In this thesis, the Generalized Finite Difference (GFD) method is applied to analyze the elastoplastic deformation behavior of a long functionally graded (FGM) tube subjected to internal pressure. First, the method is explained in detail by considering the elastic response of a rotating FGM tube. Then, the pressurized tube problem is treated. A long FGM tube with fixed ends (axially constrained ends) is taken into consideration. The two cases in which the modulus of elasticity only and both the modulus of elasticity and the yield limit are graded properties are analyzed. The plastic model here is based on incremental theory of plasticity, Tresca&#039 / s yield criterion and its associated flow rule. The numerical results are compared to those of analytical ones. Furthermore, the elastic response of an FGM tube with free ends is studied considering graded modulus of elasticity and Poisson&#039 / s ratio. The results of these computations are compared to those of Shooting solutions. In the light of analyses and comparisons stated above, the applicability of the GFD method to the solution of similar problems is discussed. It is observed that, in purely elastic deformations the accuracy of the method is sufficient. However, in case of elastic-plastic deformations, the discrepancies between numerical and analytical results may increase in determining plastic displacements. It is also noteworthy that the predictions for tubes with two graded properties, i. e. the modulus of elasticity and the yield limit, turn out to be better than those with one graded property in this regard.

An elastic FGM layer bonded to a semi-infinite linear elastic, isotropic, homogeneous half plane is considered. The half plane contains periodic cracks perpendicular to the interface. Mechanical loading is applied through crack surface pressure, resulting in a mode I crack problem. The plane elasticity problem described above is formulated by using Fourier transforms and Fourier series. A singular integral equation is obtained for the auxiliary variable, namely derivative of the crack surface displacement. Solution is obtained, and stress intensity factors are calculated for various values of crack period, crack length, crack location, layer thickness and material gradation.

Les propriétés idéales d’un matériau de blindage sont la combinaison d’une extrême dureté pour casserles noyaux des projectiles et d’une grande ductilité pour résister à l’impact et arrêter les fragments du projectile. Or cettecombinaison de propriétés est incompatible avec un matériau unique. Pour pallier ce problème, les concepteurs de blindageassocient un matériau dur (céramique) à un matériau ductile (métal). Une autre solution serait de réaliser un matériauprésentant un gradient de propriétés mécaniques : dans le cas présent, d’une très grande dureté de la face avant à une grandeductilité de la face arrière. Les technologies non conventionnelles de frittage telles que le Spark Plasma Sintering (SPS)permettent d’assembler ou de fritter/assembler des matériaux aux caractéristiques aussi différentes et complémentaires. Ils’agit donc d’étudier les conditions d’assemblage ou de cofrittage de tels matériaux (dans le cas présent, Al2O3 et Ti) ainsique l’influence de la microstructure résultante de l’ensemble sur sa performance balistique.La première partie de ce travail a porté sur la caractérisation de l’alumine et du titane. Cinq poudres d’alumines ontété étudiées d’un point de vue comportement au frittage. Trois d’entre elles sont retenues en raison de leurs microstructuresintéressantes, proches en termes de densité et de taille de grains. Ces alumines ont été caractérisées mécaniquement (dureté,ténacité, résistance à la rupture) et balistiquement pour n’en garder qu’une dans la deuxième partie du travail. Le titane, frittédans les mêmes conditions que l’alumine, a montré qu’il n’avait malheureusement pas les propriétés attendues (absence deductilité).La seconde partie du travail a montré que l’obtention de MGFs sains à partir de Al2O3 et Ti uniquement est délicate,que ce soit avec un intercalaire sous forme de monocouche ou de multicouche. La forte affinité du titane avec l’oxygène(formation d’oxyde ou en insertion) et le carbone (formant des carbures), ainsi que sa réactivité avec l’alumine (produisantdes intermétalliques) rend le MGF fragile et incapable d’accommoder les contraintes résiduelles d’élaboration. L’insertiond’une faible proportion de nickel (plus ductile et moins réactif vis-à-vis de l’oxygène que le titane) dans les composites apermis d’obtenir des MGFs sains, dont le comportement balistique a pu être évalué. / The objective is to improve ballistic performance of armors. A perfect armor combines ductility to resistto the impact and high hardness to stop projectile’s fragments. However, such an association of properties is inconsistent witha single material. The solution is to perform a functionally graded material (FGM) with a ductile metal at the back side of thesample and a hard ceramic on the top side. Non-conventional technologies like Spark Plasma Sintering allow joining orsintering all types of materials with different and additional properties. Furthermore, with this technique, high heating ratescan be achieved, limiting grain growth and resulting in a fine microstructure. The goal is to study joining conditions or cosinteringof such materials (in this case, Al2O3 and Ti), as well as the resulting microstructure on the ballistic efficiency.The first part of the study focused on the characterization of alumina and titanium. Five powders of alumina werestudied from a sintering point of view. Three of which were selected because of their interesting microstructures, close indensities and grain sizes. These ceramics have been characterized mechanically (hardness, toughness and strength) andballistically. One of them is adopted to realize FGM. Titanium, sintered with the same conditions, unfortunately, doesn’t haveexpected properties (absence of ductility).The second part of the work showed that the preparation of FGM without cracks from Al2O3 and Ti only ischallenging, with an interlayer with one or more layers. The strong affinity of Ti with oxygen (formation of oxides orinsertion) with C (forming carbides) and its reactivity with alumina (forming intermetallics) make the FGM brittle and enablethe release of residual stresses during the process. By adding a low amount of nickel (more ductile and less reactive withoxygen and titanium) in composites, FGMs almost without cracks were obtained. The latter were evaluated ballistically.

