Search results for: finite element modeling

Authors: M. Khal, Ab. Algouti, A. Algouti

Abstract:

Water erosion is the major cause of the erosion that shapes the earth's surface. Modeling water erosion requires the use of software and GIS programs, commercial or closed source. The very high prices for commercial GIS licenses, motivates users and researchers to find open source software as relevant and applicable as the proprietary GIS. The objective of this study is the modeling of water erosion and the hydrogeological and morphophysical characterization of the Oued M'Goun watershed (southern flank of the Central High Atlas) developed by free programs of GIS. The very pertinent results are obtained by executing tasks and algorithms in a simple and easy way. Thus, the various geoscientific and geostatistical analyzes of a digital elevation model (SRTM 30 m resolution) and their combination with the treatments and interpretation of satellite imagery information allowed us to characterize the region studied and to map the area most vulnerable to water erosion.

Keywords: Central High-Atlas, hydrogeology, M’Goun watershed, OpenGIS, water erosion.

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Authors: Jaroslav Krutil, František Pochylý, Simona Fialová, Vladimír Habán

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A mathematical model of the additional effects of the liquid in the hydrodynamic gap is presented in the paper. An incompressible viscous fluid is considered. Based on computational modeling are determined the matrices of mass, stiffness and damping. The mathematical model is experimentally verified.

Keywords: Computational modeling, mathematical model, hydrodynamic gap, matrices of mass, stiffness and damping.

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Authors: Shigeyuki Haruyama , Didik Nurhadiyanto, Moch Agus Choiron, Ken Kaminishi

Abstract:

The previous study of new metal gasket that contact width and contact stress an important design parameter for optimizing metal gasket performance. The optimum design based on an elastic and plastic contact stress was founded. However, the influence of flange surface roughness had not been investigated thoroughly. The flange has many kinds of surface roughness. In this study, we conducted a gasket model include a flange surface roughness effect. A finite element method was employed to develop simulation solution. A uniform quadratic mesh used for meshing the gasket material and a gradually quadrilateral mesh used for meshing the flange. The gasket model was simulated by using two simulation stages which is forming and tightening simulation. A simulation result shows that a smoother of surface roughness has higher slope for force per unit length. This mean a squeezed against between flange and gasket will be strong. The slope of force per unit length for gasket 400-MPa mode was higher than the gasket 0-MPa mode.

Keywords: Surface roughness, flange, metal gasket, leakage, simulation.

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Authors: Jiajia Pan, Hung Tao Shen

Abstract:

Freeze and thaw occurs seasonally in river banks in northern countries. Little is known on how the riverbank soil temperature responds to air temperature changes and how freeze and thaw develops in a river bank seasonally. This study presents a two-dimensional heat conduction model for numerical investigations of seasonal freeze and thaw processes in an idealized river bank. The model uses the finite difference method and it is convenient for applications. The model is validated with an analytical solution and a field case with soil temperature distributions. It is then applied to the idealized river bank in terms of partially and fully saturated conditions with or without ice cover influence. Simulated results illustrate the response processes of the river bank to seasonal air temperature variations. It promotes the understanding of freeze and thaw processes in river banks and prepares for further investigation of frost and thaw impacts on riverbank stability.

Keywords: Freeze and thaw, river banks, 2D model, heat conduction.

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Authors: W. M. Wan Muhamad, E. Sujatmika, M.R. Idris, S.A. Syed Ahmad

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A finite element analysis (FEA) computer software HyperWorks is utilized in re-designing an automotive component to reduce its mass. Reduction of components mass contributes towards environmental sustainability by saving world-s valuable metal resources and by reducing carbon emission through improved overall vehicle fuel efficiency. A shape optimization analysis was performed on a rear spindle component. Pre-processing and solving procedures were performed using HyperMesh and RADIOSS respectively. Shape variables were defined using HyperMorph. Then optimization solver OptiStruct was utilized with fatigue life set as a design constraint. Since Stress-Number of Cycle (S-N) theory deals with uni-axial stress, the Signed von Misses stress on the component was used for looking up damage on S-N curve, and Gerber criterion for mean stress corrections. The optimization analysis resulted in mass reduction of 24% of the original mass. The study proved that the adopted approach has high potential use for environmental sustainability.

