Search results for: Numerical field computation

Authors: Ahmad Attiq Al-Ogaibi, Ahmad Sharieh, Moh’d Belal Al-Zoubi, R. Bremananth

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In pattern clustering, nearest neighborhood point computation is a challenging issue for many applications in the area of research such as Remote Sensing, Computer Vision, Pattern Recognition and Statistical Imaging. Nearest neighborhood computation is an essential computation for providing sufficient classification among the volume of pixels (voxels) in order to localize the active-region-of-interests (AROI). Furthermore, it is needed to compute spatial metric relationships of diverse area of imaging based on the applications of pattern recognition. In this paper, we propose a new methodology for finding the nearest neighbor point, depending on making a virtually grid of a hexagon cells, then locate every point beneath them. An algorithm is suggested for minimizing the computation and increasing the turnaround time of the process. The nearest neighbor query points Φ are fetched by seeking fashion of hexagon holistic. Seeking will be repeated until an AROI Φ is to be expected. If any point Υ is located then searching starts in the nearest hexagons in a circular way. The First hexagon is considered be level 0 (L0) and the surrounded hexagons is level 1 (L1). If Υ is located in L1, then search starts in the next level (L2) to ensure that Υ is the nearest neighbor for Φ. Based on the result and experimental results, we found that the proposed method has an advantage over the traditional methods in terms of minimizing the time complexity required for searching the neighbors, in turn, efficiency of classification will be improved sufficiently.

Keywords: Hexagon cells, k-nearest neighbors, Nearest Neighbor, Pattern recognition, Query pattern, Virtually grid

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Authors: Kui Du

Abstract:

Recently, Uhlig [Numer. Algorithms, 52(3):335-353, 2009] proposed open questions about the ratios between the spectral norm, the numerical radius and the spectral radius of a square matrix. In this note, we provide some observations to answer these questions.

Keywords: Spectral norm, Numerical radius, Spectral radius, Ratios

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Authors: H. Ahmed, A. Schlenkhoff

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Recently, permeable breakwaters have been suggested to overcome the disadvantages of fully protection breakwaters. These protection structures have minor impacts on the coastal environment and neighboring beaches where they provide a more economical protection from waves and currents. For regular waves, a numerical model is used (FLOW-3D, VOF) to investigate the hydraulic performance of a permeable breakwater. The model of permeable breakwater consists of a pair of identical vertical slotted walls with an impermeable upper and lower part, where the draft is a decimal multiple of the total depth. The middle part is permeable with a porosity of 50%. The second barrier is located at distant of 0.5 and 1.5 of the water depth from the first one. The numerical model is validated by comparisons with previous laboratory data and semi-analytical results of the same model. A good agreement between the numerical results and both laboratory data and semi-analytical results has been shown and the results indicate the applicability of the numerical model to reproduce most of the important features of the interaction. Through the numerical investigation, the friction factor of the model is carefully discussed.

Keywords: Coastal structures, permeable breakwater, slotted wall, numerical model, energy dissipation coefficient.

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Authors: P. Zamani, S. Mohajerzadeh, R. Masoudinejad, Kh. Farhangdoost

Abstract:

Riveting process is one of the important ways to keep fastening the lap joints in aircraft structures. Failure of aircraft lap joints directly depends on the stress field in the joint. An important application of riveting process is in the construction of aircraft fuselage structures. In this paper, a 3D finite element method is carried out in order to optimize residual stress field in a riveted lap joint and also to estimate its fatigue life. In continue, a number of experiments are designed and analyzed using design of experiments (DOE). Then, Taguchi method is used to select an optimized case between different levels of each factor. Besides that, the factor which affects the most on residual stress field is investigated. Such optimized case provides the maximum residual stress field. Fatigue life of the optimized joint is estimated by Paris-Erdogan law. Stress intensity factors (SIFs) are calculated using both finite element analysis and experimental formula. In addition, the effect of residual stress field, geometry and secondary bending are considered in SIF calculation. A good agreement is found between results of such methods. Comparison between optimized fatigue life and fatigue life of other joints has shown an improvement in the joint’s life.

Keywords: Fatigue life, Residual stress, Riveting process, Stress intensity factor, Taguchi method.

