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Pouzdanost analiza geotehničkih problema numeričkih metoda kao što su metoda konačnih elemenata..., Accuracy and reliability of geotechical analysis by numerical methods such ....

REZIME Funkcionalno gradijentno raspoređeni materijali (FGM), kao grupa savremenih materijala u porodici inženjerskih kompozita dobijaju sve širu primenu u raznim granama industrije sa ciljem da se, odgovarajućim kombinovanjem potencijala dostupnih materijala, njihove osobine iskoriste na najbolji mogući način. Otkaz ili delaminacija, izazvana visokim lokalnim interlaminarnim naponima, je najveći i najčešće proučavani problem kod konvencionalnih kompozitnih laminata. U cilju prevazilaženja pomenutih problema, u okviru ove disertacije proučavane su i implementirane teorijske osnove, kao i analitičke i numeričke procedure kojima se može obezbediti predviđanje ponašanja ploča od funkcionalno gradijentno raspoređenih materijala izloženih različitim vrstama opterećenja. Prikazane su osnovne karakteristike FGM i ukazano je na njihove prednosti u odnosu na konvencionalne kompozitne laminate. Izvršena je njihova klasifikacija u odnosu na različite kriterijume i opisan je širok spektar oblasti u kojima se primenjuju. Posebna pažnja je posvećena definisanju matematičkih funkcija, koje na adekvatan način mogu da opišu njihovu gradijentnu strukturu. Te funkcije su poslužile kao osnova za dobijanje matematičkog modela FGM za naponsko-deformacionu analizu ploča koja je urađena u okviru ove disertacije Izvršena je sistematizacija teorija ploča koje se koriste u analizi konvencionalnih kompozitnih lamina. Data je analiza prednosti i nedostataka klasične teorije ploča i smicajnih deformacionih teorija prvog i višeg reda. Smicajna deformaciona teorija višeg reda zasnovana na 13 različitih funkcija oblika, koje su prvenstveno razvijene od strane različitih autora za analizu kompozitnih laminata, u ovoj disertaciji je prilagođena i implementirana u teorijske postavke za analizu ploča od FGM. Kako se veliki broj inženjerskih problema matematički opisuje modelom ploče na elastičnoj podlozi, proučene su i teorijske postavke ploče od FGM na elastičnoj podlozi. Primenjen je Vinkler-Pasterna, Functionally graded materials (FGM), as a group of modern materials in the family of engineering composite materials, are being increasingly used in various branches of industry, striving to make the best use of their characteristics by combining adequately the potentials of available materials. Failure or delamination, caused by high local interlaminar stresses, is the biggest and the most commonly studied problem with conventional composite laminates. With the aim of overcoming those problems, this thesis provides a study and implementation of theoretical basis, as well as analytical and numerical procedures which can predict the behaviour of plates of functionally graded materials exposed to different kinds of loading. The basic characteristics of FGM are presented and it is pointed to their advantages over conventional composite laminates. They have been classified according to various criteria and a wide range of areas of their use has been presented. Special attention has been given to defining mathematical functions which can adequately describe their graded structure. Those functions were used as a basis for getting a mathematical model of FGM for stress-strain analysis of plates which has been done within this thesis. A systematization of plate theories which are used in the analysis of conventional composite laminates has been done. The thesis also gives an analysis of advantages and disadvantages of the classical plate theory as well as of the first order and high order shear deformation theories. High order shear deformation theory based on 13 different shape functions, which were previously developed by various authors for the analysis of conventional composite laminates, has been adjusted and implemented into theoretical postulates for the analysis of FGM plates. Since a big number of engineering problems are mathematically described by a model of plate on an elastic foundation, the thesis studies theoretical postulates for FGM plates on an el

