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Within the theory of thermo-elasticity, the temperature field of thin plates is commonly defined via two parameters: temperature in the mid-plane and linear temperature gradient normal to the mid-plane. First, the paper analytically proves the justification of that assumption in machine structures. Then, in an analytical closed form, applying the integral transformation method, the thin plate deflection caused by a constant temperature gradient is defined. It is shown that, in that case, the plate deflection does not depend on its thickness but only on the plate dimensions in the mid-plane. Analytically defined values are compared to corresponding values obtained by applying the thin plate finite element, where the temperature field is described using the two mentioned parameters. This finite element is defined and programmed within the Komips program package. The influence of the temperature gradient on the behavior of constructions mostly depends on the type of material. That is why the behavior of some structural elements made of brass, steel, and concrete is analyzed in this paper.

Temperature distribution in the metallic plate influenced by high-frequency electromagnetic wave depends on thermal and electrical properties of the plate material. The goal of the paper is to present the significance of the temperature dependence of the electrical resistivity and its influence on the plate heating. A mathematical model of the problem was established and an analytical closed-form solution to the problem was presented. The active power of the electromagnetic wave was calculated by Poynting vector. Temperature field was obtained by integral-transform technique. Numerical examples were presented for three different materials (copper, aluminum, and steel). Calculated results show the large influence of temperature dependent electrical resistance on heating of the metallic plate.

The paper presents analytical and numerical determina-tion of the equivalent stress and strain of the open section thin-walled ‘’ cantilever beams loaded with torsion. Ana-lytical calculation was used to calculate the equivalent stress and strain values for the model encastred across the entire cross-section at one end, while the other end is free (model 1). The finite element method is applied for the calculation of the same ‘’ cantilever beam model exposed to torsion, and the stress and strain values are obtained by numerical calculation. Numerical simulations have been performed using KOMIPS software. Analytical and numerical results are compared and discussed. In this paper, a numerical model for constrained torsion is also created in ABAQUS® and SolidWorks® software. A cantilever beam with an omega profile is encastred at one end, while at the other end there is a welded plate (model 2). Numerical models are created, and static calculation is done using the finite element method. The zones of stress concentration are identified and presented. Finally, the equivalent stress values of models 1 and 2 are compared. Conclusions obtained by examining this type of structures may be involved in the design process of new similar structures. The findings obtained during the implementation of this work can be directly applied to iden-tify the behaviour of real structures in their working condi-tions.

The aim of this paper is to present the application of thin-walled beams on cargo raft load-bearing structure from the aspect of strength and reliability. The beams have an open cross section. Analytical and numerical determination of equivalent stresses and deformations of open section thinwalled ‘U’ and ‘Z’ cantilever beams, loaded with torsion, is presented. Work is divided into three parts. In the first part, equivalent stress and deformation are obtained analytically for cantilever beam model in the whole cross section. In the second part, the finite element method is applied in beam models, and the results are compared with the analytical calculation. The third part presents the profiles installed in load-bearing structures of vessels (rafts) and solutions are shown to apply results of the presented analyses in order to increase reliability. Finally, the design calculation of the raft load-bearing structure is shown., Cilj ovog rada jeste da prikaže primenu tankozidih nosača na noseće konstrukcije teretnog splava sa aspekta čvrstoće i pouzdanosti. Nosači su sa otvorenim poprečnim presekom. U radu je prikazano analitičko i numeričko određivanje ekvivalentnog napona i deformacije kod U i Z tankozidih konzola otvorenog poprečnog preseka opterećenih na uvijanje. U radu se izdvajaju tri celine. U prvom delu je analitički dobijen ekvivalentni napon i deformacija za model sa uklještenjem, po celom poprečnom preseku. U drugom delu se primenjuje metoda konačnih elemenata na modele nosača, a dobijeni rezultati su upoređeni sa analitičkim proračunom. U trećem delu su prikazani profili koji se ugrađuju u noseće konstrukcije plovnih objekata (splavova) i dat je način kako bi mogli da se iskoriste rezultati prikazanih analiza u cilju povećanja njihove pouzdanosti. Takođe, u trećem delu rada je urađen proračun noseće konstrukcije splava.

Industrial robots are used for high-precision tasks and in intensive production. One of the most reliable methods for monitoring robots’ work is vibrodiagnostics, which provides recommendations and maintenance procedures, and also serves as a reliable diagnostic method for determining the causes of industrial robot failures. Connection of robot and the supporting structure is very important and it affects on dynamic behavior of the robot. This paper presents the process of diagnosing dynamic condition of the structure with painting robots, after the failure of the robot motion reducer. To analyze the causes of the failure, a numerical analysis was performed, which included: static calculation, dynamic calculation, determining transfer function in frequency domain and reinforcement factors. Supporting structure has very low eigen-frequencies (3,5 to 9.5 Hz), it cannot accept inertial forces and large deformations and resonant behavior occur. Using FEM analysis is shown that the behavior of the structure is unfavorable because 20 eigen-oscillations had a frequency less than 17 Hz, and all are located in the robots’ working space. Determination of the transfer functions showed that the dynamic gain factor in all three directions of the excitation force is extremely large, while the corresponding frequencies are 5 ÷ 20 Hz. It was determined that the main problem was the rigidity of the supporting structure.

U ovoj disertaciji je prezentiran rad autora pod nazivom: "Numeričko - eksperimentalna analiza čvrstoće strukturnih elemenata hidroelektrane". Na bazi definisane metodologije dijagnostike ponašanja strukturnih elemanata hidroelektrane izvršeno je dijagnosticiranje ponašanja najvažnijih strukturnih elemenata hidroelektrane kao što su: cjevovod, račva i vratilo hidroagregata. Primjenom analitičkih i numeričkih metoda izvršena je analiza napona, dilatacija i pomjeranja cjevovoda kao cjeline. Definisana su kritična mjesta na cjevovodu sa aspekta i napona i deformacija pod različitim uslovima rada i opterećenja cjevovoda (unutrašnji pritisak, trenje, temperatura). Što se tiče napona to su mjesta na kojima se nalaze račve, a što se pomjeranja tiče to je kraj glavne cijevi cjevovoda..., This doctoral dissertation presents the work of the author entitled: "Numerical - experimental analysis of strength of structural elements in hydro - power plants". Diagnostics of the behavior of basic elements of the hydro - power plant such as: pipeline or penstock, bifurcation, and shafts is done on the basis of previously defined methodology of the diagnostics of the hydro - power plant structural elements behavior. Analysis of the stress, dilatations and deformations of pipeline as whole is done through the application of analytical and numerical methods. Critical places on the pipeline from stress and deformations point of view are defined under different exploitation conditions and regimes of work and also under different loads of pipeline (internal pressure, friction, temperature). As far as stresses are concerned those are the places where bifurcations are placed, and as far as deformations are concerned this is the place of the main pipe ends...

The possibilities of testing real constructions are often limited, especially in case of large constructions. The idea of model testing is to create a sub-scaled model in order to anticipate the behavior of the real construction, regarding the behavior of the model, with sufficient accuracy. The aim of this paper is to demonstrate that model testing of bucket wheel excavator structure, from the aspect of the strength of the constructions, is possible. In order to prove this assumption, firstly, numerical calculations of a real construction and its sub-scaled model were performed using the Finite Element Method. Sub-scaled structure is 10 times scaled real structure (in size and plates thickness). Within the static calculation, the analysis of the stress mapping from sub-scaled model to real structure was carried out, by partial groups of construction. The coefficients connecting stresses of sub-scaled model and stresses of real construction were formulated. Dynamic calculations of sub-scaled model and real structure were also performed. Then, a physical model was produced and subjected to experimental testing. Experimental testing was performed in order to verify the numerical models. A parallel testing of the model with strain gauges and a system for non-contact measurement of displacement and deformation was performed. High matching results were obtained of two experimental methods on one side, and numerical calculation on the other side. The physical model and the successful experiments carried out on it confirmed that these structures can be subjected to model testing, without important constraints and with sufficient accuracy.

The electrochemical behaviour of the P/T91 steel with martensitic microstructure as well as its behaviour in cavitation conditions has been investigated in this study. The electrochemical techniques used to analyze corrosion behaviour include Linear Polarization Resistance (LPR), Electrochemical Impedance Spectroscopy (EIS) and Linear Sweep Voltammetry (LSV). Corrosion rate determination was performed in a solution that simulates the industrial atmosphere. In laboratory conditions, ultrasonic vibratory cavitation test set up (stationary specimen method) has been applied on specimens made of P/T91 steel. Scanning electron microscopy technique has been applied to analyze the morphology of the eroded surfaces and to interpret the results of the cavitation tests. Test results have shown that, from the point of view of corrosion, P/T91 steel has a favourable chemical composition but the unfavourable lamellar martensite microstructure. Also, the morphology of surface damage from cavitation of P/T91 steel resembles the features of the fatigue failure. In order to evaluate the resistance to cavitation of investigated material, its cavitation rate was compared with those of some other martensitic steels used in fabrication of various industrial components for application in thermal power plants.

The paper presents an analytical closed-form solution to the problem of dynamic change in the temperature field of a steel sample model during a short-term heating up and thereafter intense heat removal. It is demonstrated how a relatively complex thermal problem can be solved analytically based on differential equation that describes the temperature field. Differential equation that describes the temperature field is formed via the power of several heat sources with limited action time, as shown mathematically by applying the Dirac and Heaviside functions. In the present paper the example provided includes two heat sources. In accordance with boundary conditions the differential equation is solved by applying the finite Fourier transforms and Laplace transform. Based on obtained analytical solution of the problem, a numerical model was created corresponding to the simulation of steel sample heating on a thermomechanical welding simulator. The welding thermal simulator is a device used to achieve controlled heating and cooling, similar to the one in welding. Analytically calculated temperature fields were utilized to obtain the strain distribution in the heat source environment by applying the finite element method.

The present paper describes numerical and experimental methodology for the analysis of stress and deformation state in structural elements with geometrical discontinuities. The research is based on structural elements of the connecting lug type. The stress and deformation state was determined as the contact area size between the axle and the connecting lug was changing. Numerical analysis was conducted by applying the finite element method in a ''KOMIPS'' software package. Experiments were performed at the Laboratory for stress and deformation measurements, Faculty of Mechanical Engineering, University of Belgrade, using ''GOM'' equipment and ''ARAMIS'' software application (DIC). This paper demonstrates how it is possible to anticipate the results by applying FEM. A short review of current research in the field of structural elements with geometrical discontinuities is given within the framework of the paper.

The purpose of this work is to present analytical and numerical determination of equivalent stress and deformation of open section thin-walled U and Z cantilever beams loaded with torsion. This work can be divided into two parts. In the first part of this paper, equivalent stress and deformation are obtained by analytical calculation for encastered model over the whole cross section. In the second part, the finite element method is applied for four different encastered models and the obtained results are compared with the analytical calculation.

