Search results for: nonlinear shell element

Authors: Muhammad Umair Shahid, Abdul Rehman, Mudassir Mukhtar, Muhammad Nauman

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The smart antenna is the prominent technology that has become known in recent years to meet the growing demands of wireless communications. In an overcrowded atmosphere, its application is growing gradually. A methodical evaluation of the performance of Fixed Beamforming algorithms for smart antennas such as Multiple Sidelobe Canceller (MSC), Maximum Signal-to-interference ratio (MSIR) and minimum variance (MVDR) has been comprehensively presented in this paper. Simulation results show that beamforming is helpful in providing optimized response towards desired directions. MVDR beamformer provides the most optimal solution.

Keywords: fixed weight beamforming, array pattern, signal to interference ratio, power efficiency, element spacing, array elements, optimum weight vector

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Authors: Nursen Saklakoglu, Adnan Turker

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The main objective of this study is to reveal the effect of the Thixoforming process on the microstructure and mechanical properties of the AlSi12 alloy with trace amounts of silver. It is concluded that Thixoforming has an important effect on the morphology of intermetallics and Si formation, as well as globular α-Al morphology. The intermetallics have been fractured during thixoforming. It is believed that the fine distribution of the intermetallics is one mechanism for the improved mechanical properties of Thixoformed alloys. The discrete Si particles have been observed during both isothermal heating to the semi-solid range and Thixoforming, also have an important effect on mechanical properties. The Thixoforming process has a greater effect on hardness than the addition of Ag does.

Keywords: AlSi alloys, intermetallic phases, mechanical properties trace element, silver, thixoforming

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Authors: Roselyn T. Bustos

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Literature is an imitation of life. It depicts man's culture as well as his struggles. In short, literature is a part of man's way of life- a reflection of his personal or vicarious experiences. Using the qualitative-descriptive content analysis, this study investigates the mimetic signification in the five select sonnets of William Shakespeare.An in- depth analysis of the poetic elements such as the figurative language used and the themes extracted is made to draw out the universal meaning of his works. It is found out that his select sonnets use figurative languages such as simile, metaphor, personification, and hyperbaton which becomes a potent element that allows his sonnets to convey the themes of love and perseverance. With these findings, it is concluded that William Shakespeare's sonnets are evidently written within the context of the universals and that they are worthy of wide readership not only because of him being a renowned English poet and playwright but most importantly of the realities his sonnets signify.

Keywords: imitation, mimesis, potent, realities

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Authors: Yakin Hajlaoui, Richard Labib, Jean-François Plante, Michel Gamache

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This study introduces the Multi-Layer Inverse Distance Weighting Model (ML-IDW), inspired by the mathematical formulation of both multi-layer neural networks (ML-NNs) and Inverse Distance Weighting model (IDW). ML-IDW leverages ML-NNs' processing capabilities, characterized by compositions of learnable non-linear functions applied to input features, and incorporates IDW's ability to learn anisotropic spatial dependencies, presenting a promising solution for nonlinear spatial interpolation and learning from complex spatial data. it employ gradient descent and backpropagation to train ML-IDW, comparing its performance against conventional spatial interpolation models such as Kriging and standard IDW on regression and classification tasks using simulated spatial datasets of varying complexity. the results highlight the efficacy of ML-IDW, particularly in handling complex spatial datasets, exhibiting lower mean square error in regression and higher F1 score in classification.

Keywords: deep learning, multi-layer neural networks, gradient descent, spatial interpolation, inverse distance weighting

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Authors: Hammoudi Abderazek

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The present paper introduces a modified adaptive mixed differential evolution (MAMDE) to select the main geometry parameters of specific cylindrical spur gear. The developed algorithm used the self-adaptive mechanism in order to update the values of mutation and crossover factors. The feasibility rules are used in the selection phase to improve the search exploration of MAMDE. Moreover, the elitism is performed to keep the best individual found in each generation. For the constraints handling the normalization method is used to treat each constraint design equally. The finite element analysis is used to confirm the optimization results for the maximum bending resistance. The simulation results reached in this paper indicate clearly that the proposed algorithm is very competitive in precision gear design optimization.