Granularne materijale čini skup vema velikog broja sitnih solida (zrna, granula, čestica) čije ponašanje zavisi od energije koju solidi poseduju i predstavljaju nakon vode drugu najmanipulisaniju materiju u inženjerstvu. Za numeričku analizu uređaja za transport, skladištenje i obradu granularnih materijala, neophodno je tačno modeliranje opterećenja kojima granularni materijal deluje na pomenute uređaje. U okviru ove disertacije data je teorijska analiza ponašanja granularnih materijala od mikro nivoa gde je analiziran kontakt između dva zrna, do makro nivoa u kome se analizira ponašanje celokupnog materijala. Metoda diskretnih elemenata je korišćena za modeliranje troosnog testa, eksperimenta koji se najčešće koristi za određivanje materijalnih karakteristika, kao i traka smicanja i vrtolga koji se pri tom javljaju u granularnom materijalu. Opterećenja u granularnom materijalu nisu ravnomerno raspoređena, već najopterećenija zrna formiraju lance sila dok ostala zrna igraju potpornu ulogu. Deformacije granularnog materijala izazivaju kidanje starih i formiranje novih lalnaca sila, a promene opterećenja su analizirane za izabrana zrna. Glatka čestična hidrodinamika je numerička metoda zasnovana na mehanici kontinuuma, a njen bezmrežni karakter omogućava analizu velikih deformacija u realnim problemima, pa je generalisani materijalni model sa kapom ugrađen u program i korišćen za modeliranje granularnih materijala. Metoda konačnih elementata je najčešće korišćena numerička metoda u inženjerstvu, a da bi se koristila za analizu uređaja za transport, skladištenje i obradu granularnih materijala povezana je sa glatkom čestičnom hidrodinamikom po principima fluid-solid interakcije, a kontaktni algoritam između ove dve metode je proširen tretmanom trenja na osnovu Kulonovog zakona. Metodologija analize podrazumeva korišćenje dva programa za pre-procesiranje i jednog za post-procesiranje koji su povezani sa solverima pomoću programa prevodioca. Materijalni model, sprezanje, The granular materials consists of large number of small solids (grains, granules, particles) whose behavior depends on the energy they have and represent the second most manipulated matter in engineering (water is the first). For numerical analysis of devices for transport, storage and processing of granular materials, it is necessary to accurately model load which granular materials exert on the aforementioned devices. As a part of this dissertation the theoretical analysis of granular materials behavior is presented, both at the micro levels where the contact between two grains is analyzed, and a macro level in which the behavior of the whole material is analyzed. Discrete element method was used for modeling of triaxial tests, experiments that are commonly used to determine material characteristics, as well as shear bands and vortexes which occur in the granular material during these tests. Loads in the granular material are not evenly distributed, with most loaded grains forming force chains, while other grains play only a supporting role. Deformation of granular materials causes breaking of old and the formation of new force chains and load changes are analyzed in selected grains. Smoothed particle hydrodynamics is a numerical method based on continuum mechanics, and its meshless character allows analysis of large deformation in real problems, so generalized material model with cap was coded into the program and used to model granular materials. Finite element analysis is the most widely used numerical methods in engineering, but in order to be used for the evaluation of construction for transportation, storage and processing of granular materials it needed to be connected with smoothed particle hydrodynamics using the principles of fluid-solid interactions, and contact algorithm between these two methods is expanded by friction treatment on the basis of Coulomb's law. The methodology of analysis involves the use of two programs for pre-processing and one for