Keywords: Environmental Sustainability, Shape Optimization, Fatigue, Rear Spindle.

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Authors: Mohammad Reza Baradaran, Farhad Hamzezarghani, Mehdi Rastegari Ghiri, Zahra Mirsanjari

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Passive control methods can be utilized to build earthquake resistant structures, and also to strengthen the vulnerable ones. In this paper, we studied the effect of this system in increasing the ductility and energy dissipation and also modeled the behavior of this type of eccentric bracing, and compared the hysteresis diagram of the modeled samples with the laboratory samples. We studied several samples of frames with vertical shear-links in order to assess the behavior of this type of eccentric bracing. Each of these samples was modeled in finite element software ANSYS 9.0, and was analyzed under the static cyclic loading. It was found that vertical shear-links have a more stable hysteresis loops. Another analysis showed that using honeycomb beams as the horizontal beam along with steel reinforcement has no negative effect on the hysteresis behavior of the sample.

Keywords: Vertical shear-link, passive control, cyclic analysis, energy dissipation, honeycomb beam.

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Authors: T.F.Lai, Wan Nor Liza Mahadi, Norhayati Soin

Abstract:

This paper present a circular patch microstrip array antenna operate in KU-band (10.9GHz – 17.25GHz). The proposed circular patch array antenna will be in light weight, flexible, slim and compact unit compare with current antenna used in KU-band. The paper also presents the detail steps of designing the circular patch microstrip array antenna. An Advance Design System (ADS) software is used to compute the gain, power, radiation pattern, and S11 of the antenna. The proposed Circular patch microstrip array antenna basically is a phased array consisting of 'n' elements (circular patch antennas) arranged in a rectangular grid. The size of each element is determined by the operating frequency. The incident wave from satellite arrives at the plane of the antenna with equal phase across the surface of the array. Each 'n' element receives a small amount of power in phase with the others. There are feed network connects each element to the microstrip lines with an equal length, thus the signals reaching the circular patches are all combined in phase and the voltages add up. The significant difference of the circular patch array antenna is not come in the phase across the surface but in the magnitude distribution.

Keywords: Circular patch microstrip array antenna, gain, radiation pattern, S-Parameter.

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Authors: Kazuki Murakami, Takashige Nakamura, Noriko Sakamoto, Kunio Aizawa

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A Watson-Crick automaton is recently introduced as a computational model of DNA computing framework. It works on tapes consisting of double stranded sequences of symbols. Symbols placed on the corresponding cells of the double-stranded sequences are related by a complimentary relation. In this paper, we investigate a variation of Watson-Crick automata in which both heads read the tape in reverse directions. They are called reverse Watson-Crick finite automata (RWKFA). We show that all of following four classes, i.e., simple, 1-limited, all-final, all-final and simple, are equal to non-restricted version of RWKFA.

Keywords: automaton, DNA computing, formal languages, Watson-Crick automaton

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Authors: Pattamad Panedpojaman

Abstract:

For fire safety purposes, the fire resistance and the structural behavior of reinforced concrete members are assessed to satisfy specific fire performance criteria. The available prescribed provisions are based on standard fire load. Under various fire scenarios, engineers are in need of both heat transfer analysis and structural analysis. For heat transfer analysis, the study proposed a modified finite difference method to evaluate the temperature profile within a cross section. The research conducted is limited to concrete sections exposed to a fire on their one side. The method is based on the energy conservation principle and a pre-determined power function of the temperature profile. The power value of 2.7 is found to be a suitable value for concrete sections. The temperature profiles of the proposed method are only slightly deviate from those of the experiment, the FEM and the FDM for various fire loads such as ASTM E 119, ASTM 1529, BS EN 1991-1-2 and 550 oC. The proposed method is useful to avoid incontinence of the large matrix system of the typical finite difference method to solve the temperature profile. Furthermore, design engineers can simply apply the proposed method in regular spreadsheet software.

Keywords: temperature profile, finite difference method, concrete section, one-side fire exposed, energy conservation

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Authors: Eldin Wee Chuan Lim

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The mixing behaviors of dry and wet granular materials in gas fluidized bed systems were investigated computationally using the combined Computational Fluid Dynamics and Discrete Element Method (CFD-DEM). Dry particles were observed to mix fairly rapidly during the fluidization process due to vigorous relative motions between particles induced by the flow of gas. In contrast, due to the presence of strong cohesive forces arising from capillary liquid bridges between wet particles, the mixing efficiencies of wet granular materials under similar operating conditions were observed to be reduced significantly.

Keywords: Computational Fluid Dynamics, Discrete Element Method, Gas Fluidization, Mixing, Wet particles

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Authors: Alaoua Bouaicha, Fahim Kahlouche, Abdelhamid Benouali

Abstract:

Many embankment dams have suffered failures during earthquakes due to the increase of pore water pressure under seismic loading. After analyzing of the behavior of embankment dams under severe earthquakes, major advances have been attained in the understanding of the seismic action on dams. The present study concerns numerical analysis of the seismic response of earth dams. The procedure uses a nonlinear stress-strain relation incorporated into the code FLAC2D based on the finite difference method. This analysis provides the variation of the pore water pressure and horizontal displacement.

Keywords: Earthquake, numerical analysis, FLAC2D, displacement, Embankment Dam, pore water pressure.

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Authors: Fadi Eleiwi, Taous Meriem Laleg-Kirati

Abstract:

This paper presents a complete dynamic modeling of a membrane distillation process. The model contains two consistent dynamic models. A 2D advection-diffusion equation for modeling the whole process and a modified heat equation for modeling the membrane itself. The complete model describes the temperature diffusion phenomenon across the feed, membrane, permeate containers and boundary layers of the membrane. It gives an online and complete temperature profile for each point in the domain. It explains heat conduction and convection mechanisms that take place inside the process in terms of mathematical parameters, and justify process behavior during transient and steady state phases. The process is monitored for any sudden change in the performance at any instance of time. In addition, it assists maintaining production rates as desired, and gives recommendations during membrane fabrication stages. System performance and parameters can be optimized and controlled using this complete dynamic model. Evolution of membrane boundary temperature with time, vapor mass transfer along the process, and temperature difference between membrane boundary layers are depicted and included. Simulations were performed over the complete model with real membrane specifications. The plots show consistency between 2D advection-diffusion model and the expected behavior of the systems as well as literature. Evolution of heat inside the membrane starting from transient response till reaching steady state response for fixed and varying times is illustrated.

Keywords: Membrane distillation, Dynamical modeling, Advection-diffusion equation, Thermal equilibrium, Heat equation.

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Authors: Tsuyoshi Okita, Tatsuya Niwa

Abstract:

For a given specific problem an efficient algorithm has been the matter of study. However, an alternative approach orthogonal to this approach comes out, which is called a reduction. In general for a given specific problem this reduction approach studies how to convert an original problem into subproblems. This paper proposes a formal modeling language to support this reduction approach. We show three examples from the wide area of learning problems. The benefit is a fast prototyping of algorithms for a given new problem.

Keywords: Formal language, statistical inference problem, reduction.

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Authors: A. Shafaghat, H. Khabbaz, S. Moravej, Ah. Shafaghat

Abstract:

The bearing capacity of closely spaced shallow footings alters with their spacing and the shape of footing. In this study, the bearing capacity and settlement of two adjacent footings constructed on a sand layer are investigated. The effect of different footing shapes including square, circular, ring and strip on sandy soil is captured in the calculations. The investigations are carried out numerically using PLAXIS-3D software and analytically employing conventional settlement equations. For this purpose, foundations are modelled in the program with practical dimensions and various spacing ratios ranging from 1 to 5. The spacing ratio is defined as the centre-to-centre distance to the width of foundations (S/B). Overall, 24 models are analyzed; and the results are compared and discussed in detail. It can be concluded that the presence of adjacent foundation leads to the reduction in bearing capacity for round shape footings while it can increase the bearing capacity of rectangular footings in some specific distances.

Keywords: Bearing capacity, finite element analysis, loose sand, settlement equations, shallow foundation.

