{"id":{"repo_id":"greece","oai_identifier":"oai:10442/1660"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/1660","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"ΜΗ ΓΡΑΜΜΙΚΑ ΠΡΟΒΛΗΜΑΤΑ ΛΕΠΤΟΤΟΙΧΩΝ ΔΙΑΤΟΜΩΝ","abstract":"INEQUALITY CONSTRAINTS HAVE BEEN STUDIED IN RECENT YEARS IN SEVERAL AREAS OF STRUCTURAL ANALYSIS. WE MENTION, THE THEORY OF IDEAL PLASTICITY AND VISCOPLASTICITY, THE UNILATERAL CONTACT PROBLEMS OF A BODY WITH RIGID OR DEFORMABLE BODY, THE FRICTION PROBLEMS E.T.C. MOREOVER, SUCH PROBLEMS HAVE NOT BEEN FORMULATED ANDSTUDIED IN THE FRAMEWORK OF STRUCTURES INCLUDING THIN WALLED BEAMS, BUT ONLY FOR CLASSICAL BEAMS AND PLATES AS WELL AS FOR FRAMES AND TRUSSES. THIS IS ATTEMPTED IN THE PRESENT WORK, FOR OPEN CROSS SECTION THIN WALLED BEAMS AND GENERALLYFOR STRUCTURES CONTAINING SUCH ELEMENTS. SEVERAL CONTACT, PLASTICITY AND FRICTION PROBLEMS ARE FORMULATED AND STUDIED AND THE RESPECTIVE VARIATIONAL EXPRESSIONS ARE DERIVED. NOTE THAT IN THE CASE OF INEQUALITY CONSTRAINTS THE PRINCIPLE OF VIRTUAL WORK AND THE COMPLEMENTARY VIRTUAL WORK HOLD IN INEQUALITY FORMS WHICH CONSTITUTE VARIATIONAL INEQUALITIES. THIS IS CAUSED BY THE FACT THAT THE VARIATIONS OF THE INEQUALITY CONSTRAINED QUANTITIES ARE UNILATERAL I.E. WHEN ΔΧ=Χ*-Χ IS ADMISSIBLE -ΔΧ IS NOT ADMISSIBLE. FINALLY THE RESULTING PROBLEMS ARE FORMULATED AS INEQUALITY CONSTRAINED MINIMUM PROBLEMS AND THE THEORY IS ILLUSTRATEDBY NUMERICAL EXAMPLES. HERE WE HAVE CONSIDERED INEQUALITY CONSTRAINTS ARISING FROM REACTION-DISPLACEMENT OR MOMENT-ROTATION DIAGRAM OF MONOTONE TYPE. THE MORE GENERAL CASE OF LOCK OF MONOTONICITY LEADS TO HEMIRATIONAL INEQUALITIES. THE PRESENT WORK DIVIDED INTO FIVE CHAPTERS DEALS WITH THE ANALYSIS OF STRUCTURES WHOSE STRUCTURAL ELEMENTS ARE OF THIN WALLED OPEN CROSS SECTION TYPE AND