Locating inclusions of the same material in finite plane isotropic elastic media by using complex path-independent integrals

• Main Author: Ioakimidis, Nikolaos
• Other Authors: Ιωακειμίδης, Νικόλαος
• Format: Technical Report
• Language: English
• Published: 2018
• Subjects: Inclusions; Location of inclusions; Plane isotropic elasticity; Complex path-independent integrals; Closed contours; Contour integrals; Cauchy-type integrals; Complex potentials; Complex analysis; Analytic functions; Holomorphic functions; Residues; Εγκλείσματα; Εντοπισμός εγκλεισμάτων; Επίπεδη ισότροπη ελαστικότητα; Μιγαδικά ολοκληρώματα ανεξάρτητα του δρόμου ολοκληρώσεως; Κλειστές καμπύλες; Επικαμπύλια ολοκληρώματα; Ολοκληρώματα τύπου Cauchy; Μιγαδικά δυναμικά; Μιγαδική ανάλυση; Αναλυτικές συναρτήσεις; Ολόμορφες συναρτήσεις; Ολοκληρωτικά υπόλοιπα

The method of complex path-independent integrals on a closed contour is used for the location of an inclusion (of arbitrary but known shape) of the same material with the matrix and welded with the matrix in plane isotropic elasticity for a finite medium. Only the position of the inclusion and the external loading are not known in advance. The first complex potential of Kolosov–Muskhelishvili (or one of its two first derivatives) is used, together with optical methods for its evaluation, on the aforementioned contour. Beyond the location of the inclusion, a variety of generalizations of the proposed technique as well as a long discussion are also included.