A one-dimensional hypersingular integral equation for axisymmetric planar cracks in three-dimensional isotropic elasticity

• Main Author: Ioakimidis, Nikolaos
• Other Authors: Ιωακειμίδης, Νικόλαος
• Format: Technical Report
• Language: English
• Published: 2018
• Subjects: Boundary integral equations; Fracture mechanics; Crack problems; Planar cracks; Axisymmetric cracks; Penny-shaped cracks; Three-dimensional elasticity; Isotropic elasticity; Axisymmetric loading; Finite-part integrals; Hadamard-type integrals; Hypersingular integrals; Hypersingular integral equations; Elliptic integrals; Συνοριακές ολοκληρωτικές εξισώσεις; Θραυστομηχανική; Προβλήματα ρωγμών; Επίπεδες ρωγμές; Αξονοσυμμετρικές ρωγμές; Κυκλικές ρωγμές; Τριδιάστατη ελαστικότητα; Ισότροπη ελαστικότητα; Αξονοσυμμετρική φόρτιση; Ολοκληρώματα πεπερασμένου μέρους; Oλοκληρώματα τύπου Hadamard; Υπεριδιόμορφα ολοκληρώματα; Υπεριδιόμορφες ολοκληρωτικές εξισώσεις; Ελλειπτικά ολοκληρώματα

The problem of an axisymmetric planar crack (or a system of such cracks) under an arbitrary axisymmetric normal loading distribution inside an infinite three-dimensional isotropic elastic medium is reduced to a one-dimensional hypersingular integral equation (with a second-order, a first-order and a logarithmic singularity in its kernel). This equation seems to be most appropriate for the solution of the aforementioned crack problem. On the other hand, this equation seems to be unique in physical and engineering problems and may draw the interest in its investigation from the mathematical (theoretical and numerical) point of view.