Ph.D. Theses

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Finite-element analysis of radiative transport in gray participating media
(Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 1980., 1980.) Kalenderoğlu, Vahan.; Tezel, Akın.
A finite-element solution scheme for radiative transport problems in gray participating media is devised, and its validity is substantiated through application to representative problems involving plane-parallel geometry with azimuthal symmetry. The governing boundary value problem of radiative transport in gray participating media is first posed, and its, simplification in the case of plane-parallel geometry with azimuthal symmetry is considered in great detail with emphasis on the physics assumed in the simplification process. To provide the necessary basis for the application of the finite-element approximation technique, the governing boundary value problem is formu.lated in the weak sense, and subsequently the Galerkin approximation of the resulting weak formulation is stated. In the weak formulation. and therefore in its corresponding Galerkin approximation boundary conditions are incorporated as natural rather than essential conditions.The advantages of such an approach are clear and are discusied briefly. After a short discussion of the relevant concepts of the finite-element approximatio technique, the finite-element model of the Galerkin approximation of the weak formulation of the governing boundary value problem is developed. The resulting equations describing this model are simple, well-conditioned algebraic equations. With the general underlying theory thus established, a specific finite-element model applicable to any radiative transport problem in plane-parallel azimuthally symmetric gray participating media is, derived, vlith particular emphasis laid on accounting for the angular discontinuities in the intensity distribution. For the sake of simplicity, linear rectangular finite elements are incorporated in this specific model. For this particular choice of elements, specific expressions for the (elevant element matrices and the element vectors are derived and presehted with the intention of facilitating the tailoring of a finite-element solution scheme to problems in the application range of the aforementioned specific model. Finally; the application of this specific model to selected homogeneous as viell as nonhomogeneous problems, which are well-documented, is considered. Numerical results obtained for these problems are tabulated and compared with the corresponding exact results reported in the literature. The agreement between the finite-element and the corresponding exact results is seen to be highly satisfactory. On the basis of the aforementioned theoretical and numerical results, it is found that the finite-element approximation technique provides an efficient and reliable solution scheme for radiative transport problems in gray participating media.
Three-dimensional solution of compressible potential flow in turbomachinery by a finite element method
(Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 1983., 1983.) Güneş, Doğan.; Mengütürk, Muhsin.
The present study is concerned with the analysis of three-dimensional, compressible flows in axial-, radial-, or mixed-flow turbomachinery under the limitations of steady and potential flow conditions. The basic approach is to isolate a single blade row (which may be stationary or rotating at a constant speed) and consider the flow in one of the blade passages as representative of the total flow through the entire row of blades. It is assumed that the fluid is inviscid and enters this "characteristic" passage with uniform entropy, uniform total enthalpy and zero vorticity. Under these conditions, Kelvin's circulation theorem ensures irrotationality of the absolute flow throughout. The analysis is restricted to subsonic flows which may have local suporsonic spots. The fluid is either incompressible or assumed to be accurately represented by the perfect gas law. The analysis begins with the development of the classical velocity potential formulation of the problem stated above. An equivalent variational formulation is then described. This formulation incorporates a quasilinearization concept which leads to iterative solution. Density distribution is assumed to be given by a previous solution and therefore has no variation. The problem of three dimensional, compressible, potentiai flow in turbomachinery is thus reduced to the determination of the absolute velocity potential distribution which minimizes an equivalent functional in the solution domain with appropriate boundary conditions. A computer code has been developed to solve this problem based on the finite element analysis presented in this thesis. The solution domain is discretized by using hexahedral superelements each composed of six ten-node tetrahedral elements enabling quadratic interpolation of velocity potential. The code offers the flexibility of using a com. bination of subparametric and isoparametric elements. which provides high accuracy at reasonable cost in the treatment of turbomachinery flows that exhibit complicated design features. Applications of the code to the Gostelow cascade, an experimental turbine stator, the first stage stator and rotor of an electric utility axial-flow turbine and finally to a mixed-flow turbine rotor are presented. The validity of the code is established by comparing the results with the exact solution, experimental data and calculations by other numerical methods.
A deterministic approach to transition to turbulance in plane shear flows
(Thesis (Ph.D.)- Bogazici University. Institute for Graduate Studies in Science and Engineering, 1999., 1999.) Atalık, Salim Kunt.; Tezel, Akın.