Iz inženjerske prakse je poznato da su vagonske čelične konstrukcije tokom eksploatacije izložene složenim kombinovanim opterećenjima. Modernizacijom pruga, povećavanjem brzine kretanja, optimizacijom vagonskih konstrukcija, korišćenjem novih materijala, stvoreni su veliki izazovi u oblasti vagonske industrije. Paralelno sa povećanjem izazova, zahtevi u pogledu pouzdanosti i bezbednosti vagonskih konstrukcija postajali su sve veći. Predmet proučavanja i cilj rada na ovoj disertaciji je razvoj pouzdane metodologije za eksperimentalnu i numeričku procenu integriteta vagonskih konstrukcija izloženih promenljivim dinamičkim opterećenjima. Za potrebe procene integriteta delova vagonskih konstrukcija eksperimentalno su određivane karakteristike konstrukcionih čelika i čelika koji su već bili u fazi eksploatacije. Cilj ovih eksperimentalnih istraživanja je dobijanje dovoljnog broja podataka o materijalima i geometriji kritičnih zona vagonskih konstrukcija. Sistematizacijom dobijenih rezultata i onih koji su već dostupni u raznim oblicima literature napravljena je osnova za tumačenje rezultata dobijenih numeričkim proračunima. Kao plod razvijene metodologije, na realnim primerima iz prakse, prikazan je postupak procene integriteta nosećih delova rekonstruisane vagonske konstrukcije, koja je izložena promenljivim zamornim opterećenjima. Na osnovu eksperimentalnih i numeričkih rezultata izvršena je analiza postavljenog problema u skladu sa standardima u oblasti vagonskih konstrukcija. Drugi primer predstavlja procenu preostalog radnog veka, određivanje broja ciklusa do otkaza kritičnih zona nosećih delova vagonske konstrukcije na osnovu eksperimentalno dobijenih podataka i numeričkih rezultata proračuna. Korišćenje razvijene metodologije na konkretnim primerima i njena verifikacija u praksi, dovodi do znatne uštede pri veoma skupim ispitivanjima različitih prototipova vagona. Praktična primena razvijene metodologije u budućnosti bi mogla ostvariti pozitivan uticaj u oblasti v, It is well known from the engineering experience that, during exploitation, steel structures of wagons are exposed to the complex combined loads. Modernization of rails by increasing the velocity, optimization of the wagon structures, using new materials, created great challenges in the field of wagon industry. Together with increasing challenges, the requirements in terms of reliability and safety of the wagon structure have increased as well. The subject of studying and purpose of this thesis is to develop a reliable methodology for the experimental and numerical evaluation of the integrity of the wagon structures exposed to the alternating dynamic loads. For the purpose of integrity estimation of the wagon parts, the characteristics of structural steel and steel in the phase of exploitation have been experimentally determined. The aim of this experimental research is to obtain sufficient data on materials and geometry relating to the critical zones of the wagon structures. Systematization of the obtained results and those that are already available in various forms of literature enabled forming the basis for the interpretation of the results of the numerical calculations. As a result of the developed methodology, the procedure of assessment of the integrity of loadbearing parts of the reconstructed wagon structure exposed to fatigue loads, is presented on the real examples in practice. The analysis of a problem was performed in accordance with the standards in the field of the wagon industry and based on the experimental and numerical results. Another example presents the remaining service life assessment, determination of the number of cycles to failure of critical load-bearing parts of the wagon structure according to the experimental data and numerical calculation results. Using of the developed methodology on concrete examples and its verification in practice lead to the significant savings in the very expensive tests of different prototypes of the wagon. Pra

