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master's thesis
Numerička metoda za problem elastičnog štapa uz prepreku
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:058264
Sočo, Petra
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Sočo, P. (2022). Numerička metoda za problem elastičnog štapa uz prepreku (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:058264

Sočo, Petra. "Numerička metoda za problem elastičnog štapa uz prepreku." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:058264

Sočo, Petra. "Numerička metoda za problem elastičnog štapa uz prepreku." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:058264

Sočo, P. (2022). 'Numerička metoda za problem elastičnog štapa uz prepreku', Master's thesis, University of Zagreb, Faculty of Science, accessed 08 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:058264

Sočo P. Numerička metoda za problem elastičnog štapa uz prepreku [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 December 08] Available at: https://urn.nsk.hr/urn:nbn:hr:217:058264

P. Sočo, "Numerička metoda za problem elastičnog štapa uz prepreku", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:058264

Metadata
TitleNumerička metoda za problem elastičnog štapa uz prepreku
Title (english)Numerical method for the problem of elastic beam with an obstacle
AuthorPetra Sočo
MentorJosip Tambača (mentor)
Committee memberJosip Tambača (predsjednik povjerenstva)
Committee memberLuka Grubišić (član povjerenstva)
Committee memberMarko Vrdoljak (član povjerenstva)
Committee memberBoris Muha (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-05-10, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu se upoznajemo s teorijom varijacijskih nejednakosti koje dovodimo u vezu sa problemom minimizacije funkcije na zatvorenom, konveksnom podskupu Hilbertovog prostora. Također, izvodimo dovoljne uvjete za postojanje jedinstvenog rješenja takvih problema i prezentiramo rezultate iz teorije aproksimacije rješenja. Upoznajemo se i s metodom penalizacije pomoću koje rješenje varijacijske nejednakosti dobijemo kao limes niza rješenja penaliziranih nejednakosti koje su definirane na cijelom prostoru V. U okviru uvedene teorije analiziramo problem prepreke za elastični štap opisan Euler-Bernoullijevom jednadžbom s Dirichletovim rubnim uvjetima koji rješavamo penalizacijom na konačnodimenzionalnom prostoru do kojeg dolazimo metodom konačnih elemenata. Tako definirana aproksimacija će se svesti na rješavanje niza nelinearnih jednadžbi ili, ekvivalentno, na niz problema minimizacije. Stoga prezentiratiramo i numeričke metode kojima možemo doći do danog rješenja: Newtonova i gradijentna metoda.
Abstract (english)
In this thesis, we present the fundamentals of the theory of variational inequalities that we associate with problems of minimization of functions on closed, convex subsets of a Hilbert space. Furthermore, we obtain sufficient conditions for a variational inequality to have a unique solution. We’ll employ penalty method that enables us to obtain a solution of variational inequality as a limit of solutions to penalized inequalities defined on the whole space. Within such a theoretical framework, we analyze the obstacle problem for an elastic beam determined by the Euler-Bernoulli equation subject to Dirichlet boundary conditions. The finite element method is used to derive a formulation of discrete obstacle problem, which we then solve by penalization in the finite-dimensional space. Approximation involves solving a series of nonlinear equations or, equivalently, minimization problems. Therefore, we also present numerical methods that yield a solution, namely gradient and Newton’s method.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:058264
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 on2022-06-08 10:15:40