Search

The dissertation is a contribution in defining and studying different types of partial orders on rings, particularly on von Neumann regular and Rickart rings, as well as on the algebras of bounded operators on Banach and Hilbert spaces. In the first part of the dissertation, using generalized inverses of elements, the definitions of the minus, star, sharp, core and dual core partial orders are extended from the set of complex matrices to an arbitrary ring (with or without an involution). In a unified approach it is shown that the condition a

Tlo kao osnovni materijala za izradu nasutih brana ima izrazito nelinearno mehaničko ponašanje koje se bitno razlikuje od mehaničkog ponašanja drugih inženjerskih materijala. Kako bi sprovođenje detaljne analize stabilnosti nasutih brana primenom metode konačnih elemenata bilo moguće, neophodno je korišćenje materijalnih modela za opisivanje mehaničkog ponašanja materijala tla. Sa tim ciljem u okviru ove disertacije su razvijeni algoritmi za integraciju napona materijalnih modela najčešćih tipova tla. Razvijeni materijalni modeli su namenjeni statičkoj i dinamičkoj analizi tla, odnosno nasutih brana. Pored poznatih materijalnih modela za koje su razvijeni algoritmi za integraciju napona, razvijen je I implementiran nov materijalni model za simulaciju mehaničkog ponašanja granularnih materijala zasnovan na uslovu loma Maksimovića. Verifikacija materijalnih modela je izvršena kroz više primera numeričke simulacije eksperimentalnih ispitivanja uzoraka materijala tla kao i kroz primere u kojima su numerički rezultati poređeni sa teorijskim rešenjima. Razvijen je i implementiran algoritam za dinamičku analizu problema mehanike tla sa posebnim osvrtom na primenu u seizmičkoj analizi stabilnosti nasutih brana. Kako bi se analiziralo realno ponašanje materijala tla kao poroznog medija čije su pore ispunjene fluidom i u obzir uzela interakcija ove dve faze, izvršeno je sprezanje ravnotežnih jednačina čvrste i tečne faze. Sa ciljem redukovanja domena numeričke integracije pri analizi nasutih brana izloženih seizmičkom opterećenju, razvijene su i implementirane apsorbujuće granice modela. Korišćenjem ovih granica sprečava se pojava refleksije talasa od granica modela. Izvršena je analiza i sistematizacija kriterijuma za analizu stabilnosti nasutih brana I predložene metode određivanja njihove stabilnosti primenom razvijenih algoritama. U okviru ovog dela je obrađena metoda redukovanja smičuće čvrstoće primenom materijalnih modela razvijenih u okviru disertacije. Razvijeni softver i predložene metode analize stabilnosti nasutih brana su primenjene u analizi stabilnosti brane Prvonek. Soil as a basic material for construction of embankment dams is of a very non-linear and fundamentally different mechanical behavior compared to mechanical behavior of other engineering materials. In order to enable performance of detailed stability analysis of this structure type using the finite element method, it is necessary to use constitutive models to describe mechanical behavior of soil. With such an objective, algorithms for integration of material model stress of most common soil types were developed in this thesis. Developed material models are applied in static and dynamic soil analysis especially in embankment dams. Apart from familiar material models with developed algorithms for stress integration, there is also a new material model developed and implemented to simulate mechanical behavior of granular materials based on Maksimovic’s failure envelope. Verification of the material model was performed using a number of numerical simulations of experimental tests of soil material samples as well as examples in which numerical results were compared to theoretical solutions of the problems. Algorithm for dynamic analysis of the soil mechanics problems was developed and implemented with a special emphasis on the application in embankment dam seismic stability analysis. In order to analyze realistic behavior of soil materials as porous media whose pores are filled with fluid and to consider the interaction of these two phases, coupling of the equilibrium equations in solid and fluid phases was performed. With the aim to reduce numerical integration domain in the analysis of embankment dams subjected to seismic loads, absorbing boundary conditions were developed and implemented. These boundaries prevent the occurrence of reflection waves from the artificial boundaries. The analysis and systematization of stability analysis criteria for embankment dams were performed with suggested methods of their stability determination using developed algorithms. Sheer strength reduction method is also processed within this section using material models developed in the thesis. Developed software and suggested methods of embankment dam stability analysis were applied in the Prvonek dam stability analysis.

