Search results for: FVM (Finite Volume Method)

Authors: P. M. Keshtiban, M. Zdshakoyan, G. Faragi

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Different severe plastic deformation (SPD) methods are the most successful ways to build nano-structural materials from coarse grain samples without changing the cross-sectional area. One of the most widely used methods in the SPD process is equal channel angler pressing (ECAP). In this paper, ECAP process on Al1050 sheets was evaluated at room temperature by both experiments and finite element method. Since, one of the main objectives of SPD processes is to achieve high equivalent plastic strain (PEEQ) in one cycle, the values of PEEQ obtained by finite element simulation. Also, force-displacement curve achieved by FEM. To study the changes of mechanical properties, micro-hardness tests were conducted on samples and improvement in the mechanical properties were investigated. Results show that there is the good proportion between FEM, theory and experimental results.

Keywords: AL1050, experiments, finite element method, severe plastic deformation

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Authors: Wiem Zaabi, Yemna Bensalem, Hafedh Trabelsi

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The paper presents a finite element (FE) based efficient analysis procedure for induction machine (IM). The FE formulation approaches are proposed to achieve this goal: the magnetostatic and the non-linear transient time stepped formulations. The study based on finite element models offers much more information on the phenomena characterizing the operation of electrical machines than the classical analytical models. This explains the increase of the interest for the finite element investigations in electrical machines. Based on finite element models, this paper studies the influence of the stator and the rotor faults on the behavior of the IM. In this work, a simple dynamic model for an IM with inter-turn winding fault and a broken bar fault is presented. This fault model is used to study the IM under various fault conditions and severity. The simulation results are conducted to validate the fault model for different levels of fault severity. The comparison of the results obtained by simulation tests allowed verifying the precision of the proposed FEM model. This paper presents a technical method based on Fast Fourier Transform (FFT) analysis of stator current and electromagnetic torque to detect the faults of broken rotor bar. The technique used and the obtained results show clearly the possibility of extracting signatures to detect and locate faults.

Keywords: Finite element Method (FEM), Induction motor (IM), short-circuit fault, broken rotor bar, Fast Fourier Transform (FFT) analysis

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Authors: Mohammad Tahmasebipour, Hosein Salarpour

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Micro cantilevers are one of the components used in the manufacture of micro-electromechanical systems. Epoxy microcantilevers have a variety of applications in the manufacture of micro-sensors and micro-actuators. In this paper, the Timoshenko Micro cantilever was statically and dynamically analyzed using the finite element method. First, all boundary conditions and initial conditions governing micro cantilevers were considered. The effect of size on the deflection, angle of rotation, natural frequencies, and mode shapes were then analyzed and evaluated under different frequencies. It was observed that an increased micro cantilever thickness reduces the deflection, rotation, and resonant frequency. A good agreement was observed between our results and those obtained by the couple stress theory, the classical theory, and the strain gradient elasticity theory.

Keywords: microcantilever, microsensor; epoxy, dynamic behavior, static behavior, finite element method

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Authors: Khaled Saad Eldin Mohamed Ragab

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This paper investigates analytically the torsion behavior of steel fibered high strength self compacting concrete beams reinforced by GFRP bars. Nonlinear finite element analysis on 12­ beams specimens was achieved by using ANSYS software. The nonlinear finite element analysis program ANSYS is utilized owing to its capabilities to predict either the response of reinforced concrete beams in the post elastic range or the ultimate strength of a reinforced concrete beams produced from steel fiber reinforced self compacting concrete (SFRSCC) and reinforced by GFRP bars. A general description of the finite element method, theoretical modeling of concrete and reinforcement are presented. In order to verify the analytical model used in this research using test results of the experimental data, the finite element analysis were performed. Then, a parametric study of the effect ratio of volume fraction of steel fibers in ordinary strength concrete, the effect ratio of volume fraction of steel fibers in high strength concrete, and the type of reinforcement of stirrups were investigated. A comparison between the experimental results and those predicted by the existing models are presented. Results and conclusions thyat may be useful for designers have been raised and represented.