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Authors: Basmah H. Shafee

Abstract:

In this paper, we will generate the wreath product 11 12 M wrM using only two permutations. Also, we will show the structure of some groups containing the wreath product 11 12 M wrM . The structure of the groups founded is determined in terms of wreath product k (M wrM ) wrC 11 12 . Some related cases are also included. Also, we will show that 132K+1 S and 132K+1 A can be generated using the wreath product k (M wrM ) wrC 11 12 and a transposition in 132K+1 S and an element of order 3 in 132K+1 A . We will also show that 132K+1 S and 132K+1 A can be generated using the wreath product 11 12 M wrM and an element of order k +1.

Keywords: Group presentation, group generated by n-cycle, Wreath product, Mathieu group.

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Authors: Rezaul Azim, A. Toaha Mobashsher, M. Tariqul Islam

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In this paper a novel ultra-wideband (UWB) slot antenna with band notch characteristics for world interoperability for microwave access (WiMAX) is proposed. The designed antenna consists of a rectangular radiating patch and a ground plane with tapered shape slot. To realize a notch band, a curved parasitic element has been etched out along with the radiating patch. It is observed that by adjusting the length, thickness and position of the parasitic element, the proposed antenna can achieved an impedance bandwidth of 8.01GHz (2.84 to 10.85GHz) with a notched band of 3.28-3.85GHz. Compared to the recently reported band notch antennas, the proposed antenna has a simple configuration to realize band notch characteristics in order to mitigate the potential interference between WiMAX and UWB system. Furthermore, a stable radiation pattern and moderate gain except at the notched band makes the proposed antenna suitable for various UWB applications. 

Keywords: Band notch, Filter element, Ultra-wideband (UWB), WiMAX.

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Authors: Shan Gao

Abstract:

This paper treats a discrete-time finite buffer batch arrival queue with a single working vacation and partial batch rejection in which the inter-arrival and service times are, respectively, arbitrary and geometrically distributed. The queue is analyzed by using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at prearrival, arbitrary and outside observer-s observation epochs. We also present probability generation function (p.g.f.) of actual waiting-time distribution in the system and some performance measures.

Keywords: Discrete-time, finite buffer, single working vacation, batch arrival, partial rejection.

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Authors: Ziad. Sh. Al Sarraf

Abstract:

Ultrasonic metal welding has been the subject of ongoing research and development, most recently concentrating on metal joining in miniature devices, for example to allow solder-free wire bonding. As well as at the small scale, there are also opportunities to research the joining of thicker sheet metals and to widen the range of similar and dissimilar materials that can be successfully joined using this technology. This study presents the design, characterisation and test of a lateral-drive ultrasonic metal spot welding device. The ultrasonic metal spot welding horn is modelled using finite element analysis (FEA) and its vibration behaviour is characterised experimentally to ensure ultrasonic energy is delivered effectively to the weld coupon. The welding stack and fixtures are then designed and mounted on a test machine to allow a series of experiments to be conducted for various welding and ultrasonic parameters. Weld strength is subsequently analysed using tensile-shear tests. The results show how the weld strength is particularly sensitive to the combination of clamping force and ultrasonic vibration amplitude of the welding tip, but there are optimal combinations of these and also limits that must be clearly identified.

Keywords: Ultrasonic welding, vibration amplitude, welding force, weld strength.

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Authors: S. Chokri

Abstract:

Load modeling is one of the central functions in power systems operations. Electricity cannot be stored, which means that for electric utility, the estimate of the future demand is necessary in managing the production and purchasing in an economically reasonable way. A majority of the recently reported approaches are based on neural network. The attraction of the methods lies in the assumption that neural networks are able to learn properties of the load. However, the development of the methods is not finished, and the lack of comparative results on different model variations is a problem. This paper presents a new approach in order to predict the Tunisia daily peak load. The proposed method employs a computational intelligence scheme based on the Fuzzy neural network (FNN) and support vector regression (SVR). Experimental results obtained indicate that our proposed FNN-SVR technique gives significantly good prediction accuracy compared to some classical techniques.

Keywords: Neural network, Load Forecasting, Fuzzy inference, Machine learning, Fuzzy modeling and rule extraction, Support Vector Regression.

