Search results for: finite%20memory%20filter

Authors: Tun Myat Aung, Ni Ni Hla

Abstract:

This paper begins by describing basic properties of finite field and elliptic curve cryptography over prime field and binary field. Then we discuss the discrete logarithm problem for elliptic curves and its properties. We study the general common attacks on elliptic curve discrete logarithm problem such as the Baby Step, Giant Step method, Pollard’s rho method and Pohlig-Hellman method, and describe in detail experiments of these attacks over prime field and binary field. The paper finishes by describing expected running time of the attacks and suggesting strong elliptic curves that are not susceptible to these attacks.c

Keywords: discrete logarithm problem, general attacks, elliptic curve, prime field, binary field

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Authors: N. Jinesh, K. Shankar

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This article presents a method of using the one dimensional piezo-electric patch on beam model for structural identification. A hybrid element constituted of one dimensional beam element and a PZT sensor is used with reduced material properties. This model is convenient and simple for identification of beams. Accuracy of this element is first verified against a corresponding 3D finite element model (FEM). The structural identification is carried out as an inverse problem whereby parameters are identified by minimizing the deviation between the predicted and measured voltage response of the patch, when subjected to excitation. A non-classical optimization algorithm Particle Swarm Optimization is used to minimize this objective function. The signals are polluted with 5% Gaussian noise to simulate experimental noise. The proposed method is applied on beam structure and identified parameters are stiffness and damping. The model is also validated experimentally.

Keywords: inverse problem, particle swarm optimization, PZT patches, structural identification

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Authors: Nasiru Aliyu, Glyn Atkinson, Nick Stannard

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With increasing demand for electric motors used in nearly all sectors of our day to day activities, which range from the motor that rotates the washing machine and dishwasher to the tens of thousands of motors used in domestic appliance. The number of applications for soft magnetic composites (SMC) material is growing significantly. This paper presents the development of a compact single sided concentrated winding axial flux PM motor using soft magnetic composite as core for reducing core losses and cost. The effects of changing the flux carrying component to pressed SMC parts are investigated based on a comprehensive understanding of the properties of the material. A 3-D finite-element analysis is performed for accurate parameter calculation. To validate the simulation, a new static test measurement was fully conducted on a prototype motor and agree with the theoretical calculations and old measured static test.

Keywords: SMC, compact development, axial field motor, 3DFA

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Authors: P. Saleh, G. Challita, R. Hazimeh, K. Khalil

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In this paper 3D FEM analysis was carried out on double lap bonded joint with composite adherents subjected to dynamic shear. The adherents are made of Carbon/Epoxy while the adhesive is epoxy Araldite 2031. The maximum average shear stress and the stress homogeneity in the adhesive layer were examined. Three fibers textures were considered: UD; 2.5D and 3D with same volume fiber then a parametric study based on changing the thickness and the type of fibers texture in 2.5D was accomplished. Moreover, adherents’ dissimilarity was also investigated. It was found that the main parameter influencing the behavior is the longitudinal stiffness of the adherents. An increase in the adherents’ longitudinal stiffness induces an increase in the maximum average shear stress in the adhesive layer and an improvement in the shear stress homogeneity within the joint. No remarkable improvement was observed for dissimilar adherents.

Keywords: adhesive, composite adherents, impact shear, finite element

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Authors: Ezio Bassi, Francesco Vercesi, Francesco Benzi

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The aim of this study is to evaluate the potentiality of synchronous reluctance motors for lift systems by also evaluating the vibroacoustic behaviour of the motor. Two types of synchronous machines are designed, analysed, and compared with an equivalent induction motor, which is the more common solution in such gearbox applications. The machines' performance are further improved with optimization procedures based on multiobjective optimization genetic algorithm (MOGA). The difference between the two synchronous motors consists in the rotor geometry; a symmetric and an asymmetric rotor design were investigated. The evaluation of the vibroacoustic performance has been conducted with a multi-variable model and finite element software taking into account electromagnetic, mechanical, and thermal features of the motor, therefore carrying out a multi-physics analysis of the electrical machine.

