Ιεραρχική βελτίωση της προσομοίωσης με την μέθοδο της ισογεωμετρικής ανάλυσης - Κάρρας, Δημήτριος (Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Πολιτικών Μηχανικών. Τομέας Δομοστατικής. Εργαστήριο Στατικής και Αντισεισμικών Ερευνών, 2015)
The aim of the present thesis is to introduce and examine in depth the possibilities of local refinement in Isogeometric Analysis with B-SPLines and NURBS. A major drawback of the Isogeometric Analysis was the lack of local refinement in a fast and efficient way. For the past years many have tried to tackle this issue in order to make IGA even faster. The answer came by Vuong et al in 2011, where by utilizing the hierarchical refinement theory proposed for computer graphics by Rainer Kraft, she was able to locally refine a B-SPLine and NURBS geometry admissible for analysis with the Isogeometric method. Hierarchical refinement is a technique of enriching the approximation space locally, which replaces the selected coarse grid with a fine one. However the initial proposal by Vuong itself had quite a lot drawbacks that needed to be handled. In this thesis we examined and reviewed all the later proposed methodologies and strategies which have been based on Vuongs theory and tried to overcome all the drawbacks that this methodology had. Our ultimate goal, is to compare all the methods of the literature in order to decide which one is the best, for IGA applications. We have also constructed our own algorithm for solving this kind of problems. Hieararchical refinement is currently one of the most trending topics in computational engineering and hopefully in the near future we will be able to issue our work and propose a new aspect of dealing with it efficiently. In order to compare appropriately the methods, the bandwidth of the stiffness matrices, the time consumption for the inversion of [K] and the time consumption for solving of the equations must be taken into account.