Αξιολόγηση μεθόδων τοπολογικής βελτιστοποίησης κατασκευών σε μη δομημένα πλέγματα

Φιλιππίδης, Αχιλλέας; Filippidis, Achilleas

dc.contributor.author	Φιλιππίδης, Αχιλλέας	el
dc.contributor.author	Filippidis, Achilleas	en
dc.date.accessioned	2019-07-10T08:47:50Z
dc.date.available	2019-07-10T08:47:50Z
dc.date.issued	2019-07-10
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/49026
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.16363
dc.rights	Default License
dc.subject	Βελτιστοποίηση Τοπολογίας	el
dc.subject	Μη δομημένο	el
dc.subject	Τριγωνικό στοιχείο	el
dc.subject	Topology Optimization	en
dc.subject	Unstructured	el
dc.subject	Triangular Element	el
dc.subject	Ανάλυση Πεπερασμένων Στοιχείων	el
dc.subject	Finite Element Analysis	el
dc.title	Αξιολόγηση μεθόδων τοπολογικής βελτιστοποίησης κατασκευών σε μη δομημένα πλέγματα	el
dc.title	Assessment of topology optimization methods in unstructured mesh	en
heal.type	bachelorThesis
heal.classification	Αναλύσεις Πεπερασμένων Στοιχείων	el
heal.classification	Βελτιστοποίηση Τοπολογίας	el
heal.language	el
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2019-03-14
heal.abstract	Σύγκριση και αποτίμηση των μεθόδων τοπολογικής βελτιστοποίησης φορέων με τις μεθόδους SIMP, BESO και Level Set σε μη δομημένα πλέγματα πεπερασμένων στοιχείων με την χρήση ενός εξακομβικού τριγωνικού στοιχείου βασισμένου στην θεωρία Reissner-Mindlin	el
heal.abstract	Which is the optimal structural model that could receive a given loadcase and steer it towards its supports while undergoing the least deformation? A question that any engineer is called to answer with each project he decides to take on, having though in his possession the modern tool of numerical analyses with the use of the finite element theory. The advantages of this numerical approach are exploited by the purely mathematical methods for the optimization of structures developed in the recent years, confronting a structural model as a function which could give after differentiation local, or even the deeply desired global, maxima. A reliable application of these optimization methods with the use of finite elements hopefully is represented by this thesis. In particular, in the first part the theory for the construction of a six node triangular finite element for thick plates is laid out, with each of the nodes having five degrees of freedom. Using this triangular element for the discretization of shell structural models the topology optimization of them is attempted with three different methods, the method of SIMP, the BESO method and finally the Level Set method. The unique and noteworthy part that this thesis will try to add in the work revolving these methods is their implementation on completely unstructured grids such as those provided by the Delaunay triangulation algorithm, a discretization that seldom one encounters on relevant research. Apart from the mathematical side of the methods, their algorithmic realization is also presented in order to further understand them in a practical level and display their distinctive details and the problems occurring from their implementation with the use of triangular finite elements, in comparison with the usually encountered quadrilateral elements in similar projects. For the execution of the analyses the programming structure MSolve was used, which was developed in the Institute of Structural Analysis and Antiseismic Research of National Technical University of Athens. MSolve is written in the programming language C#, in which the code for the triangular six node finite element was added, as well as those parts responsible for the implementation of the topology optimization methods mentioned above. However, C# isn’t one of the most popular programming languages, additionally to the fact that in order to understand the used in this thesis one should first familiarize themselves with the logic behind the ~ xii ~operations of MSolve. For this reason equivalent code written in matlab is exhibited and laid out step by step. In the final parts of this work applications of the above methods on different structural models are presented, from ones that rest in a 2D plane surface and only require the membrane behavior of the elements to shells belonging in the 3D space and require the full structural behavior of our triangular thick plate finite elements. Alongside the demonstration of the examples, the influence of the parameters used at the instantiation of each kind of problem is also discussed, such as the mesh density of the domains impact on the type, or even on the existence, of solution. The results from every approach are assessed and a thoughtful comparison between them is carried out. Ultimate goal of this thesis is to hopefully contribute in the foundations for the discussion about the optimal method for topology optimization problems of shell based structural models.	en
heal.advisorName	Λαγαρός, Νικόλαος Δ.	el
heal.committeeMemberName	Κουμούσης, Βλάσης Κ.	el
heal.committeeMemberName	Παπαδόπουλος, Βησσαρίων	el
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Πολιτικών Μηχανικών	el
heal.academicPublisherID	ntua
heal.fullTextAvailability	true