Keywords: synchronous reluctance motor, vibro-acoustic, lift systems, genetic algorithm

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Authors: Han-Taw Chen, Tzu-Hsiang Lin, Chung-Hou Lai

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This study applies the inverse method and three-dimensional CFD commercial software in conjunction with the experimental temperature data to investigate the heat transfer and fluid flow characteristics of the plate-fin heat sink in a rectangular closed enclosure. The inverse method with the finite difference method and the experimental temperature data is applied to determine the approximate heat transfer coefficient. Later, based on the obtained results, the zero-equation turbulence model is used to obtain the heat transfer and fluid flow characteristics between two fins. To validate the accuracy of the results obtained, the comparison of the heat transfer coefficient is made. The obtained temperature at selected measurement locations of the fin is also compared with experimental data. The effect of the height of the rectangular enclosure on the obtained results is discussed.

Keywords: inverse method, fluent, heat transfer characteristics, plate-fin heat sink

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Authors: Seung-Yeon Kim

Abstract:

The Ising model, consisting magnetic spins, is the simplest system showing phase transitions and critical phenomena at finite temperatures. The Ising model has played a central role in our understanding of phase transitions and critical phenomena. Also, the Ising model explains the gas-liquid phase transitions accurately. However, the Ising model in a nonzero magnetic field has been one of the most intriguing and outstanding unsolved problems. We study analytically the partition function zeros in the complex magnetic-field plane and the Yang-Lee edge singularity of the infinite-range Ising model in an external magnetic field. In addition, we compare the Yang-Lee edge singularity of the infinite-range Ising model with that of the square-lattice Ising model in an external magnetic field.

Keywords: Ising ferromagnet, magnetic field, partition function zeros, Yang-Lee edge singularity

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Authors: H. Nouri, I. E. Achouri, A. Grimes, H. Ait Said, M. Aissou, Y. Zebboudj

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This paper aims to analysis the behaviour of DC corona discharge in wire-to-plate electrostatic precipitators (ESP). Current-voltage curves are particularly analysed. Experimental results show that discharge current is strongly affected by the applied voltage. The proposed method of current identification is to use the method of least squares. Least squares problems that of into two categories: linear or ordinary least squares and non-linear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares problem occurs in statistical regression analysis; it has a closed-form solution. A closed-form solution (or closed form expression) is any formula that can be evaluated in a finite number of standard operations. The non-linear problem has no closed-form solution and is usually solved by iterative.

Keywords: electrostatic precipitator, current-voltage characteristics, least squares method, electric field, magnetic field

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Authors: I. Made Gatot Karohika, Shigeyuki Haruyama, Ken Kaminishi, Oke Oktavianty, Didik Nurhadiyanto

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Contact width and contact stress are important parameters related to the leakage behavior of corrugated metal gasket. In this study, contact width and contact stress of three-layer corrugated metal gasket are investigated due to the modulus of elasticity and thickness of surface layer for 2 type gasket (0-MPa and 400-MPa mode). A finite element method was employed to develop simulation solution to analysis the effect of each parameter. The result indicated that lowering the modulus of elasticity ratio of surface layer will result in better contact width but the average contact stresses are smaller. When the modulus of elasticity ratio is held constant with thickness ratio increase, its contact width has an increscent trend otherwise the average contact stress has decreased trend.

