Search results for: finite element methods

Authors: Abdelaziz Guerrouat, Harald Richter

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In this paper test generation methods and appropriate fault models for testing and analysis of embedded systems described as (extended) finite state machines ((E)FSMs) are presented. Compared to simple FSMs, EFSMs specify not only the control flow but also the data flow. Thus, we define a two-level fault model to cover both aspects. The goal of this paper is to reuse well-known FSM-based test generation methods for automation of embedded system testing. These methods have been widely used in testing and validation of protocols and communicating systems. In particular, (E)FSMs-based specification and testing is more advantageous because (E)FSMs support the formal semantic of already standardised formal description techniques (FDTs) despite of their popularity in the design of hardware and software systems.

Keywords: Formal methods, testing and validation, finite state machines, formal description techniques.

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Authors: Anish H. Gandhi, Harit K. Raval

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Carbon steel is used in boilers, pressure vessels, heat exchangers, piping, structural elements and other moderatetemperature service systems in which good strength and ductility are desired. ASME Boiler and Pressure Vessel Code, Section II Part A (2004) provides specifications of ferrous materials for construction of pressure equipment, covering wide range of mechanical properties including high strength materials for power plants application. However, increased level of springback is one of the major problems in fabricating components of high strength steel using bending. Presented work discuss the springback simulations for five different steels (i.e. SA-36, SA-299, SA-515 grade 70, SA-612 and SA-724 grade B) using finite element analysis of air V-bending. Analytical springback simulations of hypothetical layered materials are presented. Result shows that; (i) combination of the material property parameters controls the springback, (ii) layer of the high ductility steel on the high strength steel greatly suppresses the springback.

Keywords: Carbon steel, Finite element analysis, Layeredmaterial, Springback

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Authors: Jin Sup Kim, Woo Young Jung, Minho Kwon

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In general dynamic analyses, lower mode response is of interest, however the higher modes of spatially discretized equations generally do not represent the real behavior and not affects to global response much. Some implicit algorithms, therefore, are introduced to filter out the high-frequency modes using intended numerical error. The objective of this study is to introduce the P-method and PC α-method to compare that with dissipation method and Newmark method through the stability analysis and numerical example. PC α-method gives more accuracy than other methods because it based on the α-method inherits the superior properties of the implicit α-method. In finite element analysis, the PC α-method is more useful than other methods because it is the explicit scheme and it achieves the second order accuracy and numerical damping simultaneously.

Keywords: Dynamic, α-Method, P-Method, PC α-Method, Newmark method.

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Authors: Thomas Jin-Chee Liu, Yu-Shen Chen

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Using the numerical and experimental methods, this paper discusses some primary studies on the vibration and cooling performances of the piezoelectric cooling fan with the rectangular blade. When the fan works at its natural frequency, the vibrating displacement is largest and the cooling performance is best. Due to the vibration behavior, the cooling performance is affected by the geometry, material property, and working frequency of the piezoelectric cooling fan. 

Keywords: Piezoelectric cooling fan, finite element, vibration, natural frequency.

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Authors: Ming Wen, Nasim Nezamoddini

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Sophisticated numerical simulations like finite element analysis (FEA) involve a complicated process from model setup to post-processing tasks that require replication of time-consuming steps. Utilizing FEA automation program simplifies the complexity of the involved steps while minimizing human errors in analysis set up, calculations, and results processing. One of the main challenges in designing FEA automation programs is to identify user requirements and link them to possible design alternatives. This paper presents a decision-making framework to design a Python based FEA automation program for modal analysis, frequency response analysis, and random vibration fatigue (RVF) analysis procedures. Analytical hierarchy process (AHP) and technique for order preference by similarity to ideal solution (TOPSIS) are applied to evaluate design alternatives considering the feedback received from experts and program users.

Keywords: FEA, random vibration fatigue, process automation, AHP, TOPSIS, multiple-criteria decision-making, MCDM.