Keywords: nonlinear analysis, torsionally loaded, self compacting concrete, steel fiber reinforced self compacting concrete (SFRSCC), GFRP bars and sheets

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Authors: Zhengyi Kong, Xueqing Wang, Quang-Viet Vu

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In this study, the structural behavior of high strength steel (HSS) hot-finished elliptical hollow section (EHS) subjected to uniaxial eccentric compression is investigated. A finite element method for predicting the cross-section resistance of HSS hot-finished EHS is developed using ABAQUS software, which is then verified by comparison with previous experiments. The validated finite element method is employed to carry out parametric studies for investigating the structural behavior of HSS hot-finished EHS under uniaxial eccentric compression and evaluate the current design guidance for HSS hot-finished EHS. Different parameters, such as the radius of the larger and smaller outer diameter of EHS, thickness of EHS, eccentricity, and material property, are considered. The resulting data from 84 finite element models are used to obtain the relationship between the cross-section resistance of HSS hot-finished EHS and cross-section slenderness. It is concluded that current design provisions, such as EN 1993-1-1, BS 5950-1, AS4100, and Gardner et al., are conservative for predicting the HSS hot-finished EHS under uniaxial eccentric compression.

Keywords: hot-finished, elliptical hollow section, uniaxial eccentric compression, finite element method

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Authors: Mohammad Hadi Jalali, Behrooz Shahriari, Mostafa Ghayour, Saeed Ziaei-Rad, Shahram Yousefi

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Most flexible rotors can be considered as beam-like structures. In many cases, rotors are modeled as one-dimensional bodies, made basically of beam-like shafts with rigid bodies attached to them. This approach is typical of rotor dynamics, both analytical and numerical, and several rotor dynamic codes, based on the finite element method, follow this trend. In this paper, a finite element model based on Timoshenko beam elements is utilized to analyze the lateral dynamic behavior of a certain rotor-bearing system in operating conditions.

Keywords: finite element method, Timoshenko beam elements, operational deflection shape, unbalance response

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Authors: Zineddine Bouyahiaoui, Rabah Haoui

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The aim of this work is to analyze a flow around the axisymmetric blunt body taken into account the chemical and vibrational nonequilibrium flow. This work concerns the entry of spacecraft in the atmosphere of the planet Mars. Since the equations involved are non-linear partial derivatives, the volume method is the only way to solve this problem. The choice of the mesh and the CFL is a condition for the convergence to have the stationary solution.

Keywords: blunt body, finite volume, hypersonic flow, viscous flow

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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: Partha P. Gopmandal, S. Bhattacharyya

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We investigate the thermal end effect on the pseudo-steady state behavior of the isotachophoretic transport of ionic species in a 2-D microchannel. Both ends of the channel are kept at a constant temperature which may lead to significant changes in electrophoretic migration speed. A mathematical model based on Nernst-Planck equations for transport of ions coupled with the equation for temperature field is considered. In addition, the charge conservation equations govern the potential field due to the external electric field. We have computed the equations for ion transport, potential and temperature in a coupled manner through the finite volume method. The diffusive terms are discretized via central difference scheme, while QUICK (Quadratic Upwind Interpolation Convection Kinematics) scheme is used to discretize the convective terms. We find that the thermal end effect has significant effect on the isotachophoretic (ITP) migration speed of the analyte. Our result shows that the ITP velocity for temperature dependent case no longer varies linearly with the applied electric field. A detailed analysis has been made to provide a range of the key parameters to minimize the Joule heating effect on ITP transport of analytes.

Keywords: finite volume method, isotachophoresis, QUICK scheme, thermal effect

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Authors: Mohammadamin Esmaeilzadehazimi, Morteza Shayan Arani, Mohammad Toorani, Aouni Lakis

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This study uses a hybrid finite element method to predict the dynamic behavior of both fully and partially-filled truncated conical shells stiffened with ring stiffeners. The method combines classical shell theory and the finite element method, and employs displacement functions derived from exact solutions of Sanders' shell equilibrium equations for conical shells. The shell-fluid interface is analyzed by utilizing the velocity potential, Bernoulli's equation, and impermeability conditions to determine an explicit expression for fluid pressure. The equations of motion presented in this study apply to both conical and cylindrical shells. This study presents the first comparison of the method applied to ring-stiffened shells with other numerical and experimental findings. Vibration frequencies for conical shells with various boundary conditions and geometries in a vacuum and filled with water are compared with experimental and numerical investigations, achieving good agreement. The study thoroughly investigates the influence of geometric parameters, stiffener quantity, semi-vertex cone angle, level of water filled in the cone, and applied boundary conditions on the natural frequency of fluid-loaded ring-stiffened conical shells, and draws some useful conclusions. The primary advantage of the current method is its use of a minimal number of finite elements while achieving highly accurate results.