In this work, a parametrical study of the transition to turbulence in two-dimensional shear flows has been conducted. For this purpose, the solutions of the full two-dimensional Navier-Stokes equations have been investigated numerically using spectral methods. In parallel, a new spectral integration algorithm, called the Nonlinear Galerkin Method, stemming from dynamical systems theory and developed for the integration of dissipative evolution equations such as Navier-Stokes equations, has been tested and applied for the study cases. Different nonlinear Galerkin methods have been compared for this purpose with respect to each other in terms of convergence and efficiency and the improvements on the classical Galerkin spectral method have been shown numerically. Transition to turbulence has been analyzed by the parametrical investigation of qualitatively different solutions in the phase space of two-dimensional Navier-Stokes equations for bounded and unbounded shear flows with one nonhomogeneous direction. The applications were plane channel (Poiseuille) flow and oscillatory plane Poiseuille flow for the bounded flow case, and temporally growing mixing layer and plane jet flows for the unbounded flow case. With this work, we aim to contribute to the enlightening of the structure of the phase space of two-dimensional Navier-Stokes equations as well as to the testing of a new integration algorithm which seems to be promising in the direct numerical simulation of Navier-Stokes equations.
Physical based analysis and model reduction of engineering systems
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2003., 2003.) Orbak, Ali Yurdun.; Eşkinat, Eşref.; Türkay, Osman S.
There is a need for obtaining low order approximations of high order models of physical systems as low order models result in several advantages including the reduction of computational complexity and improved understanding of the original system structure. Different methods have been suggested in literature for obtaining suitable low order approximations, but these approaches do not reflect the relation between the mathematical model and the physical components of a system. In this thesis, some new approaches are provided for model reduction in the physical domain. The approaches that are presented use the idea of decomposition of physical systems, which is useful for the identification of dominant components or subsystems. The procedures are applied to the physical systems that are represented by bond graphs as they lead to better understanding of the system structure. One of the proposed methodologies exploits the idea of decomposition of physical systems. The proposed decomposition and model reduction procedures are directly implemented on the model providing a better perception of the physical model reduction and a better design point of view. As a second methodology, the determination of subsystems and/or components that influence a given eigenvalue of the overall system has been explored. A set of theorems and definitions are proposed that lead to an efficient procedure for this aim. After the calculation of eigenvectors, effect matrices are produced that indicate the relative importance of physical parameters in a selected eigenvalue. Using these matrices, an efficient physical model reduction procedure is constructed. The advantages of the presented approaches over existing methodologies are emphasized through several examples.
Characterization of NiMnGa magnetic shape memory alloys
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2005., 2005.) Pirge, Gürsev.; Altıntaş, Sabri.
Magnetic shape memory (MSM) alloys are a new class of actuator materials withhigh actuation frequency, energy density and strain and they can be used in themanufacturing of actuators, smart structures, sensors and transducers. NiMnGa alloys experience a reversible martensitic transformation, which is a temperature-dependent phasetransformation from a highly symmetric crystallographic structure (austenite) to lowsymmetry (martensite). These materials are ferromagnetic. Ferromagnetism is aphenomenon by which a material can exhibit a spontaneous magnetization, and is one of the strongest forms of magnetization. Ferromagnetic metal alloys whose constituents arenot ferromagnetic in their pure forms are called Heusler alloys, named after Friedrich Heusler. Applying a strong magnetic field to some of the Heusler alloys may inducereorientation of martensite variants with high magneto-crystalline anisotropy energy, which leads to a net shape change of the material. In this study, the effect of alloycomposition, cutting direction and heat treatment on the microstructure, local composition,and thermal and dilatometric properties of NiMnGa alloys were investigated.Characterization tests involved various crystals, with and without post-crystal growth heat treatment, by chemical analysis, differential scanning calorimetry (DSC), dilatometry,optical microscopy, scanning electron microscopy and radiography. Metallographic studies showed that as solidified, off-stoichiometric alloys had three distinct microstructural features-a Heusler phase, a Mn rich phase and a eutectic or eutectoid region. Various heattreatment procedures were applied to successfully remove the last phase and produce MSM effect. Heat treatment was also essential for the production of a distinct martensitetransformation in DSC and dilatometry traces and a martensitic transformation to occurover a narrow temperature range. Bulk and microanalysis showed that there are significant concentration variations in the boules grown by the Bridgman method, that lead to changesin phase transformation behavior which were observed by DSC. The presence of composition variations in the boules is a major issue because of its effect on the martensitetransformation temperature. For boules with composition variations, both transformed anduntransformed regions will exist over some temperature range, degrading the performanceof any actuator made from them. Clearly, further effort on the improvement of the crystalgrowth technique is needed to remove the composition gradient and variations and toobtain a fine dendritic structure, which would be much easier to homogenize. For thecurrent growth conditions, coarse cellular structures have been obtained which showsignificant solute segregation. An increase in the thermal gradient during the directionalsolidification process resulted in a finer cellular structure.