In this study, we quantified the Chemistry-Process-Structure-Property (CPSP) relations of a Ti-6Al-4V/TiB functionally graded material to assess its ability to withstand large deformations in a high throughput manner. The functionally graded Ti-6Al-4V/TiB alloy was created by using a Laser Engineered Net Shaping (LENS) process. A complex thermal history arose during the LENS process and thus induced a multiscale hierarchy of structures that in turn affected the mechanical properties. Here, we quantified the functionally graded chemical composition; functionally graded TiB particle size, number density, nearest neighbor distance, and particle fraction; grain size gradient; porosity gradient. In concert with these multiscale structures, we quantified the associated functionally graded elastic moduli and overall stress-strain behavior of eight materials with differing amounts of titanium, vanadium, aluminum, and boron with just one experiment under compression using digital image correlation techniques. We then corroborated our experimental stress behavior with independent hardening experiments. This paper joins not only the Process-Structure-Property (PSP) relations, but couples the different chemistries in an efficient manner to effectively create the CPSP relationships for analyzing titanium, aluminum, vanadium, and boron together. Since this methodology admits the CPSP coupling, the development of new alloys can be solved by using an inverse method. Finally, this experimental data now lays down the gauntlet for modeling the sequential CPSP relationships.

No description available.

Yes / The ever-increasing demand for high performance electronic and computer systems has unequivocally called for increased microprocessor performance. However, increasing microprocessor performance requires increasing the power and on-chip power density of the microprocessor, both of which are associated with increased heat dissipation. In recent times, thermal management of electronic systems has gained intense research attention due to increased miniaturization trend in the electronics industry. In the paper, we present a numerical study on the performance of a convective-radiative porous heat sink with functionally graded material for improved cooling of various consumer electronics. For the theoretical investigation, the thermal property of the functionally graded material is assumed as a linear and power-law function. We solved the developed thermal models using the Chebyshev spectral collocation method. The effects of inhomogeneity index of FGM, convective and radiative parameters on the thermal behaviour of the porous heat sink are investigated. The present study shows that increase in the inhomogeneity index of FGM, convective and radiative parameter improves the thermal efficiency of the porous fin heat sink. Moreover, for all values of Nc and Rd, the temperature gradient along the fin of FGM is negligible compared to HM fin in both linear and power-law functions. For comparison, the thermal predictions made in the present study using Chebyshev spectral collocation method agrees excellently with the established results of Runge-Kutta with shooting and homotopy analytical method. / Supported in part from PhD sponsorship of the first author by the Tertiary Education Trust Fund of the Federal Government of Nigeria.

Functionally graded materials (FGMs) are an advanced class of material which seeks to leverage the strengths of one material to mitigate the weaknesses of another. This allows for operation in extreme environments or conditions where materials properties must change at various locations within a structure. Fabrication of this advanced class of material is limited due to geometric, economic, and material constraints inherent in the various methods. For this reason, a model was developed to discretize continuous gradient curves to allow for the use of a step-wise approximations to such gradients. These alternative step-wise gradients would allow for the use of numerous manufacturing techniques which have improved composition control, cost of processing, cost of equipment, and equipment availability. One such technique, tape casting, was explored due to its robustness and ability to create layered ceramics. Since ceramics are inherently brittle materials, they serve to be strengthened by the thermal residual stresses that form in the creation of these step-wise graded composites. With models to calculate these residual stresses and determine step-wise approximations of various compositional gradients, the process of designing these layered ceramics can be significantly improved.

