Search results for: parametric model

Authors: S. Benzarti, H. Mhiri, H. Bournot

Abstract:

In the current work, a numerical parametric study was performed in order to model the fluid mechanics in the riser of a bubbling fluidized bed (BFB). The gas-solid flow was simulated by mean of a multi-fluid Eulerian model incorporating the kinetic theory for solid particles. The bubbling fluidized bed was simulated two dimensionally by mean of a Computational Fluid Dynamic (CFD) commercial software package, Fluent. The effects of using different inter-phase drag function (the drag model of Gidaspow, Syamlal and O-Brien and the EMMS drag model) on the model predictions were evaluated and compared. The results showed that the drag models of Gidaspow and Syamlal and O-Brien overestimated the drag force for the FCC particles and predicted a greater bed expansion in comparison to the EMMS drag model.

Keywords: Bubbling fluidized bed, CFD, drag model, EMMS

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Authors: E. Elgendy

Abstract:

There are several ways of improving the performance of a vapor compression refrigeration cycle. Use of an ejector as expansion device is one of the alternative ways. The present paper aims at evaluate the performance improvement of a vapor compression refrigeration cycle under a wide range of operating conditions. A numerical model is developed and a parametric study of important parameters such as condensation (30-50°C) and evaporation temperatures (-20-5°C), nozzle and diffuser efficiencies (0.75-0.95), subcooling and superheating degrees (0-15K) are investigated. The model verification gives a good agreement with the literature data. The simulation results revealed that condensation temperature has the highest effect (129%) on the performance improvement ratio while superheating has the lowest one (6.2%). Among ejector efficiencies, the diffuser efficiency has a significant effect on the COP of ejector expansion refrigeration cycle. The COP improvement percentage decreases from 10.9% to 4.6% as subcooling degrees increases by 15K.

Keywords: Numerical modeling, R134a, Two phase ejector, Vapor compression refrigeration system.

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Authors: Mohammad Ali Lotfollahi-Yaghin, Hamid Ahmadi

Abstract:

In the present paper, a set of parametric FE stress analyses is carried out for two-planar welded tubular DKT-joints under two different axial load cases. Analysis results are used to present general remarks on the effect of geometrical parameters on the stress concentration factors (SCFs) at the inner saddle, outer saddle, toe, and heel positions on the main (outer) brace. Then a new set of SCF parametric equations is developed through nonlinear regression analysis for the fatigue design of two-planar DKT-joints. An assessment study of these equations is conducted against the experimental data; and the satisfaction of the criteria regarding the acceptance of parametric equations is checked. Significant effort has been devoted by researchers to the study of SCFs in various uniplanar tubular connections. Nevertheless, for multi-planar joints covering the majority of practical applications, very few investigations have been reported due to the complexity and high cost involved.

Keywords: Offshore jacket structure, Parametric equation, Stress concentration factor (SCF), Two-planar tubular KT-joint

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Authors: Hamid Ahmadi, Shadi Asoodeh

Abstract:

The fatigue life of tubular joints commonly found in offshore industry is not only dependent on the value of hot-spot stress (HSS), but is also significantly influenced by the through-thethickness stress distribution characterized by the degree of bending (DoB). The determination of DoB values in a tubular joint is essential for improving the accuracy of fatigue life estimation using the stresslife (S–N) method and particularly for predicting the fatigue crack growth based on the fracture mechanics (FM) approach. In the present paper, data extracted from finite element (FE) analyses of tubular KT-joints, verified against experimental data and parametric equations, was used to investigate the effects of geometrical parameters on DoB values at the crown 0°, saddle, and crown 180° positions along the weld toe of central brace in tubular KT-joints subjected to axial loading. Parametric study was followed by a set of nonlinear regression analyses to derive DoB parametric formulas for the fatigue analysis of KT-joints under axial loads. The tubular KTjoint is a quite common joint type found in steel offshore structures. However, despite the crucial role of the DoB in evaluating the fatigue performance of tubular joints, this paper is the first attempt to study and formulate the DoB values in KT-joints.

Keywords: Tubular KT-joint, fatigue, degree of bending (DoB), axial loading, parametric formula.

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Authors: Sanmohan Krüger, Volker Krüger

Abstract:

Imitation learning is considered to be an effective way of teaching humanoid robots and action recognition is the key step to imitation learning. In this paper an online algorithm to recognize parametric actions with object context is presented. Objects are key instruments in understanding an action when there is uncertainty. Ambiguities arising in similar actions can be resolved with objectn context. We classify actions according to the changes they make to the object space. Actions that produce the same state change in the object movement space are classified to belong to the same class. This allow us to define several classes of actions where members of each class are connected with a semantic interpretation.