Keywords: contact width, contact stress, layer, metal gasket, corrugated, simulation

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Authors: Jiajia Pan, Hung Tao Shen

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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, riverbanks, 2D model, heat conduction

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Authors: Dara Singh, Keikhosrow Firouzbakhsh, Mohammad Taghi Ahmadian

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In this study, a validated 3D finite volume model of human eye is developed to study the fluid flow and heat transfer in the human eye at steady state conditions. For this purpose, discretized bio-heat transfer equation coupled with Boussinesq equation is analyzed with different anatomical, environmental, and physiological conditions. It is demonstrated that the fluid circulation is formed as a result of thermal gradients in various regions of eye. It is also shown that posterior region of the human eye is less affected by the ambient conditions compared to the anterior segment which is sensitive to the ambient conditions and also to the way the gravitational field is defined compared to the geometry of the eye making the circulations and the thermal field complicated in transient states. The effect of variation in material and boundary conditions guides us to the conclusion that thermal field of a healthy and non-healthy eye can be distinguished via computer simulations.

Keywords: bio-heat, boussinesq, conduction, convection, eye

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Authors: Ryan D. Hoult

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The inherent assumption in the elementary theory of bending that plane sections remain plane is commonly used in the design of reinforced concrete members. However, in reality, a shear flow would develop in non-rectangular sections, where the longitudinal strains in between the web and flanges of the element would lag behind those at the boundary ends. This phenomenon, known as shear lag, can significantly reduce the expected moment capacity of non-rectangular reinforced concrete walls. This study focuses on shear lag effects in reinforced concrete U-shaped walls, which are commonly used as lateral load resisting elements in reinforced concrete buildings. An extensive number of finite element modelling analyses are conducted to estimate the vertical strain distributions across the web and flanges of a U-shaped wall with different axial load ratios and longitudinal reinforcement detailing. The results show that shear lag effects are prominent and sometimes significant in U-shaped walls, particularly for the wall sections perpendicular to the direction of loading.

Keywords: shear lag, walls, U-shaped, moment-curvature

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Authors: A. Benmerkhi, A. Bounouioua, M. Bouchemat, T. Bouchemat

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In this paper, we present a numerical optical properties of a triangular periodic lattice of elliptical air holes. We report the influence of the ratio (semi-major axis length of elliptical hole to the filling ratio) on the photonic band gap. Then by using the finite difference time domain (FDTD) algorithm, the resonant wavelength of the point defect microcavities in a two-dimensional photonic crystal (PC) shifts towards the low wavelengths with significantly increased filing ratio. It can be noted that the Q factor is gradually changed to higher when the filling ratio increases. It is due to an increase in reflectivity of the PC mirror. Also we theoretically investigate the H1 cavity, where the value of semi-major axis (Rx) of the six holes surrounding the cavity are fixed at 0.5a and the Rx of the two edge air holes are fixed at the optimum value of 0.52a. The highest Q factor of 4.1359 × 10⁶ is achieved at the resonant mode located at λ = 1.4970 µm.

Keywords: photonic crystal, microcavity, filling ratio, elliptical holes

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Authors: Zulfiqar Ali, Umar Saleem, Muhammad Junaid, Rizwan Tahir

Abstract:

Gulzar Mahal is a heritage site located in the city of Bahawalpur, Pakistan. The site is under a process of degradation, as cracks are appearing on the walls, roofs, and floor around the building due to differential settlement. To preserve the integrity of the structure, a geotechnical distress evaluation was carried out to evaluate the causal factors and recommend remediation measures. The research involved the characterization of the problematic soil and analysis of the observed distress with respect to the geotechnical properties. Both conventional lab and field tests were used in conjunction with the unconventional techniques like; Electrical Resistivity Tomography (ERT) and FEA. The temporal, geophysical and geotechnical evaluations have concluded that the foundation soil over the past was subjected to variations in the land use, poor drainage patterns, overloading and fluctuations in groundwater table all contributing to the differential settlements manifesting in the form of the visible shear crack across the length and breadth of the building.