U makromehaničkoj linearno-elastičnoj analizi kompozitnih laminata moguće je koristi dva usvojena teorijska pristupa: pristup kontinualnosti napona i princip kontinualnosti deformacija. U ovoj disertaciji primarno je razvijen postupak analize laminata zasnovan na kontinualnosti deformacija. U tu svrhu razrađene su smicajne deformacione teorije višeg reda. Nedostatke klasične teorije ploča i smicajne deformacione teorije prvog reda, koje ne uzimaju u obzir geometrijsku nelinearnost, pri deformisanju, normale na srednju površ laminatne ploče, moguće je otkloniti uvođenjem smicajnih deformacionih teorija višeg reda. U ovoj disertaciji detaljno su opisane deformacione teorije zasnovane na funkcijama oblika, kao i polinomne deformacione teorije drugog i trećeg reda. Na osnovu pretpostavljenih oblika pomeranja izvedene su komponente vektora deformacije i urađena makromehanička analiza laminata uz definisanja matrica koje nastaju kao rezultat slaganja slojeva u laminatu. Prikazane su osnove varijacionog računa koji se koristi za dobijanje statičkih jednačina ravnoteže i dinamičkih jednačina kretanja. Razrađeni su najbitniji varijacioni principi koji se koriste u pomenute svrhe. Razrađene su analitičke metode za proučavanje statičkih problema savijanja i izvijanja slobodno oslonjenih laminatnih ploča uz primenu smicajnih deformacionih teorija višeg reda. Takođe su razrađeni postupci za proučavanje modova slobodnog oscilovanja laminatnih ploča. Implementiran je nov postupak za analizu slobodnih vibracija ukrštenih i umreženih simetričnih i antisimetričnih laminatnih ploča. Uveden je i nov postupak za određivanje slobodnih vibracija umreženih antisimetričnih laminata uz primenu proizvoljne smicajne deformacione teorije trećeg reda. Analizirana je propagacija elastičnih talasa u kompozitnim laminatima. Pažnja je usresređena na Lambove talase. Problemi propagacije su posmatrani sa aspekta 3D elastične teorije, kao i sa aspekta primene deformacionih teorija višeg reda. Prikazan, In macro mechanical linear-elastic analysis of composite laminates‚ it is possible to use two adopted theoretical approaches: stress continuity approach and the principle of strain continuity. This thesis primarily develops the process of strain continuity based laminate analysis. With this aim higher-order shear deformation theories are developed. The disadvantages of the classical plate theory and the first-order shear deformation theory, which do not take into consideration geometric non-linearity of the line normal to the middle plane of a laminate plate upon deformations, can be eliminated by introducing higher-order shear deformation theories. The present thesis presents in details deformation theories based on shape functions as well as second and third order polynomial deformation theories. Based on the assumed displacement fields, components of deformation vector are derived and macro mechanical analysis of laminates is done defining the matrices which occur as a result of stacking of plies in a laminate. Moreover, the basics of variation calculations are presented, which is used for obtaining static equations of equilibrium and dynamic equations of movement. The thesis develops the most important variation principles that are used for these purposes. Analytical methods are developed for examining bending and buckling static problems of simply supported laminate plates using higher-order shear deformation theories. The thesis also elaborates the models of examining the modes of laminate plate free vibrations. A new approach is implemented for analysing free vibrations of cross-ply and angle-ply symmetric and antisymmetric laminate plates. Moreover a new approach is introduced for determining free vibrations of angle-ply anti-symmetric laminates applying any third-order shear deformation theory. The propagation of elastic waves in composite laminates is analysed with the focus on Lamb's waves. Propagation problems are considered from the aspect of 3D elastic