Keywords: Parametric actions, Action primitives, Hand gesture recognition, Imitation learning

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Authors: E. Mat Tokit, Yusoff M. Z, Mohammed H.

Abstract:

Numerical investigation on the generality of nanoparticle velocity equation had been done on the previous published work. The three dimensional governing equations (continuity, momentum and energy) were solved using finite volume method (FVM). Parametric study of thermal performance between pure water-cooled and nanofluid-cooled are evaluated for volume fraction in the range of 1% to 4%, and nanofluid type of gamma-Al₂O₃ at Reynolds number range of 67.41 to 286.77. The nanofluid is modeled using single and two phase approach. Three different existing Brownian motion velocities are applied in comparing the generality of the equation for a wide parametric condition. Deviation in between the Brownian motion velocity is identified to be due to the different means of mean free path and constant value used in diffusion equation.

Keywords: Brownian nanoparticle velocity, heat transfer enhancement, nanofluid, two phase model.

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Authors: Zuodong Liang, Dong-Sheng Jeng

Abstract:

Seabed instability around an offshore pipeline is one of key factors that need to be considered in the design of offshore infrastructures. Unlike previous investigations, a three-dimensional numerical model for the wave-induced soil response around an offshore pipeline is proposed in this paper. The numerical model was first validated with 2-D experimental data available in the literature. Then, a parametric study will be carried out to examine the effects of wave, seabed characteristics and confirmation of pipeline. Numerical examples demonstrate significant influence of wave obliquity on the wave-induced pore pressures and the resultant seabed liquefaction around the pipeline, which cannot be observed in 2-D numerical simulation.

Keywords: Pore pressure, 3D wave model, seabed liquefaction, pipeline.

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Authors: J. Mendoza-López, S. Sánchez-Solano, J. L. Huertas-Díaz

Abstract:

An array of piezoelectric micro actuators can be used for radiation of an ultrasonic carrier signal modulated in amplitude with an acoustic signal, which yields audio frequency applications as the air acts as a self-demodulating medium. This application is known as the parametric array. We propose a parametric array with array elements based on existing piezoelectric micro ultrasonic transducer (pMUT) design techniques. In order to reach enough acoustic output power at a desired operating frequency, a proper ratio between number of array elements and array size needs to be used, with an array total area of the order of one cm square. The transducers presented are characterized via impedance, admittance, noise figure, transducer gain and frequency responses.

Keywords: Pizeoelectric, Microspeaker, MEMS, pMUT, Parametric Array

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Authors: Maysam Saidi, Reza Maddahian, Bijan Farhanieh

Abstract:

Hydrocyclones flow field study is conducted by performing a parametric study. Effect of cone angle on deoiling hydrocyclones flow behaviour is studied in this research. Flow field of hydrocyclone is obtained by three-dimensional simulations with OpenFOAM code. Because of anisotropic behaviour of flow inside hydrocyclones LES is a suitable method to predict the flow field since it resolves large scales and model isotropic small scales. Large eddy simulation is used to predict the flow behavior of three different cone angles. Differences in tangential velocity and pressure distribution are reported in some figures.

Keywords: Deoiling hydrocyclones, Flow field, Hydrocyclone cone angle, Large Eddy Simulation, Pressure distribution

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Authors: E. A. Azrulhisham, Y. M. Asri, A. W. Dzuraidah, A. H. Hairul Fahmi

Abstract:

The aim of this paper is to introduce a parametric distribution model in fatigue life reliability analysis dealing with variation in material properties. Service loads in terms of responsetime history signal of Belgian pave were replicated on a multi-axial spindle coupled road simulator and stress-life method was used to estimate the fatigue life of automotive stub axle. A PSN curve was obtained by monotonic tension test and two-parameter Weibull distribution function was used to acquire the mean life of the component. A Pearson system was developed to evaluate the fatigue life reliability by considering stress range intercept and slope of the PSN curve as random variables. Considering normal distribution of fatigue strength, it is found that the fatigue life of the stub axle to have the highest reliability between 10000 – 15000 cycles. Taking into account the variation of material properties associated with the size effect, machining and manufacturing conditions, the method described in this study can be effectively applied in determination of probability of failure of mass-produced parts.

