{"id":{"repo_id":"greece","oai_identifier":"oai:10442/0693"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/0693","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"Η ΕΦΑΡΜΟΓΗ ΤΗΣ ΣΥΜΜΟΡΦΟΥ ΑΠΕΙΚΟΝΙΣΕΩΣ ΣΤΑ ΠΕΠΕΡΑΣΜΕΝΑ ΣΤΟΙΧΕΙΑ ΓΙΑ ΤΗΝ ΕΠΙΛΥΣΗ ΠΡΟΒΛΗΜΑΤΩΝ ΡΩΓΜΩΝ","abstract":"USING A CONFORMAL MAPPING, THE SINGULAR STRESS FIELD AROUND CRACK TIPS IS TRANSFORMED TO A REGULAR ONE WITH RESPECT TO THE NEW VARIABLES. THUS, THE DISPLACEMENT FIELD IS APPROXIMATED IN THE MAPPED PLANE. THE INVERSE MAPPING GIVES SHAPE FUNCTIONS WHICH ARE NOT POLYNOMIALS. THE STRAIN FIELD, OBTAINED AFTER A DERIVATION OF THE DISPLACEMENT FIELD, HAS THE APPROPRIATE SQUARE ROOT SINGULARITY. THE ELEMENTS CONSTRUCTED BY USING THIS PROCEDURE ARE CALLED \"MAPPED ELEMENTS\". GEOMETRICAL DISCONTINUITIES CREATE SINGULAR FIELDS. FOR THE CONFRONTATION OF SUCH SINGULARITIES, A GRADUAL CONCENTRATION OF THE FINITE ELEMENT MESH IS NEEDED AROUND THE POINT OF GEOMETRICAL DISCONTINUITY. THE AUTOMATIC GENERATION OF AN OPTIMAL MESH IS OBTAINED BY USING A SCHWARZ-CHRISTOFFEL CONFORMAL TRANSFORMATION.","abstract_html":"USING A CONFORMAL MAPPING, THE SINGULAR STRESS FIELD AROUND CRACK TIPS IS TRANSFORMED TO A REGULAR ONE WITH RESPECT TO THE NEW VARIABLES. THUS, THE DISPLACEMENT FIELD IS APPROXIMATED IN THE MAPPED PLANE. THE INVERSE MAPPING GIVES SHAPE FUNCTIONS WHICH ARE NOT POLYNOMIALS. THE STRAIN FIELD, OBTAINED AFTER A DERIVATION OF THE DISPLACEMENT FIELD, HAS THE APPROPRIATE SQUARE ROOT SINGULARITY. THE ELEMENTS CONSTRUCTED BY USING THIS PROCEDURE ARE CALLED "MAPPED ELEMENTS". GEOMETRICAL DISCONTINUITIES CREATE SINGULAR FIELDS. FOR THE CONFRONTATION OF SUCH SINGULARITIES, A GRADUAL CONCENTRATION OF THE FINITE ELEMENT MESH IS NEEDED AROUND THE POINT OF GEOMETRICAL DISCONTINUITY. THE AUTOMATIC GENERATION OF AN OPTIMAL MESH IS OBTAINED BY USING A SCHWARZ-CHRISTOFFEL CONFORMAL TRANSFORMATION.","abstract_has_math":false,"creators":["Giannakopoulos, Antonios","Γιαννακόπουλος, Αντώνιος"],"institution":"National Technical University of Athens (NTUA)","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1987,"date_issued":"1987","date_published":"1987","updated_at":"2026-07-24T02:25:24Z","subjects":["Asymptotics","CONFORMAL MAPPING","CRACK-TIP ELEMENTS","Finite elements","Fractures","MAPPED ELEMENTS","OPTIMUM MESH","ΑΠΕΙΚΟΝΙΣΜΕΝΑ ΣΤΟΙΧΕΙΑ","Ασυμπτωτική ανάλυση","ΒΕΛΤΙΣΤΟΣ ΚΑΝΝΑΒΟΣ","ΕΙΔΙΚΑ ΣΤΟΙΧΕΙΑ","ΜΗΧΑΝΙΚΗ ΤΩΝ ΡΩΓΜΩΝ","Πεπερασμένα στοιχεία","ΣΥΜΜΟΡΦΗ ΑΠΕΙΚΟΝΙΣΗ","Επιστήμες Μηχανικού και Τεχνολογία","Επιστήμη Πολιτικού Μηχανικού","Engineering and Technology","Civil Engineering"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/0693"],"render_values":[{"text":"10.12681/eadd/0693","href":"https://doi.org/10.12681/eadd/0693","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/0693","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Giannakopoulos, Antonios","Γιαννακόπουλος, Αντώνιος"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1987"]},{"key":"dc:publisher","label":"Institution","values":["National Technical University of Athens (NTUA)","Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ)"]},{"key":"dc:type","label":"Dc Type","values":["PhD Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Asymptotics","CONFORMAL MAPPING","CRACK-TIP ELEMENTS","Finite elements","Fractures","MAPPED ELEMENTS","OPTIMUM MESH","ΑΠΕΙΚΟΝΙΣΜΕΝΑ ΣΤΟΙΧΕΙΑ","Ασυμπτωτική ανάλυση","ΒΕΛΤΙΣΤΟΣ ΚΑΝΝΑΒΟΣ","ΕΙΔΙΚΑ ΣΤΟΙΧΕΙΑ","ΜΗΧΑΝΙΚΗ ΤΩΝ ΡΩΓΜΩΝ","Πεπερασμένα στοιχεία","ΣΥΜΜΟΡΦΗ ΑΠΕΙΚΟΝΙΣΗ","Επιστήμες Μηχανικού και Τεχνολογία","Επιστήμη Πολιτικού Μηχανικού","Engineering and Technology","Civil Engineering"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["gre"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/0693","http://hdl.handle.net/10442/hedi/0693"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["USING A CONFORMAL MAPPING, THE SINGULAR STRESS FIELD AROUND CRACK TIPS IS TRANSFORMED TO A REGULAR ONE WITH RESPECT TO THE NEW VARIABLES. THUS, THE DISPLACEMENT FIELD IS APPROXIMATED IN THE MAPPED PLANE. THE INVERSE MAPPING GIVES SHAPE FUNCTIONS WHICH ARE NOT POLYNOMIALS. THE STRAIN FIELD, OBTAINED AFTER A DERIVATION OF THE DISPLACEMENT FIELD, HAS THE APPROPRIATE SQUARE ROOT SINGULARITY. THE ELEMENTS CONSTRUCTED BY USING THIS PROCEDURE ARE CALLED \"MAPPED ELEMENTS\". GEOMETRICAL DISCONTINUITIES CREATE SINGULAR FIELDS. FOR THE CONFRONTATION OF SUCH SINGULARITIES, A GRADUAL CONCENTRATION OF THE FINITE ELEMENT MESH IS NEEDED AROUND THE POINT OF GEOMETRICAL DISCONTINUITY. THE AUTOMATIC GENERATION OF AN OPTIMAL MESH IS OBTAINED BY USING A SCHWARZ-CHRISTOFFEL CONFORMAL TRANSFORMATION.","ΧΡΗΣΙΜΟΠΟΙΩΝΤΑΣ ΤΗΝ ΣΥΜΜΟΡΦΗ ΑΠΕΙΚΟΝΙΣΗ, ΤΟ ΙΔΙΟΜΟΡΦΟ ΤΑΣΙΚΟ ΠΕΔΙΟ ΓΥΡΩ ΑΠΟ ΤΑ ΑΚΡΑ ΡΩΓΜΩΝ, ΜΕΤΑΣΧΗΜΑΤΙΖΕΤΑΙ ΣΕ ΕΝΑ ΟΜΑΛΟ ΩΣ ΠΡΟΣ ΤΙΣ ΝΕΕΣ ΜΕΤΑΒΛΗΤΕΣ. ΕΤΣΙ, ΤΟ ΠΕΔΙΟ ΜΕΤΑΤΟΠΗΣΕΩΝ ΠΡΟΣΕΓΓΙΖΕΤΑΙ ΣΤΟ ΑΠΕΙΚΟΝΙΣΜΕΝΟ ΕΠΙΠΕΔΟ. Η ΑΝΤΙΣΤΡΟΦΗ ΑΠΕΙΚΟΝΙΣΗ ΔΙΝΕΙ ΣΥΝΑΡΤΗΣΕΙΣ ΣΧΗΜΑΤΟΣ ΠΟΥ ΔΕΝ ΕΙΝΑΙ ΠΟΛΥΩΝΥΜΑ. ΤΟ ΠΕΔΙΟ ΠΑΡΑΜΟΡΦΩΣΕΩΝ ΠΟΥ ΠΡΟΚΥΠΤΕΙ ΕΠΕΙΤΑ ΑΠΟ ΠΑΡΑΓΩΓΙΣΗ ΤΟΥ ΠΕΔΙΟΥ ΤΩΝ ΜΕΤΑΤΟΠΗΣΕΩΝ ΕΧΕΙ ΤΗΝ ΚΑΤΑΛΛΗΛΗ ΙΔΙΟΜΟΡΦΙΑ (1/ R). ΤΑ ΣΤΟΙΧΕΙΑ ΠΟΥ ΚΑΤΑΣΚΕΥΑΖΟΝΤΑΙ ΜΕ ΑΥΤΟΝ ΤΟΝ ΤΡΟΠΟ ΛΕΓΟΝΤΑΙ \"ΑΠΕΙΚΟΝΙΣΜΕΝΑ ΣΤΟΙΧΕΙΑ\". ΟΙ ΓΕΩΜΕΤΡΙΚΕΣ ΙΔΙΟΜΟΡΦΙΕΣ ΔΗΜΙΟΥΡΓΟΥΝ ΙΔΙΟΜΟΡΦΑ ΠΕΔΙΑ . ΓΙΑ ΤΗΝ ΑΝΤΙΜΕΤΩΠΙΣΗ ΤΕΤΟΙΩΝ ΙΔΙΟΜΟΡΦΙΩΝ, ΑΠΑΙΤΕΙΤΑΙ ΜΙΑ ΣΤΑΔΙΑΚΗ ΠΥΚΝΩΣΗ ΤΟΥ ΚΑΝΝΑΒΟΥ ΤΩΝ ΠΕΠΕΡΑΣΜΕΝΩΝ ΣΤΟΙΧΕΙΩΝ ΓΥΡΩ ΑΠΟ ΤΟ ΣΗΜΕΙΟ ΤΗΣ ΓΕΩΜΕΤΡΙΚΗΣ ΙΔΙΟΜΟΡΦΙΑΣ. Η ΑΥΤΟΜΑΤΗ ΚΑΤΑΣΚΕΥΗ ΕΝΟΣ ΒΕΛΤΙΣΤΟΥ ΚΑΝΝΑΒΟΥ ΠΕΤΥΧΑΙΝΕΤΑΙ ΧΡΗΣΙΜΟΠΟΙΩΝΤΑΣ ΤΟΝ ΣΥΜΜΟΡΦΟ ΜΕΤΑΣΧΗΜΑΤΙΣΜΟ SCHWARZ-CHRISTOFFEL."]},{"key":"dc:title","label":"Title","values":["Η ΕΦΑΡΜΟΓΗ ΤΗΣ ΣΥΜΜΟΡΦΟΥ ΑΠΕΙΚΟΝΙΣΕΩΣ ΣΤΑ ΠΕΠΕΡΑΣΜΕΝΑ ΣΤΟΙΧΕΙΑ ΓΙΑ ΤΗΝ ΕΠΙΛΥΣΗ ΠΡΟΒΛΗΜΑΤΩΝ ΡΩΓΜΩΝ","THE APPLICATION OF CONFORMAL MAPPING IN THE FINITE ELEMENT METHOD FOR THE SOLUTION OF CRACKED BODIES"]}]}],"canonical_facts":{"dc:creator":["Giannakopoulos, Antonios","Γιαννακόπουλος, Αντώνιος"],"dc:date":["1987"],"dc:description":["USING A CONFORMAL MAPPING, THE SINGULAR STRESS FIELD AROUND CRACK TIPS IS TRANSFORMED TO A REGULAR ONE WITH RESPECT TO THE NEW VARIABLES. THUS, THE DISPLACEMENT FIELD IS APPROXIMATED IN THE MAPPED PLANE. THE INVERSE MAPPING GIVES SHAPE FUNCTIONS WHICH ARE NOT POLYNOMIALS. THE STRAIN FIELD, OBTAINED AFTER A DERIVATION OF THE DISPLACEMENT FIELD, HAS THE APPROPRIATE SQUARE ROOT SINGULARITY. THE ELEMENTS CONSTRUCTED BY USING THIS PROCEDURE ARE CALLED \"MAPPED ELEMENTS\". GEOMETRICAL DISCONTINUITIES CREATE SINGULAR FIELDS. FOR THE CONFRONTATION OF SUCH SINGULARITIES, A GRADUAL CONCENTRATION OF THE FINITE ELEMENT MESH IS NEEDED AROUND THE POINT OF GEOMETRICAL DISCONTINUITY. THE AUTOMATIC GENERATION OF AN OPTIMAL MESH IS OBTAINED BY USING A SCHWARZ-CHRISTOFFEL CONFORMAL TRANSFORMATION.","ΧΡΗΣΙΜΟΠΟΙΩΝΤΑΣ ΤΗΝ ΣΥΜΜΟΡΦΗ ΑΠΕΙΚΟΝΙΣΗ, ΤΟ ΙΔΙΟΜΟΡΦΟ ΤΑΣΙΚΟ ΠΕΔΙΟ ΓΥΡΩ ΑΠΟ ΤΑ ΑΚΡΑ ΡΩΓΜΩΝ, ΜΕΤΑΣΧΗΜΑΤΙΖΕΤΑΙ ΣΕ ΕΝΑ ΟΜΑΛΟ ΩΣ ΠΡΟΣ ΤΙΣ ΝΕΕΣ ΜΕΤΑΒΛΗΤΕΣ. ΕΤΣΙ, ΤΟ ΠΕΔΙΟ ΜΕΤΑΤΟΠΗΣΕΩΝ ΠΡΟΣΕΓΓΙΖΕΤΑΙ ΣΤΟ ΑΠΕΙΚΟΝΙΣΜΕΝΟ ΕΠΙΠΕΔΟ. Η ΑΝΤΙΣΤΡΟΦΗ ΑΠΕΙΚΟΝΙΣΗ ΔΙΝΕΙ ΣΥΝΑΡΤΗΣΕΙΣ ΣΧΗΜΑΤΟΣ ΠΟΥ ΔΕΝ ΕΙΝΑΙ ΠΟΛΥΩΝΥΜΑ. ΤΟ ΠΕΔΙΟ ΠΑΡΑΜΟΡΦΩΣΕΩΝ ΠΟΥ ΠΡΟΚΥΠΤΕΙ ΕΠΕΙΤΑ ΑΠΟ ΠΑΡΑΓΩΓΙΣΗ ΤΟΥ ΠΕΔΙΟΥ ΤΩΝ ΜΕΤΑΤΟΠΗΣΕΩΝ ΕΧΕΙ ΤΗΝ ΚΑΤΑΛΛΗΛΗ ΙΔΙΟΜΟΡΦΙΑ (1/ R). ΤΑ ΣΤΟΙΧΕΙΑ ΠΟΥ ΚΑΤΑΣΚΕΥΑΖΟΝΤΑΙ ΜΕ ΑΥΤΟΝ ΤΟΝ ΤΡΟΠΟ ΛΕΓΟΝΤΑΙ \"ΑΠΕΙΚΟΝΙΣΜΕΝΑ ΣΤΟΙΧΕΙΑ\". ΟΙ ΓΕΩΜΕΤΡΙΚΕΣ ΙΔΙΟΜΟΡΦΙΕΣ ΔΗΜΙΟΥΡΓΟΥΝ ΙΔΙΟΜΟΡΦΑ ΠΕΔΙΑ . ΓΙΑ ΤΗΝ ΑΝΤΙΜΕΤΩΠΙΣΗ ΤΕΤΟΙΩΝ ΙΔΙΟΜΟΡΦΙΩΝ, ΑΠΑΙΤΕΙΤΑΙ ΜΙΑ ΣΤΑΔΙΑΚΗ ΠΥΚΝΩΣΗ ΤΟΥ ΚΑΝΝΑΒΟΥ ΤΩΝ ΠΕΠΕΡΑΣΜΕΝΩΝ ΣΤΟΙΧΕΙΩΝ ΓΥΡΩ ΑΠΟ ΤΟ ΣΗΜΕΙΟ ΤΗΣ ΓΕΩΜΕΤΡΙΚΗΣ ΙΔΙΟΜΟΡΦΙΑΣ. Η ΑΥΤΟΜΑΤΗ ΚΑΤΑΣΚΕΥΗ ΕΝΟΣ ΒΕΛΤΙΣΤΟΥ ΚΑΝΝΑΒΟΥ ΠΕΤΥΧΑΙΝΕΤΑΙ ΧΡΗΣΙΜΟΠΟΙΩΝΤΑΣ ΤΟΝ ΣΥΜΜΟΡΦΟ ΜΕΤΑΣΧΗΜΑΤΙΣΜΟ SCHWARZ-CHRISTOFFEL."],"dc:identifier":["10.12681/eadd/0693","http://hdl.handle.net/10442/hedi/0693"],"dc:language":["gre"],"dc:publisher":["National Technical University of Athens (NTUA)","Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ)"],"dc:subject":["Asymptotics","CONFORMAL MAPPING","CRACK-TIP ELEMENTS","Finite elements","Fractures","MAPPED ELEMENTS","OPTIMUM MESH","ΑΠΕΙΚΟΝΙΣΜΕΝΑ ΣΤΟΙΧΕΙΑ","Ασυμπτωτική ανάλυση","ΒΕΛΤΙΣΤΟΣ ΚΑΝΝΑΒΟΣ","ΕΙΔΙΚΑ ΣΤΟΙΧΕΙΑ","ΜΗΧΑΝΙΚΗ ΤΩΝ ΡΩΓΜΩΝ","Πεπερασμένα στοιχεία","ΣΥΜΜΟΡΦΗ ΑΠΕΙΚΟΝΙΣΗ","Επιστήμες Μηχανικού και Τεχνολογία","Επιστήμη Πολιτικού Μηχανικού","Engineering and Technology","Civil Engineering"],"dc:title":["Η ΕΦΑΡΜΟΓΗ ΤΗΣ ΣΥΜΜΟΡΦΟΥ ΑΠΕΙΚΟΝΙΣΕΩΣ ΣΤΑ ΠΕΠΕΡΑΣΜΕΝΑ ΣΤΟΙΧΕΙΑ ΓΙΑ ΤΗΝ ΕΠΙΛΥΣΗ ΠΡΟΒΛΗΜΑΤΩΝ ΡΩΓΜΩΝ","THE APPLICATION OF CONFORMAL MAPPING IN THE FINITE ELEMENT METHOD FOR THE SOLUTION OF CRACKED BODIES"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:25:24Z"}