Sharif Digital Repository

In this study, elastic analysis of a functionally graded full-space with quadratic variations under various types of loading is addressed. The elastic responses of the medium are obtained in closed-form under various types of loading including point load, concentrated moment, distributed patch load of rectangular and circular shape, normal ring load, and concentrated torsion. The displacement fields are derived by virtue of the appropriate Green’s functions corresponding to the FGMs with a quadratic variation of elastic moduli and constant poisons ratio of = 0.25 .For the special case of homogeneous medium, the results are verified with available solutions. Furthermore, effects of degree of... 

The purpose of the present study was to investigate the Grade 9 students' ability to solve real-life and modelling problems, focusing on proof and reasoning. The study conducted using qualitative method in which, six volunteer students participated. The data collected via eight problems mostly chosen from Chapter 3 of the 9th grade mathematics textbook and using Adobe Connect Platform, because of Covid-19 Pandemic and schools clousure. The data were analyzed using a problem solving framework developed by Mason, Burton and Stacey (2010) including three stages of entry, attack and review. The results showed that considering these three steps, is effective to understand students' problem... 

The ever increasing usage of modified binders in road construction requires that the effect of different modifiers on the performance characteristics of the asphalt binder be determined through laboratory testing. The current Superpave protocol for performance grading asphalt binders has proven to be insufficient to properly characterize modified binders, thus researchers have searched for other testing methods to complement or possibly replace some of the Superpave tests. Most notable are the time sweep test for fatigue resistance, the multiple stress creep and recovery test (MSCR) for rutting resistance and the direct tension test (DTT) for low temperature cracking characteristics. In the... 

In this thesis, concerning Eigenstrain Theory, the micromechanical formulation of dental implants has been derived for the first time in the fields of Mechanics and Medical Science. The proliferation of using dental implants as a prosthesis for the people who lost their teeth because of poor maintenance and smoking cigarette results in scientists think more about the design of these implants and their stress fields inside the mandible. It is crystal clear that these stress fields cause stress shielding, which is a phenomenon that brings about bone loss or decrement in the bone density. Hence, if we know the stress that is produced by the implants inside the mandible, we can optimize the... 

Discontinuously reinforced aluminum matrix composites (DRA) are candidates as a substantial class of materials for improved strength, stiffness, and wear resistance. However, the low fracture resistance of DRA's has restricted the widespread use of these materials as structural components. Consequently, intrinsic and extrinsic mechanisms have been considered in order to enhance the damage tolerance of composite materials based on microstructural and architectural modification, respectively. The intrinsic toughening technique has shown to elevate fracture resistance to some extent; usually at the expense of reducing several other properties such as strength. The more recent approach to... 

In this study, flexural vibration of a functionally graded nanotube under an initial stress is investigated. The small scale effect is taken into consideration based on Eringen’s nonlocal elasticity theory. The material properties are assumed to vary exponentially along the depth direction. The complete effect of the initial stress is taken into account in the problem formulation. The governing equations of motion are derived by using the Hamilton’s principle on the basis of the nonlocal Timoshenko beam theory. An analytical solution of the governing equations, for free vibration of a simply-supported nanotube is presented. Numerical results are presented to investigate the effect of the... 

Boric acid (H3BO3) is a weak monobasic acid that exist as a white powder in the standard conditions. In industry, it is used in manufacturing of fiberglas filaments, precious metals soldering and production of flat panel LCD displays. In all of these applications, normal grade boric acid is used, but nuclear industry demands an ultrapure boric acid (UPA) for controlling of the reactivity and power levels in pressurized water reactors. Annual consumption of UPA in Bushehr Power Plant (BPP) is around 60 metric tons. Currently, this amount is imported from Russia, but atomic energy organization of Iran plans to displace it by the acid made inside the country. Domestic production of UPA in... 

A numerical algorithm is proposed to design microstructure of a two-phase functionally graded material under dynamic loading. In order to direct energy propagation through the desired regions in the domain, we introduced a regularized Heaviside function, H(x), in our objective functional, namely the time-averaged sum of the elastic strain energy and the kinetic energy. Real-life systems are however, not undamped, but possess some kind of energy dissipation mechanism or damping. In order to apply modal analysis of undamped systems to damped systems, we use Rayleigh damping model in our formulations. To generate a well-posed topology optimization, we used homogenization via a solid isotropic... 

When swellable elastomer are surrounded by suitable fluid, they absorb the fluid and swell. This capability is used to design different tools. For example, drug release devises, sensors and actuators, in microfluidic devises such as micro-valves and micro-mixers, and seal devises. Most of these devises are shaped cylindrically. Therefore, have a thorough knowledge about how cylindrical swellable elastomer behavior, give us a good vision about how to design such actuators. In this thesis we have used constitutive equation of such materials and have investigated behavior of cylindrical swellable elastomers analytically and numerically. Analytical investigation is focused of transient behavior... 

Nowadays, regarding to knowledge progresses in various fields,advanced materials for which have acceptable performance in sensitive and special conditions must be used. Functionally graded materials are advanced multiphase composite materials that are characterized by continues spatial variations in mechanical and thermal properties. Clearly, studying on fracture mechanics of FGMs is important because they are used in igh-tech and sensitive applications.In this research, numerical modeling of fracture mechanics in isotropic/orthotropic/ transversely isotropic FGMs via interaction integral method is performed. Both incompatible and non-equilibrium formulations of interaction integral are... 