Keywords: evolutionary algorithm, spur gear, tooth profile, meta-heuristics

Procedia PDF Downloads 126

Authors: C. F. Ocoleanu, G. Cividjian, Gh. Manolea

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In this paper, we present two solutions for connections quality pre-control of Crimp Contacts and to identify in the first moments the connections improperly executed, before final assembly of a electrical machines. The first solution supposed experimental determination of specific losses by calculated the initial rate of temperature rise. This can be made drawing the tangent at the origin at heating curve. The method can be used to identify bad connections by passing a current through the winding at ambient temperature and simultaneously record connections temperatures in the first few minutes since the current is setting. The second proposed solution is to apply to each element crimping a thermal indicator one level, and making a test heating with a heating current corresponding to critical temperature indicator.

Keywords: temperature, crimp contact, thermal indicator, current distribution, specific losses

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Authors: Silas A. Ihedioha

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In this work; it is considered that an investor’s portfolio is comprised of two assets; a risky stock which price process is driven by the geometric Brownian motion and a risk-free asset with Ornstein-Uhlenbeck Stochastic interest rate of return, where consumption, taxes, transaction costs and dividends are involved. This paper aimed at the optimization of the investor’s expected utility of consumption and terminal return on his investment at the terminal time having power utility preference. Using dynamic optimization procedure of maximum principle, a second order nonlinear partial differential equation (PDE) (the Hamilton-Jacobi-Bellman equation HJB) was obtained from which an ordinary differential equation (ODE) obtained via elimination of variables. The solution to the ODE gave the closed form solution of the investor’s problem. It was found the optimal investment in the risky asset is horizon dependent and a ratio of the total amount available for investment and the relative risk aversion coefficient.

Keywords: optimal, investment, Ornstein-Uhlenbeck, utility maximization, stochastic interest rate, maximum principle

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Authors: Mnasri Faiza, El Ganaoui Mohammed, Khelifa Mourad, Gabsi Slimane

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The main objective of this paper is to describe the hydrothermal behavior through porous material of construction due to temperature gradient. The construction proposed a bi-layer structure which composed of two different materials. The first is a bio-sourced panel named IBS-AKU (inertia system building), the second is the Neopor material. This system (IBS-AKU Neopor) is developed by a Belgium company (Isohabitat). The study suggests a multi-layer structure of the IBS-AKU panel in one dimension. A numerical method was proposed afterwards, by using the finite element method and a refined mesh area to strong gradients. The evolution of temperature fields and the moisture content has been processed.

Keywords: heat transfer, moisture diffusion, porous media, composite IBS-AKU, simulation

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Authors: Ramezani M., Neitzert T.

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This paper investigates mechanical properties and formability of the AZ61 magnesium alloy at high temperatures. Tensile tests were performed at elevated temperatures of up to 400ºC. The results showed that as temperature increases, yield strength and ultimate tensile strength decrease significantly, while the material experiences an increase in ductility (maximum elongation before break). A finite element model has been developed to further investigate the formability of the AZ61 alloy by deep drawing a square cup. Effects of different process parameters such as punch and die geometry, forming speed and temperature as well as blank-holder force on deep drawability of the AZ61 alloy were studied and optimum values for these parameters are achieved which can be used as a design guide for deep drawing of this alloy.

Keywords: AZ61, formability, magnesium, mechanical properties

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Authors: Tao Qu, Chandra Prakash, Vikas Tomar

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The interfaces between organic and inorganic phases in natural materials have been shown to be a key factor contributing to their high performance. This work analyzes crack propagation in a 2-ply laminate subjected to uniaxial tensile mode-I crack propagation loading that has laminate properties derived based on biological material constituents (marine exoskeleton- chitin and calcite). Interfaces in such laminates are explicitly modeled based on earlier molecular simulations performed by authors. Extended finite element method and cohesive zone modeling based simulations coupled with theoretical analysis are used to analyze crack propagation. Analyses explicitly quantify the effect that interface mechanical property variation has on the delamination as well as the transverse crack propagation in examined 2-ply laminates.