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Authors: M.Zadshakouyan, E.Abdi Sobbouhi, H.Jafarzadeh

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In this study, the precision heading process of spur gears has been investigated by means of numerical analysis. The effect of some parameters such as teeth number and module on the forming force and material flow were presented. The simulation works were performed rigid-plastic finite element method using DEFORM 3D software. In order to validate the estimated numerical results, they were compared with those obtained experimentally during heading of spur gear using lead as a model material. Results showed that the optimum number of gear teeth is between 10 to 20, that is because of being the specific pressure in its minimum value.

Keywords: Heading, spur gear, numerical analysis, experiments.

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Authors: P.S. Prakash, S. Selvan

Abstract:

Quality of Service (QoS) Routing aims to find path between source and destination satisfying the QoS requirements which efficiently using the network resources and underlying routing algorithm and to fmd low-cost paths that satisfy given QoS constraints. One of the key issues in providing end-to-end QoS guarantees in packet networks is determining feasible path that satisfies a number of QoS constraints. We present a Optimized Multi- Constrained Routing (OMCR) algorithm for the computation of constrained paths for QoS routing in computer networks. OMCR applies distance vector to construct a shortest path for each destination with reference to a given optimization metric, from which a set of feasible paths are derived at each node. OMCR is able to fmd feasible paths as well as optimize the utilization of network resources. OMCR operates with the hop-by-hop, connectionless routing model in IP Internet and does not create any loops while fmding the feasible paths. Nodes running OMCR not necessarily maintaining global view of network state such as topology, resource information and routing updates are sent only to neighboring nodes whereas its counterpart link-state routing method depend on complete network state for constrained path computation and that incurs excessive communication overhead.

Keywords: QoS Routing, Optimization, feasible path, multiple constraints.

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Authors: Sirapat Lookrak, Anol Paisal

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Space debris has numerous manifestations including ferro-metalize and non-ferrous. The electric field will induce negative charges to split from positive charges inside the space debris. In this research, we focus only on conducting materials. The assumption is that the electric charge density of a conducting surface is proportional to the electric field on that surface due to Gauss's law. We are trying to find the induced charge density from an external electric field perpendicular to a conducting spherical surface. An object is a sphere on which the external electric field is not uniform. The electric field is, therefore, considered locally. The localised spherical surface is a tangent plane so the Gaussian surface is a very small cylinder and every point on a spherical surface has its own cylinder. The electric field from a circular electrode has been calculated in near-field and far-field approximation and shown Explanation Touchless manoeuvring space debris orbit properties. The electric charge density calculation from a near-field and far-field approximation is done.

Keywords: Near-field approximation, far-field approximation, localized Gauss’s law, electric charge density.

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Authors: N. M. Nusi, M. Othman, M. Suleiman, F. Ismail, N. Alias

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In this paper, an alternating implicit block method for solving two dimensional scalar wave equation is presented. The new method consist of two stages for each time step implemented in alternating directions which are very simple in computation. To increase the speed of computation, a group of adjacent points is computed simultaneously. It is shown that the presented method increase the maximum time step size and more accurate than the conventional finite difference time domain (FDTD) method and other existing method of natural ordering.

Keywords: FDTD, Scalar wave equation, alternating direction implicit (ADI), alternating group explicit (AGE), asymmetric approximation.

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Authors: Mohammad R. Kavian Nezhad, Carlos F. Lange, Brian A. Fleck

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This research presents the validation study of a computational fluid dynamics (CFD) model developed to simulate the scalar dispersion emitted from rooftop sources around the buildings at the University of Alberta North Campus. The ANSYS CFX code was used to perform the numerical simulation of the wind regime and pollutant dispersion by solving the 3D steady Reynolds-averaged Navier-Stokes (RANS) equations on a building-scale high-resolution grid. The validation study was performed in two steps. First, the CFD model performance in 24 cases (eight wind directions and three wind speeds) was evaluated by comparing the predicted flow fields with the available data from the previous measurement campaign designed at the North Campus, using the standard deviation method (SDM), while the estimated results of the numerical model showed maximum average percent errors of approximately 53% and 37% for wind incidents from the North and Northwest, respectively. Good agreement with the measurements was observed for the other six directions, with an average error of less than 30%. In the second step, the reliability of the implemented turbulence model, numerical algorithm, modeling techniques, and the grid generation scheme was further evaluated using the Mock Urban Setting Test (MUST) dispersion dataset. Different statistical measures, including the fractional bias (FB), the mean geometric bias (MG), and the normalized mean square error (NMSE), were used to assess the accuracy of the predicted dispersion field. Our CFD results are in very good agreement with the field measurements.

