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An Integral Equation Solution for a Bounded Elastic Body Containing a Crack: Mode I Deformation
International Journal of Fracture (1978)
  • Thomas J. Rudolphi, Wright-Patterson Air Force Base
An integral-equation solution for the two dimensional problem of a stress-free crack in a bounded, linearly elastic, isotropic medium subjected to in-plane forces is presented. A set of coupled equations, involving integrals over the outer boundary and the line of the crack, is obtained my the simultaneous solution of a crack problem in an unbounded medium - the perturbed problem - and a problem in an unflawed region having the same outer boundary as the medium containing the crack - the equable problem. The solution for the perturbed problem is given in quadrature form in terms of the derivative of the normal displacement of the crack surface. The solution for the equable problem is given by a set of boundary integral equations. The character of the stress-field singularity at the crack tips is provided by the solution for the perturbed problem. For a numerical evaluation the set of coupled integral equations is approximated by a set of simultaneous, linear algebraic equations. Since the stress intensity factors and the crack surface displacement are incorporated into the integral equations, the values of these quantities are obtained directly from the numerical solution. Several sample problems are presented in order to determine the versatility and accuracy of this approach.
Publication Date
October, 1978
Publisher Statement
Works produced by employees of the U.S. Government as part of their official duties are not copyrighted within the U.S. The content of this document is not copyrighted.
Citation Information
Thomas J. Rudolphi. "An Integral Equation Solution for a Bounded Elastic Body Containing a Crack: Mode I Deformation" International Journal of Fracture Vol. 14 Iss. 5 (1978) p. 527 - 541
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