Keywords: differential settlement, distress evaluation, finite element analysis, Gulzar Mahal

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Authors: Radek Doubrava, Roman Ruzek

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Nonstandard tests are necessary for analyses and verification of new developed structural and technological solutions with application of composite materials. One of the most critical primary structural parts of a typical aerospace structure is T-joint. This structural element is loaded mainly in shear, bending, peel and tension. The paper is focused on the shear loading simulations. The aim of the work is to obtain a representative uniform distribution of shear loads along T-joint during the mechanical testing is. A new design of T-joint test procedure, numerical simulation and optimization of representative boundary conditions are presented. The different conditions and inaccuracies both in simulations and experiments are discussed. The influence of different parameters on stress and strain distributions is demonstrated on T-joint made of CFRP (carbon fiber reinforced plastic). A special test rig designed by VZLU (Aerospace Research and Test Establishment) for T-shear test procedure is presented.

Keywords: T-joint, shear, composite, mechanical testing, finite element analysis, methodology

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Authors: James A. Adeyanju, John O. Olajide, Akinbode A. Adedeji

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A predictive mathematical model based on the fundamental principles of mass transfer was developed to simulate the moisture content and oil content during Deep-Fat Frying (DFF) process of dodo. The resulting governing equation, that is, partial differential equation that describes rate of moisture loss and oil uptake was solved numerically using explicit Finite Difference Technique (FDT). Computer codes were written in MATLAB environment for the implementation of FDT at different frying conditions and moisture loss as well as oil uptake simulation during DFF of dodo. Plantain samples were sliced into 5 mm thickness and fried at different frying oil temperatures (150, 160 and 170 ⁰C) for periods varying from 2 to 4 min. The comparison between the predicted results and experimental data for the validation of the model showed reasonable agreement. The correlation coefficients between the predicted and experimental values of moisture and oil transfer models ranging from 0.912 to 0.947 and 0.895 to 0.957, respectively. The predicted results could be further used for the design, control and optimization of deep-fat frying process.

Keywords: frying, moisture loss, modelling, oil uptake

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Authors: M. J. Uddin, M. M. Rahman

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Transient natural convective flow dynamics of nanofluids in a horizontal homocentric annulus using nonhomogeneous dynamic model has been experimented numerically. The simulation is carried out for four different shapes of the inner wall, which is either cylindrical, elliptical, square or triangular. The outer surface of the annulus is maintained at constant low temperature while the inner wall is maintained at a uniform temperature; higher than the outer one. The enclosure is permeated by a uniform magnetic field having variable orientation. The Brownian motion and thermophoretic deposition phenomena of the nanoparticles are taken into account in model construction. The governing nonlinear momentum, energy, and concentration equations are solved numerically using Galerkin weighted residual finite element method. To find the best performer, the local Nusselt number is demonstrated for different shapes of the inner wall. The heat transfer enhancement for different nanofluids for four different shapes of the inner wall is exhibited.

Keywords: nanofluids, annulus, nonhomogeneous dynamic model, heat transfer

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Authors: Subrato Saha, Yun-Hyun Cho

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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: Hyungoo Kang, Minsung Kim, Jinkoo Kim

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This study investigates the performance of a 2D and 3D steel moment frame subjected to vehicle collision at a first story column using LS-DYNA. The finite element models of vehicles provided by the National Crash Analysis Center (NCAC) are used for numerical analysis. Nonlinear dynamic time history analysis of the 2D and 3D model structures are carried out based on the arbitrary column removal scenario, and the vertical displacement of the damaged structures are compared with that obtained from collision analysis. The analysis results show that the model structure remains stable when the speed of the vehicle is 40km/h. However, at the speed of 80 and 120km/h both the 2D and 3D structures collapse by progressive collapse. The vertical displacement of the damaged joint obtained from collision analysis is significantly larger than the displacement computed based on the arbitrary column removal scenario.