A hydrocode and an explicit finite element code were used to evaluate functionally graded material impacts, meteor impacts, and split Hopkinson pressure bar specimens. Modeling impacts of functionally graded projectiles revealed that density was the primary material characteristic controlling the shock wave profile. A parametric study of material order for functionally graded armor showed that arranging the weaker material in front created the greater stopping power. By modeling an array of meteor impact scenarios, deformation and stress were shown to occur at great depths and possibly cause tectonic movement, like subduction. Three proposed Hopkinson specimens, which were designed to produce either shear or tensile reactions under compressive loading, were evaluated. For two of these specimens, improved stress and strain equations were presented.

The Element Free Galerkin (EFG) method, which is based on the Moving Least Squares (MLS) approximation, is developed here for vibration, buckling and static analysis of homogenous and FGM plate with curvilinear stiffeners. Numerical results for different stiffeners configurations and boundary conditions are presented. All results are verified using the commercial finite element software ANSYS® and other available results in literature. In addition, the vibration analysis of plates with curvilinear stiffeners is carried out using Ritz method. A 24 by 28 in. curvilinear stiffened panel was machined from 2219-T851 aluminum for experimental validation of the Ritz and meshfree methods of vibration mode shape predictions. Results were obtained for this panel mounted vertically to a steel clamping bracket using acoustic excitation and a laser vibrometer. Experimental results appear to correlate well with the meshfree and Ritz method results. In reality, many engineering structures are subjected to random pressure loads in nature and cannot be assumed to be deterministic. Typical engineering structures include buildings and towers, offshore structures, vehicles and ships, are subjected to random pressure. The vibrations induced from gust loads, engine noise, and other auxiliary electrical system can also produce noise inside aircraft. Consequently, all flight vehicles operate in random vibration environment. These random loads can be modeled by using their statistical properties. The dynamical responses of the structures which are subjected to random excitations are very complicated. To investigate their dynamic responses under random loads, the meshfree method is developed for random vibration analysis of curvilinearly-stiffened plates. Since extensive efforts have been devoted to study the buckling and vibration analysis of stiffened panel to maximize their natural frequencies and critical buckling loads, these structures are subjected to in-plane loading while the vibration analysis is considered. In these cases the natural frequencies calculated by neglecting the in-plane compression are usually over predicted. In order to have more accurate results it might be necessary to take into account the effects of in-plane load since it can change the natural frequency of plate considerably. To provide a better view of the free vibration behavior of the plate with curvilinear stiffeners subjected to axial/biaxial or shear stresses several numerical examples are studied. The FEM analysis of curvilinearly stiffened plate is quite computationally expensive, and the meshfree method seems to be a proper substitution to reduce the CPU time. However it will still require many simulations. Because of the number of simulations may be required in the solution of an engineering optimization problem, many researchers have tried to find approaches and techniques in optimization which can reduce the number of function evaluations. In these problems, surrogate models for analysis and optimization can be very efficient. The basic idea in surrogate model is to reduce computational cost and giving a better understanding of the influence of the design variables on the different objectives and constrains. To use the advantage of both meshfree method and surrogate model in reducing CPU time, the meshfree method is used to generate the sample points and combination of Kriging (a surrogate model) and Genetic Algorithms is used for design of curvilinearly stiffened plate. The meshfree and kriging results and CPU time were compared with those obtained using EBF3PanelOpt. / Ph. D.

This work is a numerical and analytical study of wave motion through dynamic materials (DM). This work focuses on showing several results that greatly extend the applicability of the checkerboard focusing effect. First, it is shown that it is possible to simultaneously focus dilatation and shear waves propagating through a linear elastic checkerboard structure. Next, it is shown that the focusing effect found for the original €œperfect€� checkerboard extends to the case of the checkerboard with smooth transitions between materials, this is termed a functionally graded (FG) checkerboard. With the additional assumption of a linear transition region, it is shown that there is a region of existence for limit cycles that takes the shape of a parallelogram in (m,n)-space. Similar to the perfect case, this is termed a €œplateau€� region. This shows that the robustness of the characteristic focusing effect is preserved even when the interfaces between materials are relaxed. Lastly, by using finite volume methods with limiting and adaptive mesh refinement, it is shown that energy accumulation is present for the functionally graded checkerboard as well as for the checkerboard with non-matching wave impedances. The main contribution of this work was to show that the characteristic focusing effect is highly robust and exists even under much more general assumptions than originally made. Furthermore, it provides a tool to assist future material engineers in constructing such structures. To this effect, exact bounds are given regarding how much the original perfect checkerboard structure can be spoiled before losing the expected characteristic focusing behavior.