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dc.contributor.advisorHermann, G. Matthies
dc.contributor.otherŽivković, Miroslav
dc.creatorRosić, Bojana V.
dc.date.accessioned2016-01-05T13:08:43Z
dc.date.available2016-01-05T13:08:43Z
dc.date.available2020-07-03T15:11:43Z
dc.date.issued2012-11-16
dc.identifier.urihttp://eteze.kg.ac.rs/application/showtheses?thesesId=65
dc.identifier.urihttp://nardus.mpn.gov.rs/handle/123456789/3649
dc.identifier.urihttps://fedorakg.kg.ac.rs/fedora/get/o:124/bdef:Content/download
dc.description.abstractWithin the framework of innitesimal and large displacement elastoplasticity theory we consider a class of abstract stochastic variational inequalities of the second kind described by uncertain parameters. Particularly we focus on the rate-independent evolutionary problem with general hardening whose material characteristics are assumed to be distributed according to the maximum entropy law. By exhibiting the structure of the evolutionary equations in a convex setting we study the existence and uniqueness of the solution and carry the mathematical formulation over to the computationally more suitable mixed variational description. Within one time-backward Euler step the inequality reduces to a minimisation problem for smooth convex energy functional on discrete tensor product subspaces whose unique minimizer is obtained via a stochastic closest point projection algorithm based on white noise analysis". To this end we use a description in the language of nondissipative and dissipative operators and introduce the stochastic Galerkin method into the computational process in fully intrusive and non-intrusive variant. The former method represents the direct, purely algebraic way of computing the response in each iteration of Newton-like methods. As the solution is given in a form of polynomial chaos expansion, i.e. an explicit functional relationship between the independent random variables, the subsequent evaluations of its functionals (the mean, variance, or probabilities of exceedence) are shown to be very cheap, but with limited accuracy. Furthermore, the method is contrasted to the less-ecient but more accurate non-intrusive variant which evaluates the residuum in each iteration via highdimensional integration rules based on random or deterministic sampling - Monte Carlo and related techniques. In addition to these, we also present the stochastic collocation method via sparse grid techniques. Finally the methods are validated on a series of test examples in plain strain conditions whose reference solution is computed via direct integration methods.en
dc.description.abstractU okviru teorije malih i velikih plasticnih deformacija razmatrana je klasa apstraktnih stohastičkih varijacionih nejednakosti opisanih slučajnim promenljivama. Poseban fokus je stavljen na asocijativni evolucioni problem sa generalnim ojačanjem čije materijalne karakteristike imaju distribuciju odredenu zakonom maksimalne entropije. Proučavajući strukturu evolucionih jednačina uz pomoć konveksne teorije uslovi za postojanje i jedinstvenost rešenja su analizirani uz dodatnu matematičku reformulaciju problema u numerički prikladan mešoviti varijacioni opis. Dobijena nejednakost se nakon implicitne diskretizacije svodi na minimizaciju konveksnog funkcionala denisanog u tenzorskom prostoru dobijenom kao proizvod determinističkog i stohastičkog podprostora. Rešenje tako postavljenog problema se može dobiti novouvedenom stohastiškom metodom projekcije najbliže tačke uz pomoć teorije analize belog šuma. Pomenuta metoda se sastoji od dva koraka: elastičnog i plastičnog, koji zajedno čine stohastičku Galerkinovu metodu, ovde formulisanu na dva načina: direktan (intruzivan) i posredan (neintruzivan). Prva varijanta predstavlja direktan, algebarski način dobijanja rešenja u svakoj iteraciji Njutnove metode. Zahvaljujući polinomnoj formi rešenja sve predstojeće evaluacije njegovih funkcionala kao što su srednja vrednost, varijansa itd. postaju računski jako efikasne, ali ograničene tačnosti. U cilju unapredenja tačnosti Galekinova methoda je implementirana i u svojoj manje efikasnoj neintruzivnoj varijanti, koja računa rezidual u svakoj Njutnovoj iteraciji numeričkom (determinističkom ili stohastičkom) integracijom. Obe varijante Galerkinovih metoda su uporedene sa metodom stohastičke kolokacije zasnovane na sparse grid pravilu. Konačno sve predstavljene metode su verikovane na seriji test primera u ravanskom stanju deformacije i za referentno rešenje dobijeno uz pomoć direktne integracije.sr
dc.formatapplication/pdf
dc.languageen
dc.publisherУниверзитет у Крагујевцу, Факултет инжењерских наукаsr
dc.rightsopenAccessen
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.sourceУниверзитет у Крагујевцуsr
dc.subjectstohastička metodasr
dc.titleVariational formulations and functional approximation algorithms in stochastic plasticity of materialsen
dc.typedoctoralThesisen
dc.rights.licenseBY-NC-ND
dcterms.abstractХерманн, Г. Маттхиес; Живковић, Мирослав; Росић, Бојана В.;
dc.identifier.fulltexthttp://nardus.mpn.gov.rs/bitstream/id/71266/disertacija.pdf
dc.identifier.doi10.2298/kg20121116rosic
dc.identifier.rcubhttps://hdl.handle.net/21.15107/rcub_nardus_3649


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