Abstract
A new singular integral equation (with a kernel with a logarithmic singularity) is proposed for the crack problem inside an elastic medium under plane or antiplane conditions. In this equation the integral is considered in the sense of a finite-part integral of Hadamard because the unknown function presents singularities of order −3/2 at the crack tips. The Galerkin and the collocation methods are proposed for the numerical solution of this equation and the determination of the values of the stress intensity factors at the crack tips and numerical results are presented. Finally, the advantages of this equation are also considered.
Résumé
Une nouvelle équation intégrale singulière (à noyau avec une singularité logarithmique) est proposée pour le problème de la fissure dans un milieu élastique à conditions planes ou antiplanes. Dans cette équation l'intégrale est considerée au sens des parties finies d'Hadamard car la fonction inconnue présente des singularités d'ordre −3/2 aux extrémités de la fissure. Les méthodes de Galerkin et de la collocation sont proposées pour la solution numérique de cette équation et la détermination des valeurs des facteurs d'intensité de contrainte aux extrémités de la fissure et des résultats numériques sont présentés. Finalement, les avantages de cette équation sont aussi considerés.
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Ioakimidis, N.I. A new singular integral equation for the classical crack problem in plane and antiplane elasticity. Int J Fract 21, 115–122 (1983). https://doi.org/10.1007/BF00941868
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DOI: https://doi.org/10.1007/BF00941868