INVOLVEMONOTE LAWS OF THEIR BOUNDARIES.","abstract_html":"INEQUALITY CONSTRAINTS HAVE BEEN STUDIED IN RECENT YEARS IN SEVERAL AREAS OF STRUCTURAL ANALYSIS. WE MENTION, THE THEORY OF IDEAL PLASTICITY AND VISCOPLASTICITY, THE UNILATERAL CONTACT PROBLEMS OF A BODY WITH RIGID OR DEFORMABLE BODY, THE FRICTION PROBLEMS E.T.C. MOREOVER, SUCH PROBLEMS HAVE NOT BEEN FORMULATED ANDSTUDIED IN THE FRAMEWORK OF STRUCTURES INCLUDING THIN WALLED BEAMS, BUT ONLY FOR CLASSICAL BEAMS AND PLATES AS WELL AS FOR FRAMES AND TRUSSES. THIS IS ATTEMPTED IN THE PRESENT WORK, FOR OPEN CROSS SECTION THIN WALLED BEAMS AND GENERALLYFOR STRUCTURES CONTAINING SUCH ELEMENTS. SEVERAL CONTACT, PLASTICITY AND FRICTION PROBLEMS ARE FORMULATED AND STUDIED AND THE RESPECTIVE VARIATIONAL EXPRESSIONS ARE DERIVED. NOTE THAT IN THE CASE OF INEQUALITY CONSTRAINTS THE PRINCIPLE OF VIRTUAL WORK AND THE COMPLEMENTARY VIRTUAL WORK HOLD IN INEQUALITY FORMS WHICH CONSTITUTE VARIATIONAL INEQUALITIES. THIS IS CAUSED BY THE FACT THAT THE VARIATIONS OF THE INEQUALITY CONSTRAINED QUANTITIES ARE UNILATERAL I.E. WHEN ΔΧ=Χ*-Χ IS ADMISSIBLE -ΔΧ IS NOT ADMISSIBLE. FINALLY THE RESULTING PROBLEMS ARE FORMULATED AS INEQUALITY CONSTRAINED MINIMUM PROBLEMS AND THE THEORY IS ILLUSTRATEDBY NUMERICAL EXAMPLES. HERE WE HAVE CONSIDERED INEQUALITY CONSTRAINTS ARISING FROM REACTION-DISPLACEMENT OR MOMENT-ROTATION DIAGRAM OF MONOTONE TYPE. THE MORE GENERAL CASE OF LOCK OF MONOTONICITY LEADS TO HEMIRATIONAL INEQUALITIES. THE PRESENT WORK DIVIDED INTO FIVE CHAPTERS DEALS WITH THE ANALYSIS OF STRUCTURES WHOSE STRUCTURAL ELEMENTS ARE OF THIN WALLED OPEN CROSS SECTION TYPE AND INVOLVEMONOTE LAWS OF THEIR BOUNDARIES.","abstract_has_math":false,"creators":["Ποτήρη, Θεοδώρα"],"institution":"Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1991,"date_issued":"1991","date_published":"1991","updated_at":"2026-07-24T02:25:02Z","subjects":["INEQUALITY