Objektno orijentirane biblioteke za realizaciju metode konačnih elemenata s primjenom u brodogradnji

master's thesis

• Author: Tadej-Ivan Zečević
• Mentor: Luka Grubišić (mentor)
• Committee member: Luka Grubišić (predsjednik povjerenstva)
• Committee member: Goranka Nogo (član povjerenstva)
• Committee member: Zvonimir Bujanović (član povjerenstva)
• Committee member: Ilja Gogić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-07-17, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu opisana je metoda konačnih elemenata, generatori, alati i algoritmi koji se koriste da bi se ona ostvarila u praksi te praktičan zadatak kreiranja mreže konačnih elemenata na brodskoj konstrukciji. Na početku rada smo sklopili matricu krutosti i opisali osnovne elemente koji su bitni za jednostavnije integriranje po površini konačnih elemenata te za ispunjenje uvjeta kvalitete mreže. Opisali smo glavne algoritme gmsh generatora te prikazali njihove rezultate u dobivanju mreže na brodskom modelu. Objasnili smo zašto je važno napraviti dobru triangulaciju prije rekombinacije te naveli Frontal-Delaunay triangulaciju kao pozitivan primjer. Definirali smo pozitivne strane dobivene mreže, opisali prostor za napredak u kvaliteti mreže i kako to postići.

Abstract (english)

This paper describes a finite element method together with the generators, tools and algorithms needed for its use. It also provides an example of generating the mesh of finite elements for a ship structure. The first part of the paper assembles the stiffness matrix and describes basic finite elements necessary for simple integration over the surface of finite elements as well as for meeting the conditions of mesh quality. (In the second part), the main algorithms of the gmsh mesh generator are described and these outcomes are further used for making the mesh of the ship structure. We explained why it was important to make good triangulation before recombination. Frontal-Delaunay triangulation was indicated as a positive example. The advantages of the generated mesh are clearly explained. The paper also indicates possible improvements in mesh quality as well as the methods of achieving these improvements.

• Keywords: metoda konačnih elemenata; gmsh generator; Frontal-Delaunay triangulacija
• Keywords (english): finite element method; gmsh mesh generator; Frontal-Delaunay triangulation
• Language: croatian
• URN:NBN: urn:nbn:hr:217:536735
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-07-09 09:28:49