Keywords: finite element method, fluid–structure interaction, conical shell, natural frequency, ring-stiffener

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Authors: Armansyah, I. P. Almanar, M. Saiful Bahari Shaari, M. Shamil Jaffarullah

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Finite element approach have been used via three-dimensional models by using Altair Hyper Work, a commercially available software, to describe heat gradients along the welding zones (axially and coronaly) in Friction Stir Welding (FSW). Transient thermal finite element analyses are performed in AA 6061-T6 Aluminum Alloy to obtain temperature distribution in the welded aluminum plates during welding operation. Heat input from tool shoulder and tool pin are considered in the model. A moving heat source with a heat distribution simulating the heat generated by frictions between tool shoulder and work piece is used in the analysis. The developed model was then used to show the effect of various input parameters such as total rate of welding speed and rotational speed on temperature distribution in the work piece.

Keywords: Frictions Stir Welding (FSW), temperature distribution, Finite Element Method (FEM), altair hyperwork

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Authors: Mohamed Hafid, Marcel Lacroix

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This study presents a simple inverse heat transfer procedure for predicting the wall erosion and the time-varying thickness of the protective bank that covers the inside surface of the refractory brick wall of a melting furnace. The direct problem is solved by using the Finite-Volume model. The melting/solidification process is modeled using the enthalpy method. The inverse procedure rests on the Levenberg-Marquardt method combined with the Broyden method. The effect of the location of the temperature sensors and of the measurement noise on the inverse predictions is investigated. Recommendations are made concerning the location of the temperature sensor.

Keywords: melting furnace, inverse heat transfer, enthalpy method, levenberg–marquardt method

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Authors: M. Sasajima, M. Watanabe, T. Yamaguchi Y. Kurosawa, Y. Koike

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In very narrow pathways, the speed of sound propagation and the phase of sound waves change due to the air viscosity. We have developed a new Finite Element Method (FEM) that includes the effects of air viscosity for modeling a narrow sound pathway. This method is developed as an extension of the existing FEM for porous sound-absorbing materials. The numerical calculation results for several three-dimensional slit models using the proposed FEM are validated against existing calculation methods.

Keywords: simulation, FEM, air viscosity, slit

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Authors: Norhashidah Hj Mohd Ali, Teng Wai Ping

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In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two-dimensional Helmholtz equation. The formulation is based on the nine-point fourth-order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation.

Keywords: explicit group method, finite difference, Helmholtz equation, five-point formula, nine-point formula

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Authors: Djamel Remache, Serge Dos Santos, Michael Cliez, Michel Gratton, Patrick Chabrand, Jean-Marie Rossi, Jean-Louis Milan

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Skin tissue is an inhomogeneous and anisotropic material. Uniaxial tensile testing is one of the primary testing techniques for the mechanical characterization of skin at large scales. In order to predict the mechanical behavior of materials, the direct or inverse analytical approaches are often used. However, in case of an inhomogeneous and anisotropic material as skin tissue, analytical approaches are not able to provide solutions. The numerical simulation is thus necessary. In this work, the uniaxial tensile test and the FEM (finite element method) based inverse method were used to identify the anisotropic mechanical properties of porcine skin tissue. The uniaxial tensile experiments were performed using Instron 8800 tensile machine®. The uniaxial tensile test was simulated with FEM, and then the inverse optimization approach (or the inverse calibration) was used for the identification of mechanical properties of the samples. Experimentally results were compared to finite element solutions. The results showed that the finite element model predictions of the mechanical behavior of the tested skin samples were well correlated with experimental results.

Keywords: mechanical skin tissue behavior, uniaxial tensile test, finite element analysis, inverse optimization approach

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Authors: S. Bennoud, M. Zergoug

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The numerical simulation of electromagnetic interactions is still a challenging problem, especially in problems that result in fully three dimensional mathematical models. The goal of this work is to use mathematical modeling to characterize the reliability and capacity of eddy current technique to detect and characterize defects embedded in aeronautical in-service pieces. The finite element method is used for describing the eddy current technique in a mathematical model by the prediction of the eddy current interaction with defects. However, this model is an approximation of the full Maxwell equations. In this study, the analysis of the problem is based on a three dimensional finite element model that computes directly the electromagnetic field distortions due to defects.

