Search results for: Finite Difference methods

Authors: M. Mahdi, N. Shariatmadari

Abstract:

Since, both the relative position of tunnels and the construction procedure affect the soil movement and internal forces in the lining, it is of major concern to study the influence of these factors on the tunnel design. Construction procedures of tunnels have considerable effects on the magnitude of surface movements and lining stresses. This paper describes numerical analysis of construction procedure of a three adjacent shallow tunnels at high groundwater levels using the commercial finite difference software (FLAC-3D). The aim of this study is to determinate the most suitable construction procedure for the three tunnels and the optimum excavation step in Tehran Metro tunnels in order to optimize the surface settlements and lining stresses.

Keywords: Shallow tunnel, multiple tunnels, construction procedure, surface movement, numerical modeling.

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Authors: Ruediger Schmidt, Thang Duy Vu

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Two geometrically nonlinear plate theories, based either on first- or third-order transverse shear deformation theory are used for finite element modeling and simulation of the transient response of smart structures incorporating piezoelectric layers. In particular the time histories of nonlinear vibrations and sensor voltage output of a thin beam with a piezoelectric patch bonded to the surface due to an applied step force are studied.

Keywords: Nonlinear vibrations, piezoelectric patches, sensor voltage output, smart structures.

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Authors: S. Alih, A. Khelil

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In the present work, behavior of inoxydable steel as reinforcement bar in composite concrete is being investigated. The bar-concrete adherence in reinforced concrete (RC) beam is studied and focus is made on the tension stiffening parameter. This study highlighted an approach to observe this interaction behavior in bending test instead of direct tension as per reported in many references. The approach resembles actual loading condition of the structural RC beam. The tension stiffening properties are then applied to numerical finite element analysis (FEA) to verify their correlation with laboratory results. Comparison with laboratory shows a good correlation between the two. The experimental settings is able to determine tension stiffening parameters in RC beam and the modeling strategies made in ABAQUS can closely represent the actual condition. Tension stiffening model used can represent the interaction properties between inoxydable steel and concrete.

Keywords: Inoxydable steel, Finite element modeling, Reinforced concrete beam, Tension-stiffening.

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Authors: Shi Qi Koo, Ahmad Beng Hong Kueh

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In the present work, the finite element formulation for the investigation of the effects of a localized interfacial degeneration on the dynamic behavior of the [90°/0°] laminated composite plate employing the state-space technique is performed. The stiffness of the laminate is determined by assembling the stiffnesses of subelements. This includes an introduction of an interface layer adopting the virtually zero-thickness formulation to model the interfacial degeneration. Also, the kinematically consistent mass matrix and proportional damping have been formulated to complete the free vibration governing expression. To simulate the interfacial degeneration of the laminate, the degenerated areas are defined from the center propagating outwards in a localized manner. It is found that the natural frequency, damped frequency and damping ratio of the plate decreases as the degenerated area of the interface increases. On the contrary, the loss factor increases correspondingly.

Keywords: Dynamic finite element, localized interface degeneration, proportional damping, state-space modeling.

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Authors: Thomas Jin-Chee Liu, Yu-Shen Chen

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Using the numerical and experimental methods, this paper discusses some primary studies on the vibration and cooling performances of the piezoelectric cooling fan with the rectangular blade. When the fan works at its natural frequency, the vibrating displacement is largest and the cooling performance is best. Due to the vibration behavior, the cooling performance is affected by the geometry, material property, and working frequency of the piezoelectric cooling fan. 

Keywords: Piezoelectric cooling fan, finite element, vibration, natural frequency.

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Authors: M. Azadbakht, Y. Fadakar

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Since fuel must be injected with appropriate pressure and time for accurate performance of diesel engines, then proper function of engine is influenced by accurate function of injector pump. At first total pump was designed by SolidWorks 2012 software. Then the total relationship of rotor, roller, internal cam ring, pole shoe and plunger in injector pump in MF285 tractor and their performance was shown. During suction state rollers connect with dents in internal cam ring and in pressure course pole shoes have drawer move in rotor and perform tappet action between rollers and plungers. The maximum stress was obtained by using analysis of finite element method. The maximum stress in contact surface of roller and internal cam ring and on roller surface. The maximum amount of this stress is 288.12 MPa. According to conducted analyses, the minimum value for safety factor is related to roller surface and it equals to 2.0477.

Keywords: Rotary injector pump, MF285 tractor, finite element, stress.