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Authors: S. Boria

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In the last years, the crashworthiness of an automotive body structure can be improved, since the beginning of the design stage, thanks to the development of specific optimization tools. It is well known how the finite element codes can help the designer to investigate the crashing performance of structures under dynamic impact. Therefore, by coupling nonlinear mathematical programming procedure and statistical techniques with FE simulations, it is possible to optimize the design with reduced number of analytical evaluations. In engineering applications, many optimization methods which are based on statistical techniques and utilize estimated models, called meta-models, are quickly spreading. A meta-model is an approximation of a detailed simulation model based on a dataset of input, identified by the design of experiments (DOE); the number of simulations needed to build it depends on the number of variables. Among the various types of meta-modeling techniques, Kriging method seems to be excellent in accuracy, robustness and efficiency compared to other ones when applied to crashworthiness optimization. Therefore the application of such meta-model was used in this work, in order to improve the structural optimization of a bumper for a racing car in composite material subjected to frontal impact. The specific energy absorption represents the objective function to maximize and the geometrical parameters subjected to some design constraints are the design variables. LS-DYNA codes were interfaced with LS-OPT tool in order to find the optimized solution, through the use of a domain reduction strategy. With the use of the Kriging meta-model the crashworthiness characteristic of the composite bumper was improved.

Keywords: Composite material, crashworthiness, finite element analysis, optimization.

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Authors: A.H. Akhaveissy

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Nonlinear finite element method and Serendipity eight nodes element are used for determining of ground surface settlement due to tunneling. Linear element with elastic behavior is used for modeling of lining. Modified Generalized plasticity model with nonassociated flow rule is applied for analysis of a tunnel in Sao Paulo – Brazil. The tunnel had analyzed by Lades- model with 16 parameters. In this work modified Generalized Plasticity is used with 10 parameters, also Mohr-Coulomb model is used to analysis the tunnel. The results show good agreement with observed results of field data by modified Generalized Plasticity model than other models. The obtained result by Mohr-Coulomb model shows less settlement than other model due to excavation.

Keywords: Non-associated flow rule, Generalized plasticity, tunnel excavation, Excavation method.

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Authors: R. Ziaie Moayed, A. Mahigir

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Stone column technique has been successfully employed to improve the load-settlement characteristics of foundations. A series of finite element numerical analyses of harmonic dynamic loading have been conducted on strengthened raft footing to study the effects of single and group stone columns on settlement of circular footings. The settlement of circular raft footing that improved by single and group of stone columns are studied under harmonic dynamic loading. This loading is caused by heavy machinery foundations. A detailed numerical investigation on behavior of single column and group of stone columns is carried out by varying parameters like weight of machinery, loading frequency and period. The result implies that presence of single and group of stone columns enhanced dynamic behavior of the footing so that the maximum and residual settlement of footing significantly decreased. 

Keywords: Finite element analysis, harmonic loading, settlement, stone column.

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Authors: Liu Ying-jie, Lu Wen-bo, Peng Cheng-jian

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With the development of the automotive technology and electric vehicle, the contribution of the wind noise on the interior noise becomes the main source of noise. The main transfer path which the exterior excitation is transmitted through is the greenhouse panels and side windows. Simulating the wind noise transmitted into the vehicle accurately in the early development stage can be very challenging. The basic methodologies of this study were based on the Lighthill analogy; the exterior flow field around a passenger car was computed using unsteady Computational Fluid Dynamics (CFD) firstly and then a Finite Element Method (FEM) was used to compute the interior acoustic response. The major findings of this study include: 1) The Sound Pressure Level (SPL) response at driver’s ear locations is mainly induced by the turbulence pressure fluctuation; 2) Peaks were found over the full frequency range. It is found that the methodology used in this study could predict the interior wind noise induced by the exterior aerodynamic excitation in industry.

Keywords: Wind noise, computational fluid dynamics, finite element method, passenger car.

