Abstract
In this paper, an application of the periodic Riemann boundary value problem to a periodic crack problem is considered. At first, we mainly treat the first fundamental bundary value problem. By approaches using the solutions of periodic Riemann boundary value problems and a singular integral equation with Hilbert kernel, we obtain the expression for the Stress Intensity Factors (SIF) in closed form for any loading on the crack face. As a concrete application of practical interest, the first fundamental boundary value problem with polynomial traction applied on the crack face and the second fundamental boundary value problem with the prescribed polynomial crack opening displacement are investigated by employing the Lobatto-Chebyshev quadrature formula. The numerical solution of the singular integral equation and the SIF are obtained.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Begehr, H., Gilbert, R.P.: Transformations, transmutations, and kernel functions, 1. Longman, Harlow, 1992.
Chen, Y.Z.: Single crack problem with polynomial traction on the crack face. Engineering Fracture Mechanics 46 (1993), 353–355.
Howland, R.C.J.: Stress in a plate containing an infinite row of holes. Proc. Royal Soc. London Ser. A 148 (1935), 471–491.
Ioakimidis, N.I., Theocaris, P.S.: Array of periodic curvilinear cracks in an infinite isotropic medium. Acta Mechnica 28 (1977), 239–254.
Isida, M.: On some plane problems of an infinite plate containing an infinite row of circular holes. Bull. JSME 10 (1960), 259–265.
Kuznetsov, E.A.: Periodic fundamental mixed problem of elastic theory for a half-plane. Prik. Mech. 12 (1976), no. 9, 89–97.
Li, X., Li, Z.: Effect of a periodic elastic gasket on periodic cracks. Engineering Fracture Mechanics 46 (1993), 127–131.
Li, X.: Effect of periodic elastic gasket on periodic contact problem. Partial differential and integral equations. Eds. H. Begehr, R.P. Gilbert, G.-C. Wen. Kluwer, Dordrecht, 1999, 249–254.
Lu, C.K., Cai, H.T.: Periodic problems in the classical theory of elasticity. Hunan Sci. Tech. Press, Hunan, 1986 (Chinese).
Muskhelishvili, N.I.: Some basic problems of the mathematical theory of elasticity. 2nd English ed., Noordhoff, Groningen, 1963.
Savruk, M.P.: Two-dimensional problems of elasticity for bodies with cracks. Naukova Dumka, Kiev, 1981 (Russian).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Kluwer Academic Publishers
About this chapter
Cite this chapter
Li, X. (1999). An Application of the Periodic Riemann Boundary Value Problem to a Periodic Crack Problem. In: Begehr, H.G.W., Celebi, A.O., Tutschke, W. (eds) Complex Methods for Partial Differential Equations. International Society for Analysis, Applications and Computation, vol 6. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3291-6_7
Download citation
DOI: https://doi.org/10.1007/978-1-4613-3291-6_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-3293-0
Online ISBN: 978-1-4613-3291-6
eBook Packages: Springer Book Archive