Numerical investigation of high Knudsen number flow in rectangular enclosures
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2006., 2006.) Orhan, Mehmet.; Ecder, Ali.; Tezel, Akın.
Nowadays, enlightening unknown aspects of rarefied gas flow is one of the critical issues of fluid dynamic research to ensure correct and proper operations of manyMicro- Electro-Mechanical-Systems (MEMS). Thermally driven motion of rarefied gases is gaining in importance to develop Knudsen compressors having better performance or to improve single crystal growth processes. Therefore, accurate prediction of the physics lying behind the thermal creep in the transition regime as well as slip flow regime is one of the main motivations of this study. The other emphasis is possible flow instability of the rarefied gases in enclosures. For this purpose, an asymptotic approximation has been performed in the first part of the study to find analytical solutions. In the second one, linear disturbance theory of hydrodynamic stability has been applied to the problem to determine bounds of instabilities. Analytical solutions of two-dimensional stability analysis have been introduced. Critical states have been identified for different models and for varying Knudsen numbers. More generally, eigen-spectrum of the perturbation equations has been identified in three-dimensions. At the last part, by applications of an artificial viscosity scheme, a computer program has been constructed to solve Burnett and also Navier-Stokes equations. Mechanisms of the thermal creep flow have also been verified by inspecting stress tensors of Burnett equations. Most importantly, the insufficiency and the failure of Navier-Stokes equations for the creeping flows have been proved. Moreover, it has been shown that Burnett equations can correctly model such creeping flows.
LPV modeling and robust control of yaw and roll modes of road vehicles
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2007., 2007.) Başlamışlı, Selahattin Çağlar.; Köse, İbrahim Emre.; Anlaş, Günay.
In this thesis, the usefulness of linear parameter varying (LPV) modeling of vehicle dynamics is investigated for controller synthesis to take nonlinear tire behavior into account. The H infinity control framework is used to design combined active steering and differential controllers to improve vehicle handling during maneuvers involving large driver commanded steering angles. Two approaches are undertaken to reduce the size of the parameter set to minimize solver time during the controller synthesis step. The first approach is built on modeling tire stiffnesses as parametric uncertainties. This leads to a linear fractional transformation (LFT) model of the combined vehicle body and tire subsystems and to the design of a static state feedback controller intended to be robust against large variations in parameters. In the second approach, a rational fit is proposed for the nonlinear tire model used, and original parametric vehicle models are derived by integrating the fitting model into the equations of motion. This leads to the design of gainscheduled LPV controllers where scheduling is based on lateral and longitudinal tire slips. At small driver commanded steering angles, both controllers achieve decoupling of sideslip and yaw rate modes. However, at large driver commanded steering angles, the steering response of the first controller is observed to be unstable at the physical limit of the vehicle due to the shortcomings of the parametric uncertainty model in predicting tire behavior at large lateral slip. Meanwhile, the second controller achieves decoupling of all vehicle modes for the whole range of driver commanded steering angles up to and at the physical limit of the vehicle, revealing the importance of incorporating the tire friction circle concept into the controller synthesis.
Hydroxyapatite coating on Ti and Ti6A14V substrates by using electrophoretic deposition method
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2008., 2008.) Albayrak, Önder.; Altıntaş, Sabri.