Keywords: CFD, plume dispersion, complex urban geometry, validation study, wind flow.

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Authors: Marco Antonio Cruz-Chávez, Juan Frausto-Solís, Fernando Ramos-Quintana

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A procedure commonly used in Job Shop Scheduling Problem (JSSP) to evaluate the neighborhoods functions that use the non-deterministic algorithms is the calculation of the critical path in a digraph. This paper presents an experimental study of the cost of computation that exists when the calculation of the critical path in the solution for instances in which a JSSP of large size is involved. The results indicate that if the critical path is use in order to generate neighborhoods in the meta-heuristics that are used in JSSP, an elevated cost of computation exists in spite of the fact that the calculation of the critical path in any digraph is of polynomial complexity.

Keywords: Job Shop, CPM, critical path, neighborhood, meta-heuristic.

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Authors: Khosrow Maleknejad, Reza Mollapourasl, Parvin Torabi, Mahdiyeh Alizadeh,

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Sinc-collocation scheme is one of the new techniques used in solving numerical problems involving integral equations. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. So, in this paper, some properties of the Sinc-collocation method required for our subsequent development are given and are utilized to reduce integral equation of the first kind to some algebraic equations. Then convergence with exponential rate is proved by a theorem to guarantee applicability of numerical technique. Finally, numerical examples are included to demonstrate the validity and applicability of the technique.

Keywords: Integral equation, Fredholm type, Collocation method, Sinc approximation.

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Authors: R. Varalakshmi

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For the last decade, researchers have started to focus their interest on Multicast Group Key Management Framework. The central research challenge is secure and efficient group key distribution. The present paper is based on the Bit model based Secure Multicast Group key distribution scheme using the most popular absolute encoder output type code named Gray Code. The focus is of two folds. The first fold deals with the reduction of computation complexity which is achieved in our scheme by performing fewer multiplication operations during the key updating process. To optimize the number of multiplication operations, an O(1) time algorithm to multiply two N-bit binary numbers which could be used in an N x N bit-model of reconfigurable mesh is used in this proposed work. The second fold aims at reducing the amount of information stored in the Group Center and group members while performing the update operation in the key content. Comparative analysis to illustrate the performance of various key distribution schemes is shown in this paper and it has been observed that this proposed algorithm reduces the computation and storage complexity significantly. Our proposed algorithm is suitable for high performance computing environment.

Keywords: Multicast Group key distribution, Bit model, Integer Multiplications, reconfigurable mesh, optimal algorithm, Gray Code, Computation Complexity, Storage Complexity.

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Authors: Aníbal Rodríguez Fuentes, Juan V. Lorenzo Ginori, Ricardo Grau Ábalo

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Identifying protein coding regions in DNA sequences is a basic step in the location of genes. Several approaches based on signal processing tools have been applied to solve this problem, trying to achieve more accurate predictions. This paper presents a new predictor that improves the efficacy of three techniques that use the Fourier Transform to predict coding regions, and that could be computed using an algorithm that reduces the computation load. Some ideas about the combination of the predictor with other methods are discussed. ROC curves are used to demonstrate the efficacy of the proposed predictor, based on the computation of 25 DNA sequences from three different organisms.

Keywords: Bioinformatics, Coding region prediction, Computational load reduction, Digital Signal Processing, Fourier Transform.

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Authors: Jalal Karam

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In real-field applications, the correct determination of voice segments highly improves the overall system accuracy and minimises the total computation time. This paper presents reliable measures of speech compression by detcting the end points of the speech signals prior to compressing them. The two different compession schemes used are the Global threshold and the Level- Dependent threshold techniques. The performance of the proposed method is tested wirh the Signal to Noise Ratios, Peak Signal to Noise Ratios and Normalized Root Mean Square Error parameter measures.

Keywords: Wavelets, End-points Detection, Compression.