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Authors: Remigijus Janulionis, Marijus Šeporaitis, Aleksandra Legha, Raimundas Ručys

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All types of farms have a waste problem. Livestock farms have huge amounts of manure and vegetable farms have to deal with inedible parts of vegetables or rotten, damaged and unacceptable vegetable waste. All of this waste needs to be disposed of safely, ecologically, and as quickly as possible. One of the options is composting using bioreactors, which are rotating drum composters. This type of composting allows biodegradable waste to be disposed of quickly and in an environmentally friendly manner, turning it into a useful product such as soil fertilizer or livestock bedding. This paper presents the fatigue and stiffness analysis of a rotating drum composter. The analysis was performed using a 3D finite element model. It was found that the analyzed composter design has good mechanical strength, good fatigue strength for a cylinder, and acceptable fatigue strength for tire rings. The deformation analysis of the cylinder indicated that the front and rear door support mechanisms should allow the positioning angle to be changed to ensure tightness.

Keywords: 3D modeling, fatigue, Finite Element Method, Goodman’s diagram.

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Authors: Kazeem K. Adewole, Steve J. Bull

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Tensile armour wires provide a flexible pipe's resistance to longitudinal stresses. Flexible pipe manufacturers need to know the effect of defects such as scratches and cracks, with dimensions less than 0.2mm which is the limit of the current nondestructive detection technology, on the fracture stress and fracture strain of the wire for quality assurance purposes. Recent research involving the determination of the fracture strength of cracked wires employed laboratory testing and classical fracture mechanics approach using non-standardised fracture mechanics specimens because standard test specimens could not be manufactured from the wires owing to their sizes. In this work, the effect of miniature cracks on the fracture properties of tensile armour wires was investigated using laboratory and finite element tensile testing simulations with the phenomenological shear fracture model. The investigation revealed that the presence of cracks shallower than 0.2mm is worse on the fracture strain of the wire.

Keywords: Cracks, Finite Element Simulations, Fracture Mechanics, Shear Fracture Model, Tensile Armour Wire

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Authors: M. Chaichanyut, S. Tungjitkusolmun

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This paper is concerned with microwave (MW) ablation for a liver cancer tissue by using helix antenna. The antenna structure supports the propagation of microwave energy at 2.45 GHz. A 1½ turn spiral catheter-based microwave antenna applicator has been developed. We utilize the three-dimensional finite element method (3D FEM) simulation to analyze where the tissue heat flux, lesion pattern and volume destruction during MW ablation. The configurations of helix antenna where Helix air-core antenna and Helix Dielectric-core antenna. The 3D FEMs solutions were based on Maxwell and bio-heat equations. The simulation protocol was power control (10 W, 300s). Our simulation result, both helix antennas have heat flux occurred around the helix antenna and that can be induced the temperature distribution similar (teardrop). The region where the temperature exceeds 50°C the microwave ablation was successful (i.e. complete destruction). The Helix air-core antenna and Helix Dielectric-core antenna, ablation zone or axial ratios (Widest/length) were respectively 0.82 and 0.85; the complete destructions were respectively 4.18 cm³ and 5.64 cm³

Keywords: Liver cancer, Helix antenna, Finite element, Microwave ablation.

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Authors: Yee-Ting Lee, Jyun-Rong Zhuang, Wen-Hsin Hsieh, An-Shik Yang

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Additive manufacturing (AM) is increasingly crucial in biomedical and aerospace industries. As a recently developed AM technique, selective laser melting (SLM) has become a commercial method for various manufacturing processes. However, the molten pool configuration during SLM of metal powders is a decisive issue for the product quality. It is very important to investigate the heat transfer characteristics during the laser heating process. In this work, the finite element method (FEM) software ANSYS^® (work bench module 16.0) was used to predict the unsteady temperature distribution for resolving molten pool dimensions with consideration of temperature-dependent thermal physical properties of TiAl6V4 at different laser powers and scanning speeds. The simulated results of the temperature distributions illustrated that the ratio of laser power to scanning speed can greatly influence the size of molten pool of titanium alloy powder for SLM development.

Keywords: Additive manufacturing, finite element method, molten pool dimensions, selective laser melting.