Electrophoretic deposition method was used to coat hydroxyapatite (HA) on titanium (Ti) and its alloy (Ti6Al4V). Main focus was elimination or decreasing the crack occurrence and increasing adhesion strength. For this purpose, chemically synthesized nano sized and naturally derived submicron sized HA powders were produced. First, these powders both in calcined and uncalcined states were deposited on Ti and Ti6Al4V substrates under different coating voltages to investigate the effect of calcination and coating voltage on coating quality. The cracks became less pronounced with decreasing applied voltage. Coatings obtained using calcined powders were seen to be free of cracks before and after sintering. Further studies were conducted to increase the adhesion strength by depositing nano-sized titanium dioxide (TiO2) powders using different coating voltages, as an inner layer between Ti6Al4V substrate and HA coating. Adhesion strength of the overall coating was found to increase with decreasing voltage used in TiO2 deposition. Furthermore, use of the TiO2 inner layer prevented HA decomposition. Finally, studies were conducted to create coating surface consisting of calcium phosphate (Ca-P) based bioceramics and TiO2. This surface was expected to combine the advantages of Ca-P (osseointegration) and TiO2 (photocatalytic bactericidal effect). TiO2 was allowed to grow from the titanium substrate to fill in the cracks in the Ca-P coating at sintering stage, and coalescence of Ca-P/TiO2 was observed.
Dynamic analysis of diesel engine crankshaft system using finite elements and multibody system simulation programs
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2008., 2008.) Yılmaz, Yasin.; Anlaş, Günay.
In this thesis, dynamic analysis of in-line six cylinder diesel engine crankshaft system is carried out using analytical and numerical methods. The dynamic analysis of the crankshaft system consists of calculation of forces, displacements and stresses over a complete engine cycle (two revolutions of the crankshaft) under steady state (constant speed) conditions with a model of the whole cranktrain. Crankshaft system consists of crankshaft, engine block, pistons, piston pins, connecting rods, flywheel, torsional vibration damper, bearings and mounts that support the engine block. The loading on the system comes from the cylinder gas pressure and inertia of crankshaft system components. In the analytical part of the study, first, the forces acting on the crankshaft system are determined. Then, main bearing loads are calculated using a statically determinate system approach for each crank throw. Finally, torsional vibration and stress analyses of the crankshaft system are performed. In the numerical analysis of the crankshaft system, Msc. Nastran and Msc. Adams programs are used. The dynamic stress distribution in the crankshaft is evaluated using a flexible crankshaft model that is obtained through finite elements and Component Mode Synthesis (CMS) technique. To study the effect of oil holes on crankshaft dynamic stresses, crankshaft models with and without oil holes are used. The effect of TV damper on crankshaft stresses is investigated. Bearings are modeled using hydrodynamic bearing models of ADAMS. Coupled axial, bending and torsional vibrations of the crankshaft system are considered. Effect of each part of the crankshaft system on crankshaft dynamic stress and vibration characteristics are investigated. A separate chapter is devoted to effects of counterweight mass and position on main bearing load and crankshaft bending stresses. In the analysis, rigid, beam and 3D solid (flexible) crankshaft models are used. Main bearing load results for rigid, beam and 3D solid models are compared and beam model is used in counterweight configuration analyses. Twelve-counterweight configurations with a zero degree counterweight angle and eight-counterweight configurations with thirty degree counterweight angle, each for 0%, 50% and 100% counterweight balancing rates, are considered. It is found that maximum main bearing load and web bending stress increase with increasing balancing rate, and average main bearing load increases with decreasing balancing rate. Both configurations show the same trend. For this specific engine, the load from gas pressure rather than inertia forces is the parameter with the most important influence on design of the crankshaft. Results of bearing loads and web bending stresses are tabulated.
Mechanical behavior of low density polymeric foams under multiple loading and unloading
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2008., 2008.) Öztürk, Umud Esat.; Anlaş, Günay.
In this thesis, mechanical behavior and energy absorption characteristics of low density polymeric foams under multiple loading and unloading are investigated for uniaxial and hydrostatic compression, uniaxial tension, simple shear, and cylinder and block indentation. Constitutive models and energy absorption diagrams available in literature for uniaxial compressive loading are reviewed. A new phenomenological constitutive model for accurate calculation of load, deformation, and absorbed energy is proposed for multiple loading and unloading. Results of the available and the new models are compared to those of experiments for expanded polystyrene (EPS) and polyethylene (PE) foams. A design procedure for multiple compressive loading and unloading is presented. A drop test rig for measuring uniaxial compressive behavior of foams at high loading speed and a hydrostatic compression test setup to study the mechanical behavior of foams under multiple hydrostatic loading and unloading are built. Tools to be used with Zwick Z020 universal tensile testing machine are prepared for uniaxial tension, simple shear, and cylinder and block indentation tests. Stressstrain results are presented for EPS and PE foam specimens. Finite element simulations of EPS and PE foam specimens under multiple loading and unloading for uniaxial and hydrostatic compression, uniaxial tension, simple shear, and cylinder and block indentation are performed using Abaqus finite element package for volumetric and isotropic hardening. The results of finite element simulations are compared to those of experiments.
