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master's thesis
Optimizacija forme zakrivljenog štapa
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:611704
Jelašić, Mislav
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Jelašić, M. (2022). Optimizacija forme zakrivljenog štapa (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:611704

Jelašić, Mislav. "Optimizacija forme zakrivljenog štapa." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:611704

Jelašić, Mislav. "Optimizacija forme zakrivljenog štapa." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:611704

Jelašić, M. (2022). 'Optimizacija forme zakrivljenog štapa', Master's thesis, University of Zagreb, Faculty of Science, accessed 27 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:611704

Jelašić M. Optimizacija forme zakrivljenog štapa [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 December 27] Available at: https://urn.nsk.hr/urn:nbn:hr:217:611704

M. Jelašić, "Optimizacija forme zakrivljenog štapa", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:611704

Metadata
TitleOptimizacija forme zakrivljenog štapa
Title (english)Optimizing form of an elastic curved rod
AuthorMislav Jelašić
MentorJosip Tambača (mentor)
Committee memberJosip Tambača (predsjednik povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
Committee memberPavle Pandžić (član povjerenstva)
Committee memberNela Bosner (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-11-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu prezentiramo optimizaciju forme elastičnog zakrivljenog štapa. Najprije uvodimo jednodimenzionalni Antman-Cosseratov model, definiran za neproduljive i nesmičljive štapove, koji je zadan sustavom diferencijalnih jednadžbi. Zakrivljeni štap je zatim aproksimiran konačnom unijom ravnih štapića. Uz određene rubne uvjete, izvodimo slabu (varijacijsku) formulaciju našeg problema (prvo za pojedini ravni štapić, a onda i za cijeli zakrivljeni štap). Glavni zadatak je pronaći optimalnu debljinu štapa, za koju je štap najkrući, kada na njega djeluje vanjska sila. Iz mješovite formulacije, definiramo minimizacijsku zadaću koristeći podatljivost kao funkciju cilja. Također pokazujemo da postoji rješenje zadanog problema. Za računanje optimalne debljine prezentiramo iterativni algoritam. Na kraju, definiramo metodu konačnih elemenata za zakrivljeni štap, koju koristimo za numeričko određivanje rješenja.
Abstract (english)
In this paper we present the optimization of the form of an elastic curved rod. First, we introduce a one-dimensional Antman-Cosserat model, defined for inextensible and unshearable rods, which is given by a system of differential equations. The curved rod is then approximated by a finite union of straight rods. Using certain boundary conditions, we derive a weak (variational) formulation of our problem (firstly for a single straight rod, and then for the entire curved rod). The main goal is to find the thickness of rod for which the rod is the most stiff, when an external force acts on it. From the mixed formulation, we prescribe minimization problem using compliance as a cost function. We also show that there is a solution to the given problem. For calculating the optimal thickness, we present an iterative algorithm. Finally, we define the finite element method for a curved rod, which we use to numerically calculate the solution.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:611704
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-12-15 15:25:11