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Authors: S. Yamini Sudha, Ashok Khanna

Abstract:

Owing to the stringent environmental legislations, CO2 capture and sequestration is one of the viable solutions to reduce the CO2 emissions from various sources. In this context, Ionic liquids (ILs) are being investigated as suitable absorption media for CO2 capture. Due to their non-evaporative, non-toxic, and non-corrosive nature, these ILs have the potential to replace the existing solvents like aqueous amine solutions for CO2 separation technologies. Thus, the present work aims at studying the important aspects such as the interactions of CO2 molecule with different anions (F-, Br-, Cl-, NO3 -, BF4 -, PF6 -, Tf2N-, and CF3SO3 -) that are commonly used in ILs through molecular modeling. In this, the minimum energy structures have been obtained using Ab initio based calculations at MP2 (Moller-Plesset perturbation) level. Results revealed various degrees of distortion of CO2 molecule (from its linearity) with the anions studied, most likely due to the Lewis acid-base interactions between CO2 and anion. Furthermore, binding energies for the anion-CO2 complexes were also calculated. The implication of anion-CO2 interactions to the solubility of CO2 in ionic liquids is also discussed.

Keywords: CO2, Ionic liquids, capture, molecular modeling, sequestration.

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Authors: Design of 3-Step Skew BLAC Motor for Better Performance in Electric Power Steering System

Abstract:

In Electric Power Steering (EPS), spoke type Brushless AC (BLAC) motors offer distinct advantages over other electric motor types in terms torque smoothness, reliability and efficiency. This paper deals with the shape optimization of spoke type BLAC motor, in order to reduce cogging torque. This paper examines 3 steps skewing rotor angle, optimizing rotor core edge and rotor overlap length for reducing cogging torque in spoke type BLAC motor. The methods were applied to existing machine designs and their performance was calculated using finite- element analysis (FEA). Prototypes of the machine designs were constructed and experimental results obtained. It is shown that the FEA predicted the cogging torque to be nearly reduce using those methods.

Keywords: EPS, 3-Step skewing, spoke type BLAC, cogging torque, FEA, optimization.

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

Abstract:

The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

Keywords: Curved stretching sheet, finite difference method, MHD, variable thermal conductivity.

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Authors: B. Engel, Sara Salman Hassan Al-Maeeni

Abstract:

Human consumption of the Earth's resources increases the need for a sustainable development as an important ecological, social, and economic theme. Re-engineering of machine tools, in terms of design and failure analysis, is defined as steps performed on an obsolete machine to return it to a new machine with the warranty that matches the customer requirement. To understand the future fatigue behavior of the used machine components, it is important to investigate the possible causes of machine parts failure through design, surface, and material inspections. In this study, the failure modes of the shaft of the rotary draw bending machine are inspected. Furthermore, stress and deflection analysis of the shaft subjected to combined torsion and bending loads are carried out by an analytical method and compared with a finite element analysis method. The theoretical fatigue strength, correction factors, and fatigue life sustained by the shaft before damaged are estimated by creating a stress-cycle (S-N) diagram. In conclusion, it is seen that the shaft can work in the second life, but it needs some surface treatments to increase the reliability and fatigue life.

Keywords: Failure analysis, fatigue life, FEM analysis, shaft, stress analysis.

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Authors: I. Ioannou, I. M. Gitman

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This study focused on the contribution of micro-mechanical parameters on the macro-mechanical response of short fiber composites, namely polypropylene matrix reinforced by glass fibers. In the framework of this paper, an attention has been given to the glass fibers length, as micromechanical parameter influences the overall macroscopic material’s behavior. Three dimensional numerical models were developed and analyzed through the concept of a Representative Volume Element (RVE). Results of the RVE-based approach were compared with analytical Halpin-Tsai’s model.

Keywords: Effective properties, representative volume element, short fiber reinforced composites.

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Authors: A. Ja, J. Belabid, A. Cheddadi

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This paper reports the numerical simulation of doublediffusive natural convection flows within a horizontal annular filled with a saturated porous medium. The analysis concerns the influence of the different parameters governing the problem, namely, the Rayleigh number Ra, the Lewis number Le and the buoyancy ratio N, on the heat and mass transfer and on the flow structure, in the case of a fixed radius ratio R = 2. The numerical model used for the discretization of the dimensionless equations governing the problem is based on the finite difference method, using the ADI scheme. The study is focused on steady-state solutions in the cooperation situation.

Keywords: Natural convection, double-diffusion, porous medium, annular geometry, finite differences.