Polimerni materijali sa svojstvom pamćenja oblika (eng. Shape Memory Polymers – SMP) predstavljaju brzo rastuću grupu, čak i među naprednim materijalima. Ova grupa materijala odlikuje se sposobnošću obnove oblika nakon deformacije primenom adekvatnog spoljašnjeg stimulansa. Efekat pamćenja oblika prati složenom termomehaničko ponašanje koje se manifestuje dvojako: izraženom osetljivošću materijala na temperaturu ispitivanja/eksploatacije i osetljivost na brzinu deformacije/ispitivanja. Takođe, materijali sa navedenim svojstvom mogu biti izloženi izuzetno velikim deformacijama (> 300 %) pa se usled toga moraju koristiti formulacije za rešavanje velikih deformacija. Predočeni zahtevi su rešeni u nekoliko koraka (1) Predložen je modifikovani materijalni model sačinjen od više mikromehanizama, koji svaki ponaosob daje odgovarajući doprinos ukupnom naponskom stanju. (2) Za simulacije termo-mehančkog ponašanja polimera sa pamćenjem oblika korišćeno je spregnuto modeliranje povezivanjem programa za strukturnu analizu i prenos toplote, čime se pored efekta pamćenja oblika modelira i porast temperature u materijalu usled plastične disipacije. Kod problema velikih deformacija korišćena je logaritamska deformacija. (3) Multiplikativna dekompozicija ukupnog gradijenta deformacije izvršena je za svaki od mikromehanizama posebno, na elastični i plastični deo. (4) Odlike materijala potvrđene su eksperimentalnim ispitivanjima na uzorcima od PLA i fotopolimera. Izrada uzoraka i eksperimenti su sprovedeni na opremi Fakulteta inženjerskih nauka. Deo rezultata koji nije bilo moguće dobiti usled ograničenja opreme preuzet je iz dostupne literature. Dobro slaganje eksperimentalnih rezultata sa rezultatima modela pokazalo je ispravnost teorijskih pretpostavki i opravdalo formulisanje modela. Shape memory polymers (SMP) are a fast-growing group, even among advanced materials. This group of materials is characterized by the ability to recover permanent shape after deformation by applying an adequate external stimulus. The shape memory effect is accompanied by complex thermo-mechanical behaviour, which is manifested in two ways: strong temperature and strain rate dependence. Also, materials with this property can be exposed to extremely large deformations (> 300%), so large deformation theory must be applied. These tasks are solved in several steps: (1) A modified material model consisting of several micro-mechanisms is proposed, each of which individually makes an appropriate contribution to the overall stress state. (2) For simulations of thermo-mechanical behavior of SMPs, coupled modeling was used by connecting programs for structural analysis and heat transfer, allowing to model the temperature increase in the material due to plastic dissipation. For large deformation problems, logarithmic deformation was applied. (3) Multiplicative decomposition of total deformation gradient is applied for each micromechanism individually, separating total deformation gradient in plastic and elastic part. (4) Experimental testing is conducted on PLA and photopolymers specimens. All specimen and experiments are produced at the Faculty of Engineering. Missing results which were not possible to measure with given equipment are taken from literature. Good agreement of experiments with numerical results approve theoretical assumptions i accuracy of the proposed model.

