Abstract
Abstract A new method is proposed for the analysis of an elastic space weakened by a flat crack of arbitrary shape under the action of a uniform normal pressure. The method is based on an integral representation for the reciprocal distance between two points obtained earlier by the author. A simple but yet accurate relationship is established between the crack face displacements and the applied pressure for an arbitrary flat crack. Specific formulae are derived for a crack in the shape of a polygon, a rectangle, a rhombus, a cross, a circular sector and a circular segment. All the formulae are checked against the solutions known in the literature, and their accuracy is confirmed. A similar approach can be used for the analysis of a crack under a general polynomial loading.
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