Kardiovaskularni sistem je jedan od najvažnijih sistema u ljudskom organizmu. Istraživanja strujanja krvi su klinički veoma značajna zbog mogućnosti poboljšane dijagnostike bolesti, planiranja odgovarajućih preventivnih mera, analize transporta lekova itd. Ove pojave se teško eksperimentalno ispituju i zbog toga u ovoj oblasti numeričke simulacije mogu da doprinesu dobijanju mnogo novih i korisnih informacija. U okviru ovog rada predstavljen je kompletan numerički model koji uspešno simulira trodimenzionalno strujanje krvi kroz krvne sudove u ljudskom organizmu. Ovo je pokazano na nekoliko primera, gde je modelirano strujanje krvi kroz ljudsku aortu, karotidnu i koronarnu arteriju. Takođe, predstavljen je numerički model koji simulira kretanje crvenih krvnih zrnaca i sfernih čestica kroz kompleksne geometrijske domene, kao što su mali krvni sudovi sa stenozom, bifurkacijom, kao i kroz mikrofluidne čipove za separaciju kancer ćelija, ali i kroz realne domene dobijene eksperimentalnim snimanjem protoka krvi kroz posebnu vrstu ribe, tzv. zebra ribu. S obzirom da jedan ovakav softver za naučne simulacije zahteva mnogo računarskih resursa i da izvršavanje jedne simulacije traje dosta dugo, prilikom implementacije numeričke metode posebna pažnja posvećena je tehnikama paralelizacije. Kompjuterski program je razvijan tako da pored rada na standardnim PC računarima, može da se izvršava i na kompjuterskim klasterima sa velikim brojem procesora, kao što su Tesla superkompjuteri, koje proizvodi svetska kompanija NVIDIA. Postignuta su značajna ubrzanja razvijenog softvera, tako da se numeričke simulacije mogu izvršavati za samo nekoliko minuta, naspram par sati koliko je potrebno za izvršavanje iste simulacije na standardnom PC računaru, što omogućava praktično interaktivno praćenje kretanja deformabilnih tela u realnom vremenu. Zbog numeričke metode koja dosta realno oslikava uslove u ljudskom organizmu, velike tačnosti koja je pokazana kroz poređenje sa eksperimentalnim rezul, Cardiovascular system is one of the most important systems in human organism. Investigation of blood flow is clinically very relevant due to the possibility of improved diagnostic of diseases, planning of appropriate preventive measures, analisys of drug transport etc. Experimental investigation of these phenomena is difficult and therefore numerical simulation can contribute to the acquisition of manu new and useful information. Within this dissertation a complete numerical model is presented, that is capable of simulating three-dimensional blood flow through the blood vessels in human organism. This is demonstrated on several examples, where blood flow through human aorta, carotid and coronary arteries is modelled. Also, numerical model that simulates solid-fluid interaction is presented and this model is used to simulate motion of red blood cells and spherical particles through complex geometric domains, such as small blood vessels with stenosis and bifurcation, as well as microfluidic chips for cancer cell separation and real domains obtained by experimental recording of blood flow through a specific type of fish, so called zebrafish. This type of software for numerical simulation requires a lot of computer resources and the execution of one simulation lasts quite long. Therefore, during the implementation of the numerical method, special attention was dedicated to parallelisation techniques. The software was developed such that beside execution on standarad PC computer, it is possible to execute the program on computer clusters with large number of processors, such as Tesla supercomputers, that are manufactured by the world known company NVIDIA. Significant speed-ups were obtained and numerical simulation can now be executed in several minutes, instead of several hours, which was the case when the same simulation was executed on standard PC computer. This enables interactive tracking of motion of deformable bodies in real time. Due to the numerical method that