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Authors: Thomas Rowan, Mohammed Seaid

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A fast finite volume solver for multi-layered shallow water flows with mass exchange and an erodible bed is developed. This enables the user to solve a number of complex sediment-based problems including (but not limited to), dam-break over an erodible bed, recirculation currents and bed evolution as well as levy and dyke failure. This research develops methodologies crucial to the under-standing of multi-sediment fluvial mechanics and waterway design. In this model mass exchange between the layers is allowed and, in contrast to previous models, sediment and fluid are able to transfer between layers. In the current study we use a two-step finite volume method to avoid the solution of the Riemann problem. Entrainment and deposition rates are calculated for the first time in a model of this nature. In the first step the governing equations are rewritten in a non-conservative form and the intermediate solutions are calculated using the method of characteristics. In the second stage, the numerical fluxes are reconstructed in conservative form and are used to calculate a solution that satisfies the conservation property. This method is found to be considerably faster than other comparative finite volume methods, it also exhibits good shock capturing. For most entrainment and deposition equations a bed level concentration factor is used. This leads to inaccuracies in both near bed level concentration and total scour. To account for diffusion, as no vertical velocities are calculated, a capacity limited diffusion coefficient is used. The additional advantage of this multilayer approach is that there is a variation (from single layer models) in bottom layer fluid velocity: this dramatically reduces erosion, which is often overestimated in simulations of this nature using single layer flows. The model is used to simulate a standard dam break. In the dam break simulation, as expected, the number of fluid layers utilised creates variation in the resultant bed profile, with more layers offering a higher deviation in fluid velocity . These results showed a marked variation in erosion profiles from standard models. The overall the model provides new insight into the problems presented at minimal computational cost.

Keywords: Erosion, finite volume method, sediment transport, shallow water equations.

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Authors: Ali Pour Yazdanpanah, Farideh Foroozandeh Shahraki, Emma Regentova

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The reconstruction from sparse-view projections is one of important problems in computed tomography (CT) limited by the availability or feasibility of obtaining of a large number of projections. Traditionally, convex regularizers have been exploited to improve the reconstruction quality in sparse-view CT, and the convex constraint in those problems leads to an easy optimization process. However, convex regularizers often result in a biased approximation and inaccurate reconstruction in CT problems. Here, we present a nonconvex, Lipschitz continuous and non-smooth regularization model. The CT reconstruction is formulated as a nonconvex constrained L1 − L2 minimization problem and solved through a difference of convex algorithm and alternating direction of multiplier method which generates a better result than L0 or L1 regularizers in the CT reconstruction. We compare our method with previously reported high performance methods which use convex regularizers such as TV, wavelet, curvelet, and curvelet+TV (CTV) on the test phantom images. The results show that there are benefits in using the nonconvex regularizer in the sparse-view CT reconstruction.

Keywords: Computed tomography, sparse-view reconstruction, L1 −L2 minimization, non-convex, difference of convex functions.

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Authors: G. Revathi, P. Saikrishnan

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In the present analysis an unsteady laminar forced convection water boundary layer flow is considered. The fluid properties such as viscosity and Prandtl number are taken as variables such that those are inversely proportional to temperature. By using quasi-linearization technique the nonlinear coupled partial differential equations are linearized and the numerical solutions are obtained by using implicit finite difference scheme with the appropriate selection of step sizes. Non-similar solutions have been obtained from the starting point of the stream-wise coordinate to the point where skin friction value vanishes. The effect non-uniform mass transfer along the surface of the cylinder through slot is studied on the skin friction and heat transfer coefficients.

Keywords: Boundary layer, heat transfer, non-similar solution, non-uniform mass, unsteady flow.

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Authors: Migbar Assefa

Abstract:

The performance of a machine tool is eventually assessed by its ability to produce a component of the required geometry in minimum time and at small operating cost. It is customary to base the structural design of any machine tool primarily upon the requirements of static rigidity and minimum natural frequency of vibration. The operating properties of machines like cutting speed, feed and depth of cut as well as the size of the work piece also have to be kept in mind by a machine tool structural designer. This paper presents a novel approach to the design of machine tool column for static and dynamic rigidity requirement. Model evaluation is done effectively through use of General Finite Element Analysis software ANSYS. Studies on machine tool column are used to illustrate finite element based concept evaluation technique. This paper also presents results obtained from the computations of thin walled box type columns that are subjected to torsional and bending loads in case of static analysis and also results from modal analysis. The columns analyzed are square and rectangle based tapered open column, column with cover plate, horizontal partitions and with apertures. For the analysis purpose a total of 70 columns were analyzed for bending, torsional and modal analysis. In this study it is observed that the orientation and aspect ratio of apertures have no significant effect on the static and dynamic rigidity of the machine tool structure.

