On the boundary integral equation method for the problem of a plane crack inside a three-dimensional elastic medium

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Ioakimidis, Nikolaos
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The problem of a plane crack of arbitrary shape and under an arbitrary normal pressure distribution inside an infinite three-dimensional isotropic elastic medium is reconsidered by the boundary integral equation method. This method is seen to be capable to produce the singular integral equation of this problem with one unknown function, i.e. the displacements of the points of the crack faces (and not the derivatives of this function), and this is achieved in two ways. This is an alternative and probably interesting new method for the derivation of the aforementioned singular integral equation having been previously derived by two other methods. Generalizations of the present results to more complicated problems follow trivially.
Boundary integral equations, Crack problems, Fracture mechanics, Three-dimensional elasticity, Isotropic elasticity, Principal value integrals, Cauchy-type integrals, Singular integral equations, Finite-part integrals, Hypersingular integrals, Hypersingular integral equations