Abstract
In this paper, numerical solutions of the singular integral equations of the body force method in the crack problems are discussed. The stress fields induced by ‘two kinds of displacement discontinuity’ are used as fundamental solutions. Then, the problem is formulated as a hypersingular integral equation with the singularity of the form r 2. In the numerical calculation, two kinds of unknown functions are approximated by the products of the fundamental density function and the Chebyshev polynomials. As examples, the stress intensity factors of the oblique edge crack, kinked crack, branched crack and zig-zag crack are analyzed. The calculation shows that the present method gives accurate results even for the extremely oblique edge crack and kinked crack with extremely short bend which has been difficult to analyze by the previous method using the approximation by the products of the fundamental density function and the stepped functions etc.
Similar content being viewed by others
References
H. Nisitani, Journal of the Japan Society of Mechanical Engineers 70 (1967) 627–635.
H. Nisitani, Mechanics of Fracture 5, G. C. Sih (ed.), Noordhoff International Publishing, Leyden (1978)1–68.
S. Krenk, International Journal of Solids and Structures 11 (1975) 693–708.
N.I. Ioakimidis, Engineering Fracture Mechanics 26 (1987) 783–788.
A.C. Kaya and F. Erdogan, Quarterly of Applied Mathematics 45 (1987) 105–122.
H. Nisitani, Transactions of the Japan Society of Mechanical Engineers 41 (1987) 1103–1111.
M. Isida, Transactions of the Japan Society of Mechanical Engineers 44 (1978) 1122–1132.
M. Isida, Transactions of the Japan Society of Mechanical Engineers 45 A (1979) 306–317.
H. Kitagawa and R. Yuuki, Transactions of the Japan Society of Mechanical Engineers 41 (1975) 1641–1649.
N. Hasebe and S. Inohara, Ingenieur-Archiv 49 (1980) 51–62.
M.P. Stallybrass, International Journal of Engineering Science 8 (1970) 351–362.
H. Nisitani and Y. Oda, Transactions of the Japan Society of Mechanical Engineers 46 (1980) 745–755.
M. Isida and T. Nishino, Engineering Fracture Mechanics 36 (1990) 697–711.
K. Kageyama and H. Okamura, Transactions of the Japan Society of Mechanical Engineers 48 A (1983) 783–791.
M. Isida and H. Noguchi, Transactions of the Japan Society of Mechanical Engineers 49 A (1983) 469–479.
H. Nisitani, D.H. Chen and M. Isida, Transactions of the Japan Society of Mechanical Engineers 50 A (1984) 341–350.
H. Nisitani and D.H. Chen, The Body Force Method, Baifukan Publication, Tokyo (1987) (Taisekiryokuhou inJapanese).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Noda, NA., Oda, K. Numerical solutions of the singular integral equations in the crack analysis using the body force method. Int J Fract 58, 285–304 (1992). https://doi.org/10.1007/BF00048950
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00048950