Abstract
The classical problem of a straight crack in a finite, plane, isotropic, elastic medium of arbitrary shape is reconsidered by the well-known method of Muskhelishvili for such a crack (but in an infinite medium). Both the crack and the boundary of the medium are assumed loaded in an arbitrary way. It is shown that this problem can be completely solved if the numerical values of the first complex potential Φ(z) of Muskhelishvili are known along a closed contour surrounding the crack, probably along the boundary of the medium. To this end, complex path-independent integrals associated with Φ(z) and Chebyshev polynomials have been used. Numerical results for the stress intensity factors are displayed in an application. Generalizations of the method are also proposed and the second fundamental crack problem, the problem of a crack in an anisotropic medium and the problem of an interface crack between two isotropic media are considered in some detail.
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Ioakimidis, N.I. Application of complex path-independent integrals to the solution of the problem of a straight crack in a finite plane isotropic elastic medium. J Elasticity 16, 441–456 (1986). https://doi.org/10.1007/BF00041767
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DOI: https://doi.org/10.1007/BF00041767