Pravilan rad svih čula omogućava čoveku normalno funkcionisanje u sredini koja ga okružuje. Oštećenje ili gubitak čula sluha otežava svakodnevni život, smanjuje mogućnosti za rad i društveni život i može dovesti osobu u stanje depresije. Gubitak sluha može biti posledica različitih uzroka, oštećenja različitih delova uva ili auditornih nerava. Poboljšanje sluha je najčešće moguće ostvariti primenom slušnih aparata i slušnih implanata. U zavisnosti od stepena i vrste oštećenja predlaže se odgovarajući implant – pasivni ili aktivni, kohlearni ili implant srednjeg uva, implant koji radi na principu provođenja zvuka kroz vazduh ili zvuka kroz temporalnu kost. Iako doprinose poboljšanju sluha svi implanti se ugrađuju operativnim putem što nosi dozu rizika. O čulu sluha se zna dosta i opet nedovoljno. O uvu, kao organu čula sluha, se zna dosta o njegovoj strukturi i funkciji. Kohlea, koja čini deo unutrašnjeg uva, ima složenu strukturu i dosta procesa se odvija unutar nje. Problem sa izučavanjem kohlee se ogleda u tome što je teško prikupiti eksperimentalne podatke. Kohlea je smeštena duboko u lobanji, gotovo nepristupačna i velika je verovatnoća da će doći do oštećenja prilikom merenja na živom pacijentu. Na taj način eksperimentalni pristup je veoma ograničen. S druge strane, kohlea brzo gubi svoja svojstva po nastupanju smrti, tako da nije moguć u velikoj meri ni rad na mrtvim kohleama. Zbog toga kompjutersko modeliranje kohlee i analiza odziva imaju veliku ulogu u ovoj oblasti istraživanja. Cilj ove teze je razvoj mehaničkih i elektro-mehaničkih modela kohlee koji opisuju normalno funkcionisanje kohlee i omogućavaju analizu odziva – posmatranje promene odziva sa promenom izvesnih parametara. Dovođenje u vezu uzroka oštećenja sa njegovom posledicom, odnosno promenom odgovarajućeg parametra koji utiče na oštećenje sluha, omogućava primenu modela u praksi. Modeliranje kohlee ima za cilj i utvrđivanje postojanja određenih signala koji ukazuju na oštećenje i predlog načina merenja. Na ovaj način je ustanovljena kohlearna mikrofonija i pojava otoakustičnih emisija koje se koriste za detektovanje čula sluha kod novorođenih beba. Modeli kohlee mogu da doprinesu i poboljšanju karakteristika slušnih implanata i njihovom boljem pozicioniranju. U ovom radu su predstavljeni mehanički i elektro-mehanički modeli kohlee koji su rešavani metodom konačnih elemenata i kao modeli u prostoru stanja. Prikazani su osnovni odzivi, izvršeno je poređenje sa određenim eksperimentalnim merenjima i rezultatima drugih modela iz literature i data je analiza dobijenih odziva. Dalji rad na razvoju ovih modela mogao bi da vodi do njihove primene u pretkliničkoj praksi, a nastavak istraživanja je usmeren na primenu u oblasti slušnih implanata. Proper work of human senses allows normal functioning in the surrounding environment. Damage or hearing loss makes difficult everyday life, decreases possibilities for work and social life and can bring person to the state of depression. Hearing loss can be consequence of different causes, damage of different part of the ear or auditory nerves. Hearing improvement is usually possible to accomplish by applying hearing aids and hearing implants. In dependence of the level and type of damage certain implant is suggested – passive or active, cochlear or middle ear implant, implant that works on principle of air conduction of sound or bone conduction of sound, through the temporal bone. Although all implants contribute to improving of hearing, they are implanted during the surgery, which carrying a dose of risk. About hearing sense is known a lot of, but yet not enough. About ear, as organ of hearing sense, is known a lot about his structure and function. Cochlea, which makes part of the inner ear, has complex structure and a lot of processes are happening inside her. Problem with cochlear research is that it is hard to collect experimental data. Cochlea is placed deep inside the skull, almost unreachable and there is great possibility that it will be harmed during the experimental measurement on alive human. On that way experimental approach is very limited. On the other side, cochlea quickly loses its properties after death occurs, so it is not possible in larger scale to work with dead cochlea. That is the reason why computer modeling of cochlea and response analysis have great role in this research area. The goal of this thesis is to develop mechanical and electro-mechanical cochlea models which describe proper functioning of the cochlea and allow response analysis – observation of the response change with change of certain parameters. By combining cause of damage with his consequence, namely change of the certain parameter which has influence on hearing damage, model can be applied in practice. Modeling of cochlea has as one of the goal to establish existence of certain signals which pointing on damage and to propose way of signals measurement. On this way were established cochlear microphonic and appearance of otoacoustic emissions which are used for detection of hearing in newborn babies. Cochlea models can contribute in improvement of characteristics of hearing implants and their better positioning. In this work are presented mechanical and electro-mechanical cochlea models which were solved with finite element method and as models in state space representation. Most common responses are shown, comparison with specific experimental measurements and with results from other models from literature are performed and analysis of obtained responses is given. Further work on development of these models could lead to their application in preclinical practice, while future investigations in this area are directed to application in area of hearing implants.

