. 1939 Orthogonal polynomials, vol. XXIII. Providence, RI: American Mathematical Society.
20. Yakimiw, E. 1996 Accurate computation of weights in classical Gauss-Christoffel quadrature rules. J. Computat. Phys. 129, 406-430.