Keywords: chitin, composites, interfaces, fracture

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Authors: Buntheng Chhorn, WooYoung Jung

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Large-scale swing has been used in entertainment and performance, especially in circus, for a very long time. To increase the safety of this type of structure, a thorough analysis for displacement and bearing stress was performed for an extreme condition where a full cycle swing occurs. Different masses, ranging from 40 kg to 220 kg, and velocities were applied on the swing. Then, based on the solution of differential dynamics equation, swing velocity response to harmonic force was obtained. Moreover, the resistance capacity was estimated based on ACI steel structure design guide. Subsequently, numerical analysis was performed in ABAQUS to obtain the stress on each frame of the swing. Finally, the analysis shows that the expansion of swing structure frame section was required for mass bigger than 150kg.

Keywords: swing structure, displacement, bearing stress, dynamic loads response, finite element analysis

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Authors: H. Nabaei, M. Joghataie

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In this article, we study the design methods of matched filter with commercial software including CST Studio and ADS in specific frequency: 900 MHz. At first, we select two amounts of impedance for studying matching of them. Then, using by matched filter utility tool in ADS software, we simulate and deviate the elements of matched filters. In the following, we implement matched filter in CST STUDIO software. The simulated results show the great conformity in this field. Also, we peruse scattering and Impedance parameters in the Derivative structure. Finally, the layout of matched filter is obtained by the schematic tool of CST STUDIO. In fact, here, we present the design process of matched filters in the specific frequency.

Keywords: impedance matching, lumped element, transmission line, maximum power transmission, 3D layout

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Authors: Yujeong Shin, Seong Jin Cho, Jin Ho Kim

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In the textile-weaving machine, the reed is the core component to separate thousands of strands of yarn and to produce the fabric in a continuous high-speed movement. In addition, the reed affects the quality of the fiber. Therefore, the wire forming analysis of the main raw materials of the reed needs to be considered. Roll-forming is a key technology among the manufacturing process of reed wire using textile machine. A simulation of roll-forming line in accordance with the reduction rate is performed using LS-DYNA. The upper roller, fixed roller and reed wire are modeled by finite element. The roller is set to be rigid body and the wire of SUS430 is set to be flexible body. We predict the variation of the cross-sectional shape of the wire depending on the reduction ratio.

Keywords: textile machine, reed, rolling, reduction ratio, wire

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Authors: Sabina Hublova, Kristyna Hrabova, Petr Cikrle

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Sustainable development and preservation of existing buildings are becoming increasingly important worldwide. In order to reduce the amount of CO2 emissions in the air and to reduce the amount of waste from building structures, we can predict an increasing demand for maintenance of some existing buildings in the future. The use of modern diagnostic methods, which allow detailed determination of the properties of structures, the identification of critical points, could be the great importance for the better assessment of existing structures. Non-destructive methods could be one of the options. From these methods, ultrasonic appears to be a highly perspective method, thanks to which we are able to identify critical points of an element or a structure. The experiment will focus on the use of electroacoustic methods for defectoscopy in reinforced concrete columns.

Keywords: sustainability, defectoscopy, ultrasonic method, non-destructive methods, electroacoustic methods

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Authors: Wei-Zhao, Yannian-Bao, Xing-Fan, Lei-Cao

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An isostatic pressing working cylinder automatic exhaust valve is designed. The finite element models of valve core and valve body under ultra-high pressure work environment are built to study the influence of interact of valve core and valve body to sealing performance. The contact stresses of metal sealing surface with different sizes are calculated and the automatic exhaust valve is optimized. The result of simulation and experiment shows that the sealing of optimized exhaust valve is more reliable and the service life is greatly improved. The optimized exhaust valve has been used in the warm isostatic pressing equipment.

Keywords: exhaust valve, sealing, ultra-high pressure, isostatic pressing

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Authors: I. Apostol, M. Mosoarca

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Romania is a seismic country, with two major seismic zones, Vrancea and Banat. One of the most important cities from Banat seismic area is Timisoara, where a lot of valuable historical buildings were built before any design codes, but still they kept their stability during past earthquakes. This article presents the influence of the adjacent buildings during an earthquake and the way that the specific failure mechanism is changed when the building is part of an aggregate. The investigation was made using nonlinear analysis based on Tremuri software, first analyzing the buildings as isolated and second, considering the entire aggregate of buildings. There were noticed significant differences through the two situations regarding the specific failure mechanism activated for each building, showing the fact that in some situations, the presence of the adjacent buildings has positive or negative contribution for the seismic behavior of the analyzed one. The difference between the failure mechanism of the same buildings considered isolated and in aggregate aims to provide explications for the good structural state of the existing historical areas of Timisoara, as part of a larger multidisciplinary study, which will help local authorities to prioritize the consolidation works for the historical buildings in order to assure that the history of the city will be kept alive for the next generations.