PROBLEMS IN MECHANICS","NON SMOOTH ANALYSIS: APPLICATIONS","NONLINEARSTRUCTURAL ANALYSIS","STRUCTURAL ANALYSIS OF THIN-WALLED SECTIONS","THE MINIMUM OF THE COPLEMENTARY ENERGY","THE MINIMUM OF THE VIRTUAL ENERGY","UNILATERAL BOUNDARY CONDITIONS","VARIATIONAL PROBLEMS IN MECHANICS","ΑΝΙΣΟΤΗΤΕΣ ΜΕΤΑΒΟΛΩΝ ΑΡΧΗΣ ΤΩΝ ΔΥΝΑΤΩΝ ΕΡΓΩΝ","ΑΝΙΣΟΤΗΤΕΣ ΜΕΤΑΒΟΛΩΝ ΑΡΧΗΣ ΤΩΝ ΣΥΜΠΛΗΡ. ΕΡΓΩΝ","ΑΝΙΣΟΤΙΚΑ ΠΡΟΒΛΗΜΑΤΑ ΜΗΧΑΝΙΚΗΣ","ΕΛΑΧΙΣΤΟ ΔΥΝΑΜΙΚΗΣ ΕΝΕΡΓΕΙΑΣ","ΕΛΑΧΙΣΤΟ ΣΥΜΠΛΗΡΩΜΑΤΙΚΗΣ ΕΝΕΡΓΕΙΑΣ","Μη γραμμική ανάλυση","ΜΗ ΛΕΙΑ ΑΝΑΛΥΣΗ-ΕΦΑΡΜΟΓΕΣ","ΜΟΝΟΠΛΕΥΡΕΣ ΣΥΝΟΡΙΑΚΕΣ ΣΥΝΘΗΚΕΣ","ΠΡΟΒΛΗΜΑΤΑ ΜΕΤΑΒΟΛΩΝ ΣΤΗΝ ΜΗΧΑΝΙΚΗ","ΣΤΑΤΙΚΗ ΜΕΛΕΤΗ ΦΟΡΕΩΝ ΛΕΠΤΟΤΟΙΧΗΣ ΔΙΑΤΟΜΗΣ","Engineering and Technology","Civil Engineering","Επιστήμες Μηχανικού και Τεχνολογία","Επιστήμη Πολιτικού Μηχανικού"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1660"],"render_values":[{"text":"10.12681/eadd/1660","href":"https://doi.org/10.12681/eadd/1660","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/1660","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Ποτήρη, Θεοδώρα"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1991"]},{"key":"dc:publisher","label":"Institution","values":["Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)","Aristotle University Of Thessaloniki (AUTH)"]},{"key":"dc:type","label":"Dc Type","values":["PhD Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["INEQUALITY PROBLEMS IN MECHANICS","NON SMOOTH ANALYSIS: APPLICATIONS","NONLINEARSTRUCTURAL ANALYSIS","STRUCTURAL ANALYSIS OF THIN-WALLED SECTIONS","THE MINIMUM OF THE COPLEMENTARY ENERGY","THE MINIMUM OF THE VIRTUAL ENERGY","UNILATERAL BOUNDARY CONDITIONS","VARIATIONAL PROBLEMS IN MECHANICS","ΑΝΙΣΟΤΗΤΕΣ ΜΕΤΑΒΟΛΩΝ ΑΡΧΗΣ ΤΩΝ ΔΥΝΑΤΩΝ ΕΡΓΩΝ","ΑΝΙΣΟΤΗΤΕΣ ΜΕΤΑΒΟΛΩΝ ΑΡΧΗΣ ΤΩΝ ΣΥΜΠΛΗΡ. ΕΡΓΩΝ","ΑΝΙΣΟΤΙΚΑ ΠΡΟΒΛΗΜΑΤΑ ΜΗΧΑΝΙΚΗΣ","ΕΛΑΧΙΣΤΟ ΔΥΝΑΜΙΚΗΣ ΕΝΕΡΓΕΙΑΣ","ΕΛΑΧΙΣΤΟ ΣΥΜΠΛΗΡΩΜΑΤΙΚΗΣ ΕΝΕΡΓΕΙΑΣ","Μη γραμμική ανάλυση","ΜΗ ΛΕΙΑ ΑΝΑΛΥΣΗ-ΕΦΑΡΜΟΓΕΣ","ΜΟΝΟΠΛΕΥΡΕΣ ΣΥΝΟΡΙΑΚΕΣ ΣΥΝΘΗΚΕΣ","ΠΡΟΒΛΗΜΑΤΑ ΜΕΤΑΒΟΛΩΝ ΣΤΗΝ ΜΗΧΑΝΙΚΗ","ΣΤΑΤΙΚΗ ΜΕΛΕΤΗ ΦΟΡΕΩΝ ΛΕΠΤΟΤΟΙΧΗΣ ΔΙΑΤΟΜΗΣ","Engineering and Technology","Civil Engineering","Επιστήμες Μηχανικού και Τεχνολογία","Επιστήμη Πολιτικού Μηχανικού"]}]},{"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/1660","http://hdl.handle.net/10442/hedi/1660"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["INEQUALITY CONSTRAINTS HAVE BEEN STUDIED IN RECENT YEARS IN SEVERAL AREAS OF STRUCTURAL ANALYSIS. WE MENTION, THE THEORY OF IDEAL PLASTICITY AND VISCOPLASTICITY, THE UNILATERAL CONTACT PROBLEMS OF A BODY WITH RIGID OR DEFORMABLE BODY, THE FRICTION PROBLEMS E.T.C. MOREOVER, SUCH PROBLEMS HAVE NOT BEEN FORMULATED ANDSTUDIED IN THE FRAMEWORK OF STRUCTURES INCLUDING THIN WALLED BEAMS, BUT ONLY FOR CLASSICAL BEAMS AND PLATES AS WELL AS FOR FRAMES AND TRUSSES. THIS IS ATTEMPTED IN THE PRESENT WORK, FOR OPEN CROSS SECTION THIN WALLED BEAMS AND GENERALLYFOR STRUCTURES CONTAINING SUCH ELEMENTS. SEVERAL CONTACT, PLASTICITY AND FRICTION PROBLEMS ARE FORMULATED AND STUDIED AND THE RESPECTIVE VARIATIONAL EXPRESSIONS ARE DERIVED. NOTE THAT IN THE CASE OF INEQUALITY CONSTRAINTS THE PRINCIPLE OF VIRTUAL WORK AND THE COMPLEMENTARY VIRTUAL WORK HOLD IN INEQUALITY FORMS WHICH CONSTITUTE VARIATIONAL INEQUALITIES. THIS IS CAUSED BY THE FACT THAT THE VARIATIONS OF THE INEQUALITY CONSTRAINED QUANTITIES ARE UNILATERAL I.E. WHEN ΔΧ=Χ*-Χ IS ADMISSIBLE -ΔΧ IS NOT ADMISSIBLE. FINALLY THE RESULTING PROBLEMS ARE FORMULATED AS INEQUALITY CONSTRAINED MINIMUM PROBLEMS AND THE THEORY IS ILLUSTRATEDBY NUMERICAL EXAMPLES. HERE