Aorta, kao osnovni i najveći krvni sud u čoveku, neprekidno je izložena visokom pulzativnom pritisku i smičućim silama. Disekcija aorte predstavlja veoma ozbiljno i urgentno stanje, u kojem dolazi do cepanja i raslojavanja unutrašnjeg sloja aortnog zida, dok spoljnji sloj ostaje netaknut. Numeričke simulacije dinamičkog ponašanja fluida-krvi u aorti sa disekcijom mogu dosta pomoći lekarima, jer daju uvid u dalji razvoj bolesti. Osnovni metod koji je korišćen u ovom radu jeste metod konačnih elemenata (MKE). Brzine strujanja fluida, pritisaka i smičućih napona u čvorovima konačnih elemenata određuju se u karakterističnim tačkama pulzatornog strujanja krvi. U jednom delu rada, primenom komercijalnih softvera, izvršene su trodimenzionalne rekonstrukcije medicinskih snimaka, a potom, primenom softvera koji je razvijen u Istraživačko razvojnom centru za bioinženjering, sprovedeno je numeričko rešavanje odnosa pravog i lažnog lumena akutne aortne disekcije. Osnovni cilj teze je da se primenom numeričkih simulacija odrede pritisci, smičući naponi i brzine u pravom i lažnom lumenu čime se dobija jasna slika njihovog međusobnog odnosa. Virtuelnim simuliranjem efekta operacije (isecanjem uzlazne aorte i zamene tubus graftom) određuju se protoci kroz bočne opstruirane grane aorte zahvaćene disekcijom, što pokazuje kako hirurški zahvat zamene uzlazne aorte i prekidanje protoka lažnog lumena, ima uticaj na protok kroz grane aortnog luka i visceralne grane (grane abdominalne aorte). Određivanjem von Mizesovih napona u zidu lažnog lumena dobijaju se potencijalna mesta rupture aorte. Ovim putem se neinvazivnim pristupom određuje rizik od nastanka rupture aorte i daje prednost ovom metodu, umesto kriterijuma maksimalnog prečnika. Aorta, as the main and the largest blood vessel in the human body, is constantly exposed to high pulse pressure and shear forces. Aortic dissection is a very serious condition and medical emergency, which leads to tearing and delamination of the inner layer of the aortic wall, while the outer layer remains intact. Numerical simulations of the dynamic behavior of fluid-blood in the aorta dissection can be of great help to doctors, because they provide insight into further development of the disease. The main method used in this paper is the finite element method (FEM). Fluid velocity, pressure and wall shear stress in nodes of finite elements are determined by specific points of the pulsatile blood flow. One section of the paper focuses on a three-dimensional reconstruction of medical images using a commercial software and in the next section, by using the software developed in the Research and Development Centre for Bioengineering, the numerical solution of relations between true and false lumens of acute aortic dissection is performed. The main objective of the thesis is to determine pressures, wall shear stress and velocity in the true and false lumen by applying numerical simulations, which gives a clear picture of their relationship. Virtual simulation of the effects of the operation (by cutting the ascending aorta and replacing it with the stent graft) determines the flow through the obstructed side branches of aortic dissection, which shows how the surgical intervention of replacing the ascending aorta and interrupting the flow in the false lumen has an impact on the flow through the branches of the aortic arch and the visceral branches (branches of the abdominal aorta). By determining von Mises stresses in the wall of the false lumen, potential points of rupture of the aorta are obtained. In this manner, the risk of rupture of the aorta is determined by using a non-invasive approach, giving this method an advantage over the maximum diameter criterion.