Keywords: failure mechanism, analysis, aggregate, masonry, earthquake

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Authors: Nusrat T. Chowdhury

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Green Supply Chain Management (GSCM) is becoming a key to success for profitable businesses. The various activities contributing to carbon emissions in a supply chain are transportation, ordering and holding of inventory. This research work develops a mixed-integer nonlinear programming (MINLP) model that considers the scenario of a supply chain with multiple periods, multiple products and multiple suppliers. The model assumes that the demand is deterministic, the buyer has a limited storage space in each period, the buyer is responsible for the transportation cost, a supplier-dependent ordering cost applies for each period in which an order is placed on a supplier and inventory shortage is permissible. The model provides an optimal decision regarding what products to order, in what quantities, with which suppliers, and in which periods in order to maximize the profit. For the purpose of evaluating the carbon emissions, three different carbon regulating policies i.e., carbon cap-and-trade, the strict cap on carbon emission and carbon tax on emissions, have been considered. The proposed MINLP has been validated using a randomly generated data set.

Keywords: green supply chain, carbon emission, mixed integer non-linear program, inventory shortage, carbon cap-and-trade

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Authors: K. Asanimoghadam, M. Salahi, A. Jamalian

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Data envelopment analysis is an approach to measure the efficiency of decision making units with multiple inputs and outputs. The structure of many decision making units also has decision-making subunits that are not considered in most data envelopment analysis models. Also, the inputs and outputs of the decision-making units usually are considered desirable, while in some real-world problems, the nature of some inputs or outputs are undesirable. In this thesis, we study the evaluation of the efficiency of two stage decision-making units, where some outputs are undesirable using two non-radial models, the SBM and the ASBM models. We formulate the nonlinear ASBM model as a second order cone optimization problem. Finally, we compare two models for both external and internal evaluation approaches for two real world example in the presence of undesirable outputs. The results show that, in both external and internal evaluations, the overall efficiency of ASBM model is greater than or equal to the overall efficiency value of the SBM model, and in internal evaluation, the ASBM model is more flexible than the SBM model.

Keywords: network DEA, conic optimization, undesirable output, SBM

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Authors: Sagardeep Talukdar, Riki Dutta, Gautam Kumar Saharia, Sudipta Nandy

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across the optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain a bright soliton solution. We have obtained bright 1-soliton and 2-soliton solutions and propose a scheme for obtaining an N-soliton solution. We have used an additional parameter that is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. In the non-vanishing boundary condition, we obtain the dark 1-soliton solution. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: Chakshu Baweja, Ishaan Prakash, Deepak Giri, Prithwish Mukherjee, Herambraj Ashok Nalawade

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The need to prevent and control rampant and indiscriminate usage of energy in present-day realm on earth has motivated active research efforts aimed at understanding of controlling mechanisms leading to sustained energy. Although much has been done but complexity of the problem has prevented a complete understanding due to nonlinear interaction between flow, heat and mass transfer in terrestrial environment. Therefore, there is need for a systematic study to clearly understand mechanisms controlling energy-spreading phenomena to increase a system’s efficiency. The present work addresses the issue of sustaining energy and proposes a devoted technique of optimizing energy in the automotive domain. The proposed method focus on utilization of the mechanical and thermal energy of an automobile IC engine by converting and storing energy due to motion of a piston in form of electrical energy. The suggested technique utilizes piston motion of the engine to generate high potential difference capable of working as a secondary power source. This is achieved by the use of a gear mechanism and a flywheel.