Keywords: eddy current, finite element method, non destructive testing, numerical simulations

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Authors: I Made Gatot Karohika, Shigeyuki Haruyama, Ken Kaminishi

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In this study, we proposed a three-layer metal gasket with Al, Cu, and SUS304 as the material, respectively. A finite element method was employed to develop simulation solution and design of experiment (DOE). Taguchi method was used to analysis the effect of each parameter design and predicts optimal design of new 25A-size three layer corrugated metal gasket. The L18 orthogonal array of Taguchi method was applied to design experiment matrix for eight factors with three levels. Based on elastic mode and plastic mode, optimum design gasket is gasket with core metal SUS304, surface layer aluminum, p1 = 4.5 mm, p2 = 4.5 mm, p3 = 4 mm, Tg = 1.2 mm, R = 3.5 mm, h = 0.4 mm and Ts = 0.3 mm.

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

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Authors: Benseghir Omar, Bahmed Mohamed

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In this work, we presented a numerical study of the phenomenon of heat transfer through the laminar, incompressible and steady mixed convection in a closed square cavity with the left vertical wall of the cavity is subjected to a warm temperature, while the right wall is considered to be cold. The horizontal walls are assumed adiabatic. The governing equations were discretized by finite volume method on a staggered mesh and the SIMPLER algorithm was used for the treatment of velocity-pressure coupling. The numerical simulations were performed for a wide range of Reynolds numbers 1, 10, 100, and 1000 numbers are equal to 0.01,0.1 Richardson, 0.5,1 and 10.The analysis of the results shows a flow bicellular (two cells), one is created by the speed of the fan placed in the inner cavity, one on the left is due to the difference between the temperatures right wall and the left wall. Knowledge of the intensity of each of these cells allowed us to get an original result. And the values obtained from each of Nuselt convection which allow to know the rate of heat transfer in the cavity.Finally we find that there is a significant influence on the position of the fan on the heat transfer (Nusselt evolution) for values of Reynolds studied and for low values of Richardson handed this influence is negligible for high values of the latter.

Keywords: thermal transfer, mixed convection, square cavity, finite volume method

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Authors: Shangerganesh Lingeshwaran

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In this presentation, we have performed numerical simulations for a reaction-diffusion equation with various nonlinear density-dependent diffusion operators and proliferation functions. The mathematical model represented by parabolic partial differential equation is considered to study the invasion of gliomas (the most common type of brain tumors) and to describe the growth of cancer cells and response to their treatment. The unknown quantity of the given reaction-diffusion equation is the density of cancer cells and the mathematical model based on the proliferation and migration of glioma cells. A standard Galerkin finite element method is used to perform the numerical simulations of the given model. Finally, important observations on the each of nonlinear diffusion functions and proliferation functions are presented with the help of computational results.

Keywords: glioma invasion, nonlinear diffusion, reaction-diffusion, finite eleament method

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Authors: A. Fettahoglu

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Theory of viscoelasticity is used by many researchers to represent the behavior of many materials such as pavements on roads or bridges. Several researches used analytical methods and rheology to predict the material behaviors of simple models. Today, more complex engineering structures are analyzed using Finite Element Method, in which material behavior is embedded by means of three dimensional viscoelastic material laws. As a result, structures of unordinary geometry and domain can be analyzed by means of Finite Element Method and three dimensional viscoelastic equations. In the scope of this study, rheological models embedded in ANSYS, namely, generalized Maxwell model and Prony series, which are two methods used by ANSYS to represent viscoelastic material behavior, are presented explicitly. Afterwards, a guide is illustrated to ease using of viscoelasticity tool in ANSYS.

Keywords: ANSYS, generalized Maxwell model, finite element method, Prony series, viscoelasticity, viscoelastic material curve fitting

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Authors: Aymen Laadhari

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We present in this paper a fully implicit finite element method tailored for the numerical modeling of inextensible fluidic membranes in a surrounding Newtonian fluid. We consider a highly simplified version of the Canham-Helfrich model for phospholipid membranes, in which the bending force and spontaneous curvature are disregarded. The coupled problem is formulated in a fully Eulerian framework and the membrane motion is tracked using the level set method. The resulting nonlinear problem is solved by a Newton-Raphson strategy, featuring a quadratic convergence behavior. A monolithic solver is implemented, and we report several numerical experiments aimed at model validation and illustrating the accuracy of the proposed method. We show that stability is maintained for significantly larger time steps with respect to an explicit decoupling method.