U ovoj doktorskoj disertaciji zavarena konstrukcija je posmatrana kao složen sistem elemenata sa kompleksnim interakcijama koji su heterogeni iz aspekta materijala, oblika i dimenzija, mehaničkih karakteristika, kao i eksploatacionih i funkcionalnih uslova. Heterogenost elemenata zavarene konstrukcije uslovljava njihove različite karakteristike i odgovore na opterećenje, dok nehomogenost njihove mikrostrukture uslovljava i dodatno usložnjava naponsko-deformaciono stanje. Specifičnosti projektovanja zavarenih mašinskih konstrukcija sagledane su iz aspekta složenosti oblika, materijala, koncentracije napona i temperature eksploatacije. Eksperimentalno određivanje mehaničkih karakteristika i analiza ponašanja u eksploatacionim uslovima, na sobnoj i povišenim temperaturama, izvedena je na modelima od mikrolegiranog čelika povišene jačine. Ispitivani modeli pored zone zavarenog spoja sadrže i zonu geometrijskog diskontinuiteta kao dodatni izvor koncentracije napona što je čest slučaj kod elemenata zavarenih konstrukcija. Skup faktora koji uslovljavaju projektovanje zavarenih konstrukcija identifikovan je sveobuhvatnom analizom eksperimentalnih rezultata i verifikovan je teorijskim razmatranjem naponsko-deformacionog stanja koje nastaje kod razmatranih modela. Posebna pažnja je posvećena analizi mehaničkih osobina i karakteristika mikrolegiranih čelika povišene jačine za izradu veoma odgovornih zavarenih mašinskih konstrukcija, kao savremenog materijala, čija upotreba omogućava ostvarivanje niza prednosti, ali sa sobom donosi i specifične probleme koji moraju biti adekvatno rešeni tokom procesa projektovanja ovih konstrukcija. Identifikovanjem faktora koji određuju konstrukciono rešenje zavarenih mašinskih konstrukcija i utvrđivanjem njihovog uticaja date su preporuke kojima se utemeljuje racionalno korišćenje materijala i energije, ostvaruje smanjenje ukupnih troškova uz prihvatljive ekološke efekte i istovremeno unapređuje sigurnost i pouzdanost zavarenih mašinskih kons, In this dissertation welded constructions are analyzed as complex systems of elements with complex mechanisms of interactions that are heterogeneous from the aspects of materials, shape and dimensions, mechanical properties, so as exploitation and functional conditions. Heterogeneity of elements of welded constructions cause their different characteristics and their different response to load, while inhomogeneity of their microstructure cause complex stress-strain state so as additional complication of this state. The specific characteristics of welded constructions design are highlighted from the aspect of shape complexity, material, stress concentrations and exploitation temperature. Experimental determination of mechanical properties and analysis of mechanical response to load during exploitation at room and elevated temperatures were done at models made of low alloyed high strength steel. Tested models besides zone of welded joint have zone of geometrical discontinuities as additional source of stress concentration that is common case at elements of welded mechanical constructions. Set of parameters that influent to design of welded constructions is identificated by analysis of experimental results and verified by theoretical considerations of stress-strain state at tested models. Special focus is put on analysis of characteristics and mechanical properties of low alloyed high strength steels for welded mechanical constructions as present material with usage that obtain number of advances, but also bring some specific problems that must be solved during process of design of those constructions. By identification of factors that influent to constructional solution of welded construction and determination of their influence, recommendations are given to establish rational usage of material and energy, obtained reduction of total costs with minimal ecological impact and with simultaneous improve of safety and reliability of welded constructions.

Shape memory alloys (SMA) have wider and more frequent application in cases when it is useful to employ their advantages through specific behavior (pseudoelasticity and shape memory effect) in various conditions. As a side effect due to the high thermosensitivity, strong thermomechanical coupling occurs what increases the need for simulation of complex thermomechanical response in realistic problems. The complex stress states and deformation range impose the requirements for accurate analysis of large strain problems. The presented requirements are solved in several steps: (1) Phenomenological constitutive SMA model (Lagoudas) has been reformulated by derivation of variables to depend on effective values of stress and strain and martensitic volume fraction. Gibbs free energy is reduced to scalar form what provides stress integration in the direction of deviatoric stress for forward transformation or total transformation strain for the reverse transformation. (2) Simulation of SMA thermomechanical behavior is realized using partitioned approach by coupling of programs for structural analysis - PAK-S and heat transfer PAK-T. Dissipative energy of martensitic phase transformation imposes change of the material temperature as an internal heat source. As a communication interface between the PAK-S and PAK-T, Component Template Library (CTL) is used. (3) Extension to the large strain problems is based on multiplicative decomposition of the deformation gradient to decompose deformation on elastic and inelastic part. Using the energy conjugated stress and strain measures, easy extension of the algorithm for small strain is provided to solve complex stress states for large strains. (4) Experimental investigation of TiNi SMA samples under various loading rates is used for verification of thermo-mechanical coupling. Numerical simulation of initiation, development and saturation of the martensitic phase transformation under various loading rates is compared to experimental resu

Indikatori ponašanja brane su relevantne veličine, čijim se praćenjem utvrđuje da li je stvarno stanje brane u eksploataciji u saglasnosti sa onim što je predviđeno i očekivano u fazi projektovanja. Veličine koje se prate treba da se kreću u nekom unapred definisanom opsegu koji garantuje stanje stabilnosti brane. U ovoj disertaciji su predloženi različiti pristupi modeliranja i parametarske identifikacije indikatora ponašanja brane, poput horizontalnih pomeranja i nivoa vode u pijezometrima, tehnikama računarske inteligencije. Prvi pristup je da se linearno preslikavanje uzročnih veličina u indikatore ponašanja, koje se koristi kod višestruke linearne regresije, zameni nelinearnim. Drugi pristup, predložen u ovom radu, zasniva se na primeni postupka parametarske identifikacije nelinearnih sistema. Horizontalna pomeranja i nivoi vode u pijezometrima su nelinearne, složene funkcije uzročnih veličina, pa je za njihovo modeliranje korišćena NARX (Nonlinear Auto Regresive eXogenous- nelinearni auto-regresioni model sa spoljašnjim ulazom) struktura, kojom je opisana široka klasa nelinearnih dinamičkih procesa. Predloženi pristupi formiranja modela primenjeni su za modeliranje i parametarsku identifikaciju horizontalnih pomeranja tačaka brane Bočac, kao i nivoa vode u pijezometrima brana Đerdap II i Prvonek. Nelinearni modeli zasnovani na tehnikama računarske inteligencije implementirani su korišćenjem programskog jezika Java i programskog paketa Matlab. Tehnike računarske inteligencije korišćene u ovom radu su višeslojni perceptron, RBF (RBF - Radial Basis Function – radijalna osnovna funkcija) neuronska mreža i ANFIS (ANFIS - Adaptive-Network-Based Fuzzy Inference System - fazi sistem za zaključivanje zasnovan na adaptivnoj mreži). Nedostajući podaci u skupu merenja mogu biti uzrok problema u okviru procesa učenja i loših performansi dobijenih modela. U cilju nadomeštanja nedostajućih podataka korišćene su tehnike iz domena matematičke statistike. Prisustvo autlajera u, The dam behavior indicators are relevant factors whose monitoring indicates whether the actual operational state of the dam is in accordance with what is expected and anticipated in the design phase. Such indicators should move in a predefined range, in order to guarantee stability of the dam. This dissertation proposes different approaches to modeling and parametric identification of the dam behavior indicators, such as radial displacements or piezometric water levels, using the techniques of artificial intelligence. The first approach is to replace linear mapping of causal variables into behavior indicators, which is used in multiple linear regression, with nonlinear. The second approach proposed in this paper is based on applying the method of parametric nonlinear system identification. Radial displacements and piezometric water levels are nonlinear, complex functions of causal variables, so for their modeling NARX (Nonlinear Auto Regresive eXogenous), which is employed to describe a wide class of nonlinear dynamic systems, is used. These proposed approaches are used for modeling and parametric identification of radial displacements of dam Bočac, and piezometric water levels of dams Iron Gate II and Prvonek. Nonlinear models based on artificial intelligence techniques have been implemented using the Java programming language and MATLAB. Artificial intelligence techniques used in this work are the multilayer perceptron, RBF (Radial Basis Function) neural network and ANFIS (Adaptive-Network-Based Fuzzy Inference System). The presence of missing data in a set of measurements may be causing problems in the learning process and the poor performance of the obtained models. In order to predict the missing data, the techniques of mathematical statistics have been used. Outliers present in a set of measurements have a big effect on the prediction of missing data, and their presence is specifically analyzed. The problem of optimizing the inputoutput model, which involves d