Keywords: internal combustion engine, energy, electromagnetic induction, efficiency, gear ratio, hybrid vehicle, engine shaft

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Authors: P. Naresh, Amir Iqbal

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Satellite transportation is inevitable step during the course of integration testing and launch. Large satellites are transported in horizontal mode due to constraints on commercially available cargo bay dimensions & on road obstacles. To facilitate transportation of bigger size spacecraft in horizontal mode a tilting system is released. This tilting system consists of tilt table, columns, hinge pin, angular contact bearings, slewing bearing and linear actuators. The tilting system is very compact and easy to use however it is also serves the purpose of a fixture so it is of immense interest to know the stress and fundamental frequency of the system in transportation configuration. This paper discusses design aspects and finite element analysis of tilting system-cum-fixture using Hypermesh/Nastran.

Keywords: tilt table, column, slewing bearing, stress, modal analysis

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Authors: HyunSu Seo, HoYoung Son, Sungjin Kim, WooYoung Jung

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In order to understand the seismic behavior of steel frame structure with infill FRP composite panel, simple models for simulation on the steel frame with the panel systems were developed in this study. To achieve the simple design method of the steel framed structure with the damping panel system, 2-D finite element analysis with the springs and dashpots models was conducted in ABAQUS. Under various applied spring stiffness and dashpot coefficient, the expected hysteretic energy responses of the steel frame with damping panel systems we re investigated. Using the proposed simple design method which decides the stiffness and the damping, it is possible to decide the FRP and damping materials on a steel frame system.

Keywords: numerical analysis, FEM, infill, GFRP, damping

Procedia PDF Downloads 414

Authors: N. K. Mohd Affendi, T. A. R. Tuan Abdullah, S. A. Syed Mustaffa

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In power industry transformer is an important component and most of us familiar by the functioning principle of a transformer electrically. There are many losses occur during the operation of a transformer that causes heat generation. This heat, if not dissipated properly will reduce the lifetime and effectiveness of the transformer. Transformer cooling helps in maintaining the temperature rise of various paths. This paper proposed to minimize the ambient temperature of the transformer room in order to lower down the temperature of the transformer. A simulation has been made using finite element methods programs called FEMM (Finite Elements Method Magnetics) to create a virtual model based on actual measurement of a transformer. The generalization of the two-dimensional (2D) FEMM results proves that by minimizing the ambient temperature, the heat of the transformer is decreased. The modeling process and of the transformer heat flow has been presented.

Keywords: heat generation, temperature rise, ambient temperature, FEMM

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Authors: Harish Ramesh Babu, Marco Böcker, Mario Raddatz, Sebastian Henkel, Horst Biermann, Uwe Gampe

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Thermal power machines are subjected to cyclic loading conditions under elevated temperatures. At these extreme conditions, the durability of the components has a significant influence. The material mechanical behaviour has to be known in detail for a failsafe construction. For this study a nickel-based alloy is considered, the deformation and fatigue behaviour of the material is analysed under cyclic loading. A viscoplastic model is used for calculating the deformation behaviour as well as to simulate the rate-dependent and cyclic plasticity effects. Finally, the cyclic deformation results of the finite element simulations are compared with low cycle fatigue (LCF) experiments.

Keywords: complex low cycle fatigue, elevated temperature, fe-simulation, viscoplastic

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Authors: Mehdi Fuladipanah

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Stepped spillway includes several steps from the crest to the toe. The steps of stepped spillway could cause to decrease the energy with making energy distribution in the longitude mode and also to reduce the outcome speed. The aim of this study was to stimulate the stepped spillway combined with stilling basin-step using Fluent model and the turbulent superficial flow using RNG, K-ε. The free surface of the flow was monitored by VOF model. The velocity and the depth of the flow were measured by tail water depth by the numerical model and then the dissipated energy was calculated along the spillway. The results indicated that the stilling basin-step complex may cause energy dissipation increment in the stepped spillway. Also, the numerical model was suggested as an effective method to predict the circular and complicated flows in the stepped spillways.

