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master's thesis
Metoda homogenizacije u topološkoj optimizaciji
Zagreb: University of Zagreb, Faculty of Science, 2017. urn:nbn:hr:217:789883
Ševerdija, Nela
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Ševerdija, N. (2017). Metoda homogenizacije u topološkoj optimizaciji (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:789883

Ševerdija, Nela. "Metoda homogenizacije u topološkoj optimizaciji." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:789883

Ševerdija, Nela. "Metoda homogenizacije u topološkoj optimizaciji." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:789883

Ševerdija, N. (2017). 'Metoda homogenizacije u topološkoj optimizaciji', Master's thesis, University of Zagreb, Faculty of Science, accessed 29 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:789883

Ševerdija N. Metoda homogenizacije u topološkoj optimizaciji [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2017 [cited 2024 December 29] Available at: https://urn.nsk.hr/urn:nbn:hr:217:789883

N. Ševerdija, "Metoda homogenizacije u topološkoj optimizaciji", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:217:789883

Metadata
TitleMetoda homogenizacije u topološkoj optimizaciji
AuthorNela Ševerdija
MentorJosip Tambača (mentor)
Committee memberJosip Tambača (predsjednik povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
Committee memberMladen Jurak (član povjerenstva)
Committee memberMarko Tadić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2017-09-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu iznesen je kratki pregled primjene metode homogenizacije na problem topološke optimizacije dvodimenzionalne elastične strukture načinjene od izotropnog elastičnog materijala. Najprije je uveden pojam H-konvergencije na kojem je temeljena metoda homogenizacije. Izvedeni su uvjeti optimalnosti takve strukture, takozvane Hashin-Shtrikmanove ocjene, te je dokazano da se struktura maksimalne krutosti postiže sekvencijalnim laminatom ranga 2 za čije su određivanje izvedene eksplicitne formule. Konačno je implementiran algoritam kojim su izračunate optimalne strukture u odabranim primjerima.
Abstract (english)
In this thesis we present a short summary of the homogenization method and its application to problems of shape optimization in the elasticity setting in two dimensions when the domain is filled with an isotropic elastic medium. First we introduce the notion of H-convergence on which the method of homogenization is based. Next, the optimality conditions for such a structure, namely Hashin-Shtrikman energy bounds, are computed and it is proved that an optimal shape in terms of compliance could be achieved by a rank-2 sequential laminate for which the effective properties are then explicitly determined. Finally, a numerical algorithm is developed and applied to computing the optimal shape of a structure in a few select examples.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:789883
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 on2018-03-15 14:15:05