Keywords: vehicle collision, progressive collapse, FEM, LS-DYNA

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Authors: Aurore Cauquis, Philippe Heinrich, Mario Ricchiuto, Audrey Gailler

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In this talk, we look for an accurate time scheme to model the propagation of waves. Several numerical schemes have been developed to solve the extended weakly nonlinear weakly dispersive Boussinesq Equations. The temporal schemes used are two Lax-Wendroff schemes, second or third order accurate, two Runge-Kutta schemes of second and third order and a simplified third order accurate Lax-Wendroff scheme. Spatial derivatives are evaluated with fourth order accuracy. The numerical model is applied to two monodimensional benchmarks on a flat bottom. It is also applied to the simulation of the Algerian tsunami generated by a Mw=6 seism on the 18th March 2021. The tsunami propagation was highly dispersive and propagated across the Mediterranean Sea. We study here the effects of the order of temporal discretization on the accuracy of the results and on the time of computation.

Keywords: numerical analysis, tsunami propagation, water wave, boussinesq equations

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Authors: Cha’o-Kuang Chen, Ching-Chang Cho

Abstract:

This paper investigates the natural convection heat transfer performance in a complex-wavy-wall cavity filled with power-law fluid. In performing the simulations, the continuity, Cauchy momentum and energy equations are solved subject to the Boussinesq approximation using a finite volume method. The simulations focus specifically on the effects of the flow behavior index in the power-law model and the Rayleigh number on the flow streamlines, isothermal contours and mean Nusselt number within the cavity. The results show that pseudoplastic fluids have a better heat transfer performance than Newtonian or dilatant fluids. Moreover, it is shown that for Rayleigh numbers greater than Ra=103, the mean Nusselt number has a significantly increase as the flow behavior index is decreased.

Keywords: non-Newtonian fluid, power-law fluid, natural convection, heat transfer enhancement, cavity, wavy wall

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Authors: Kitjapat Phuvoravan, Phattaraphong Ponsorn

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In the design of Castellated beams (CB), the web post buckling acted by horizontal shear force is one of the important failure modes that have to be considered. It is also a dominant governing mode when design following the AISC 31 design guideline which is just published. However, the equation of the web post buckling given by the guideline is still questionable for most of the engineers. So the purpose of this paper is to study and provide a proposed equation for design the web post buckling with more simplified and convenient to use. The study is also including the improper of the safety factor given by the guideline. The proposed design equation is acquired by regression method based on the results of finite element analysis. An amount of Cellular beam simulated to study is modelled by using shell element, analysis with both geometric and material nonlinearity. The results of the study show that the use of the proposed equation to design the web post buckling in Castellated beams is more simple and precise for computation than the equations provided from the guideline.

Keywords: castellated beam, web opening, web post buckling, design equation

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Authors: Waheed Ahmad Safi, Shunichi Nakamura

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Steel/concrete composite bridge with the concrete filled steel I-girder (CFIG) was proposed, and the bending and shear strength was studied by experiments and FEM analysis. The area surrounded by the upper and lower flanges and the web is filled with concrete in CFIG, which is used at the intermediate support of a continuous girder. The bending and shear tests of the CFIG were carried out, showing that the bending strength of CFIG was 2.8 times of the conventional steel I-girder and the shear strength was 3.0 times of the steel I-girder. Finite element models were established to clarify bending and shear behaviors and the load transfer mechanism of CFIG. FEM result agreed very well with the test results. The FEM model was also applied to simulate the shear tests of the CFIG specimens. A trail design was carried out for a four-span continuous highway bridge and the design method was established.

Keywords: bending strength, concrete filled steel I-girder, steel I-girder, FEM, limit states design and shear strength

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Authors: Masoud Nasiri Sarvi, Yunhua Luo

Abstract:

Low-trauma hip fracture, usually caused by fall from standing height, has become a main source of morbidity and mortality for the elderly. Factors affecting hip fracture include sex, race, age, body weight, height, body mass distribution, etc., and thus, hip fracture risk in fall differs widely from subject to subject. It is therefore necessary to develop a subject-specific biomechanical model to predict hip fracture risk. The objective of this study is to develop a two-level, image-based, subject-specific biomechanical model consisting of a whole-body dynamics model and a proximal-femur finite element (FE) model for more accurately assessing the risk of hip fracture in lateral falls. Required information for constructing the model is extracted from a whole-body and a hip DXA (Dual Energy X-ray Absorptiometry) image of the subject. The proposed model considers all parameters subject-specifically, which will provide a fast, accurate, and non-expensive method for predicting hip fracture risk.