У овој тези проучене су осцилације и стабилност запремински оптерећене правоугаоне нано-плоче уз коришћење Ерингенове теорије еластичности. Запреминско оптерећење је константно са правцем који је у равни плоче. Гранични услови су моделовани као покретна укљештења. Класична теорија плоча и Карманова теорија плоча, које су надограђене Ерингеновом теоријом еластичности, искоришћене су за формирање диференцијалне једначине стабилности и осциловања нано-плоче. Галеркиновом методом одређене су сопствене фреквенције трансверзалних осцилација нано-плоче у зависности од ефеката запреминског оптерећења и нелокалности. Одређене су критичне вредности параметра запреминског оптерећења при којима нано-плоча губи стабилност. Приказан је утицај ефеката запреминског оптерећења и нелокалности на неколико облика осциловања. Верификација резултата извршена је помоћу методе диференцијалних квадратура., U ovoj tezi proučene su oscilacije i stabilnost zapreminski opterećene pravougaone nano-ploče uz korišćenje Eringenove teorije elastičnosti. Zapreminsko opterećenje je konstantno sa pravcem koji je u ravni ploče. Granični uslovi su modelovani kao pokretna uklještenja. Klasična teorija ploča i Karmanova teorija ploča, koje su nadograđene Eringenovom teorijom elastičnosti, iskorišćene su za formiranje diferencijalne jednačine stabilnosti i oscilovanja nano-ploče. Galerkinovom metodom određene su sopstvene frekvencije transverzalnih oscilacija nano-ploče u zavisnosti od efekata zapreminskog opterećenja i nelokalnosti. Određene su kritične vrednosti parametra zapreminskog opterećenja pri kojima nano-ploča gubi stabilnost. Prikazan je uticaj efekata zapreminskog opterećenja i nelokalnosti na nekoliko oblika oscilovanja. Verifikacija rezultata izvršena je pomoću metode diferencijalnih kvadratura., In this thesis, the problem of stability and vibration of a rectangular single-layer graphene sheet under body force is studied using Eringen’s theory. The body force is constant and parallel with the plate. The boundary conditions correspond to the dynamical model of a nanoplate clamped at all its sides. Classical plate theory and von Kármán plate theory, upgraded with nonlocal elasticity theory, is used to formulate the differential equation of stability and vibration of the nanoplate. Natural frequencies of transverse vibrations, depending on the effects of body load and nonlocality, are obtained using Galerkin’s method. Critical values of the body load parameter, i.e., the values of the body load parameter when the plate loses its stability, are determined for different values of nonlocality parameter. The mode shapes of nanoplate under influences of body load and nonlocality are presented as well. Differential quadrature method is used for verification of obtained results.

Предмет истраживања докторске дисертације чини домен пројектовања набораних конструкција. Код оваквих конструктивних система је изражена међузависност форме и структуре због начина на који преноси оптерећење. Односно, утицај геометрије система у великој мери одређује ефикасност конструкције. Oбзиром да конструкција у исто време има носећу функцију и функцију форме у изгледу, сам рад је имао за циљ да сагледа како архитектонске, тако и прорачунске (статичко-динамичке карактеристике) захтеве које конструкција треба да испуни. Мултидисциплинаран приступ проблему је подразумевао израду рачунарских алгоритама за генерисање структуре, затим пројектовање примитива, интеграцију групно суперматричне процедуре у метод коначних елемената, дефинисање макро коначног елемента и прорачун еквиваленте матрице крутости равне плоче са којом се улази у статичко – динамичку анализу конструкције. Приказана је предност параметарског генерисања набора и дефинисање заменског, једноставног, макро коначног елемента погодног за прорачун ГСП процедуром. Имплементација процедуре потврђује иновацију и унапређење процеса архитектонско – инжењерског пројектовања сложених конструктивних система., The research subject of the doctoral dissertation is within domain of folded plate structures designing. Because of the load distribution way, this type of construction has very strong interdependence between form and structure. Respectively system geometry has significant impact on structure efficiency. Since structure has simultaneously form and bearing function, this paper has a goal to perceive and apply both, architectural and structural (static – dynamic analysis) demands that structure must fulfill. The multidisciplinary problem approach has considered development of software algorithm for generating of structure, then primitive designing, following with integration of the group supermatrices procedure in finite element method, determination of macro finite element and computing of equivalent stiffness matrices of flat plate which is the main input for static- dynamic structure analysis. The advantage of parametric folded plate generator and defining of simple equivalent macro finite element suitable for GPS analysis is presented. Procedure implementation confirms innovation and improvement of architectural – engineering designing of the complex structural systems.