Keywords: Finite Element Modeling, Modal Analysis, Machine tool structure, Static Analysis.

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Authors: Z. Salehi Dehyagani, A. L. Yusoff

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BEAMnrc was used to calculate the spectrum and HVL for X-ray Beam during low energy X-ray radiation using tube model: SRO 33/100 /ROT 350 Philips. The results of BEAMnrc simulation and measurements were compared to the IPEM report number 78 and SpekCalc software. Three energies 127, 103 and 84 Kv were used. In these simulation a tungsten anode with 1.2 mm for Be window were used as source. HVLs were calculated from BEAMnrc spectrum with air Kerma method for four different filters. For BEAMnrc one billion particles were used as original particles for all simulations. The results show that for 127 kV, there was maximum 5.2 % difference between BEAMnrc and Measurements and minimum was 0.7% .the maximum 9.1% difference between BEAMnrc and IPEM and minimum was 2.3% .The maximum difference was 3.2% between BEAMnrc and SpekCal and minimum was 2.8%. The result show BEAMnrc was able to satisfactory predict the quantities of Low energy Beam as well as high energy X-ray radiation.

Keywords: BEAMnr , Monte Carlo , HVL

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Authors: U. Amin, A. Talib, S. A. Qureshi, M. J. Hossain, G. Ahmad

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The choice evaluation between oil-immersed and dry-type transformers is often controlled by cost, location, and application. This paper compares the electrical performance of liquid- filled and dry-type transformers, which will assist the customer to choose the right and efficient ones for particular applications. An accurate assessment of the time-average flux density, electric field intensity and voltage distribution in an oil-insulated and a dry-type transformer have been computed and investigated. The detailed transformer modeling and analysis has been carried out to determine electrical parameter distributions. The models of oil-immersed and dry-type transformers are developed and solved by using the finite element method (FEM) to compare the electrical parameters. The effects of non-uniform and non-coherent voltage gradient, flux density and electric field distribution on the power losses and insulation properties of transformers are studied in detail. The results show that, for the same voltage and kilo-volt-ampere (kVA) rating, oil-immersed transformers have better insulation properties and less hysteresis losses than the dry-type.

Keywords: Finite element method, flux density, transformer, voltage gradient.

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Authors: Alberto Hananel

Abstract:

The aim of this work is to modelize the occlusion of a person with temporomandibular disorders as an evolutionary equation and approach its solution by the construction and characterizing of discrete variational splines. To formulate the problem, certain boundary conditions have been considered. After showing the existence and the uniqueness of the solution of such a problem, a convergence result of a discrete variational evolutionary spline is shown. A stress analysis of the occlusion of a human jaw with temporomandibular disorders by finite elements is carried out in FreeFem++ in order to prove the validity of the presented method.

Keywords: Approximation, evolutionary PDE, finite element method, temporomandibular disorders, variational spline.

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Authors: Thanh-Duoc Phan, Saden H. Zahiri, S. H. Masood, Mahnaz Jahedi

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In this article, using finite element analysis (FEA) and an X-ray diffractometer (XRD), cold-sprayed titanium particles on a steel substrate is investigated in term of cooling time and the development of residual strains. Three cooling-down models of sprayed particles after deposition stage are simulated and discussed: the first model (m1) considers conduction effect to the substrate only, the second model (m2) considers both conduction as well as convection effect to the environment, and the third model (m3) which is the same as the second model but with the substrate heated to a near particle temperature before spraying. Thereafter, residual strains developed in the third model is compared with the experimental measurement of residual strains, which involved a Bruker D8 Advance Diffractometer using CuKa radiation (40kV, 40mA) monochromatised with a graphite sample monochromator. For deposition conditions of this study, a good correlation was found to exist between the FEA results and XRD measurements of residual strains.

Keywords: cold gas dynamic spray, X-ray diffraction, explicit finite element analysis, residual strain, titanium, particle impact, deformation behavior.

