Modelling of structures using the Isogeometric Method

Τσαπέτης, Δημήτριος Γ.; Tsapetis, Dimitrios

dc.contributor.author	Τσαπέτης, Δημήτριος Γ.	el
dc.contributor.author	Tsapetis, Dimitrios	en
dc.date.accessioned	2021-01-18T08:08:18Z
dc.date.issued	2021-01-18
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/52814
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.20512
dc.rights	Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/gr/	*
dc.subject	Ισογεωμετρική ανάλυση	el
dc.subject	Μέθοδος υποφορέων	el
dc.subject	Μέθοδος ταξιθεσίας	el
dc.subject	Ανάλυση πολλαπλών κλιμάκων	el
dc.subject	Λεπτότοιχα κελύφη	el
dc.subject	Isogeometric analysis	en
dc.subject	Domain decomposition	en
dc.subject	Multiscale analysis	en
dc.subject	Thin shells	en
dc.subject	Collocation method	en
dc.title	Modelling of structures using the Isogeometric Method	en
dc.title	Προσομοίωση Κατασκευών με την Ισογεωμετρική Μέθοδο	el
dc.contributor.department	Τομέας Δομοστατικής - Εργαστήριο Στατικής και Αντισεισμικών Ερευνών	el
heal.type	doctoralThesis
heal.classification	Υπολογιστική Μηχανική	el
heal.dateAvailable	2022-01-17T22:00:00Z
heal.language	en
heal.access	embargo
heal.recordProvider	ntua	el
heal.publicationDate	2021-01-14
heal.abstract	Isogeometric Analysis was proposed as an alternative spatial discretization method, that addresses the need for an integrated pipeline of Computer Aided Design and Computer Aided Engineering industries, towards the development of efficient and reliable structures. To this end, CAD shape functions ranging from B´ezier to T-Splines are utilized, that allow the exact geometrical representation of arbitrarily complex geometries, while at the same time rendering the mesh generation procedure of other spatial discretization techniques such as FEM obsolete. Due to the high smoothness of the shape functions over conventional approaches, IGA has showcased significant advantages in various computational mechanics fields such as structural dynamics, fluid mechanics and optimization problems. In addition, the description of intricate geometries with highly continuous shape functions, enables IGA to be effectively used for shell theories such as Kirchhoff-Love thin shells, that required special treatment in the case of FEM. The latter resulted in the introduction of various shell formulations, for miscellaneous materials. Unfortunately, the strongest asset of isogeometric methods, which is the increased interelement continuity of the shape functions, constitutes at the same time its greatest weakness. Despite resulting in a smooth variation of the analysis characteristics and enhanced accuracy, a significant computational burden is added to the formation and solution of the resulting linear systems due to their increased bandwidth and reduced sparsity patterns. This rendering the introduction of efficient solution schemes a necessity for the establishment of isogeometric methods. To this end, this dissertation introduces a family of methods, to address the efficient implementation of solution schemes for the purpose of isogeometric Galerkin and collocation methods. Specifically, for the case of isogeometric Galerkin method, an appropriate modification of the overlapping nature of NURBS shape functions is introduced, in the form of truncated shape functions. This modification generates a non-overlapping equivalent of the initial model that retains the same geometry, yet has reduced accuracy. As a result,with the aid of IETI domain decomposition method, applied to the interface among adjacent subdomains, the non-overlapping model can serve as an efficient preconditioner for the PCG iterative method. In a similar fashion, a non-overlapping decomposition of the non-symmetric matrices derived from isogeometric collocation methods is proposed, that allows the development of a GMRES preconditioner based on P-FETI-DP domain decomposition method. Finally, in order to unify all existing thin shell isogeometric formulations, a framework is proposed that examines isogeometric shells under the prism of semi-concurrent multiscale analysis. To this end, a nested IGA-FEM analysis scheme is introduced, where macroscale shell modeling is performed with isogeometric Kirchhoff-Love shell elements, while Representative Volume Elements are discretized with solid finite elements. The required plane-stress constitutive law is then extracted from a homogenization process, thus leading to the introduction of a framework that can efficiently address composite materials of arbitrary microstructural topology	en
heal.sponsor	Ίδρυμα Ωνάση	el
heal.sponsor	European Research Council Advanced Grant MASTER - Mastering the computational challenges in numerical modeling and optimum design of CNT reinforced composites	en
heal.sponsor	European Regional Development Fund and Greek national funds under the Grant HEAT - Optimal multiscale design of innovative materials for heat exchange applications	en
heal.advisorName	Παπαδρακάκης, Εμμανουήλ	el
heal.committeeMemberName	Σπηλιόπουλος, Κωνσταντίνος	el
heal.committeeMemberName	Παπαδόπουλος, Βησσαρίων	el
heal.committeeMemberName	Γαντές, Χαράλαμπος	el
heal.committeeMemberName	Προβατίδης, Χριστόφορος	el
heal.committeeMemberName	Φραγκιαδάκης, Μιχαήλ	el
heal.committeeMemberName	Τριανταφύλλου, Σάββας	el
heal.committeeMemberName	Παπαδρακάκης, Εμμανουήλ	el
heal.academicPublisher	Σχολή Πολιτικών Μηχανικών	el
heal.academicPublisherID	ntua
heal.numberOfPages	262 p.	en
heal.fullTextAvailability	false