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Authors: Gökhan Yüksel, Serdar Akça, İlker Kalkan

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The present study is an attempt to demonstrate the significant levels of contribution of the moment-resisting beam-column connections with side plates to the earthquake behavior of special steel moment frames. To this end, the moment-curvature relationships of a regular beam-column connection and its SidePlate counterpart were determined with the help of finite element analyses. The connection stiffness and deformability values from these finite element analyses were used in the linear time-history analyses of an example structural steel frame under three different seismic excitations. The top-story lateral drift, base shear, and overturning moment values in two orthogonal directions were obtained from these time-history analyses and compared to each other. The results revealed the improvements in the system response with the use of SidePlate connections. The paper ends with crucial recommendations for the plan and design of further studies on this very topic.

Keywords: Seismic detailing, special moment frame, steel structures, beam-column connection, earthquake-resistant design.

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Authors: K. V. Pagalthivarthi, R. J. Visintainer

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Two-dimensional Eulerian (volume-averaged) continuity and momentum equations governing multi-size slurry flow through pump casings are solved by applying a penalty finite element formulation. The computational strategy validated for multi-phase flow through rectangular channels is adapted to the present study.   The flow fields of the carrier, mixture and each solids species, and the concentration field of each species are determined sequentially in an iterative manner. The eddy viscosity field computed using Spalart-Allmaras model for the pure carrier phase is modified for the presence of particles. Streamline upwind Petrov-Galerkin formulation is used for all the momentum equations for the carrier, mixture and each solids species and the concentration field for each species. After ensuring mesh-independence of solutions, results of multi-size particulate flow simulation are presented to bring out the effect of bulk flow rate, average inlet concentration, and inlet particle size distribution. Mono-size computations using (1) the concentration-weighted mean diameter of the slurry and (2) the D50 size of the slurry are also presented for comparison with multi-size results.

Keywords: Eulerian-Eulerian model, Multi-size particulate flow, Penalty finite elements, Pump casing, Spalart-Allmaras.

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Authors: Jawad Saleem, Abdul Majid, Kent Bertilsson, Torbjörn Carlberg, Nazar Ul Islam

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Resistance spot welding process comprises of electric, thermal and mechanical phenomenon, which makes this process complex and highly non-linear and thus, it becomes difficult to model it. In order to obtain good weld nugget during spot welding, hit and trial welds are usually done which is very costly. Therefore the numerical simulation research has been conducted to understand the whole process. In this paper three different cases were analyzed by varying the tip contact area and it was observed that, with the variation of tip contact area the nugget formation at the faying surface is affected. The tip contact area of the welding electrode becomes large with long welding cycles. Therefore in order to maintain consistency of nugget formation during the welding process, the current compensation in control feedback is required. If the contact area of the welding electrode tip is reduced, a large amount of current flows through the faying surface, as a result of which sputtering occurs.

Keywords: Resistance spot welding, Finite element modeling, Nugget formation, Welding electrode, Numerical method simulation,

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Authors: A. Gherbi, L. Dahmani, A. Boudjemia

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This paper presents the Finite Element Method (FEM) for analyzing the failure pattern of rectangular slab with various edge conditions. Non-Linear static analysis is carried out using ANSYS 15 Software. Using SOLID65 solid elements, the compressive crushing of concrete is facilitated using plasticity algorithm, while the concrete cracking in tension zone is accommodated by the nonlinear material model. Smeared reinforcement is used and introduced as a percentage of steel embedded in concrete slab. The behavior of the analyzed concrete slab has been observed in terms of the crack pattern and displacement for various loading and boundary conditions. The finite element results are also compared with the experimental data. One of the other objectives of the present study is to show how similar the crack path found by ANSYS program to those observed for the yield line analysis. The smeared reinforcement method is found to be more practical especially for the layered elements like concrete slabs. The value of this method is that it does not require explicit modeling of the rebar, and thus a much coarser mesh can be defined.

Keywords: ANSYS, cracking pattern, displacements, RC Slab, smeared reinforcement.

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Authors: W. Lai, A. A. Khan

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A water surface slope limiting scheme is tested and compared with the water depth slope limiter for the solution of one dimensional shallow water equations with bottom slope source term. Numerical schemes based on the total variation diminishing Runge- Kutta discontinuous Galerkin finite element method with slope limiter schemes based on water surface slope and water depth are used to solve one-dimensional shallow water equations. For each slope limiter, three different Riemann solvers based on HLL, LF, and Roe flux functions are used. The proposed water surface based slope limiter scheme is easy to implement and shows better conservation property compared to the slope limiter based on water depth. Of the three flux functions, the Roe approximation provides the best results while the LF function proves to be least suitable when used with either slope limiter scheme.

Keywords: Discontinuous finite element, TVD Runge-Kuttascheme, slope limiters, Riemann solvers, shallow water flow.

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Authors: Huma Kanta Mishra, Akira Igarashi

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A seismic isolation pad produced by utilizing the scrap tire rubber which contains interleaved steel reinforcing cords has been proposed. The steel cords are expected to function similar to the steel plates used in conventional laminated rubber bearings. The scrap tire rubber pad (STRP) isolator is intended to be used in low rise residential buildings of highly seismic areas of the developing countries. Experimental investigation was conducted on unbonded STRP isolators, and test results provided useful information including stiffness, damping values and an eventual instability of the isolation unit. Finite element analysis (FE analysis) of STRP isolator was carried out on properly bonded samples. These types of isolators provide positive incremental force resisting capacity up to shear strain level of 155%. This paper briefly discusses the force deformation behavior of bonded STRP isolators including stability of the isolation unit.

Keywords: base isolation, buckling load, finite element analysis, STRP isolators.

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Authors: A. Abdel-Moniem, H. Madkour, K. Farah, A. Abdullah

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The reduction in dapped end beams depth nearby the supports tends to produce stress concentration and hence results in shear cracks, if it does not have an adequate reinforcement detailing. This study investigates numerically the efficiency of applying different external strengthening techniques to the dapped end of such beams. A two-dimensional finite element model was built to predict the structural behavior of dapped ends strengthened with different techniques. The techniques included external bonding of the steel angle at the re-entrant corner, un-bounded bolt anchoring, external steel plate jacketing, exterior carbon fiber wrapping and/or stripping and external inclined steel plates. The FE analysis results are then presented in terms of the ultimate load capacities, load-deflection and crack pattern at failure. The results showed that the FE model, at various stages, was found to be comparable to the available test data. Moreover, it enabled the capture of the failure progress, with acceptable accuracy, which is very difficult in a laboratory test.

Keywords: Dapped-end beams, finite element, shear failure, strengthening techniques, reinforced concrete, numerical investigation.

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Authors: Md R. Bashar, Yan Li, Peng Wen

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This study is to investigate the electroencephalogram (EEG) differences generated from a normal and Alzheimer-s disease (AD) sources. We also investigate the effects of brain tissue distortions due to AD on EEG. We develop a realistic head model from T1 weighted magnetic resonance imaging (MRI) using finite element method (FEM) for normal source (somatosensory cortex (SC) in parietal lobe) and AD sources (right amygdala (RA) and left amygdala (LA) in medial temporal lobe). Then, we compare the AD sourced EEGs to the SC sourced EEG for studying the nature of potential changes due to sources and 5% to 20% brain tissue distortions. We find an average of 0.15 magnification errors produced by AD sourced EEGs. Different brain tissue distortion models also generate the maximum 0.07 magnification. EEGs obtained from AD sources and different brain tissue distortion levels vary scalp potentials from normal source, and the electrodes residing in parietal and temporal lobes are more sensitive than other electrodes for AD sourced EEG.

Keywords: Alzheimer's disease (AD), brain tissue distortion, electroencephalogram, finite element method.

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Authors: Kaveh PourAkbar Saffar, Nima JamilPour, Ahmad Raeisi Najafi, Gholamreza Rouhi, Ahmad Reza Arshi, Abdolhossein Fereidoon

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The presence of chemical bonding between functionalized carbon nanotubes and matrix in carbon nanotube reinforced composites is modeled by elastic beam elements representing covalent bonding characteristics. Neglecting other reinforcing mechanisms in the composite such as relatively weak interatomic Van der Waals forces, this model shows close results to the Rule of Mixtures model-s prediction for effective Young-s modulus of a Representative Volume Element of composite for small volume fractions (~1%) and high aspect ratios (L/D>200) of CNTs.