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Authors: Saad Chakkor, Mostafa Baghouri, Abderrahmane Hajraoui

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ESPRIT-TLS method appears a good choice for high resolution fault detection in induction machines. It has a very high effectiveness in the frequency and amplitude identification. Contrariwise, it presents a high computation complexity which affects its implementation in real time fault diagnosis. To avoid this problem, a Fast-ESPRIT algorithm that combined the IIR band-pass filtering technique, the decimation technique and the original ESPRIT-TLS method was employed to enhance extracting accurately frequencies and their magnitudes from the wind stator current with less computation cost. The proposed algorithm has been applied to verify the wind turbine machine need in the implementation of an online, fast, and proactive condition monitoring. This type of remote and periodic maintenance provides an acceptable machine lifetime, minimize its downtimes and maximize its productivity. The developed technique has evaluated by computer simulations under many fault scenarios. Study results prove the performance of Fast- ESPRIT offering rapid and high resolution harmonics recognizing with minimum computation time and less memory cost.

Keywords: Spectral Estimation, ESPRIT-TLS, Real Time, Diagnosis, Wind Turbine Faults, Band-Pass Filtering, Decimation.

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Authors: Y. Shpungin

Abstract:

Estimating the reliability of a computer network has been a subject of great interest. It is a well known fact that this problem is NP-hard. In this paper we present a very efficient combinatorial approach for Monte Carlo reliability estimation of a network with unreliable nodes and unreliable edges. Its core is the computation of some network combinatorial invariants. These invariants, once computed, directly provide pure and simple framework for computation of network reliability. As a specific case of this approach we obtain tight lower and upper bounds for distributed network reliability (the so called residual connectedness reliability). We also present some simulation results.

Keywords: Combinatorial invariants, Monte Carlo simulation, reliability, unreliable nodes and unreliable edges.

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Authors: Suwimon Saneewong Na Ayuttaya

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This paper presents a numerical investigation of electrically driven flow for enhancing convective heat transfer in a channel flow. This study focuses on the electrode arrangements, number of electrode and electrical voltage on Electrohydrodynamics (EHD) and effect of airflow driven on solid sample surface. The inlet airflow and inlet temperature are 0.35 m/s and 60 ^oC, respectively. High electrical voltage is tested in the range of 0-30 kV and number of electrode is tested in the range of 1-5. The numerical results show that electric field intensity is depended on electrical voltage and number of electrode. Increasing number of electrodes is increased shear flow, so swirling flow is increased. The swirling flows from aligned and staggered arrangements are affecting within the solid sample. When electrical voltage is increased, temperature distribution and convective heat transfer on the solid sample are significantly increased due to the electric force much stronger.

Keywords: Electrohydrodynamics, swirling flow, convective heat transfer, solid sample.

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Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

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Due to many applications and problems in the fields of plasma physics, geophysics, and other many topics, the interaction between the strain field and the magnetic field has to be considered. Adomian introduced the decomposition method for solving linear and nonlinear functional equations. This method leads to accurate, computable, approximately convergent solutions of linear and nonlinear partial and ordinary differential equations even the equations with variable coefficients. This paper is dealing with a mathematical model of generalized thermoelasticity of a half-space conducting medium. A magnetic field with constant intensity acts normal to the bounding plane has been assumed. Adomian’s decomposition method has been used to solve the model when the bounding plane is taken to be traction free and thermally loaded by harmonic heating. The numerical results for the temperature increment, the stress, the strain, the displacement, the induced magnetic, and the electric fields have been represented in figures. The magnetic field, the relaxation time, and the angular thermal load have significant effects on all the studied fields.

Keywords: Adomian’s Decomposition Method, magneto-thermoelasticity, finite conductivity, iteration method, thermal load.

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Authors: Terrance Charles, Zhiyin Yang, Yiling Lu

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Heavy trucks are aerodynamically inefficient due to their un-streamlined body shapes, leading to more than of 60% engine power being required to overcome the aerodynamics drag at 60 m/hr. There are many aerodynamics drag reduction devices developed and this paper presents a study on a drag reduction device called Cross Vortex Trap Device (CVTD) deployed in the gap between the tractor and the trailer of a simplified tractor-trailer model. Numerical simulations have been carried out at Reynolds number 0.51×10⁶ based on inlet flow velocity and height of the trailer using the Reynolds-Averaged Navier-Stokes (RANS) approach. Three different configurations of CVTD have been studied, ranging from single to three slabs, equally spaced on the front face of the trailer. Flow field around three different configurations of trap device have been analysed and presented. The results show that a maximum of 12.25% drag reduction can be achieved when a triple vortex trap device is used. Detailed flow field analysis along with pressure contours are presented to elucidate the drag reduction mechanisms of CVTD and why the triple vortex trap configuration produces the maximum drag reduction among the three configurations tested.