Keywords: bone mineral density, hip fracture risk, impact force, sideways falls

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Authors: Dongchuan Su, Hai Xie, Naibin Jiang

Abstract:

Under severe accident cases, the nuclear reactor core may meltdown inside the lower head of the reactor pressure vessel (RPV). Retaining the melt pool inside the RPV is an important strategy of severe accident management. During this process, the inner wall of the lower head will be heated to high temperature of a thousand centigrade, and the outer wall is immersed in a large amount of cooling water. The material of the lower head will have serious creep damage under the high temperature and the temperature difference, and this produces a great threat to the integrity of the RPV. In this paper, the ANSYS program is employed to build the finite element method (FEM) model of the lower head, the creep phenomena is simulated under the severe accident case, the time dependent strain and stress distribution is obtained, the creep damage of the lower head is investigated, the integrity of the RPV is evaluated and the theoretical basis is provided for the optimized design and safety assessment of the RPV.

Keywords: severe accident, lower head of RPV, creep, FEM

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Authors: Alaa Chasib Ghaleb, Muntadher M. Abbood

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This paper presents a study of the problem of the optimum design of piled-raft foundation systems. The study has been carried out using a hypothetic problem and soil investigations of six sites locations in Basrah city to evaluate the adequacy of using the piled-raft foundation concept. Three dimensional finite element analysis method has been used, to perform the structural analysis. The problem is optimized using Hooke and Jeeves method with the total weight of the foundation as objective function and each of raft thickness, piles length, number of piles and piles diameter as design variables. It is found that the total and differential settlement decreases with increasing the raft thickness, the number of piles, the piles length, and the piles diameter. Finally parametric study for load values, load type and raft dimensions have been studied and the results have been discussed.

Keywords: Hooke and Jeeves, optimum design, piled-raft, foundations

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Authors: Shuyi Wu, Chuang Li, Quanshui Zheng, Luping Xu

Abstract:

Stretching and snipping DNA molecule by microfluidic has important application value in gene analysis by lab on a chip. Movement, deformation and fragmenting of DNA in microfluidic are typical fluid-solid coupling problems. An efficient and common simulation system for researching the movement, deformation and fragmenting of DNA by microfluidic has not been well developed. In our study, Brownian dynamics-finite element method (BD-FEM) is used to simulate the dynamic process of stretching and fragmenting DNA by contraction flow. The shape and parameters of micro-channels are changed to optimize the stretching and fragmenting properties of DNA. Our results indicate that strain rate, resulting from contraction microchannel, is the main control parameter for stretching and fragmenting DNA. There is good consistency between the simulation data and previous experimental result about the single DNA molecule behavior and averaged fragmenting properties in this study. BD-FEM method is an efficient calculating tool to research stretching and fragmenting behavior of single DNA molecule and optimize microfluidic devices for manipulating, stretching and fragmenting DNA.

Keywords: fragmenting, DNA, microfluidic, optimize.

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Authors: W. Sun, W. Wen, J. Lu, A. A. Becker

Abstract:

In this work, methods for determining creep properties which can be used to represent the full life until failure from miniature specimen creep tests based on analytical solutions are presented. Examples used to demonstrate the application of the methods include a miniature rectangular thin beam specimen creep test under three-point bending and a miniature two-material tensile specimen creep test subjected to a steady load. Mathematical expressions for deflection and creep strain rate of the two specimens were presented for the Kachanov-Rabotnov creep damage model. On this basis, an inverse procedure was developed which has potential applications for deriving the full life creep damage constitutive properties from a very small volume of material, in particular, for various microstructure constitutive  regions, e.g. within heat-affected zones of power plant pipe weldments. Further work on validation and improvement of the method is addressed.