Keywords: Beam Element, Carbon Nanotube Reinforced Composite, Cross-link, Young's modulus.

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Authors: Mahdi Fakoor, Seyed Mohammad Navid Ghoreishi

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Composite patching is a common way for reinforcing the cracked pipes and cylinders. The effects of composite patch reinforcement on fracture parameters of a cracked pipe depend on a variety of parameters such as number of layers, angle, thickness, and material of each layer. Therefore, stacking sequence optimization of composite patch becomes crucial for the applications of cracked pipes. In this study, in order to obtain the optimal stacking sequence for a composite patch that has minimum weight and maximum resistance in propagation of cracks, a coupled Multi-Objective Genetic Algorithm (MOGA) and Finite Element Method (FEM) process is proposed. This optimization process has done for longitudinal and transverse semi-elliptical cracks and optimal stacking sequences and Pareto’s front for each kind of cracks are presented. The proposed algorithm is validated against collected results from the existing literature.

Keywords: Multi objective optimization, Pareto front, composite patch, cracked pipe.

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Authors: T. Yilmaz, N. Kirac

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Beam-column elements are defined as structural members subjected to a combination of axial and bending forces. Lateral torsional buckling is one of the major failure modes in which beam-columns that are bent about its strong axis may buckle out of the plane by deflecting laterally and twisting. This study presents a compact closed-form equation that it can be used for calculating critical lateral torsional-buckling load of beam-columns with monosymmetric sections in the presence of a known axial load. Lateral-torsional buckling behavior of beam-columns subjected to constant axial force and various transverse load cases are investigated by using Ritz method in order to establish proposed equation. Lateral-torsional buckling loads calculated by presented formula are compared to finite element model results. ABAQUS software is utilized to generate finite element models of beam-columns. It is found out that lateral-torsional buckling load of beam-columns with monosymmetric sections can be determined by proposed equation and can be safely used in design.

Keywords: Lateral-torsional buckling, stability, beam-column, monosymmetric section.

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Authors: Muhammad Naseem Baig, Abdul Qudoos Khan, Jamal Ali

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Ground deformations in deep excavations are affected by wall stiffness and pile embedment ratio. This paper presents the findings of a parametric study of a 64-ft deep excavation in mixed stiff soil conditions supported by cantilever pile wall. A series of finite element analysis has been carried out in Plaxis 2D by varying the pile embedment ratio and wall stiffness. It has been observed that maximum wall deflections decrease by increasing the embedment ratio up to 1.50; however, any further increase in pile length does not improve the performance of the wall. Similarly, increasing wall stiffness reduces the wall deformations and affects the deflection patterns of the wall. The finite element analysis results are compared with the field data of 25 case studies of cantilever walls. Analysis results fall within the range of normalized wall deflections of the 25 case studies. It has been concluded that deep excavations can be supported by cantilever walls provided the system stiffness is increased significantly.

Keywords: Excavations, support systems, wall stiffness, cantilever walls.

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Authors: M. Lashgari

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Steel plate shear walls (SPSWs) in buildings are known to be an effective means for resisting lateral forces. By using un-stiffened walls and allowing them to buckle, their energy absorption capacity will increase significantly due to the postbuckling capacity. The post-buckling tension field action of SPSWs can provide substantial strength, stiffness and ductility. This paper presents the Finite Element Analysis of low yield point (LYP) steel shear walls. In this shear wall system, the LYP steel plate is used for the steel panel and conventional structural steel is used for boundary frames. A series of nonlinear cyclic analyses were carried out to obtain the stiffness, strength, deformation capacity, and energy dissipation capacity of the LYP steel shear wall. The effect of widthto- thickness ratio of steel plate on buckling behavior, and energy dissipation capacities were studied. Good energy dissipation and deformation capacities were obtained for all models.

Keywords: low yield point steel, steel plate shear wall, thin plates, elastic buckling, inelastic buckling, post-buckling.