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Authors: Pratoom Rekklang

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The purposes of this study are to study political information exposure, politicians- perceptions, political attitudes and political participations among people in Bangkok Metropolitan Area. The sample consisted of 420 which were selected by using accidental sampling method. Questionnaires were administered to all of the respondents to obtain the data for this research. T-test, one-way ANOVA and Pearson-s correlation coefficient were used to analyze the data. The findings are as follows: The difference in gender, education, income and occupation has significantly effect upon political information exposures. The difference in age, income has significantly effect upon politicians- perceptions. The difference in income has significantly effect upon political attitudes. The difference in gender, income and occupation has significantly effect upon political participations. There were a significantly relations between political information exposures, political attitudes, political participations and between politicians- perceptions, political attitudes and political participations.

Keywords: Political Information Exposures, Politicians' Perceptions, Political Attitudes, Political Participations.

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Authors: Weifeng Wang, Xianwei Zeng, Jianping Ding

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When the characteristic length of an elastic solid is down to the nanometer level, its deformation behavior becomes size dependent. Surface energy /surface stress have recently been applied to explain such dependency. In this paper, the effect of strain-independent surface stress on the deformation of an isotropic elastic solid containing a nanosized elliptical hole is studied by the finite element method. Two loading cases are considered, in the first case, hoop stress along the rim of the elliptical hole induced by pure surface stress is studied, in the second case, hoop stress around the elliptical opening under combined remote tension and surface stress is investigated. It has been shown that positive surface stress induces compressive hoop stress along the hole, and negative surface stress has opposite effect, maximum hoop stress occurs near the major semi-axes of the ellipse. Under combined loading of remote tension and surface stress, stress concentration around the hole can be either intensified or weakened depending on the sign of the surface stress.

Keywords: Surface stress, finite element method, stress concentration, nanosized elliptical hole

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Authors: Gustavo Rodrigues, Hans Weber, Larissa Driemeier

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The prevision of post-impact conditions and the behavior of the bodies during the impact have been object of several collision models. The formulation from Hertz’s theory is generally used dated from the 19^th century. These models consider the repulsive force as proportional to the deformation of the bodies under contact and may consider it proportional to the rate of deformation. The objective of the present work is to analyze the behavior of the bodies during impact using the Finite Element Method (FEM) with elastic and plastic material models. The main parameters to evaluate are, the contact force, the time of contact and the deformation of the bodies. An advantage of using the FEM approach is the possibility to apply a plastic deformation to the model according to the material definition: there will be used Johnson–Cook plasticity model whose parameters are obtained through empirical tests of real materials. This model allows analyzing the permanent deformation caused by impact, phenomenon observed in real world depending on the forces applied to the body. These results are compared between them and with the model-based Hertz theory.

Keywords: Collision, finite element method, Hertz’s Theory, impact models.

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Authors: Ho Young Son, Bu Seog Ju, Woo Young Jung

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This study presents the seismic safety evaluation of weir structure subjected to strong earthquake ground motions, as a flood defense structure in civil engineering structures. The seismic safety analysis procedure was illustrated through development of Finite Element (FE) and InFinite Element (IFE) method in ABAQUS platform. The IFE model was generated by CINPS4, 4-node linear one-way infinite model as a sold continuum infinite element in foundation areas of the weir structure and then nonlinear FE model using friction model for soil-structure interactions was applied in this study. In order to understand the complex behavior of weir structures, nonlinear time history analysis was carried out. Consequently, it was interesting to note that the compressive stress gave more vulnerability to the weir structure, in comparison to the tensile stress, during an earthquake. The stress concentration of the weir structure was shown at the connection area between the weir body and stilling basin area. The stress both tension and compression was reduced in IFE model rather than FE model of weir structures.

Keywords: Weir, Finite Element, Infinite Element, Nonlinear, Earthquake.

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Authors: Kooshyar Passbakhsh, Maryam Yazdi

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Geosynthetics have proved to be suitable for reinforced soil retaining walls. Based on the increasing uses of geosynthetic reinforced soil systems in the regions, which bear frequent earthquakes, the study of dynamic behavior of structures seems necessary. Determining the reinforcement forces is; therefore, one of the most important and main points of discussions in designing retaining walls, by which we prevent from conservative planning. Thus, this paper intended to investigate the effects of such parameters as wall height, acceleration type, vertical spacing of reinforcement, type of reinforcement and soil type on forces and deformation through numerical modeling of the geosynthetic reinforced soil retaining walls (GRSRW) under dynamic loading with finite difference method by using FLAC. The findings indicate rather positive results with each parameter.