Keywords: Aerodynamic drag, cross vortex trap device, truck, RANS.

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Authors: Mohammad Talha, B. N. Singh

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This paper deals with the thermo-mechanical deformation behavior of shear deformable functionally graded ceramicmetal (FGM) plates. Theoretical formulations are based on higher order shear deformation theory with a considerable amendment in the transverse displacement using finite element method (FEM). The mechanical properties of the plate are assumed to be temperaturedependent and graded in the thickness direction according to a powerlaw distribution in terms of the volume fractions of the constituents. The temperature field is supposed to be a uniform distribution over the plate surface (XY plane) and varied in the thickness direction only. The fundamental equations for the FGM plates are obtained using variational approach by considering traction free boundary conditions on the top and bottom faces of the plate. A C0 continuous isoparametric Lagrangian finite element with thirteen degrees of freedom per node have been employed to accomplish the results. Convergence and comparison studies have been performed to demonstrate the efficiency of the present model. The numerical results are obtained for different thickness ratios, aspect ratios, volume fraction index and temperature rise with different loading and boundary conditions. Numerical results for the FGM plates are provided in dimensionless tabular and graphical forms. The results proclaim that the temperature field and the gradient in the material properties have significant role on the thermo-mechanical deformation behavior of the FGM plates.

Keywords: Functionally graded material, higher order shear deformation theory, finite element method, independent field variables.

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Authors: Mario Mastriani

Abstract:

In this work, we developed the concept of supercompression, i.e., compression above the compression standard used. In this context, both compression rates are multiplied. In fact, supercompression is based on super-resolution. That is to say, supercompression is a data compression technique that superpose spatial image compression on top of bit-per-pixel compression to achieve very high compression ratios. If the compression ratio is very high, then we use a convolutive mask inside decoder that restores the edges, eliminating the blur. Finally, both, the encoder and the complete decoder are implemented on General-Purpose computation on Graphics Processing Units (GPGPU) cards. Specifically, the mentio-ned mask is coded inside texture memory of a GPGPU.

Keywords: General-Purpose computation on Graphics Processing Units, Image Compression, Interpolation, Super-resolution.

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Authors: D. Kim

Abstract:

Numerical simulations are performed for laminar continuous and pulsed jets impinging on a surface in order to investigate the effects of pulsing frequency on the heat transfer characteristics. The time-averaged Nusselt number of pulsed jets is larger in the impinging jet region as compared to the continuous jet, while it is smaller in the outer wall jet region. At the stagnation point, the mean and RMS Nusselt numbers become larger and smaller, respectively, as the pulsing frequency increases. Unsteady behaviors of vortical fluid motions and temperature field are also investigated to understand the underlying mechanisms of heat transfer enhancement.

Keywords: Pulsed slot jet, impingement, pulsing frequency, heat transfer enhancement.

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Authors: Wookuen Shin, Gregory R. Miller, Pedro Arduino, Peter Mackenzie-Helnwein

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This paper presents strategies for dynamically creating, managing and removing mesh cells during computations in the context of the Material Point Method (MPM). The dynamic meshing approach has been developed to help address problems involving motion of a finite size body in unbounded domains in which the extent of material travel and deformation is unknown a priori, such as in the case of landslides and debris flows. The key idea is to efficiently instantiate and search only cells that contain material points, thereby avoiding unneeded storage and computation. Mechanisms for doing this efficiently are presented, and example problems are used to demonstrate the effectiveness of dynamic mesh management relative to alternative approaches.

Keywords: Numerical Analysis, Material Point Method, Large Deformations, Moving Boundaries.

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Authors: Mohamed M. Mousa, Aidarkhan Kaltayev

Abstract:

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4th order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compared with each other, showing excellent agreement. The effects of the magnetic parameter and Prandtl number on velocity field, shear stress, temperature and heat transfer are discussed as well.

