Hypersingularities and cracks in plane and three-dimensional elasticity

• Κύριος συγγραφέας: Ioakimidis, Nikolaos
• Άλλοι συγγραφείς: Ιωακειμίδης, Νικόλαος
• Μορφή: Technical Report
• Γλώσσα: English
• Έκδοση: 2018
• Θέματα: Hypersingularities; Hyperintegrals; Hypersingular integrals; Finite-part integrals; Cracks; Fracture mechanics; Plane elasticity; Three-dimensional elasticity; Isotropic elasticity; Stresses; Displacements; Crack opening displacement; Potentials; Complex potentials; Singular stress fields; Hypersingular stress fields; Hypersingular integral equations; Υπεριδιομορφίες; Υπερολοκληρώματα; Υπεριδιόμορφα ολοκληρώματα; Ολοκληρώματα πεπερασμένου μέρους; Ρωγμές; Θραυστομηχανική; Επίπεδη ελαστικότητα; Τριδιάστατη ελαστικότητα; Ισότροπη ελαστικότητα; Τάσεις; Μετατοπίσεις; Mετατόπιση ανοίγματος των χειλέων της ρωγμής; Δυναμικά; Μιγαδικά δυναμικά; Ιδιόμορφα τασικά πεδία; Υπεριδιόμορφα τασικά πεδία; Υπεριδιόμορφες ολοκληρωτικές εξισώσεις

Crack problems in plane elasticity are often interpreted as edge dislocation arrays. Singular stress fields, such as those due to concentrated forces, dislocations and centres of rotation and dilatation, often prove useful in the interpretation and/or the solution of elasticity problems. Here a new kind of singular stress fields called hypersingularities, since these fields are straightforwardly related to hyperintegrals in mathematics, is introduced. The stress components of hypersingularities are seen to tend to infinity more rapidly than in other singular stress fields. The hypersingularities considered here are related to simple crack problems in plane and three-dimensional isotropic elasticity. Generalizations and further applications of the present results are quite possible.