Keywords: Geosynthetic Reinforced Soil Retaining Walls (GRSRW), dynamic analysis, Geosynthetic forces, Flac

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Authors: Kimia Khoshdel Vajari, Saber Saffar

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Reducing the residual stresses caused by welding is desirable for the industry. The effect of welding sequence, as well as the effect of yield stress on the number of residual stresses generated in Inconel X750 superalloy sheets and beams, have been investigated. The finite element model used in this research is a three-dimensional thermal and mechanical model, and the type of analysis is indirect coupling. This analysis is done in two stages. First, thermal analysis is performed, and then the thermal changes of the first analysis are used as the applied load in the second analysis. ABAQUS has been used for modeling, and the Dflux subroutine has been used in the Fortran programming environment to move the arc and the molten pool. The results of this study show that the amount of tensile residual stress in symmetric, discontinuous, and symmetric-discontinuous welds is reduced to a maximum of 27%, 54%, and 37% compared to direct welding, respectively. The results also show that the amount of residual stresses created by welding increases linearly with increasing yield stress with a slope of 40%.

Keywords: Residual stress, X750 superalloy, finite element, welding, thermal analysis.

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Authors: B. Marungsri, W. Onchantuek, A. Oonsivilai

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This paper presents the simulation the results of electric field and potential distributions along surface of silicone rubber polymer insulators. Near the same leakage distance subjected to 15 kV in 50 cycle salt fog ageing test, alternate sheds silicone rubber polymer insulator showed better contamination performance than straight sheds silicone rubber polymer insulator. Severe surface ageing was observed on the straight sheds insulator. The objective of this work is to elucidate that electric field distribution along straight sheds insulator higher than alternate shed insulator in salt fog ageing test. Finite element method (FEM) is adopted for this work. The simulation results confirmed the experimental data, as well.

Keywords: Electric field distribution, potential distribution, silicone rubber polymer insulator, finite element method.

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Authors: Muna Tabuni

Abstract:

The paper contains an investigation on basic problems about the zeros of analytic theta functions. A brief introduction to analytic representation of finite quantum systems is given. The zeros of this function and there evolution time are discussed. Two open problems are introduced. The first problem discusses the cases when the zeros follow the same path. As the basis change the quantum state |f transforms into different quantum state. The second problem is to define a map between two toruses where the domain and the range of this map are the analytic functions on toruses.

Keywords: open problems, constraint, change of basis.

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Authors: Seyed Ahmad Hosseini, Makan Cheraghpour, Saeed Shirali, Roya Rafie, Matin Ghanavati, Arezoo Amjadi, Meysam Alipour

Abstract:

Background: There is a mutual relationship between sleep duration and obesity. We studied the relationship between sleep duration with obesity and dietary Intake. Methods: This cross-sectional study was conducted on 444 male students in Ahvaz Jundishapur University of Medical Science. Dietary intake was analyzed by food frequency questionnaire (FFQ). Anthropometric indices were analyzed. Participants were being asked about their sleep duration and they were categorized into three groups according to their responses (less than six hours, between six and eight hours, and more than eight hours). Results: Macronutrient, micronutrient, and antioxidant intake did not show significant difference between three groups. Moreover, we did not observe any significant difference between anthropometric indices (weight, body mass index, waist circumference, and percentage body fat). Conclusions: Our study results show no significant relationship between sleep duration, nutrition pattern, and obesity. Further study is recommended.

Keywords: Sleep duration, obesity, dietary intake, cross-sectional.

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Authors: Lina Wu, Wenyi Lu, Ye Li

Abstract:

Regarding heavy video game players for boys and super online chat lovers for girls as a symbolic phrase in the current adolescent culture, this project of data analysis verifies the displacement effect on deteriorating mathematics performance. To evaluate correlation or regression coefficients between a factor of playing video games or chatting online and mathematics performance compared with other factors, we use multivariate analysis technique and take gender difference into account. We find the most important reason for the negative sign of the displacement effect on mathematics performance due to students’ poor academic background. Statistical analysis methods in this project could be applied to study internet users’ academic performance from the high school education to the college education.

Keywords: Correlation coefficients, displacement effect, gender difference, multivariate analysis technique, regression coefficients.

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Authors: M. Si Abdallah, B. Zeghmati

Abstract:

A numerical analysis used to simulate the effects of wavy surfaces and thermal radiation on natural convection heat transfer boundary layer flow over an inclined wavy plate has been investigated. A simple coordinate transformation is employed to transform the complex wavy surface into a flat plate. The boundary layer equations and the boundary conditions are discretized by the finite difference scheme and solved numerically using the Gauss-Seidel algorithm with relaxation coefficient. Effects of the wavy geometry, the inclination angle of the wavy plate and the thermal radiation on the velocity profiles, temperature profiles and the local Nusselt number are presented and discussed in detail.