Keywords: Stub axle, Fatigue life reliability, Stress-life, PSN curve, Weibull distribution, Pearson system

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Authors: M. Khalid Imran, Syed Masood, Milan Brandt, Sudip Bhattacharya, Jyotirmoy Mazumder

Abstract:

In the present investigation, H13 tool steel has been deposited on copper alloy substrate using both CO2 and diode laser. A detailed parametric analysis has been carried out in order to find out optimum processing zone for coating defect free H13 tool steel on copper alloy substrate. Followed by parametric optimization, the microstructure and microhardness of the deposited clads have been evaluated. SEM micrographs revealed dendritic microstructure in both clads. However, the microhardness of CO2 laser deposited clad was much higher compared to diode laser deposited clad.

Keywords: CO2 laser, Diode laser, Direct Metal Deposition, Microstructure, Microhardness, Porosity.

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Authors: Oladeinde Mobolaji Humphrey, Akpobi John

Abstract:

A mathematical model for the hydrodynamic lubrication of parabolic slider bearings with couple stress lubricants is presented. A numerical solution for the mathematical model using finite element scheme is obtained using three nodes isoparametric quadratic elements. Stiffness integrals obtained from the weak form of the governing equations were solved using Gauss Quadrature to obtain a finite number of stiffness matrices. The global system of equations was obtained for the bearing and solved using Gauss Seidel iterative scheme. The converged pressure solution was used to obtain the load capacity of the bearing. Parametric studies were carried out and it was shown that the effect of couple stresses and profile parameter are to increase the load carrying capacity of the parabolic slider bearing. Numerical experiments reveal that the magnitude of the profile parameter at which maximum load is obtained increases with decrease in couple stress parameter. The results are presented in graphical form.

Keywords: Finite element, numerical, parabolic slider.

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Authors: M. Rychlik, R. Roszak, M. Morzynski, M. Nowak, H. Hausa, K. Kotecki

Abstract:

Article presents the geometry and structure reconstruction procedure of the aircraft model for flatter research (based on the I22-IRYDA aircraft). For reconstruction the Reverse Engineering techniques and advanced surface modeling CAD tools are used. Authors discuss all stages of data acquisition process, computation and analysis of measured data. For acquisition the three dimensional structured light scanner was used. In the further sections, details of reconstruction process are present. Geometry reconstruction procedure transform measured input data (points cloud) into the three dimensional parametric computer model (NURBS solid model) which is compatible with CAD systems. Parallel to the geometry of the aircraft, the internal structure (structural model) are extracted and modeled. In last chapter the evaluation of obtained models are discussed.

Keywords: computer modeling, numerical simulation, Reverse Engineering, structural model

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Authors: Lenka Ševelová, Aleš Florian

Abstract:

To improve the efficiency of parametric studies or tests planning the method is proposed, that takes into account all input parameters, but only a few simulation runs are performed to assess the relative importance of each input parameter. For K input parameters with N input values the total number of possible combinations of input values equals NK. To limit the number of runs, only some (totally N) of possible combinations are taken into account. The sampling procedure Updated Latin Hypercube Sampling is used to choose the optimal combinations. To measure the relative importance of each input parameter, the Spearman rank correlation coefficient is proposed. The sensitivity and the influence of all parameters are analyzed within one procedure and the key parameters with the largest influence are immediately identified.

Keywords: Concrete, pavement, simulation, reliability, Latin Hypercube Sampling, parametric studies.

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Authors: Zhi Sheng Lin, K. C. G. Ong, Lado Riannevo Chandra, Bee Hong Angeline Tan, Chat Tim Tam, Sze Dai Pang

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Design for Disassembly (DfD) aims to reuse the structural components instead of demolition followed by recycling of the demolition debris. This concept preserves the invested embodied energy of materials, thus reducing inputs of new embodied energy during materials reprocessing or remanufacturing. Both analytical and experimental research on a proposed DfD beam-column connection for use in residential apartments is currently investigated at the National University of Singapore in collaboration with the Housing and Development Board of Singapore. The present study reports on the results of a numerical analysis of the proposed connection utilizing finite element analysis. The numerical model was calibrated and validated by comparison against experimental results. Results of a parametric study will also be presented and discussed.

Keywords: Design for Disassembly (DfD), finite element analysis, parametric study.