Keywords: Electrically conducting elastico-viscous fluid, symmetry solution, Homotopy perturbation method, Padé approximation, 4th order Runge–Kutta, Maple

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Authors: Nicolò Vaiana, Giorgio Serino

Abstract:

In this paper, an advanced Nonlinear Exponential Model (NEM), able to simulate the uniaxial dynamic behavior of seismic isolators having a continuously decreasing tangent stiffness with increasing displacement in the relatively large displacements range and a hardening or softening behavior at large displacements, is presented. The mathematical model is validated by comparing the experimental force-displacement hysteresis loops obtained during cyclic tests, conducted on a helical wire rope isolator and a recycled rubber-fiber reinforced bearing, with those predicted analytically. Good agreement between the experimental and simulated results shows that the proposed model can be an effective numerical tool to predict the force-displacement relationship of seismic isolation devices within the large displacements range. Compared to the widely used Bouc-Wen model, unable to simulate the response of seismic isolators at large displacements, the proposed one allows to avoid the numerical solution of a first order nonlinear ordinary differential equation for each time step of a nonlinear time history analysis, thus reducing the computation effort. Furthermore, the proposed model can simulate the smooth transition of the hysteresis loops from small to large displacements by adopting only one set of five parameters determined from the experimental hysteresis loops having the largest amplitude.

Keywords: Base isolation, hardening behavior, nonlinear exponential model, seismic isolators, softening behavior.

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Authors: M. Aghajani Haghighi, H. Emdad, K. Jafarpur, A. N. Ziaei

Abstract:

The effect of a uniform magnetic field on the formation of drops of specific size has been investigated numerically in a T-shaped microchannel. Previous researches indicated that the drop sizes of secondary stream decreases, with increasing main stream flow rate and decreasing interfacial tension. In the present study the effect of a uniform magnetic field on the main stream is considered, and it is proposed that by increasing the Hartmann number, the size of the drops of the secondary stream will be decreased.

Keywords: Drop formation, Magnetohydrodynamics, Microchannel, Volume-of-Fluid

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Authors: M. Zarebnia, N. Aliniya

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In this paper, a numerical solution based on sinc functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method.

Keywords: Calculus of variation; Sinc functions; Galerkin; Numerical method

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Authors: Fatema-Tuz-Zahura, Raquib Ahsan

Abstract:

Punching shear failure is usually the governing failure mode of flat plate structures. Punching failure is brittle in nature which induces more vulnerability to this type of structure. In the present study, a 3D finite element model of a flat plate with low reinforcement ratio and without any transverse reinforcement has been developed. Punching shear stress and the deflection data were obtained on the surface of the flat plate as well as through the thickness of the model from numerical simulations. The obtained data were compared with the experimental results. Variation of punching stress with respect to deflection as obtained from numerical results is found to be in good agreement with the experimental results; the range of variation of punching stress is within 5%. The numerical simulation shows an early and gradual onset of nonlinearity, whereas the same is late and abrupt as observed in the experimental results. The range of variation of punching stress for different slab thicknesses between experimental and numerical results is less than 15%. The developed numerical model is useful to complement available punching test series performed in the past. The results obtained from the numerical model will be helpful for designing retrofitting schemes of flat plates.

Keywords: Flat plate, finite element model, punching shear, reinforcement ratio.

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Authors: Md. Fazlul Karim, Esa Al-Islam

Abstract:

This paper describes the development of a boundary fitted nested grid (BFNG) model to compute tsunami propagation of 2004 Indonesian tsunami in Southern Thailand coastal waters. We develop a numerical model employing the shallow water nested model and an orthogonal boundary fitted grid to investigate the tsunami impact on the Southern Thailand due to the Indonesian tsunami of 2004. Comparisons of water surface elevation obtained from numerical simulations and field measurements are made.

Keywords: Boundary-fitted nested grid model, finite difference method, Indonesian tsunami of 2004, Southern Thailand.

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Authors: M. Zarebnia, M. Hoshyar, M. Sedaghati

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In this paper, a numerical solution based on nonpolynomial cubic spline functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method.

Keywords: Calculus of variation; Non-polynomial spline functions; Numerical method

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