Prediction of dynamic force characteristics od radial tires using finite element and experimental techniques
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2008., 2008.) Alkan, Veysel.; Anlaş, Günay.
A tire is one of the most important components of a vehicle. To predict its dynamic force characteristics, a detailed finite element model is constructed. In the finite element analysis of the tire, nonlinear stress-strain relationship of rubber, the reinforcements of the tire and contact between the tire and ground are modeled. First, a static tire model is constructed. Its vertical force-deflection characteristics on a surface with and without cleat and the pressure distribution over the cross section are obtained. Then, dynamic force characteristics of the tire are predicted. In the dynamic analysis of the tire, lateral and vertical force characteristics are examined, tire enveloping characteristics at low speed are investigated. Experimental studies are performed to validate finite element model results. All experiments are conducted using the Flat-bed Tire Test Machine at the University of Michigan Transportation Research Institute (UMTRI). Model and experimental results are compared to each other and it is concluded that to some extent, there is a good correlation between them. Error tables are also given to show the accuracy range of the proposed model.
Closed-loop actuator and sensor location selection strategies for flexible structures
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2008., 2008.) Güney, Murat.; Eşkinat, Eşref.
In this thesis, the problem of finding the optimal actuator and sensor locations for vibration control of a flexible structure is studied. An iterative search strategy is used, where the closedloop criteria are selected as the optimization metric. During iterations approximate coprime or low-authority H-infinity-controllers are designed, or alternatively quasi-controller method (residual deformations norm minimization) is used, which does not directly calculate controller but obtains some norms that instead approximate the closed-loop behavior well. In applications with controllers, the controller design is simplified by introducing simple approximate Algebraic Riccati Equation solutions and their derivatives, which are obtained by converting the state space descriptions of the physical system with signal weights into state space representations with decoupled block diagonal state matrices. Hence, based on such approximate solutions, it is possible to design computationally less complex controllers with less computational effort. Since for gradient based search techniques, the partial derivatives of the closed-loop criteria are required, Finite Element sensitivity analysis is utilized. The partial derivatives of the mass, stiffness and electromechanical coupling matrices are defined. Then, the partial derivatives of the open-loop and controller matrices are introduced. For plates with piezoelectric patches, the minimization procedure is enriched with constrained techniques, where Finite Element discretization is done automatically at iteration regarding the constraints. The modified constrained optimization technique is based on Zoutendijk's method and introduces constraints to avoid mesh generation of badly scaled finite elements
Finite element analysis of plasticity-induced fatigue crack closure
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2008., 2008.) Gökçen, Mehmet Gökhan.; Kalenderoğlu, Vahan.
Contact elements are implemented into the elastic-plastic finite element analysis of fatigue crack closure to predict crack opening stress, by developing a code using ANSYS Parametric Design Language. Although the use of contact elements in modeling crack surface contact is inherently natural, almost no effort to incorporate them has been reported in the literature. The traditional method is based on placing truss elements on the crack surface nodes. The load is applied incrementally, during which the crack surface nodes are monitored to predict crack opening stress values. In this research contact elements are used to model crack surface contact and the determination of crack opening stress is accomplished by monitoring the state of contact elements during incrementally applied loading. The results of two dimensional finite element analyses are in good agreement with previous work given in the literature. Instead of determining crack opening stress of every load cycle, an algorithm that makes it possible to find crack opening stress at predetermined load cycle intervals is developed. With the developed algorithm it was possible to analyze crack closure behavior during a larger number of load cycles with less execution time. The newly introduced parameters such as effect of the number increments of the applied load, the effect of the load cycle interval where the opening stress values are determined are investigated. Due to simulation of relatively high number of load cycles, final stabilization of crack opening stress values after a subsequent decay in the initially “stabilized” opening stress values is observed.
Optimum vibration absorbers for continuous and discrete mechanical systems
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2008., 2008.) Tursun, Murat.; Eşkinat, Eşref.