Predmet proučavanja ove disertacije su veze koje se ostvaruju između elemenata čelične konstrukcije paletnih regala. Vertikalni ramovi i horizontalne grede, najčešće proizvedeni od tankozidnih hladno oblikovanih profila formiraju prostorni ramni sistem paletnih regala. Ramovi leže u vertikalnoj ravni poprečno na pravac glavnog hodnika regala. Sastoje se od dva perforirana stuba međusobno povezana sistemom dijagonalnih i/ili horizontalnih ukrućenja zavarenih ili zavrtnjevima vezanim za stubove. Ovaj sistem ukrućenja obezbeđuje stabilnost regala u poprečnom pravcu. Grede povezuju susedne ramove i leže u podužnom pravcu paralelno glavnom hodniku regala. Gredni konektori su delovi grede zavareni ili na drugi način formirani kao njen sastavni deo i imaju posebne delove koji upadaju u otvore ili proreze na stubu. Podužna stabilnost regala se prvenstveno obezbeđuje krutošću veze greda-stub. U praksi postoje različiti tipovi i dizajni ovih veza, karakteristični za različite proizvođače regala. U disertaciji je obrađena klasifikacija i modeliranje veza u skladu sa Evrokodom 3. Kako je nemoguće da se razvije opšti analitički model proračuna ovih veza, trenutno jedini način da se odredi karakteristika takve veze je eksperiment. U disertaciji su prikazani postupak i rezultati ispitivanja veze greda-stub po proceduri definisanoj u FEM propisima u cilju određivanja krive moment-rotacija (M- krive). Uticaj veza na globalno ponašanje konstrukcije regala uvodi se pomoću M- krive, odnosno konstrukcijskih svojstava veze koje se iz nje određuju: krutost, otpornost i rotacioni kapacitet. Kako bi se izbegao veliki broj skupih ispitivanja u cilju određivanja M- krive za različite tipove veza kojih u praksi može biti jako puno, u okviru ove disertacije je razvijen numerički model za simulaciju eksperimenta primenom metode konačnih elemenata. Nakon verifikacije modela raspoloživim eksperimentalnim rezultatima, isti se može primeniti na najrazličitije kombinacije veze greda-stub. Pouzdani

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 soft, 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 stren

In developing the vane pumps the fundamental basis is experimental research and mathematical modelling of nonstationary hydraulic processes inside the pump, in thrust space and suction and thrust pipeline. By means of experimental research and results of mathematical modelling and software package KRILP, it is possible to determine the parameters of operating processes of vane pumps precisely enough. This research examines the idealized and actual flow ripple of a high-pressure vane within vane type pump. For the idealized case, a "perfect" pump is examined in which the leakage is considered to be zero and the fluid is considered to be incompressible. Based upon these assumptions, expressions describing the characteristics of the idealized flow-ripple are derived. Next, the actual flow-ripple of the pump is examined by considering the fluid compressibility and for computing these results a numerical program is used. From the idealized analysis it is shown that the idealized flow-ripple is determined by geometrical flow property.

Within 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 str, U 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.

particles, which all together affect diffusion process. Despite the increasing focus on nanofluidics in many of these applications, the laws governing molecular transport through nanoscale fluidic channels and porous media have not been fully understood. As the size of the channels and pores is reduced to the molecule size, classical continuum theories fail to predict even the basic characteristics of fluid transport.

This paper investigates the accuracy of analytical, empirical, and numerical expressions, i. e. the most favourable methods for calculating the cooling time from 800 to 500°C (t8/5). The degree of accuracy of time t8/5 is very significant, because it determines the cooling rate, and consequently the structural changes in heat affected zone for hard faced layers. Based on the presented results, one can conclude that the finite element method provides the best conformity with the experiment and among analytical and empirical formulas the same goes for the expression of Japanese authors, for the case of hard facing of plane and prismatic parts.

This study focuses on the estimation of residual life of damaged thermal power plant components. The high-pressure turbine housing was chosen as an example of thermal power plant component where, during the years of exploitation, damage appeared in the form of dominant crack. Residual life estimation procedure, based upon experimental and numerical methods has been introduced and applied. Material properties were determined experimentally both at room and operating temperature, while all necessary calculations were performed by the special finite element method, so-called X-FEM. The residual life estimation of the damaged high-pressure turbine housing was performed by applying the Paris's law for crack growth analysis.