Keywords: finite element method, level set, Newton, membrane

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Authors: Henrique C. C. Andrade, Ana Beatriz C. G. Silva, Fernando Luiz B. Ribeiro, Samir Maghous, Jose Claudio F. Telles, Eduardo M. R. Fairbairn

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The present paper aims at developing a parallel computational model for numerical simulation of poromechanics analyses of heterogeneous reservoirs. In the context of macroscopic poroelastoplasticity, the hydromechanical coupling between the skeleton deformation and the fluid pressure is addressed by means of two constitutive equations. The first state equation relates the stress to skeleton strain and pore pressure, while the second state equation relates the Lagrangian porosity change to skeleton volume strain and pore pressure. A specific algorithm for local plastic integration using a tangent operator is devised. A modified Cam-clay type yield surface with associated plastic flow rule is adopted to account for both contractive and dilative behavior.

Keywords: finite element method, poromechanics, poroplasticity, reservoir analysis

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Authors: Nikhil Padhye, Ellen Kintz, Dan Dorci

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Recent years have seen a rising interest in study and applications of materially uniform thin-structures (plates/shells) subject to finite-bending and stretching deformations. We introduce a well-posed 2D-model involving finite-bending and stretching of thin-structures to approximate the three-dimensional equilibria. Key features of this approach include: Non-Uniform Rational B-Spline (NURBS)-based spatial discretization for finite elements, method of dynamic relaxation to predict stable equilibria, and no a priori kinematic assumption on the deformation fields. The approach is validated against the benchmark problems,and the use of NURBS for spatial discretization facilitates exact spatial representation and computation of curvatures (due to C1-continuity of interpolated displacements) for this higher-order accuracy 2D-model.

Keywords: Isogeometric Analysis, Plates/Shells , Finite Element Methods, Dynamic Relaxation

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Authors: Djalal Hamed

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The aim of this paper is to perform, by mean of the finite volume method, a numerical solution of the transient natural convection in a narrow rectangular channel between two vertical parallel Material Testing Reactor (MTR)-type fuel plates, imposed under a heat flux with a cosine shape to determine the margin of the nuclear core power at which the natural convection cooling mode can ensure a safe core cooling, where the cladding temperature should not reach a specific safety limits (90 °C). For this purpose, a computer program is developed to determine the principal parameters related to the nuclear core safety, such as the temperature distribution in the fuel plate and in the coolant (light water) as a function of the reactor core power. Throughout the obtained results, we noticed that the core power should not reach 400 kW, to ensure a safe passive residual heat removing from the nuclear core by the upward natural convection cooling mode.

Keywords: buoyancy force, friction force, finite volume method, transient natural convection

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Authors: Temami Oussama, Bessais Lakhdar, Hamadi Djamal, Abderrahmani Sifeddine

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The analysis of complex structures encourages the engineer to make simplifying assumptions, sometimes attempting the analysis of the whole structure as complex as it is, and it can be done using the finite element method (FEM). In the modeling of complex structures by finite elements, various elements can be used: beam element, membrane element, solid element, plates and shells elements. These elements formulated according to the classical formulation and do not generally share the same nodal degrees of freedom, which complicates the development of a compatible model. The compatibility of the elements with each other is often a difficult problem for modeling complicated structure. This compatibility is necessary to ensure the convergence. To overcome this problem, we have proposed finite elements with a rotational degree of freedom. The study used is based on the strain approach formulation with 2D and 3D formulation with different degrees of freedom at each node. For the comparison and confrontation of results; the finite elements available in ABAQUS/Standard are used.

Keywords: compatibility requirement, complex structures, finite elements, modeling, strain approach

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Authors: D. B. Gohil

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Closed die forging is a very complex process, and measurement of actual forces for real material is difficult and time consuming. Hence, the modelling technique has taken the advantage of carrying out the experimentation with the proper model material which needs lesser forces and relatively low temperature. The results of experiments on the model material then may be correlated with the actual material by using the theory of similarity. There are several methods available to resolve the complexity involved in the closed die forging process. Finite Element Method (FEM) and Finite Difference Method (FDM) are relatively difficult as compared to the slab method. The slab method is very popular and very widely used by the people working on shop floor because it is relatively easy to apply and reasonably accurate for most of the common forging load requirement computations.