In this thesis, the optimum parameters of passive vibration absorbers for continuous and discrete mechanical systems are investigated. Two approaches are undertaken to obtain the optimum absorber parameters. The first approach is built on the continuous system analysis for minimization of vibration amplitudes and the related methodology, motivated by Lagrange’s equation and the Lyapunov equation, is derived. The second approach, based on the receptance concept, uses a new methodology which employs the Sherman- Morrison formula to minimize the vibration amplitudes in discrete systems. A method is developed for calculating the optimum parameters of n absorbers attached to a uniform beam or rectangular plate, the vibrations of which are characterized by the first M modes where n and M can be any positive integers. For the most general case, dissipation due to damping, kinetic and potential energies, and the effects of external forces are all taken into account. Lagrange’s equation is used to generate a state space representation of the system, wherein the Lyapunov equation is used to obtain the H2 norm of the transfer function. This norm is used to construct the objective function for optimization. The optimal response is compared to cases without an absorber and with randomly selected absorber parameters. Focusing on the minimization of the vibration amplitudes using the concept of receptance, a method for calculating the receptance of a generic translational mass-springdamper system with m masses and n absorbers is developed. The dynamic stiffness of the entire system is derived both directly from the equations of motion and through a linear graph representation of the system. The receptance of the combined system, in terms of the parameters of the main and absorber systems is obtained by applying Sherman-Morrison formula sequentially. The optimal absorber parameters of the system are easily obtained once the receptance is known. The complexity of the formulation is simplified with the proposed approach. Two basic models, both the continuous and discrete system modeling for suppressing vibration, are built in this thesis. It is shown that continuous and discrete systems are interrelated and the corresponding developed methods can be applied to each type of system mutually.
Design optimization of structures under fatigue loading
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2009., 2009.) Ertaş, Ahmet Hanifi.; Sönmez, Fazıl Önder.
Many of the engineering failures are caused by fatigue. Fatigue failure can be defined as the tendency of a material to fracture by means of progressive brittle cracking under cyclic stresses. Because mechanical components usually experience cyclic loading during their operation, fatigue failure prevention is the foremost design requirement. Fatigue strength, thus structural performance, can greatly be increased through design optimization. Hence in this study, the general objective is to maximize the fatigue life of structures. Firstly, high cycle fatigue assessment models for homogeneous materials were investigated. Then, they were applied to predict fatigue lives of spot welded specimens. Reliability of these models depends on accurate calculation of the cyclic stress and strain states within the structure. For this purpose, a nonlinear finite element analysis was carried out taking into account plastic deformations, residual stresses developed after unloading, and contacting surfaces. Among the general purpose fatigue models, Coffin - Manson and Morrow’s mean stress models were found to correlate best with the experimental data. After that, a parametric study on fatigue strength of spot weld joints was conducted. The design variables considered in this study that were known to affect the strength of spot weld joints were sheet thickness, spot weld nugget diameter, number of spot welds, and the joint type as exemplified in tensile shear (TS), modified tensile shear (MTS), coach peel (CP), and modified coach peel (MCP) specimens. The results provide designers with some guidelines to foresee the impact of design changes on fatigue strength of spot weld joints. Secondly, a methodology was proposed to find the optimum locations of spot welds and the optimum overlapping length of the joined plates for maximum fatigue life. Minimum weld-to-weld and weld-to-edge distances recommended by the industry were considered as side constraints. The total strain life equation was used to predict the fatigue life. In order to use this model, the strain state in the structure developed under cyclic loading was calculated. Nelder-Mead (Sequential Simplex) was employed as the search algorithm in the optimization procedure. A number of problems were solved to demonstrate the effectiveness of the proposed method. Finally, a methodology was developed to optimize composite laminates subject to inplane loads for maximum fatigue life. For this purpose, a parametric fatigue life prediction model, proposed by Fawaz and Ellyin, was coupled with a global optimization technique called Direct Simulated Annealing (DSA). Fiber orientation angles were chosen as design variables. A computer code was developed in ANSYS parametric language and results were obtained for different configurations and loading conditions.
Fabrication and characterization of Al, AlMgSi, and AlSi foams
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2010., 2010.) Mahmutyazıcıoğlu, Nazım.; Altıntaş, Sabri.