Keywords: stepped spillway, fluent model, VOF model, K-ε model, energy distribution

Procedia PDF Downloads 365

Authors: Jean Marie Ntaganda, Froduald Minani, Wellars Banzi, Lydie Mpinganzima, Japhet Niyobuhungiro, Jean Bosco Gahutu, Vincent Dusabejambo, Immaculate Kambutse

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In this paper, we present a nonlinear dynamic model for the interactive mechanism of the cardiovascular and respiratory system. The model is designed and analyzed for human during physical exercises. In order to verify the adequacy of the designed model, data collected in Rwanda are used for validation. We have simulated the impact of heart rate and alveolar ventilation as controls of cardiovascular and respiratory system respectively to steady state response of the main cardiovascular hemodynamic quantities i.e., systemic arterial and venous blood pressures, arterial oxygen partial pressure and arterial carbon dioxide partial pressure, to the stabilised values of controls. We used data collected in Rwanda for both male and female during physical activities. We obtained a good agreement with physiological data in the literature. The model may represent an important tool to improve the understanding of exercise physiology.

Keywords: exercise, cardiovascular/respiratory, hemodynamic quantities, numerical simulation, physical activity, sportsmen in Rwanda, system

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Authors: Naren Bag, S. Bhattacharyya, Partha P. Gopmandal

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In this study, we have analyzed the transport of analytes under a two dimensional steady incompressible flow of power-law fluids through rectangular nanochannel. A mathematical model based on the Cauchy momentum-Nernst-Planck-Poisson equations is considered to study the combined effect of mixed electroosmotic (EO) and pressure driven (PD) flow. The coupled governing equations are solved numerically by finite volume method. We have studied extensively the effect of key parameters, e.g., flow behavior index, concentration of the electrolyte, surface potential, imposed pressure gradient and imposed electric field strength on the net average flow across the channel. In addition to study the effect of mixed EOF and PD on the analyte distribution across the channel, we consider a nonlinear model based on general convective-diffusion-electromigration equation. We have also presented the retention factor for various values of electrolyte concentration and flow behavior index.

Keywords: electric double layer, finite volume method, flow behavior index, mixed electroosmotic/pressure driven flow, non-Newtonian power-law fluids, numerical simulation

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Authors: Nicolas Zufferey

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Ant algorithms are well-known metaheuristics which have been widely used since two decades. In most of the literature, an ant is a constructive heuristic able to build a solution from scratch. However, other types of ant algorithms have recently emerged: the discussion is thus not limited by the common framework of the constructive ant algorithms. Generally, at each generation of an ant algorithm, each ant builds a solution step by step by adding an element to it. Each choice is based on the greedy force (also called the visibility, the short term profit or the heuristic information) and the trail system (central memory which collects historical information of the search process). Usually, all the ants of the population have the same characteristics and behaviors. In contrast in this paper, a new type of ant metaheuristic is proposed, namely SMART (for Solution Methods with Ants Running by Types). It relies on the use of different population of ants, where each population has its own personality.

Keywords: ant algorithms, evolutionary procedures, metaheuristics, optimization, population-based methods

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Authors: J. H. Kim, J. H. Kwon, J. S. Park, K. J. Lim

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This paper has investigated a technique that predicts the performance of a bar-type unimorph piezoelectric vibration actuator depending on the frequency. This paper has been proposed an equivalent circuit that can be easily analyzed for the bar-type unimorph piezoelectric vibration actuator. In the dynamic analysis, rigidity and resonance frequency, which are important mechanical elements, were derived using the basic beam theory. In the equivalent circuit analysis, the displacement and bandwidth of the piezoelectric vibration actuator depending on the frequency were predicted. Also, for the reliability of the derived equations, the predicted performance depending on the shape change was compared with the result of a finite element analysis program.

Keywords: actuator, piezoelectric, performance, unimorph

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Authors: S. Lecheb, A. Nour, A. Chellil, H. Mechakra, N. Tchina, H. Kebir

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This study concerned the dynamic behavior of the wind turbine rotor. Before all, we have studied the loads applied to the rotor, which allows the knowledge their effect on the fatigue. We also studied the movement of the longitudinal cracked rotor in order to determine stress, strain and displacement. Moreover, to study the issues of cracks in the critical zone ABAQUS software is used, which based to the finite element to give the results. In the first we compared the first six modes shapes between cracking and uncracking of HAWT rotor. In the second part, we show the evolution of six first naturals frequencies with longitudinal crack propagation. Finally, we conclude that the residual change in the naturals frequencies can be used as in shaft crack diagnosis predictive maintenance.

Keywords: wind turbine rotor, natural frequencies, longitudinal crack growth, life time

Procedia PDF Downloads 578