Abstract
A general method to construct path-independent integrals in the framework of plane elasticity is presented. The proposed path-independent integrals are valid not only for the case of a single straight crack, but also for the case of any number of collinear cracks. The integrands of these integrals are classified in three classes, which satisfy some well-defined restrictions. Therefore, it is possible to construct a large number of new path-independent integrals. As an illustration some of them are derived and are applied to the theoretical computation of the stress intensity factor in five particular cases of cracked elastic plates.
Resumé
On présente une méthode générale de construction d'intégrales indépendantes du contour dans l'élasticité plane. Les intégrales independantes du contour, proposées dans cet article, sont valables non seulement dans le cas d'une seule fissure mais aussi dans le cas d'un nombre arbitraire de fissures collineaires. Les intégrands de cas intégrales sont classifiés en trois classes, qui satisfont des restrictions bien-definies. De cette façon, il est possible de construire un nombre important de nouvelles integrales indépendentes du contour. Afin d'illustrer la méthode, un certain nombre d'intégrales est appliqué pour un calcul théorique du facteur d'intensité des contraintes de cinq cas des plaques fissurées.
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Tsamasphyros, G.J., Theocaris, P.S. A new concept of path-independent integrals for plane elasticity. J Elasticity 12, 265–280 (1982). https://doi.org/10.1007/BF00054958
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DOI: https://doi.org/10.1007/BF00054958