Keywords: experimentation, forging, process modeling, strain distribution

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Authors: Mahzabin Afroz, Indubhushan Patnaikuni, Srikanth Venkatesan

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It is well-known that fly ash can be used in high volume as a partial replacement of cement to get beneficial effects on concrete. High volume fly ash (HVFA) concrete is currently emerging as a popular option to strengthen by fiber. Although studies have supported the use of fibers with fly ash, a unified model along with the incorporation into finite element software package to estimate the maximum flexural loads need to be developed. In this study, nonlinear finite element analysis of steel fiber reinforced high strength HVFA concrete beam under static loadings was conducted to investigate their failure modes in terms of ultimate load. First of all, the experimental investigation of mechanical properties of high strength HVFA concrete was done and validates with developed numerical model with the appropriate modeling of element size and mesh by ANSYS 16.2. To model the fiber within the concrete, three-dimensional random fiber distribution was simulated by spherical coordinate system. Three types of high strength HVFA concrete beams were analyzed reinforced with 0.5, 1 and 1.5% volume fractions of steel fibers with specific mechanical and physical properties. The result reveals that the use of nonlinear finite element analysis technique and three-dimensional random fiber orientation exhibited fairly good agreement with the experimental results of flexural strength, load deflection and crack propagation mechanism. By utilizing this improved model, it is possible to determine the flexural behavior of different types and proportions of steel fiber reinforced HVFA concrete beam under static load. So, this paper has the originality to predict the flexural properties of steel fiber reinforced high strength HVFA concrete by numerical simulations.

Keywords: finite element analysis, high volume fly ash, steel fibers, spherical coordinate system

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Authors: Sendi Zohra, Belhadjsalah Hedi, Labergere Carl, Saanouni Khemais

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The modeling of mechanical problems including both material and geometric nonlinearities with Finite Element Method (FEM) remains challenging. Meshless methods offer special properties to get rid of well-known drawbacks of the FEM. The main objective of Meshless Methods is to eliminate the difficulty of meshing and remeshing the entire structure by simply insertion or deletion of nodes, and alleviate other problems associated with the FEM, such as element distortion, locking and others. In this study, a robust numerical implementation of an Element Free Galerkin Method for an elastoplastic coupled to damage problem is presented. Several results issued from the numerical simulations by a DynamicExplicit resolution scheme are analyzed and critically compared with Element Finite Method results. Finally, different numerical examples are carried out to demonstrate the efficiency of this method.

Keywords: damage, dynamic explicit, elastoplasticity, isotropic hardening, meshless

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Authors: Mahmoud Lot

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In this article, we will discuss the solution of elliptic optimal control problem. First, by using the nite element method, we obtain the discrete form of the problem. The obtained discrete problem is actually a large scale constrained optimization problem. Solving this optimization problem with traditional methods is difficult and requires a lot of CPU time and memory. But split Bergman method converts the constrained problem to an unconstrained, and hence it saves time and memory requirement. Then we use the split Bregman method for solving this problem, and examples show the speed and accuracy of split Bregman methods for solving these types of problems. We also use the SQP method for solving the examples and compare with the split Bregman method.

Keywords: Split Bregman Method, optimal control with elliptic partial differential equation constraint, finite element method

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Authors: Isa Ahmadi, Ramin Khamedi

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In this paper, the elasto-plastic and cyclic torsion of a shaft is studied using a finite element method. The Prager kinematic hardening theory of plasticity with the Ramberg and Osgood stress-strain equation is used to evaluate the cyclic loading behavior of the shaft under the torsional loading. The material of shaft is assumed to follow the non-linear strain hardening property based on the Prager model. The finite element method with C1 continuity is developed and used for solution of the governing equations of the problem. The successive substitution iterative method is used to calculate the distribution of stresses and plastic strains in the shaft due to cyclic loads. The shear stress, effective stress, residual stress and elastic and plastic shear strain distribution are presented in the numerical results.

Keywords: cyclic loading, finite element analysis, Prager kinematic hardening model, torsion of shaft

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