Složenost geometrije posuda pod pritiskom obično predstavlja uzrok pojave koncentracije napona i deformacija. Savremeni pristup analize stanja napona i deformacija uključuje numerička i eksperimentalna ispitivanja. Svako eksperimentalno testiranje na realnoj konstrukciji može ugroziti samu konstrukciju. Stoga, pravljenje modela neke konstrukcije ima velike prednosti. Umanjeni model račve A6 trećeg cevovoda na HE Perućica, Nikšić je izrađen kako bi bio podvrgnut detaljnom eksperimentalnom testiranju. Cilj je bio da se odredi vrednost unutrašnjeg pritiska koji dovodi do plastične deformacije na modelu račve i da se ovi rezultati koriste za određivanje pritiska koji će stvarnu konstrukciju dovesti do plastičnog deformisanja bez ikakvih merenja na samoj konstrukciji. Eksperimentalna merenja su sprovedena metodom mernih traka. Merne trake su pozicionirane na kritične zone. Numerički model i rezultati dobijeni metodom konačnih elemenata (FEM) potvrđeni su eksperimentalnim rezultatima (u oblasti elastičnosti). Nakon verifikacije u elastičnoj oblasti, povećanjem pritiska, eksperimentalno određena je kritična vrednost unutrašnjeg pritiska koji je izazvao plastičnu deformaciju modela račve. Na osnovu ponašanja modela račve i nakon određivanja odnosa između modela i stvarne konstrukcije, procenjuje se maksimalna izračunata vrednost unutrašnjeg pritiska na koju se realna konstrukcija može izložiti. Pored toga, slabe tačke na konstrukciji su potvrđene dobijanjem istih rezultata kroz eksperiment i proračun, što daje dobre smernice za praćenje ove konstrukcije tokom eksploatacije, s obzirom na to da je ovakvom analizom moguće smanjiti broj mernih mesta za praćenje (u smislu da se kontrolišu tačno ona merna mesta koja su se pokazala kao najkritičnija)., Complexity of pressure vessels geometry usually causes stress and strain concentrations. Modern approach of stress and strain analysis involves numerical and experimental testing. Every experimental testing on the construction could endanger construction itself. Therefore, making a model of the construction has great benefits. Sub-sized model of the pipe branch of A6 third pipeline at Hydropower Plant Perućica, Nikšić was made in order to be subjected to a detailed experimental testing. The aim was to determine internal pressure value causing pipe branch model to plastically deform, and, to use these results for determining pressure causing real structure to plastically deform, without any measurements on the structure itself. Experimental measurements were carried out using strain gauge method. Strain gauges are positioned in critical zones. Numerical pipe branch model and results obtained by using finite element method (FEM) was verified with experimental results (in elasticity area). After verification in elastic area, experimentally by increasing pressure value, critical internal pressure causing plastic deformation of pipe branch model was determined. Based on the pipe branch model behaviour, and after determination of relation between the model and the real structure, maximum calculated internal pressure value to which the structure may be subjected in exploitation is assessed. Besides, weak spots on the structure were verified by obtaining the same results through experiment and calculation, which gives good guidelines for monitoring of this structure during usage, since it is possible, by using this analysis, to decrease the number of measurement locations for monitoring (in order to control exactly those measurement locations, which proved to be the most endangered).

The present paper describes numerical and experimental methodology and development of the model for stress and deformation state analysis of the connecting lug of container terminals. Numerical analysis was conducted by applying the finite element method in a "KOMI'S" software package. Experiments were performed at the Laboratory for stress and deformation measurements, Faculty of Mechanical Engineering, Belgrade University, using "GOM" equipment and "ARAMS" software application. This paper demonstrates how it is possible to anticipate the results by applying FEM. This paper will present how experimental results can be predicted using the finite element method. The paper presents an overview of the existing research and review of previous results achieved in this field. Container terminal used to supply electrical energy and management system of conveyor belts that are used in the exploitation of the mining basins. Stress and deformation state analysis of the connecting lugs is carried out at the loading of the container.

Bucket wheel excavator ERs 1250 has been in operation for over 30 years in the Grae'anica-Gacko mining basin. It is operating in very hard working conditions due to exploiting very solid material, which has adverse effects on the behavior of the whole structure. Bucket wheel excavator boom is a single tube approximately 20 m long. The crack was detected in a cylindrical root of the boom tube at nearly 270 degrees of its circumference. Finite element method was applied in calculations and the first calculation was performed for the complete usage of engine power (the least favorable case), but it didn't indicate the possibility of crack occurrence. Based on exploitation measurements of stress and accelerations, additional simulations of loading were performed (horizontal and vertical unit loads) that could cause the crack. Numerical analysis has shown that the horizontal force causes the initial crack. Measurements and realized loading cycles indicated that the effect of material fatigue is extremely strong. That is why the fatigue is the cause of a considerable crack increase. Based on numerical investigation of the failure, rehabilitation and reparation of the wheel boom were done in the manner as presented in the paper. So, bucket wheel excavator has been operating successfully for a number of years.

Могућности испитивања реалних конструкција често су ограничене, посебно уколико се ради о великим конструкцијама. Једно од решења је прављење умањеног модела са циљем да се предвиди понашање реалне конструкције, на основу понашања модела, довољне тачности. Испитивање на моделу уместо на стварној конструкцији у већини случајева резултира великом уштедом новца и времена. Осим тога, експериментални подаци добијени за једну структуру могу се искористити за предвиђање понашања групе сличних структура, односно, савремено пројектовање захтева универзалност у приступу. Циљ овог рада је да се покаже да је могуће моделско испитивање сложених структура са аспекта чврстоће конструкција, односно да се на основу напонског и деформационог стања модела предвиди напонско и деформационо стање реалне конструкције. Као испитна (огледна) конструкција усвојена је конструкција доње градње (постоља), обртне платформе и доњег дела стубова роторног багера SchRs 630, јер је за функционисање овако сложене машине од круцијалног значаја познавати напонско стање њене носеће конструкције. Дакле, полазна хипотеза ове дисертације подразумевала је, да је конструкције сложене просторне геометрије, које се састоје доминантно од плоча као конструктивних елемената, могуће испитивати моделски. Са циљем доказивања ове претпоставке, прво су урађени нумерички прорачуни, применом Методе коначних елемената, једне стварне конструкције и њеног умањеног модела. Умањеном структуром названа је структура која је од стварне структуре мања 10 пута по димензијама и по дебљинама конструктивних елемената. Умањена структура је у односу на стварну структуру оптерећена 100 пута мањим оптерећењем (у складу са поставкама Теорије сличности). У оквиру статичког прорачуна, спроведена је анализа пресликавања напона по групама градње предметне конструкције и формулисани су коефицијенти пресликавања за сваку од њих. Генерално говорећи, закључено је да је веза напона умањене структуре и стварне структуре линеарна..., The possibilities of testing real constructions are often limited, especially in case of large constructions. One of the solutions is to create a sub-scaled model in order to anticipate the behavior of the real construction, regarding the behavior of the model, with sufficient accuracy. In most cases, testing on the model instead of the actual construction results in a great saving of money and time. Beside that, the experimental data which are obtained for one structure can be used further to predict the behavior of a group of similar structures, that is, modern design requires the universality in approach. The aim of this dissertation is to demonstrate that model testing of the complex structures is possible, from the aspect of the strength of the constructions, i.e. it is possible to predict the stresses and deformations of the real structure regarding the stresses and deformations of the model. As a test example, the construction of the substructure, the slewing platform and the lower part of the pylons of the bucket wheel excavator SchRs 630 is taken, because strength of supporting structure has a crucial importance for proper functioning of these machines. Thus, the starting hypothesis of this dissertation implied that, the constructions of complex spatial geometry, consisting mostly of plates as constructive elements, can be subjected to model testing. In order to prove this assumption, firstly, numerical calculations of a real construction and its sub-scaled model were performed using the Finite Element Method. Sub-scaled structure is 10 times scaled real structure (in size and plates thickness). Sub-scaled structure is loaded with load 100 times lower than the real structure (according to similarity method). Within the static calculation, the analysis of the stress mapping from sub-scaled model to real structure was carried out, by partial groups of construction. The coefficients connecting stresses of sub-scaled model and stresses of real construction were