Keywords: Free convection, wavy surface, inclined surface, thermal radiation.

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Authors: Motahar Reza, Rajni Chahal, Neha Sharma

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This article addresses the boundary layer flow and heat transfer of Casson fluid over a nonlinearly permeable stretching surface with chemical reaction in the presence of variable magnetic field. The effect of thermal radiation is considered to control the rate of heat transfer at the surface. Using similarity transformations, the governing partial differential equations of this problem are reduced into a set of non-linear ordinary differential equations which are solved by finite difference method. It is observed that the velocity at fixed point decreases with increasing the nonlinear stretching parameter but the temperature increases with nonlinear stretching parameter.

Keywords: Boundary layer flow, nonlinear stretching, Casson fluid, heat transfer, radiation.

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Authors: Mohd Sazli Saad, Hishamuddin Jamaluddin, Intan Zaurah Mat Darus

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This paper presents the development of an active vibration control using direct adaptive controller to suppress the vibration of a flexible beam system. The controller is realized based on linear parametric form. Differential evolution optimisation algorithm is used to optimize the controller using single objective function by minimizing the mean square error of the observed vibration signal. Furthermore, an alternative approach is developed to systematically search for the best controller model structure together with it parameter values. The performance of the control scheme is presented and analysed in both time and frequency domain. Simulation results demonstrate that the proposed scheme is able to suppress the unwanted vibration effectively.

Keywords: flexible beam, finite difference method, active vibration control, differential evolution, direct adaptive controller

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Authors: Tebogo Phetla, Edison Muzenda, M Belaid

Abstract:

This study investigated possible ways to improve the efficiency of the platinum precipitation process using ammonium chloride by reducing the platinum content reporting to the effluent. The ore treated consist of five platinum group metals namely, ruthenium, rhodium, iridium, platinum, palladium and a precious metal gold. Gold, ruthenium, rhodium and iridium were extracted prior the platinum precipitation process. Temperature, reducing agent, flow rate and potential difference were the variables controlled to determine the operation conditions for optimum platinum precipitation efficiency. Hydrogen peroxide was added as the oxidizing agent at the temperature of 85-90oC and potential difference of 700-850mV was the variable used to check the oxidizing state of platinum. The platinum was further purified at temperature between 60-65oC, potential difference above 700 mV, ammonium chloride of 200 l, and at these conditions the platinum content reporting to the effluent was reduced to less than 300ppm, resulting in optimum platinum precipitation efficiency and purity of 99.9%.

Keywords: Platinum Group Metals (PGM), Potential difference, Precipitation, Redox reactions.

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Authors: Petter Eklund, Jonathan Sjölund, Sandra Eriksson, Mats Leijon

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The spoke type rotor can be used to obtain magnetic flux concentration in permanent magnet machines. This allows the air gap magnetic flux density to exceed the remanent flux density of the permanent magnets but gives problems with leakage fluxes in the magnetic circuit. The end leakage flux of one spoke type permanent magnet rotor design is studied through measurements and finite element simulations. The measurements are performed in the end regions of a 12 kW prototype generator for a vertical axis wind turbine. The simulations are made using three dimensional finite elements to calculate the magnetic field distribution in the end regions of the machine. Also two dimensional finite element simulations are performed and the impact of the two dimensional approximation is studied. It is found that the magnetic leakage flux in the end regions of the machine is equal to about 20% of the flux in the permanent magnets. The overestimation of the performance by the two dimensional approximation is quantified and a curve-fitted expression for its behavior is suggested.

Keywords: End effects, end leakage flux, permanent magnet machine, spoke type rotor.

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Authors: Pavel K. Lopatin, Artyom S. Yegorov

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An exact algorithm for a n-link manipulator movement amidst arbitrary unknown static obstacles is presented. The algorithm guarantees the reaching of a target configuration of the manipulator in a finite number of steps. The algorithm is reduced to a finite number of calls of a subroutine for planning a trajectory in the presence of known forbidden states. The polynomial approximation algorithm which is used as the subroutine is presented. The results of the exact algorithm implementation for the control of a seven link (7 degrees of freedom, 7DOF) manipulator are given.

Keywords: Manipulator, trajectory planning, unknown obstacles

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