Nowadays in high-tech industries there is a serious demand for using advanced materials. Functionally graded materials (FGMs) are in the last generations of these group of materials. FGMs have shown good behavior in special conditions. According to sensitive applications of FGMs , there is a large amount of effort to understand it’s behavior in the presence of crack. Finite element method and other numerical methods, in recent years are widely used in modeling fracture problems.Remeshing requirements and mesh sensitivity are among the disadvantages of analyzing crack growth using the conventional FEM. Recent finite element methods such as extended finite element method, are proposed to model... 

The J-integral, as a powerful tool in fracture mechanics, is used to analysis of fracture behavior of materials. In order to, evaluate of three dimensional J-integral, an integral evaluation of line and surface is required. However, because surface integral evaluation requires the calculation of the second derivative of displacement field, an commercial finite element codes cannot calculate it.In this thesis, a method for computing 3D J-integral is presented using finite element analysis. In the analysis, the second derivative evaluation of displacement field is employed. In this method, error-minimal points for stress computation are not suitable for second derivative displacement... 

The future crisis and environmental pollution led to increasing interest in alternative energy conversion systems such as solid oxide fuel cell (SOFC). One of the main obstacles in using SOFCs is their relatively high fabrication cost compared with their low amount of produced energy .Therefore, in the present study, fabrication of a more cost-efficient functionally graded NiO-YSZ composite for SOFC anode by electrophoretic deposition (EPD) method was investigated. In this research, the effect of different chemical parameters such as media, additives, particle size distribution and nano NiO addition were initially investigated on the stability of NiO-YSZ suspension by Zetasizer and turbidity... 

In this paper, a finite element formulation is presented to study the thermoelastic behavior of Functionally Graded (FG) axisymmetric coating in shell structures. The power law distribution model is assumed for the composition of the constituent materials in thickness direction. The Plasma Spray with multi steps coating method is considered for coating method. The procedure adopted to derive the finite element formulation contains the analytical through-the-thickness integration inherently. So the explicit through-the-thickness integration becomes possible after defining a two-noded, three parameters degenerated axisymmetric FG element. The nonlinear heat transfer equation is used for... 

A numerical algorithm for the optimal design of two components functionally graded materials under thermomechanical loadings is introduced in the present study. It is based on the topology optimization method. The objective function, to be minimized, is defined as the weighted combination of the thermal and mechanical compliance of structure. The design variables are defined as the local volume fractions of contributing phases. The set of constraints includes bound constraints on local volume fractions and a global constraint on the total volume fraction of the matrix phase. The corresponding heat and elasticity equations are solved by the finite element method. The local material properties... 

Functionally graded materials (FGMs) are categorized in a branch of composite materials in which the local volume fraction of contributing phases are not fixed throughout the spatial domain, but vary gradually as a function of position. This spatial variation leads to the gradual variation of physical and mechanical properties inside the materials. It provides us the opportunity of designing multiple purpose materials by the variation of local volume fractions according to our goal. The optimal distribution of local volume fractions is a function of the spatial domain geometry and loading conditions, and in general situations, due to the complexity of the problem, it is not possible to... 

Nowadays functionally graded materials have many applications in various industries. One of these applications can be the manufacturing of thick-walled vessels. Thick-walled vessels under internal pressure and high temperatures gradient require materials with higher strength, like Functionally Graded Materials (FGM) and can be reinforced by some mechanical processes like autofrettage. In this process under certain loading some part of vessels enters into plastic zone and upon unloading some residual stresses will be generated. Moreover it is very important to find out the depth of this plastic zone, In addition, minimizing the stress distribution vs. depth of plastic zone under applied... 

Functionally Graded Material (FGM)is attaining more and more interests recently due to its outstanding feature of possessing benefits of physical and mechanical properties of two materials in one part. One of the common processes to fabricate FGM is laser directed energy deposition of pre-mixed powder of two materials. The powder stream and laser attenuation in LDED of FGM is studied in this dissertation by the aid of numerical simulation and experimental investigations. Due to numerical simulation results, which is done in FLUENT software, powder particle size and axial shielding gas flow rate has significant effect on composition of powder mixture falling into the molten pool. Considering... 

Additive manufacturing can be considered as a revolution in the manufacturing industry. The unique capabilities of this technology have led to the removal of many obstacles to the construction of complex and special parts. In this study, with the aim of further understanding how the gradient region is formed, the possibility of detecting the microstructure and finally the properties of the gradient piece made, a solidification process has been simulated in direct metal deposition. The results of this study include calculating the heat distribution during the process and obtaining a thermal history of the fabricated part, calculating the dimensions of the molten pool and the heat affected... 

In this research the process of incomplete reduction of hematite low iron ore to magnetite in a fluidized bed reactor was investigated. Temperature, composition of reduction air, particle size, and stay time were investigated as effective parameters. In this way, temperatures of 560, 580, 600, 620 and 640 degrees of centigrade, input air with flows of 1.2, 1.3 and 1.4 l/s, particles size of 425-850 µm, 850 µm-1.4 mm, and 1.4-2 mm, stay times of 4, 8, 12, 16, and 20 min were used in this research. The reduced specimens were analyzed by XRD and chemical analysis. The results illustrated that increase of temperature, decrease of input air flow, decrease of particles size, and increase of stay...