Complexity of pressure vessels geometry usually causes stress and strain concentrations. Modern approach of stress and strain analysis involves numerical and experimental testing. Every experimental testing on the construction could endanger construction itself. Therefore, making a model of the construction has great benefits. Sub-sized model of the pipe branch of A6 third pipeline at Hydropower Plant Perućica, Nikšić was made in order to be subjected to a detailed experimental testing. The aim was to determine internal pressure value causing pipe branch model to plastically deform, and, to use this results for determining pressure causing real structure to plastically deform, without any measurements on the structure itself. Experimental measurements were carried out using strain gauge method. Strain gauges are positioned in critical zones. Numerical pipe branch model and results obtained by using finite element method (FEM) was verified with experimental results (in elasticity area). After verification in elastic area, experimentally by increasing pressure value, critical internal pressure causing plastic deformation of pipe branch model was determined. Based on the pipe branch model behaviour, and after determination of relation between the model and the real structure, maximum calculated internal pressure value to which the structure may be subjected in exploitation is assessed. Besides, weak spots on the structure were verified by obtaining same results through experiment and calculation, which gives good guidelines for monitoring of this structure during usage, since it is possible, by using this analysis, to decrease number of measurement locations for monitoring (in order to control exactly those measurement locations which proved to be the most endangered).

This paper deals with the problem of optimization of thin-walled open sections. They are subjected to the bending and to the constrained torsion. The particular attention is paid to the structural optimization methods. The optimal weight of the structures is obtained starting from some initial values of thicknesses and cross-sectional areas. The analytical and numerical approaches are derived for structural elements of different shapes of the open cross-section elements subjected to several loading cases. Optimization parameters have been determined by Lagrange’s multipliers method. The obtained results are used for numerical calculation.

Глобализација привреде омогућила је настајање глобалног тржишта материјала, производа и услуга као и премештање производње у ниско трошковне регије. Као последица тога логистика и логистички ланци су постали знатно сложенији. Расклопиви контејнери су тиме нашли велику примену, као и потреба за пројектовањем нових контејнера који требају да испуне све стржије крутеријуме чврстоће. У овом раду дат је приказ резултата вишегодишњег истраживања у области понашања структуре расклопивих контејнера. Основа дисертације представља анализа комплексних геометрија разнородних расклопивих контејнера и утицају геометрије на чврстоћу контејнера. У циљу сагледавања особина и понашања контејнера издвојени су параметри који их описују и разматрани су њихови утицаји на чврстоћу контејнера. Развијена је методологија карактеризације чврстоће контејнера. Карактеризацију чврстоће функционалног склопа контејнера обављена је путем нумеричког и експерименталног приступа. Нумерички приступ је изведен кроз примену методе коначних елемената и компјутерског моделирања. Експериментални приступ представља примену метода мерења деформација и чврстоће контејнера. Овим се извршава квалитетна карактеризација расклопивог контејнера, како постојећег тако и при дизајнирању нобог модела. Дефинисани су основни елементи идентификације понашања контејнера кроз одређивање крутости елемената контејнера и самог контејнера.. Идентификовани су основни проблеми повољног понашања контејнера. Они су представљени кроз немогућност преноса оптерећења са ј едне покретне површине странице на непокретну површину базе (реална грешка дизајна, израде и монтаже) и потребно максимално растерећење везе страница и базе. Дефинисане су потребне карактеристике расклопивих контејнера које он треба да испуни. Приказане су основне геометријске карактеристике развијеног модуларног дизајна контејнера. Приказане су основне геометријске карактеристике развијеног модуларног дизајна контејнера., The globalizaton of the economy has enabled the emergence of a global market of materials, products and services, as well as the relocation of production to low-cost regions. As a consequence, logistics and logistics chains have become much more complex. Folding containers are thus broadly used, and the need for the design of new containers that need to comply with increasingly stringent decision criteria strength. This paper presents the results of years of research in the field of behaviour structure of foldable container. The basis of the thesis is the analysis of complex geometries of various foldable container and the influence of geometry on the strength of the container. In order to observe the characteristics and behavior of container were extracted parameters that describe them and examined their effects on the strength of the container. Methodology has been developed characterization of the strength of the container. Functional characterization of the strength of the container assembly is performed by numerical and experimental approaches. The numerical approach is implemented through the application of finite element method and computer modeling. The experimental approach is the application of methods of measuring deformation and strength of the container. This executes the quality characterization of the foldable container, as well as existing when designing nobog models. The basic elements of behaviour identification of containers through the determination of stiffness of the container and the container itself. They identified the main problems of the favorable behavior of the container. They are represented by the inability to transfer loads from one movable surface sites on the surface of the fixed base (real fault of design, fabrication and assembly) and need maximum relief and database links page. Defines required characteristics of extractable container, it should meet. Shows the basic geometric characteristics of the developed modular design of th

The purpose of this work is to present analytical and numerical determination of the equivalent stress of the open section thin-walled „U“ profile loaded with torsion. This work can be divided into two parts. In the first part of this paper equivalent stress was obtained with analytical calculation. In the second part was applied the finite element method for calculation of equivalent stress. At the end, result of analytical method were compared with numerical method.