Keywords: creep damage property, miniature specimen, inverse approach, finite element modeling

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Authors: Muhammad Khairul Anuar Mohamed, Mohd Zuki Salleh, Anuar Ishak, Nor Aida Zuraimi Md Noar

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In this study, the numerical investigation of viscous dissipation on convective boundary layer flow towards a horizontal circular cylinder with constant wall temperature is considered. The transformed partial differential equations are solved numerically by using an implicit finite-difference scheme known as the Keller-box method. Numerical solutions are obtained for the reduced Nusselt number and the skin friction coefficient as well as the velocity and temperature profiles. The features of the flow and heat transfer characteristics for various values of the Prandtl number and Eckert number are analyzed and discussed. The results in this paper is original and important for the researchers working in the area of boundary layer flow and this can be used as reference and also as complement comparison purpose in future.

Keywords: free convection, horizontal circular cylinder, viscous dissipation, convective boundary layer flow

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Authors: Jiaying Zhang, Xin Mu, Chang Ni, Jeff L. Zhang

Abstract:

Magnetic resonance elastography (MRE) non-invasively assesses tissue elastic properties, such as shear modulus, by measuring tissue’s displacement in response to mechanical waves. The estimated metrics on tissue elasticity or stiffness have been shown to be valuable for monitoring physiologic or pathophysiologic status of tissue, such as a tumor or fatty liver. To quantify tissue shear modulus from MRE-acquired displacements (essentially an inverse problem), multiple approaches have been proposed, including Local Frequency Estimation (LFE) and Direct Inversion (DI). However, one common problem with these methods is that the estimates are severely noise-sensitive due to either the inverse-problem nature or noise propagation in the pixel-by-pixel process. With the advent of deep learning (DL) and its promise in solving inverse problems, a few groups in the field of MRE have explored the feasibility of using DL methods for quantifying shear modulus from MRE data. Most of the groups chose to use real MRE data for DL model training and to cut training images into smaller patches, which enriches feature characteristics of training data but inevitably increases computation time and results in outcomes with patched patterns. In this study, simulated wave images generated by Finite Differential Time Domain (FDTD) simulation are used for network training, and U-Net is used to extract features from each training image without cutting it into patches. The use of simulated data for model training has the flexibility of customizing training datasets to match specific applications. The proposed method aimed to estimate tissue shear modulus from MRE data with high robustness to noise and high model-training efficiency. Specifically, a set of 3000 maps of shear modulus (with a range of 1 kPa to 15 kPa) containing randomly positioned objects were simulated, and their corresponding wave images were generated. The two types of data were fed into the training of a U-Net model as its output and input, respectively. For an independently simulated set of 1000 images, the performance of the proposed method against DI and LFE was compared by the relative errors (root mean square error or RMSE divided by averaged shear modulus) between the true shear modulus map and the estimated ones. The results showed that the estimated shear modulus by the proposed method achieved a relative error of 4.91%±0.66%, substantially lower than 78.20%±1.11% by LFE. Using simulated data, the proposed method significantly outperformed LFE and DI in resilience to increasing noise levels and in resolving fine changes of shear modulus. The feasibility of the proposed method was also tested on MRE data acquired from phantoms and from human calf muscles, resulting in maps of shear modulus with low noise. In future work, the method’s performance on phantom and its repeatability on human data will be tested in a more quantitative manner. In conclusion, the proposed method showed much promise in quantifying tissue shear modulus from MRE with high robustness and efficiency.

Keywords: deep learning, magnetic resonance elastography, magnetic resonance imaging, shear modulus estimation

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