Προχωρημένες υπολογιστικές μέθοδοι υψηλών επιδόσεων για την επίλυση προβλημάτων διάδοσης ρωγμών με τη μέθοδο των εξελιγμένων πεπερασμένων στοιχείων

Μπακαλάκος, Σεραφείμ; Bakalakos, Serafeim

dc.contributor.author	Μπακαλάκος, Σεραφείμ
dc.contributor.author	Bakalakos, Serafeim
dc.date.accessioned	2022-10-12T10:01:07Z
dc.date.available	2022-10-12T10:01:07Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/55896
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.23594
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	Πεπερασμένα στοιχεία	el
dc.subject	Υποφορείς	el
dc.subject	Μετάδοση θερμότητας	el
dc.subject	Διάδοση ρωγμών	el
dc.subject	Υπολογιστικά συστήματα υψηλών επιδόσεων	el
dc.subject	XFEM	en
dc.subject	Domain decomposition	en
dc.subject	Heat transfer	en
dc.subject	Crack propagation	en
dc.subject	High performance computing	en
dc.title	Προχωρημένες υπολογιστικές μέθοδοι υψηλών επιδόσεων για την επίλυση προβλημάτων διάδοσης ρωγμών με τη μέθοδο των εξελιγμένων πεπερασμένων στοιχείων	el
dc.contributor.department	Laboratory of Structural Analysis & Antiseismic Research	el
heal.type	doctoralThesis
heal.secondaryTitle	Advanced high performance computing methods for the solution of crack propagation and material design problems using the extended Finite Element method (XFEM)	el
heal.classification	Υπολογιστική Μηχανική	el
heal.classification	Computational Mechanics	en
heal.language	en
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2022-06-16
heal.abstract	The need for advanced high-performance materials in the industry led to the development of various innovative solutions over the years, designed to possess application-specific properties, such as improved thermal conductivity. To model heat transfer in composite materials, their complex micro-structure, as well as the thermal resistance at the interfaces between materials must be taken into account. The standard finite element treatment requires very fine meshes to conform to the complex geometry of these interfaces. This thesis proposes an eXtended Finite Element Method (XFEM) formulation that captures the temperature jump by enriching the polynomial approximation around the material interfaces with appropriate discontinuous functions. Specifically, a new XFEM enrichment scheme is developed to address the issue of multiple-phase junctions, namely areas where multiple interfaces with different resistance properties intersect. In addition, a double-mesh LSM technique is developed for describing the geometry of material interfaces. A very fine mesh is employed by a Level Set Method (LSM) to represent complex interface geometries with high accuracy, whereas XFEM uses a mesh that does not conform to the material interfaces, but is instead a coarser version of the LSM mesh, to reduce the computational cost of the analysis. The combined numerical model is first validated against existing results from the literature on polycrystalline materials. Then, it is applied for heat conduction analysis of polymers reinforced with carbon-nanotubes. The unknown thermal resistance between these materials is inferred by calibrating the numerically predicted effective conductivity to corresponding experimental measurements. The proposed XFEM model can be straightforwardly extended to other similar problem types, such us elasticity or electrical conduction. XFEM is also an attractive choice for modeling crack propagation, by enriching the polynomial displacement field of FEM with specialized non-smooth functions, without the need of remeshing in the vicinity of the crack at each propagation step. However, this enrichment causes the stiffness matrix to become strongly ill-conditioned, rendering the convergence of iterative solvers very slow. On the other hand, direct solvers are inefficient in 3D problems, due to the increased bandwidth of the system matrix. In this thesis, two domain decomposition solvers, namely FETI-DP and P-FETI-DP, are proposed for solving the linear systems resulting from XFEM crack propagation analysis in large-scale 3D problems. By modifying the coarse problem of both solvers, any singularities caused by the crack propagation are avoided and the XFEM-related ill-conditioning is completely eliminated, ensuring the scalability of FETI-DP and P-FETI-DP as the number of subdomains is increased. Finally, an efficient implementation in high performance computing systems, specifically computer clusters is developed, by altering the original FETI-DP and P-FETI-DP equations to minimize communication and computation bottlenecks in distributed memory environments.	en
heal.sponsor	I gratefully acknowledge the funding received towards my Ph.D from the Special Account for Research Funding (E.L.K.E.) of National Technical University of Athens (N.T.U.A.) scholarship. Funding was also provided by participation in the project ``Optimal multiscale design of innovative materials for heat exchange applications, (HEAT-68/1286)'', from the European Regional Development Fund and Greek National Funds through the operational program Competitiveness, Entrepreneurship and Innovation, under the call Research-Create-Innovate.	el
heal.advisorName	Παπαδόπουλος, Βησσαρίων
heal.advisorName	Παπαδρακάκης, Μανόλης
heal.advisorName	Papadopoulos, Vissarion
heal.advisorName	Papadrakakis, Manolis
heal.committeeMemberName	Παπαδόπουλος, Βησσαρίων
heal.committeeMemberName	Σπηλιόπουλος, Κωνσταντίνος
heal.committeeMemberName	Λαγαρός, Νικόλαος
heal.committeeMemberName	Σαπουντζάκης, Ευάγγελος
heal.committeeMemberName	Νεραντζάκη, Μαρία
heal.committeeMemberName	Στεφάνου, Γεώργιος
heal.committeeMemberName	Τριανταφύλλου, Σάββας
heal.committeeMemberName	Papadopoulos, Vissarion
heal.committeeMemberName	Spiliopoulos, Konstantinos
heal.committeeMemberName	Lagaros, Nikolaos
heal.committeeMemberName	Sapountzakis, Euaggelos
heal.committeeMemberName	Nerantzaki, Maria
heal.committeeMemberName	Stefanou, Georgios
heal.committeeMemberName	Triantafullou, Savvas
heal.academicPublisher	Σχολή Πολιτικών Μηχανικών	el
heal.academicPublisherID	ntua
heal.numberOfPages	277
heal.fullTextAvailability	false