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Authors: Esmaeil Poursaeidi, Mostafa Kamalzadeh Yazdi

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Different problems may causes distortion of the rotor, and hence vibration, which is the most severe damage of the turbine rotors. In many years different techniques have been developed for the straightening of bent rotors. The method for straightening can be selected according to initial information from preliminary inspections and tests such as nondestructive tests, chemical analysis, run out tests and also a knowledge of the shaft material. This article covers the various causes of excessive bends and then some applicable common straightening methods are reviewed. Finally, hot spotting is opted for a particular bent rotor. A 325 MW steam turbine rotor is modeled and finite element analyses are arranged to investigate this straightening process. Results of experimental data show that performing the exact hot spot straightening process reduced the bending of the rotor significantly.

Keywords: Distortion, FEM, Hot Spot Area, Rotor Straightening

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Authors: Djamal Hamadi, Sifeddine Abderrahmani, Toufik Maalem, Oussama Temami

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In recent years many finite elements have been developed for plate bending analysis. The formulated elements are based on the strain based approach. This approach leads to the representation of the displacements by higher order polynomial terms without the need for the introduction of additional internal and unnecessary degrees of freedom. Good convergence can also be obtained when the results are compared with those obtained from the corresponding displacement based elements, having the same total number of degrees of freedom. Furthermore, the plate bending elements are free from any shear locking since they converge to the Kirchhoff solution for thin plates contrarily for the corresponding displacement based elements. In this paper the efficiency of the strain based approach compared to well known displacement formulation is presented. The results obtained by a new formulated plate bending element based on the strain approach and Kirchhoff theory are compared with some others elements. The good convergence of the new formulated element is confirmed.

Keywords: Displacement fields, finite elements, plate bending, Kirchhoff theory, strain based approach.

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Authors: Raphael de Oliveira Garcia, Samuel Rocha de Oliveira

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We have developed a new computer program in Fortran 90, in order to obtain numerical solutions of a system of Relativistic Magnetohydrodynamics partial differential equations with predetermined gravitation (GRMHD), capable of simulating the formation of relativistic jets from the accretion disk of matter up to his ejection. Initially we carried out a study on numerical methods of unidimensional Finite Volume, namely Lax-Friedrichs, Lax-Wendroff, Nessyahu-Tadmor method and Godunov methods dependent on Riemann problems, applied to equations Euler in order to verify their main features and make comparisons among those methods. It was then implemented the method of Finite Volume Centered of Nessyahu-Tadmor, a numerical schemes that has a formulation free and without dimensional separation of Riemann problem solvers, even in two or more spatial dimensions, at this point, already applied in equations GRMHD. Finally, the Nessyahu-Tadmor method was possible to obtain stable numerical solutions - without spurious oscillations or excessive dissipation - from the magnetized accretion disk process in rotation with respect to a central black hole (BH) Schwarzschild and immersed in a magnetosphere, for the ejection of matter in the form of jet over a distance of fourteen times the radius of the BH, a record in terms of astrophysical simulation of this kind. Also in our simulations, we managed to get substructures jets. A great advantage obtained was that, with the our code, we got simulate GRMHD equations in a simple personal computer.

Keywords: Finite Volume Methods, Central Schemes, Fortran 90, Relativistic Astrophysics, Jet.

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Authors: M. Cangi, T. Dolar, C. Ersoy, Y. E. Aydogdu, A. I. Aydeniz, A. Mugan

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The drum is one of the critical parts in a washing machine in which the clothes are washed and spin by the rotational movement. It is activated by the drum shaft which is attached to an electric motor and subjected to dynamic loading. Being one of the critical components, failures of the drum require costly repairs of dynamic components. In this study, tolerance bands between the drum shaft and its two bearings were examined to develop a relationship between the fatigue life of the shaft and the interaction tolerances. Optimization of tolerance bands was completed in consideration of the fatigue life of the shaft as the cost function. The following methodology is followed: multibody dynamic model of a washing machine was constructed and used to calculate dynamic loading on the components. Then, these forces were used in finite element analyses to calculate the stress field in critical components which was used for fatigue life predictions. The factors affecting the fatigue life were examined to find optimum tolerance grade for a given test condition. Numerical results were verified by experimental observations.

Keywords: Fatigue life, finite element analysis, tolerance analysis, optimization.

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