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Authors: A. Johannet, B. Vayssade, D. Bertin

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Neural networks are well known for their ability to model non linear functions, but as statistical methods usually does, they use a no parametric approach thus, a priori knowledge is not obvious to be taken into account no more than the a posteriori knowledge. In order to deal with these problematics, an original way to encode the knowledge inside the architecture is proposed. This method is applied to the problem of the evapotranspiration inside karstic aquifer which is a problem of huge utility in order to deal with water resource.

Keywords: Neural-Networks, Hydrology, Evapotranpiration, Hidden Function Modeling.

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Authors: Ali A. Al-Jazaairry, Tahsin T. Sabbagh

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The stability of a single model pile located adjacent to a continuous cavity was studied. This paper is an attempt to understand the behaviour of axially loaded single pile embedded in clayey soil with the presences of cavities. The performance of piles located in such soils was studied analytically. A verification analysis was carried out on available studies to assess the ability of analytical model to correctly interpret the system behaviour. The study was adopted by finite element program (PLAXIS). The study included many cases; in each case, there is a critical value in which the presence of cavities has shown minimum effect on the pile performance. Figures including the load carrying capacity of pile with the affecting factors are presented. These figures provide beneficial information for pile design constructed close to underground cavities. It was concluded that the load carrying capacity of the pile is reduced by the presence of the cavity within the soil mass. This reduction varies according to the size and location of cavity.

Keywords: Axial load, cavity, clay, pile, ultimate capacity.

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Authors: George Eleftherakis, Petros Kefalas, Anna Sotiriadou, Evangelos Kehris

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Recent advances in both the testing and verification of software based on formal specifications of the system to be built have reached a point where the ideas can be applied in a powerful way in the design of agent-based systems. The software engineering research has highlighted a number of important issues: the importance of the type of modeling technique used; the careful design of the model to enable powerful testing techniques to be used; the automated verification of the behavioural properties of the system; the need to provide a mechanism for translating the formal models into executable software in a simple and transparent way. This paper introduces the use of the X-machine formalism as a tool for modeling biology inspired agents proposing the use of the techniques built around X-machine models for the construction of effective, and reliable agent-based software systems.

Keywords: Biology inspired agent, formal methods, x-machines.

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Authors: Ahmed E. Hodaib, Samar F. Abdel Fattah

Abstract:

High-speed transportation is a growing concern. To develop high-speed rails and to increase high-speed efficiencies, the idea of Hyperloop was introduced. The challenge is to overcome the difficulties of managing friction and air-resistance which become substantial when vehicles approach high speeds. In this paper, we are presenting the methodologies of the capsule design which got a design concept innovation award at SpaceX competition in January, 2016. MATLAB scripts are written for the levitation and propulsion calculations and iterations. Computational Fluid Dynamics (CFD) is used to simulate the air flow around the capsule considering the effect of the axial-flow air compressor and the levitation cushion on the air flow. The design procedures of a single-sided linear induction motor are analyzed in detail and its geometric and magnetic parameters are determined. A structural design is introduced and Finite Element Method (FEM) is used to analyze the stresses in different parts. The configuration and the arrangement of the components are illustrated. Moreover, comments on manufacturing are made.

Keywords: High-speed transportation, Hyperloop, railways transportation, single-sided linear induction motor.

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Authors: Rudy Agustriyanto, Akbarningrum Fatmawati

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The utilization of cheese whey as a fermentation substrate to produce bio-ethanol is an effort to supply bio-ethanol demand as a renewable energy. Like other process systems, modeling is also required for fermentation process design, optimization and plant operation. This research aims to study the fermentation process of cheese whey by applying mathematics and fundamental concept in chemical engineering, and to investigate the characteristic of the cheese whey fermentation process. Steady state simulation results for inlet substrate concentration of 50, 100 and 150 g/l, and various values of hydraulic retention time, showed that the ethanol productivity maximum values were 0.1091, 0.3163 and 0.5639 g/l.h respectively. Those values were achieved at hydraulic retention time of 20 hours, which was the minimum value used in this modeling. This showed that operating reactor at low hydraulic retention time was favorable. Model of bio-ethanol production from cheese whey will enhance the understanding of what really happen in the fermentation process.

Keywords: Cheese whey, ethanol, fermentation, modeling.

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