Dynamic modification of structures involves the transformation of an existing model in the new one, which has better behavior and higher accuracy in comparison with the existing. The main objective of a dynamic modification of the construction is to increase the first natural frequency, and that the gap between adjacent frequencies is as big as possible. This paper focuses on the improvement of dynamic characteristics of a tubular collector in one substation. It is shown how change of boundary conditions and the geometry of the cross section can improve dynamic characteristics of the structure. In this analysis the finite element method is used for calculating the natural frequencies, potential and kinetic energy in each node. In the particular case of a tube collector is confirmed once again, what was well known, that the change in the way of support (boundary conditions) is the most efficient way of dynamic modification. Additionally is shown one way to increase the dynamic stiffness while reducing the weight of the whole structure by choosing the right cross-section.

The purpose of this work is to present a possible approach to the mass minimization of structural thin-walled open section beams of the proposed shapes (I, Z and U-beam), submitted to the stress constraints and multiple load cases. Lagrange’s multipliers method has been used to determine the optimization parameters. The area of the cross-section is used as the objective function, while the stress constraint is introduced and used as the constraint function. Finally, some numerical examples are presented in order to verify the analytically obtained values.

Transverse vibrations of a rotating annular disk composed of two annular disks of different materials are studied in this paper. The disk is clamped at the inner edge, while at the outer edge is free. Differential equations of small vibrations are solved exactly by series expansion using the Frobenius method. The solutions are separately presented for three cases corresponding to vibration with zero, one or two nodal diameters. The influence of angular velocity, moduli of elasticity and the volume densities of the materials of disks on vibration frequency is analyzed. Vibration frequencies are obtained for the disk composed of aluminum and steel. Influences of the inner radius and the radius of the connection on the vibration frequencies are also obtained.

Проблеми понашања оребрених плоча (панела), као основних јединица бродских конструкција представљају једну од најзначајнијих истраживачких тема из области чврстоће бродских консктрукција. У овом раду оребрене плоче моделиране су неоребреним плочама, са циљем да се одзиви и једне и д руге у ш то в ећој м ери п одударају. У т у с врху р азвијена ј е процедура (метода еквиваленције) којом се за сваку оребрену плочу могу прорачунати параметри еластичности неоребрене плоче, тако да маскимални угиби и напони, у обе плоче, буду једнаки. Ово подразумева и дефинисање еквивалентног коначног елемента плоче који у својој матрици крутости, хомогенизује особине плоче и укрућења. Развијени математички алгоритам узима у обзир употребу теорије ортоторпних плоча и методе коначних елемената. С о бзиром д а ј е т руп б рoда састављен од великог броја оребрених плоча, сврха моделирања чврстоће еквивалентним плочама свакако је формирање нумеричког модела бродске конструкције са редукованим бројем елемената и степени слободе. Овај модел, за разлику од конвецнионалног, не поседује укрућења, само еквивалентне неоребрене плоче. Поређењем конкретног нумеричког модела трупа брода састављеног од конвенционалних коначних елемената и оног од нових, еквивалетних елемената, добијена је јаснија слика о примени, предностима и манама развијене методе. Циљ рада је да се употребом методе еквиваленције, поједностави структурно моделирање великих нумеричких модела бродске конкстуркције, без значајнијих губитака у квалитету анализе, односно одређеним померањима и напонима у констуркцији. Такође је урађена и серија мерења на конкретним моделима оребрених плоча да би се утврдила генерална разлика у одзивима реалне консктрукције у односу на одзив добијен применом методе коначних елемената, имајући у виду да се ова нумеричка метода користи у оквиру методе еквиваленције., One of the most important research topic in the field of ship strength analysis is the problem of structural behavior of stiffened plates (panels), as the basic units of ship structures. In this paper, stiffened plates are modeled as unstiffened ones, with the purpose to achieve the compliance in their structural response, as much as possible. Therefore, the procedure (equivalence method) is developed in order to obtain elasticity parameters of unsiffened plates so that maximum displacements and stresses would be the same in both plates. Furthermore, an equivalent finite element is defined. This element has stiffness matrix that homogenize the mechanical prorerties of both plate and stiffener. Developed mathematical algorithm takes into account application of orthotropic plate theory and finite element method. Considering that ship hull consists of large number of stiffened plates, the goal of equivalent plate strength modeling is to form a numerical model of ship structure with a reduced number of elements and degrees of freedom. This model, apart from convencional one, does not have stiffeners, just equivalent unstiffened plates. Comparing the specific numerical model of ship structure that consists of conventional finite elements and one that consists of new, equivalent elements, one can get more clear view on application, advanteges and disadvantages of developed method. The goal of this thesis is to simplify structural modelling of large numerical models of ship strucutures, without any significant loss in quality of the analysis, namely resulting displacements and stresses. Furthermore, a series of measurements is performed on specific models of stiffened plates in order to achieve general comparison of the structural response of real structure as opposed to numerically modeled one, especially having in mind that finite element method is incportporeted in equivalence method.