Manufacturing of metal foams by using powder compact melting (PCM) method, with the most important considerations like material and method selection, powder blending, cold compaction, hot compaction and hot extrusion and foaming is explained briefly. The effects of Al2O3 particle addition on the heat treatment, cell structure and mechanical properties of AlMgSi foams were studied. Alloy and composite foams were manufactured by powder compact melting (PCM) method. A pre-blended mixture of Al, Mg, Si and Cu representing the wrought AlMgSi alloy (6061) were mixed with heat treated TiH2 and Al2O3 ceramic particles, hot compacted and foamed at temperatures between 750 and 800 °C. The amount of <20μm sized Al2O3 particles in the composite foams were 3, 5 and 10 per cent by volume. The effects of different heat treatments on the microhardness of the foams were investigated. Foams that were fully heat treated had the highest hardness values and they performed best with an increase in collapse strength up to 100 per cent over the untreated samples. It was found that the addition of Al2O3 did not affect the hardenability but the strength and the compression stiffness of the composite foams were increased with 3 and 5 vol. per cent Al2O3 addition. This was attributed to the improved cell structure and decreased drainage when the ceramic amount is not more than 5 per cent. The compression test results were interpreted in terms of the foam’s microstructure and correlations were made relating the unloading modulus and compression strength of the foams with the relative density. It was found that the foams were inhomogeneous and their mechanical properties were close to those expected from open cell foams. An important phenomenon in Al foam production is stabilization of the structure. Especially it is very difficult to obtain highly expanded foams made from pure Al powder. In this study, an improvement in the stabilization was achieved by Al2O3 and B4C ceramic powder addition to the Al-TiH2 mixtures. Compaction of the mixture was achieved by hot extrusion. Extruded dense semi-products (precursors) were foamed at 800 °C and the macro and microstructures of the foams were analyzed. It was found that both of the ceramics increased the number of cells and cell size homogeneity of Al foams. The stabilization seems to be enhanced with the presence of solid constituents but the mechanism acting could not be understood clearly. Most of the ceramic particles were partially wetted and segregation between the metal and gas interface was observed. The wetting of B4C particles by the aluminum matrix was relatively better and this resulted in smoother foam cell walls when compared with the cell walls of pure and Al2O3 added Al foams. Finally, a different matrix alloy, hypereutectic AlSi (AlSi14Cu2.5Mg0.6) was used for foam manufacturing by PCM method. The alloy has some advantages over the Mg, Cu and Zn added alloys like good wear resistance, high mechanical strength without aging heat treatment and dimensional stability. Foams manufactured were heat treated, in order to analyze the changes in the microstructure and the mechanical properties. The results showed that, heat treatment caused spheroidizing of eutectic Si phases and depending on the density, the compression strength of the foams could be increased up to 50 per cent. The deformation of the foam was similar to brittle foams and densification strain was higher than ductile foams which makes it a good candidate for energy absorption applications.
Gain-scheduled air path system control and compressor air mass flow estimation in diesel engines
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2010., 2010.) Atam, Ercan.; Köse, İbrahim Emre.
In this dissertation, we deal with the independent problems of air path system control and compressor air mass flow estimation in diesel engines. In this regard, the thesis can be divided into two main parts: control and estimation. In the first part, control part, we consider regulation of the air path system in diesel engines. To that end, an extensively used mean-value engine model in the literature is considered. The underlying nonlinear model is converted into a rational linear parameter-varying (LPV) form and a gain scheduled control approach is used. The main contribution here is that the commonly used simplifying assumptions in the literature (like constant engine speed, use of engine charts, assuming exhaust manifold pressure to be equal to intake manifold pressure plus some constant value, taking constant manifold temperatures, etc.) are avoided and a better engine model with a better subsequent controller design are achieved. As a result, the control system design is covering a wide range of engine operating points. In the estimation part, we present two different estimation approaches, each having advantages over the other. In the first approach, we develop a general deterministic state estimation method for states appearing linearly in nonlinear systems. The es- timation method is based on representation of input-output pairs by a linear moving model and the use of recursive-least squares with an adaptive forgetting factor. The method is on-line applicable and very easy to apply. It is shown that the developed estimation method outperforms the popular extended kalman filter (EKF) method on some case studies. Next, the developed estimation method is used for a diesel engine model to estimate compressor air mass flow, whose measurement is difficult or unreliable in some situations and therefore its estimation is important in these cases. Again, a comparison with EKF shows the advantage of the developed method. The second estimation method is based on the use of a state estimation method for affine parameter-dependent linear systems. To use this method, the underlying nonlinear engine model is first transformed into an a±ne parameter-dependent form and then the method is used. This approach has the advantage of having an asymptotic convergence nature, when compared to the first one. Again, this method is used for compressor air mass flow estimation and the results are compared with those of EKF to demonstrate the superiority of the approach.