WE HAVE CONSIDERED INEQUALITY CONSTRAINTS ARISING FROM REACTION-DISPLACEMENT OR MOMENT-ROTATION DIAGRAM OF MONOTONE TYPE. THE MORE GENERAL CASE OF LOCK OF MONOTONICITY LEADS TO HEMIRATIONAL INEQUALITIES. THE PRESENT WORK DIVIDED INTO FIVE CHAPTERS DEALS WITH THE ANALYSIS OF STRUCTURES WHOSE STRUCTURAL ELEMENTS ARE OF THIN WALLED OPEN CROSS SECTION TYPE AND INVOLVEMONOTE LAWS OF THEIR BOUNDARIES.","ΟΙ ΜΟΝΟΠΛΕΥΡΟΙ ΠΕΡΙΟΡΙΣΜΟΙ ΜΕΛΕΤΗΘΗΚΑΝ ΤΑ ΤΕΛΕΥΤΑΙΑ ΧΡΟΝΙΑ ΣΕ ΔΙΑΦΟΡΕΣ ΕΦΑΡΜΟΓΕΣ ΤΗΣ ΕΠΙΣΤΗΜΗΣ ΤΟΥ ΠΟΛΙΤΙΚΟΥ ΜΗΧΑΝΙΚΟΥ. ΑΝΑΦΕΡΟΝΤΑΙ ΕΔΩ ΩΣ ΠΑΡΑΔΕΙΓΜΑ ΤΟ ΠΡΟΒΛΗΜΑ ΤΗΣ ΘΕΩΡΙΑΣ ΙΔΑΝΙΚΗΣ ΠΛΑΣΤΙΚΟΤΗΤΑΣ, ΤΟ ΠΡΟΒΛΗΜΑ ΜΟΝΟΠΛΕΥΡΗΣ ΕΠΑΦΗΣ ΚΑΙ ΤΟ ΠΡΟΒΛΗΜΑ ΤΡΙΒΗΣ. ΤΑ ΠΡΟΗΓΟΥΜΕΝΑ ΠΡΟΒΛΗΜΑΤΑ ΜΕΛΕΤΗΘΗΚΑΝ ΓΙΑ ΤΡΙΣΔΙΑΣΤΑΤΑ ΣΩΜΑΤΑ, ΓΙΑ ΚΛΑΣΣΙΚΕΣ ΔΟΚΟΥΣ ΚΑΙ ΠΛΑΚΕΣ, ΚΑΘΩΣ ΕΠΙΣΗΣ ΚΑΙ ΓΙΑ ΠΛΑΙΣΙΩΤΕΣ ΚΑΤΑΣΚΕΥΕΣ, ΑΛΛΑ ΜΕΧΡΙ ΣΗΜΕΡΑ ΤΕΤΟΙΟΥ ΕΙΔΟΥΣ ΠΡΟΒΛΗΜΑΤΑ ΔΕΝ ΕΧΟΥΝ ΜΕΛΕΤΗΘΕΙ ΓΙΑ ΚΑΤΑΣΚΕΥΕΣ ΠΟΥ ΠΕΡΙΛΑΜΒΑΝΟΥΝ ΣΤΑ ΔΟΜΙΚΑ ΤΟΥΣ ΣΤΟΙΧΕΙΑ ΛΕΠΤΟΤΟΙΧΕΣ ΔΟΚΟΥΣ. ΑΥΤΟ ΕΠΙΧΕΙΡΕΙΤΑΙ ΣΤΗΝ ΕΡΓΑΣΙΑ ΓΙΑ ΛΕΠΤΟΤΟΙΧΕΣ ΔΟΚΟΥΣ ΑΝΟΙΚΤΗΣ ΔΙΑΤΟΜΗΣ ΑΛΛΑ ΚΑΙ ΓΕΝΙΚΟΤΕΡΑ ΓΙΑ ΚΑΤΑΣΚΕΥΕΣ ΠΟΥ ΑΠΟΤΕΛΟΥΝΤΑΙ ΚΑΙ ΑΠΟ ΤΕΤΟΙΑ ΔΟΜΙΚΑ ΣΤΟΙΧΕΙΑ. ΓΙΑ ΤΙΣ ΚΑΤΑΣΚΕΥΕΣ ΑΥΤΕΣ ΜΕΛΕΤΩΝΤΑΙ ΔΙΑΦΟΡΑ ΠΡΟΒΛΗΜΑΤΑ ΕΠΑΦΗΣ-ΤΡΙΒΗΣ ΚΑΙ ΜΟΡΦΩΝΟΝΤΑΙ ΟΙ ΑΝΤΙΣΤΟΙΧΕΣΕΚΦΡΑΣΕΙΣ ΤΗΣ ΑΡΧΗΣ ΤΩΝ ΔΥΝΑΤΩΝ ΕΡΓΩΝ. ΣΤΗΝ ΠΕΡΙΠΤΩΣΗ ΚΑΤΑΣΚΕΥΩΝ ΜΕ ΜΟΝΟΠΛΕΥΡΕΣ ΣΥΝΟΡΙΑΚΕΣ ΣΥΝΘΗΚΕΣ, Η ΑΡΧΗ ΤΩΝ ΔΥΝΑΤΩΝ ΕΡΓΩΝ ΚΑΙ ΤΩΝ ΣΥΜΠΛΗΡΩΜΑΤΙΚΩΝ ΔΥΝΑΤΩΝΕΡΓΩΝ ΙΣΧΥΕΙ ΣΕ ΜΟΡΦΗ ΑΝΙΣΟΤΗΤΑΣ. ΑΥΤΟ ΟΦΕΙΛΕΤΑΙ ΣΤΟ ΓΕΓΟΝΟΣ ΟΤΙ ΟΙ ΜΕΤΑΒΟΛΕΣ ΤΩΝ ΜΕΓΕΘΩΝ ΠΟΥ ΥΠΕΙΣΕΡΧΟΝΤΑΙ ΣΤΟΥΣ ΠΕΡΙΟΡΙΣΜΟΥΣ ΤΩΝ ΠΡΟΒΛΗΜΑΤΩΝ ΑΥΤΩΝ ΕΙΝΑΙ ΜΗ\"ΑΝΤΙΣΤΡΕΠΤΕΣ\". ΤΑ ΠΡΟΑΝΑΦΕΡΘΕΝΤΑ ΠΡΟΒΛΗΜΑΤΑ ΜΟΡΦΩΝΟΝΤΑΙ ΙΣΟΔΥΝΑΜΑ ΩΣ ΠΡΟΒΛΗΜΑΤΑ ΕΛΑΧΙΣΤΟΥ ΤΗΣ ΔΥΝΑΜΙΚΗΣ ΚΑΙ ΣΥΜΠΛΗΡΩΜΑΤΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ΚΑΙ Η ΘΕΩΡΙΑ ΣΥΜΠΛΗΡΩΝΕΤΑΙ ΑΠΟ ΑΡΙΘΜΗΤΙΚΑ ΠΑΡΑΔΕΙΓΜΑΤΑ. Η ΘΕΩΡΙΑ ΠΟΥ ΑΝΑΠΤΥΣΣΕΤΑΙ ΕΠΙΤΡΕΠΕΙ ΤΗΝ ΑΝΤΙΜΕΤΩΠΙΣΗ ΠΡΟΒΛΗΜΑΤΩΝ ΜΕ ΙΔΙΑΙΤΕΡΟ ΕΝΔΙΑΦΕΡΟΝ ΟΠΩΣ ΑΥΤΑ ΜΕ ΑΝΙΣΟΤΙΚΟΥΣ ΠΕΡΙΟΡΙΣΜΟΥΣ ΠΟΥ ΠΡΟΚΥΠΤΟΥΝ ΑΠΟ ΔΙΑΓΡΑΜΜΑΤΑ ΑΝΤΙΔΡΑΣΗΣ-ΜΕΤΑΤΟΠΙΣΗΣ, ΡΟΠΗΣ-ΣΤΡΟΦΗΣ 'Η ΔΙΡΡΟΠΗΣ-ΚΥΡΤΩΣΗΣ ΚΑΙ ΟΔΗΓΕΙ ΣΥΧΝΑ ΣΕ ΠΙΟ ΑΚΡΙΒΕΙΣ ΛΥΣΕΙΣ, ΒΟΗΘΩΝΤΑΣ ΠΑΡΑΛΛΗΛΑ ΣΤΗΝΚΑΛΥΤΕΡΗ ΚΑΤΑΝΟΗΣΗ ΤΗΣ ΜΗΧΑΝΙΚΗΣ ΣΥΜΠΕΡΙΦΟΡΑΣ ΤΗΣ ΚΑΤΑΣΚΕΥΗΣ. Η ΕΡΓΑΣΙΑ ΧΩΡΙΖΕΤΑΙ ΣΕ ΠΕΝΤΕ ΚΕΦΑΛΑΙΑ ΚΑΙ ΑΣΧΟΛΕΙΤΑΙ ΜΕ ΤΗΝ ΜΗΧΑΝΙΚΗ ΣΥΜΠΕΡΙΦΟΡΑ ΤΩΝ ΚΑΤΑΣΚΕΥΩΝΠΟΥ ΤΑ ΣΤΟΙΧΕΙΑ ΤΟΥΣ ΑΠΟΤΕΛΟΥΝΤΑΙ ΑΠΟ ΑΝΟΙΚΤΕΣ ΛΕΠΤΟΤΟΙΧΕΣ ΔΙΑΤΟΜΕΣ ΚΑΙ ΥΠΟΚΕΙΝΤΑΙ ΣΕ ΜΟΝΟΠΛΕΥΡΕΣ ΣΥΝΟΡΙΑΚΕΣ ΣΥΝΘΗΚΕΣ."]},{"key":"dc:title","label":"Title","values":["ΜΗ ΓΡΑΜΜΙΚΑ ΠΡΟΒΛΗΜΑΤΑ ΛΕΠΤΟΤΟΙΧΩΝ ΔΙΑΤΟΜΩΝ","NONLINEAR PROBLEMS OF THIN-WALLED SECTIONS"]}]}],"canonical_facts":{"dc:creator":["Ποτήρη, Θεοδώρα"],"dc:date":["1991"],"dc:description":["INEQUALITY CONSTRAINTS HAVE BEEN STUDIED IN RECENT YEARS IN SEVERAL AREAS OF STRUCTURAL ANALYSIS. WE MENTION, THE THEORY OF IDEAL PLASTICITY AND VISCOPLASTICITY, THE UNILATERAL CONTACT PROBLEMS OF A BODY WITH RIGID OR DEFORMABLE BODY, THE FRICTION PROBLEMS E.T.C. MOREOVER, SUCH PROBLEMS HAVE NOT BEEN FORMULATED ANDSTUDIED IN THE FRAMEWORK OF STRUCTURES INCLUDING THIN WALLED BEAMS, BUT ONLY FOR CLASSICAL BEAMS AND PLATES AS WELL AS FOR FRAMES AND TRUSSES. THIS IS ATTEMPTED IN THE PRESENT WORK, FOR OPEN CROSS SECTION THIN WALLED BEAMS AND GENERALLYFOR STRUCTURES CONTAINING SUCH ELEMENTS. SEVERAL CONTACT, PLASTICITY AND FRICTION PROBLEMS ARE FORMULATED AND STUDIED AND THE RESPECTIVE VARIATIONAL EXPRESSIONS ARE DERIVED. NOTE THAT IN THE CASE OF INEQUALITY CONSTRAINTS THE PRINCIPLE OF VIRTUAL WORK AND THE COMPLEMENTARY VIRTUAL WORK HOLD IN INEQUALITY FORMS WHICH CONSTITUTE VARIATIONAL INEQUALITIES. THIS IS CAUSED BY THE FACT THAT THE VARIATIONS OF THE INEQUALITY CONSTRAINED QUANTITIES ARE UNILATERAL I.E. WHEN ΔΧ=Χ*-Χ IS ADMISSIBLE -ΔΧ IS NOT ADMISSIBLE. FINALLY THE