Otvoreni i zatvoreni tankozidi preseci imaju široku primenu u industrijskim aplikacijama za dizajn mnogih mašina i strukturnih komponenti. Ove komponente su često fabrikovane zavarivanjem, a ne livenjem ili kovanjem. Tankozidi profili su obično povezani pomoću ugaonih zavarenih spojeva. Takvi spojevi su takođe korišćeni u drugim inženjerskim aplikacijama kao što su građevinske mašine, mostovi, ramovi, šasije vozila i dr.. U ovoj disertaciji ponašanje zatvorenih profila (kutija, okrugla cev) i otvoreniih profila (L, Z, C i K profili) šavnih profila, proučavani su tako što su izlagani statičkim opterećenjima i numeričko-eksperimentalnim pristupom. Sa tačke gledišta strukturne analize, uprkos široko rasprostranjenim ugaono zavarenim spojevima koji efikasno nose opterećenja na elementima, ne postoji praktičan, jednostavan i precizan pristup za njihov dizajn i analizu. U tu svrhu , inženjeri često moraju pripremiti relativno komplikovan model konačnih elemenata ploče ili zapremine. To je zato što navedeni eleementi izloženi opštim opterećenjima proizvode koncentracije napona u blizini spojeva. Jedan od doprinosa ovog istraživanja je bolje razumevanje ponašanja ugaono zavarenih spojeva izloženi naprezanju savijanja i naprezanja savjanja sa uvijanjem. Primena metode konačnih elemenata predstavlja osnovni numerički pristup. Posmatrani profili su medelilrani različitim konačnim elementima (greda, ploča i zapremina) i sa različitim slučajevima opterećenja. Primećuje se da na kratkom rastojanju od spoja putem ugaono zavarenih spojeva struktura nosećeg elementa pod izloženim opterećenjem ponaša se kao greda. Zavareni spojevi su generisani različitim tehnikama modelrianja sa primenom različitih tipova i veličina konačnih elemenata elemenata. Kompletni rezultati deformacija su, takođe, eksperimentalno dobijeni pomoću tehnike primene korelacije digitalne slike (DIC). Eksperimentalni testovi se izvode za proveru numeričkih simulacija u cilju ispitivanja mehaničkih performansi zavar, Hollow and non hollow section members are widely used in industrial applications for the design of many machine and structural components. These components are often fabricated by welding rather than by casting or forging. For example, in agricultural machinery, the hollow tubes are typically connected together through welding to form a corner welded joints. Such joint connections are also employed in other engineering applications such as construction machinery, offshore structures, bridges, and vehicle frames. In this dissertation, the behavior of tubular (box and circle profile) and non tubular (L, Z, C and X profiles) joint connections profiles, subjected to static loads were studied both experimentally and numerically. From a structural analysis point of view, despite of the wide use of corner welded joints as efficient load carrying members, there is no available practical, simple and accurate approach for their design and analysis. For this purpose, engineers must often prepare relatively complicated and time consuming Finite Element models made up of shell or solid elements. This is because unlike solid-section members, when hollow section members are subjected to general loadings, they may experience severe deformations of their cross-sections that results in stress concentrations in the connection’s vicinity. One of the objectives/contributions of this research work is the better understanding of the behavior of the corner welded joint connections under out-of- plane bending and torsion loading conditions. Through a detailed Finite Element Analysis (FEA) using shell and solid elements, the stress distribution at the connection of the tubular and non tubular corner welded joints were obtained for different loading conditions. It is observed that at a short distance away from the connection of the corner welded joints, the structure behaves similar to beams when subjected to loadings. Finite element models with different modeling techniques and meshing with

The subject of the paper is the temperature distribution in the thin metallic ferromagnetic plate influenced by moving linear high frequency induction heater. As a result of high frequency electromagnetic field, conducting currents appear in the part of the plate. Distribution of the eddy-current power across the plate thickness is obtained by use of complex analysis. The influences of the heater frequency, magnetic field intensity and plate thickness on the heat power density were discussed. By treating this power as a moving heat source, differential equations governing distribution of the temperature field are formulated. Temperature across the plate thickness is assumed to be in linear form. Differential equations are analytically solved by using integral-transform technique, Fourier finite-sine and finite-cosine transform and Laplace transform. The influence of the heater velocity to the plate temperature is presented on numerical examples based on theoretically obtained results.

Bucket wheel excavator ERs 1250 in Gacko has worked for over 30 years. Excavator was working in very difficult conditions because it was exploited very solid material which negatively affected the dynamic behavior of the whole structure. Bucket wheel boom of the excavator is a single tube approximately 20m long. Finite element method was applied in calculations and the results are presented in the paper. The first calculation was performed for two load cases. One case was for the complete usage of engine power (the worst case) and the other was static analysis based on the inertial load of the bucket wheel and the drive group. Measurements of deformations and vibrations on the bucket wheel boom were performing during process of digging. Strain and stress measurements were obtained using inductive sensors and eddy current sensors. These sensors measure the change in length between the magnets placed on the measuring points. Experiments and calculations gave the same results that show the negative effect of dynamic forces acting on a boom. Earlier this year the crack was discovered in a cylindrical root of the tube nearly 270 of its scope. Previously derived calculations and measurements didn’t indicate the possibility of the crack appearance. Therefore, additional simulations of load were performed (horizontal and vertical unit loads) that could cause the crack. Numerical analysis has shown that the horizontal force in the amount of 1000 kN could cause such a large crack.

Membrane walls are very important structural parts of water-tube boiler construction. Based on their specific geometry, one special type of finite element was defined to help model the global boiler construction. That is the element of reduced orthotropic plate with two thicknesses and two elasticity matrixes, for membrane and bending load separately. A global model of the boiler construction showed that the high value of stress is concentrated in plates of the buckstay system in boiler corners. Validation of the new finite element was done on the local model of the part of membrane wall and buckstay. A very precise model of tubes and flanges was compared to the model formed on the element of a reduced orthotropic plate. Pressure and thermal loads were discussed. Obtained results indicated that the defined finite element was quite favorable in the design and reconstruction of the boiler substructures such as a buckstay system.