Numerical analysis of surface-driven non-isothermal viscoelastic flow
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2010., 2010.) Kaptan, Yalın.; Ecder, Ali.; Atalık, Salim Kunt.
The numerical investigations of the moving edge non-isothermal viscoelastic flows are simulated by using two example problems (lid driven cavity (LDC) and rotating disc in a cylindrical enclosure (RDCE) flows) in this study. The viscoelastic behavior of the fluids is modeled by adopting three differential constitutive relations namely Upper Convected Maxwell (UCM), Oldroyd B and Giesekus models. The comparisons reveal that the Giesekus model is the most realistic one and the maximum Weissenberg number limit is higher compared to the others. Two separate solvers are used in the simulations; PETSc and IN-GMRES solvers. PETSc code is used as a solver for the Newtonian flows and a benchmark tool for the Krylov subspace methods and preconditioners. PETSc analyses reveal that BiCGStab with ILU(5) preconditioning is the most effective solver in the simulations of the Newtonian flows. IN-GMRES solver is used to simulate the non-isothermal viscoelastic flows and it is based on the matrix free preconditioned inexact Newton-Krylov methods. To obtain higher Weissenberg number limits in the simulations, the numerical tools such as the continuation, the upwind differencing scheme, the higher order discretization schemes, the slanted stencils and similar others are implemented in the IN-GMRES algorithm. In the non-isothermal part of the study, besides the advection and diffusion, the viscous dissipation is also included and it is understood that the viscous dissipation is very important in simulations of non-Newtonian flows. The viscosity is modeled as temperature dependent by adopting the approximate Arrhenius formulation and it is realized that the viscosity changes can alter the flow field. The effects of the Reynolds number, the Weissenberg number, the Prandtl number, the Brinkman number, aspect ratio and some of the material parameters are documented within this study.
Failure criteria for functionally graded materials and application of GTN model using finite elements
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2010., 2010.) Oral, Alpay.; Anlaş, Günay.
Functionally Graded Materials (FGMs) are special composites with a point to point continuous property variation. In this failure of laboratory scale FGMs is modeled using Gurson - Tvergaard -Needleman (GTN) model. Stress, energy, strain based (e.g. MTS, G, S criteria) and cohesive zone models that are used for failure modeling of FGMs are reviewed. GTN model originally used for failure of homogeneous materials is studied in detail. Because it is extremely difficult, if not possible, to obtain a closed form GTN yield function for a non homogeneous material, numerical implementation of GTN model is considered, and Abaqus is used for computational analyses. The validity of results are first checked by resolving a problem from literature using Abaqus. GTN model is numerically implemented to two different FGM specimens to study and predict failure. One of the FGM specimens is titanium monoboride / titanium (TiB / Ti) single edge notched bending (SENB) specimen, and the other one is a gradually ultraviolet irradiated polyethylene carbon monoxide (ECO) co-polymer single edge notched tension (SENT) specimen. It is concluded that GTN model is promising for failure simulations of FGMs with a proper selection of model parameters.
Design of composite structures for minumum weight
(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2010., 2010.) Akbulut, Mustafa.; Sönmez, Fazıl Önder.
The goal of this study is to develop methodologies to optimize the structural design of composite materials to achieve the minimum weight. Mainly three different problem areas were considered. Firstly, weight minimization of laminated composite plates subjected to in-plane loading; secondly, as an extension of the first problem, weight minimization of laminated composites subjected to in-plane and out-of-plane loads; thirdly, optimal design of laminated composite plates with notches using progressive failure approach. Considering that composite materials are generally used in applications where weight is critical and considering their high cost, in this study, designs with minimum material use were aimed. Fiber orientation angle and number of plies in each lamina were used as design variables. The maximum stress and Tsai-Wu criteria were used individually or together to predict static failure. Different geometries and loading conditions were considered. Because the problems considered in this study contain numerous local optimums, a global search algorithm, Simulated Annealing, was used as the optimization algorithm. A number of modifications were proposed to improve the reliability of the algorithm.

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