RESULTING PROBLEMS ARE FORMULATED AS INEQUALITY CONSTRAINED MINIMUM PROBLEMS AND THE THEORY IS ILLUSTRATEDBY NUMERICAL EXAMPLES. HERE WE HAVE CONSIDERED INEQUALITY CONSTRAINTS ARISING FROM REACTION-DISPLACEMENT OR MOMENT-ROTATION DIAGRAM OF MONOTONE TYPE. THE MORE GENERAL CASE OF LOCK OF MONOTONICITY LEADS TO HEMIRATIONAL INEQUALITIES. THE PRESENT WORK DIVIDED INTO FIVE CHAPTERS DEALS WITH THE ANALYSIS OF STRUCTURES WHOSE STRUCTURAL ELEMENTS ARE OF THIN WALLED OPEN CROSS SECTION TYPE AND INVOLVEMONOTE LAWS OF THEIR BOUNDARIES.","ΟΙ ΜΟΝΟΠΛΕΥΡΟΙ ΠΕΡΙΟΡΙΣΜΟΙ ΜΕΛΕΤΗΘΗΚΑΝ ΤΑ ΤΕΛΕΥΤΑΙΑ ΧΡΟΝΙΑ ΣΕ ΔΙΑΦΟΡΕΣ ΕΦΑΡΜΟΓΕΣ ΤΗΣ ΕΠΙΣΤΗΜΗΣ ΤΟΥ ΠΟΛΙΤΙΚΟΥ ΜΗΧΑΝΙΚΟΥ. ΑΝΑΦΕΡΟΝΤΑΙ ΕΔΩ ΩΣ ΠΑΡΑΔΕΙΓΜΑ ΤΟ ΠΡΟΒΛΗΜΑ ΤΗΣ ΘΕΩΡΙΑΣ ΙΔΑΝΙΚΗΣ ΠΛΑΣΤΙΚΟΤΗΤΑΣ, ΤΟ ΠΡΟΒΛΗΜΑ ΜΟΝΟΠΛΕΥΡΗΣ ΕΠΑΦΗΣ ΚΑΙ ΤΟ ΠΡΟΒΛΗΜΑ ΤΡΙΒΗΣ. ΤΑ ΠΡΟΗΓΟΥΜΕΝΑ ΠΡΟΒΛΗΜΑΤΑ ΜΕΛΕΤΗΘΗΚΑΝ ΓΙΑ ΤΡΙΣΔΙΑΣΤΑΤΑ ΣΩΜΑΤΑ, ΓΙΑ ΚΛΑΣΣΙΚΕΣ ΔΟΚΟΥΣ ΚΑΙ ΠΛΑΚΕΣ, ΚΑΘΩΣ ΕΠΙΣΗΣ ΚΑΙ ΓΙΑ ΠΛΑΙΣΙΩΤΕΣ ΚΑΤΑΣΚΕΥΕΣ, ΑΛΛΑ ΜΕΧΡΙ ΣΗΜΕΡΑ ΤΕΤΟΙΟΥ ΕΙΔΟΥΣ ΠΡΟΒΛΗΜΑΤΑ ΔΕΝ ΕΧΟΥΝ ΜΕΛΕΤΗΘΕΙ ΓΙΑ ΚΑΤΑΣΚΕΥΕΣ ΠΟΥ ΠΕΡΙΛΑΜΒΑΝΟΥΝ ΣΤΑ ΔΟΜΙΚΑ ΤΟΥΣ ΣΤΟΙΧΕΙΑ ΛΕΠΤΟΤΟΙΧΕΣ ΔΟΚΟΥΣ. ΑΥΤΟ ΕΠΙΧΕΙΡΕΙΤΑΙ ΣΤΗΝ ΕΡΓΑΣΙΑ ΓΙΑ ΛΕΠΤΟΤΟΙΧΕΣ ΔΟΚΟΥΣ ΑΝΟΙΚΤΗΣ ΔΙΑΤΟΜΗΣ ΑΛΛΑ ΚΑΙ ΓΕΝΙΚΟΤΕΡΑ ΓΙΑ ΚΑΤΑΣΚΕΥΕΣ ΠΟΥ ΑΠΟΤΕΛΟΥΝΤΑΙ ΚΑΙ ΑΠΟ ΤΕΤΟΙΑ ΔΟΜΙΚΑ ΣΤΟΙΧΕΙΑ. ΓΙΑ ΤΙΣ ΚΑΤΑΣΚΕΥΕΣ ΑΥΤΕΣ ΜΕΛΕΤΩΝΤΑΙ ΔΙΑΦΟΡΑ ΠΡΟΒΛΗΜΑΤΑ ΕΠΑΦΗΣ-ΤΡΙΒΗΣ ΚΑΙ ΜΟΡΦΩΝΟΝΤΑΙ ΟΙ ΑΝΤΙΣΤΟΙΧΕΣΕΚΦΡΑΣΕΙΣ ΤΗΣ ΑΡΧΗΣ ΤΩΝ ΔΥΝΑΤΩΝ ΕΡΓΩΝ. ΣΤΗΝ ΠΕΡΙΠΤΩΣΗ ΚΑΤΑΣΚΕΥΩΝ ΜΕ ΜΟΝΟΠΛΕΥΡΕΣ ΣΥΝΟΡΙΑΚΕΣ ΣΥΝΘΗΚΕΣ, Η ΑΡΧΗ ΤΩΝ ΔΥΝΑΤΩΝ ΕΡΓΩΝ ΚΑΙ ΤΩΝ ΣΥΜΠΛΗΡΩΜΑΤΙΚΩΝ ΔΥΝΑΤΩΝΕΡΓΩΝ ΙΣΧΥΕΙ ΣΕ ΜΟΡΦΗ ΑΝΙΣΟΤΗΤΑΣ. ΑΥΤΟ ΟΦΕΙΛΕΤΑΙ ΣΤΟ ΓΕΓΟΝΟΣ ΟΤΙ ΟΙ ΜΕΤΑΒΟΛΕΣ ΤΩΝ ΜΕΓΕΘΩΝ ΠΟΥ ΥΠΕΙΣΕΡΧΟΝΤΑΙ ΣΤΟΥΣ ΠΕΡΙΟΡΙΣΜΟΥΣ ΤΩΝ ΠΡΟΒΛΗΜΑΤΩΝ ΑΥΤΩΝ ΕΙΝΑΙ ΜΗ\"ΑΝΤΙΣΤΡΕΠΤΕΣ\". ΤΑ ΠΡΟΑΝΑΦΕΡΘΕΝΤΑ ΠΡΟΒΛΗΜΑΤΑ ΜΟΡΦΩΝΟΝΤΑΙ ΙΣΟΔΥΝΑΜΑ ΩΣ ΠΡΟΒΛΗΜΑΤΑ ΕΛΑΧΙΣΤΟΥ ΤΗΣ ΔΥΝΑΜΙΚΗΣ ΚΑΙ ΣΥΜΠΛΗΡΩΜΑΤΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ΚΑΙ Η ΘΕΩΡΙΑ ΣΥΜΠΛΗΡΩΝΕΤΑΙ ΑΠΟ ΑΡΙΘΜΗΤΙΚΑ ΠΑΡΑΔΕΙΓΜΑΤΑ. Η ΘΕΩΡΙΑ ΠΟΥ ΑΝΑΠΤΥΣΣΕΤΑΙ ΕΠΙΤΡΕΠΕΙ ΤΗΝ ΑΝΤΙΜΕΤΩΠΙΣΗ ΠΡΟΒΛΗΜΑΤΩΝ ΜΕ ΙΔΙΑΙΤΕΡΟ ΕΝΔΙΑΦΕΡΟΝ ΟΠΩΣ ΑΥΤΑ ΜΕ ΑΝΙΣΟΤΙΚΟΥΣ ΠΕΡΙΟΡΙΣΜΟΥΣ ΠΟΥ ΠΡΟΚΥΠΤΟΥΝ ΑΠΟ ΔΙΑΓΡΑΜΜΑΤΑ ΑΝΤΙΔΡΑΣΗΣ-ΜΕΤΑΤΟΠΙΣΗΣ, ΡΟΠΗΣ-ΣΤΡΟΦΗΣ 'Η ΔΙΡΡΟΠΗΣ-ΚΥΡΤΩΣΗΣ ΚΑΙ ΟΔΗΓΕΙ ΣΥΧΝΑ ΣΕ ΠΙΟ ΑΚΡΙΒΕΙΣ ΛΥΣΕΙΣ, ΒΟΗΘΩΝΤΑΣ ΠΑΡΑΛΛΗΛΑ ΣΤΗΝΚΑΛΥΤΕΡΗ ΚΑΤΑΝΟΗΣΗ ΤΗΣ ΜΗΧΑΝΙΚΗΣ ΣΥΜΠΕΡΙΦΟΡΑΣ ΤΗΣ ΚΑΤΑΣΚΕΥΗΣ. Η ΕΡΓΑΣΙΑ ΧΩΡΙΖΕΤΑΙ ΣΕ ΠΕΝΤΕ ΚΕΦΑΛΑΙΑ ΚΑΙ ΑΣΧΟΛΕΙΤΑΙ ΜΕ ΤΗΝ ΜΗΧΑΝΙΚΗ ΣΥΜΠΕΡΙΦΟΡΑ ΤΩΝ ΚΑΤΑΣΚΕΥΩΝΠΟΥ ΤΑ ΣΤΟΙΧΕΙΑ ΤΟΥΣ ΑΠΟΤΕΛΟΥΝΤΑΙ ΑΠΟ ΑΝΟΙΚΤΕΣ ΛΕΠΤΟΤΟΙΧΕΣ ΔΙΑΤΟΜΕΣ ΚΑΙ ΥΠΟΚΕΙΝΤΑΙ ΣΕ ΜΟΝΟΠΛΕΥΡΕΣ ΣΥΝΟΡΙΑΚΕΣ ΣΥΝΘΗΚΕΣ."],"dc:identifier":["10.12681/eadd/1660","http://hdl.handle.net/10442/hedi/1660"],"dc:language":["gre"],"dc:publisher":["Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)","Aristotle University Of Thessaloniki (AUTH)"],"dc:subject":["INEQUALITY PROBLEMS IN MECHANICS","NON SMOOTH ANALYSIS: APPLICATIONS","NONLINEARSTRUCTURAL ANALYSIS","STRUCTURAL ANALYSIS OF THIN-WALLED SECTIONS","THE MINIMUM OF THE COPLEMENTARY ENERGY","THE MINIMUM OF THE VIRTUAL ENERGY","UNILATERAL BOUNDARY CONDITIONS","VARIATIONAL PROBLEMS IN MECHANICS","ΑΝΙΣΟΤΗΤΕΣ ΜΕΤΑΒΟΛΩΝ ΑΡΧΗΣ ΤΩΝ ΔΥΝΑΤΩΝ ΕΡΓΩΝ","ΑΝΙΣΟΤΗΤΕΣ ΜΕΤΑΒΟΛΩΝ ΑΡΧΗΣ ΤΩΝ ΣΥΜΠΛΗΡ. ΕΡΓΩΝ","ΑΝΙΣΟΤΙΚΑ ΠΡΟΒΛΗΜΑΤΑ ΜΗΧΑΝΙΚΗΣ","ΕΛΑΧΙΣΤΟ ΔΥΝΑΜΙΚΗΣ ΕΝΕΡΓΕΙΑΣ","ΕΛΑΧΙΣΤΟ ΣΥΜΠΛΗΡΩΜΑΤΙΚΗΣ ΕΝΕΡΓΕΙΑΣ","Μη γραμμική ανάλυση","ΜΗ ΛΕΙΑ ΑΝΑΛΥΣΗ-ΕΦΑΡΜΟΓΕΣ","ΜΟΝΟΠΛΕΥΡΕΣ ΣΥΝΟΡΙΑΚΕΣ ΣΥΝΘΗΚΕΣ","ΠΡΟΒΛΗΜΑΤΑ ΜΕΤΑΒΟΛΩΝ ΣΤΗΝ ΜΗΧΑΝΙΚΗ","ΣΤΑΤΙΚΗ ΜΕΛΕΤΗ ΦΟΡΕΩΝ ΛΕΠΤΟΤΟΙΧΗΣ ΔΙΑΤΟΜΗΣ","Engineering and Technology","Civil Engineering","Επιστήμες Μηχανικού και Τεχνολογία","Επιστήμη Πολιτικού Μηχανικού"],"dc:title":["ΜΗ ΓΡΑΜΜΙΚΑ ΠΡΟΒΛΗΜΑΤΑ ΛΕΠΤΟΤΟΙΧΩΝ ΔΙΑΤΟΜΩΝ","NONLINEAR PROBLEMS OF THIN-WALLED SECTIONS"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:25:02Z"}