Razmatran je jedan pristup optimizaciji tankozidih otvorenih poprečnih preseka oblika Z - profila, izloženih savijanju i ograničenoj torziji. Za data opterećenja, materijal i geometrijske karakteristike, problem se svodi na određivanje minimalne mase, odnosno minimalne površine poprečnog preseka konstruktivnih tankozidih poprečnih preseka izabranog oblika. Površina poprečnog preseka je izabrana za funkciju cilja. Uvedena su naponska ograničenja. Primenjuje se Metoda Lagranžovog množitelja. Rezultati analitički dobijenih jednačina za matematički model, numerička rešenja, kao i ušteda u masi, izračunati su za tri slučaja opterećenja. Neki rezultati su provereni primenom programa COSMOS., One approach to the optimization of a thin-walled open section Z-beam subjected to the bending and to the constrained torsion is considered. For given loads, material and geometrical characteristics, the problem is reduced to the determination of minimum mass i.e. minimum crosssectional area of structural thin-walled beam of the chosen shape. The area of the cross-section is assumed to be the objective function. The stress constraints are introduced. The Lagrange multiplier method is applied. Solutions of analitically obtained expressions for the mathematical model, numerical solutions, as well as the saved mass, are calculated for three loading cases.

The aim of this paper is to use numerical analysis and fine element method-FEM to investigate the influence of furnace tube shape on the thermal strain of fire-tube boilers. Thermal stresses in corrugated furnace tubes of different shape, i.e. with different corrugation pitch and depth, were analysed first. It was demonstrated that the thermal stresses in corrugated furnace tube are significantly reduced with the increase of corrugation depth. Than deformations and stresses in the structure of a fire-tube boiler were analysed in a real operating condition, for the cases of installed plain furnace tube and corrugated furnace tubes with different shapes. It was concluded that in this fire-tube boiler, which is of larger steam capacity, the corrugated furnace tube must be installed, as well as that the maximal stress in the construction is reduced by the installation of the furnace tube with greater corrugation depth. The analysis of stresses due to pressure and thermal loads pointed out that thermal stresses are not lower-order stresses in comparison to stresses due to pressure loads, so they must be taken into consideration for boiler strength analysis.

Problemi ponašanja orebrenih ploča (panela), kao osnovnih jedinica brodskih konstrukcija predstavljaju jednu od najznačajnijih istraživačkih tema iz oblasti čvrstoće brodskih konsktrukcija. U ovom radu orebrene ploče modelirane su neorebrenim pločama, sa ciljem da se odzivi i jedne i d ruge u š to v ećoj m eri p odudaraju. U t u s vrhu r azvijena j e procedura (metoda ekvivalencije) kojom se za svaku orebrenu ploču mogu proračunati parametri elastičnosti neorebrene ploče, tako da maskimalni ugibi i naponi, u obe ploče, budu jednaki. Ovo podrazumeva i definisanje ekvivalentnog konačnog elementa ploče koji u svojoj matrici krutosti, homogenizuje osobine ploče i ukrućenja. Razvijeni matematički algoritam uzima u obzir upotrebu teorije ortotorpnih ploča i metode konačnih elemenata. S o bzirom d a j e t rup b roda sastavljen od velikog broja orebrenih ploča, svrha modeliranja čvrstoće ekvivalentnim pločama svakako je formiranje numeričkog modela brodske konstrukcije sa redukovanim brojem elemenata i stepeni slobode. Ovaj model, za razliku od konvecnionalnog, ne poseduje ukrućenja, samo ekvivalentne neorebrene ploče. Poređenjem konkretnog numeričkog modela trupa broda sastavljenog od konvencionalnih konačnih elemenata i onog od novih, ekvivaletnih elemenata, dobijena je jasnija slika o primeni, prednostima i manama razvijene metode. Cilj rada je da se upotrebom metode ekvivalencije, pojednostavi strukturno modeliranje velikih numeričkih modela brodske konksturkcije, bez značajnijih gubitaka u kvalitetu analize, odnosno određenim pomeranjima i naponima u konsturkciji. Takođe je urađena i serija merenja na konkretnim modelima orebrenih ploča da bi se utvrdila generalna razlika u odzivima realne konsktrukcije u odnosu na odziv dobijen primenom metode konačnih elemenata, imajući u vidu da se ova numerička metoda koristi u okviru metode ekvivalencije., One of the most important research topic in the field of ship strength analysis is the problem of structural behavior of stiffened plates (panels), as the basic units of ship structures. In this paper, stiffened plates are modeled as unstiffened ones, with the purpose to achieve the compliance in their structural response, as much as possible. Therefore, the procedure (equivalence method) is developed in order to obtain elasticity parameters of unsiffened plates so that maximum displacements and stresses would be the same in both plates. Furthermore, an equivalent finite element is defined. This element has stiffness matrix that homogenize the mechanical prorerties of both plate and stiffener. Developed mathematical algorithm takes into account application of orthotropic plate theory and finite element method. Considering that ship hull consists of large number of stiffened plates, the goal of equivalent plate strength modeling is to form a numerical model of ship structure with a reduced number of elements and degrees of freedom. This model, apart from convencional one, does not have stiffeners, just equivalent unstiffened plates. Comparing the specific numerical model of ship structure that consists of conventional finite elements and one that consists of new, equivalent elements, one can get more clear view on application, advanteges and disadvantages of developed method. The goal of this thesis is to simplify structural modelling of large numerical models of ship strucutures, without any significant loss in quality of the analysis, namely resulting displacements and stresses. Furthermore, a series of measurements is performed on specific models of stiffened plates in order to achieve general comparison of the structural response of real structure as opposed to numerically modeled one, especially having in mind that finite element method is incportporeted in equivalence method.