Abstract
New aspects for the generalization of the Sokhotski-Plemelj formulae are investigated, in order to show the behaviour of the limiting values of the finite-part singular integrals, defined over a smooth closed or open contour. The new formulae are more complicated when some corner points are further included in the contour. Beyond the above, when the contour is infinite, then the limiting values of the finite-part singular integrals are calculated by using an additional method. An application of two-dimensional fracture mechanics is finally given, to the determination of the stress intensity factors near a straight crack in a bimaterial infinite and isotropic solid under antiplane shear.
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