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Authors: Dursun Aydın

Abstract:

In this paper, estimation of the linear regression model is made by ordinary least squares method and the partially linear regression model is estimated by penalized least squares method using smoothing spline. Then, it is investigated that differences and similarity in the sum of squares related for linear regression and partial linear regression models (semi-parametric regression models). It is denoted that the sum of squares in linear regression is reduced to sum of squares in partial linear regression models. Furthermore, we indicated that various sums of squares in the linear regression are similar to different deviance statements in partial linear regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the partial linear regression model. For this aim, it is made two different applications. A simulated and a real data set are considered to prove the claim mentioned here. In this way, this study is supported with a simulation and a real data example.

Keywords: Partial Linear Regression Model, Linear RegressionModel, Residuals, Deviance, Smoothing Spline.

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Authors: Arshia Azam, J. Amarnath, Ch. D. V. Paradesi Rao

Abstract:

The advantage of solving the complex nonlinear problems by utilizing fuzzy logic methodologies is that the experience or expert-s knowledge described as a fuzzy rule base can be directly embedded into the systems for dealing with the problems. The current limitation of appropriate and automated designing of fuzzy controllers are focused in this paper. The structure discovery and parameter adjustment of the Branched T-S fuzzy model is addressed by a hybrid technique of type constrained sparse tree algorithms. The simulation result for different system model is evaluated and the identification error is observed to be minimum.

Keywords: Fuzzy logic, branch T-S fuzzy model, tree modeling, complex nonlinear system.

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Authors: Om Parkash, C.P.Gandhi

Abstract:

In the literature of fuzzy measures, there exist many well known parametric and non-parametric measures, each with its own merits and limitations. But our main emphasis is on applications of these measures to a variety of disciplines. To extend the scope of applications of these fuzzy measures to geometry, we need some special fuzzy measures. In this communication, we have introduced two new fuzzy measures involving trigonometric functions and simultaneously provided their applications to obtain the basic results already existing in the literature of geometry.

Keywords: Entropy, Uncertainty, Fuzzy Entropy, Concavity, Symmetry.

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Authors: Pi-Chung Hsu

Abstract:

Super-quadrics can represent a set of implicit surfaces, which can be used furthermore as primitive surfaces to construct a complex object via Boolean set operations in implicit surface modeling. In fact, super-quadrics were developed to create a parametric surface by performing spherical product on two parametric curves and some of the resulting parametric surfaces were also represented as implicit surfaces. However, because not every parametric curve can be redefined implicitly, this causes only implicit super-elliptic and super-hyperbolic curves are applied to perform spherical product and so only implicit super-ellipsoids and hyperboloids are developed in super-quadrics. To create implicit surfaces with more diverse shapes than super-quadrics, this paper proposes an implicit representation of spherical product, which performs spherical product on two implicit curves like super-quadrics do. By means of the implicit representation, many new implicit curves such as polygonal, star-shaped and rose-shaped curves can be used to develop new implicit surfaces with a greater variety of shapes than super-quadrics, such as polyhedrons, hyper-ellipsoids, superhyperboloids and hyper-toroids containing star-shaped and roseshaped major and minor circles. Besides, the newly developed implicit surfaces can also be used to define new primitive implicit surfaces for constructing a more complex implicit surface in implicit surface modeling.

Keywords: Implicit surfaces, Soft objects, Super-quadrics.

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Authors: Narbada Prasad Gupta, Mithilesh Kumar

Abstract:

A compact Ultra Wide Band (UWB) antenna with coplanar waveguide feed has been designed and results are verified in this paper. The antenna has been designed on FR4 substrate with dielectric constant (εr) of 4.4 and dimensions of 32mm x 26mm x 0.8mm. The presented antenna shows return loss characteristics in the band of 3.1 to 10.6 GHz as prescribed by FCC, USA. Parametric studies have been done and results thus obtained have been presented. Simulated results have been verified on Rohde & Swartz VNA. The measured results are in good agreement with simulated results which make the presented antenna suitable to be used for wearable applications. Performance analysis of antenna has also been shown in the presence of three layered Human Arm model. Results obtained in presence of Human Arm model has been compared with that in free space.

Keywords: CPW feed, Human Arm model, UWB, wearable antenna.

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Authors: N. P. Yadav, Deepti Verma

Abstract:

This paper focuses on the mathematical modeling for solidification of Al alloy in a cube mold cavity to study the solidification behavior of casting process. The parametric investigation of solidification process inside the cavity was performed by using computational solidification/melting model coupled with Volume of fluid (VOF) model. The implicit filling algorithm is used in this study to understand the overall process from the filling stage to solidification in a model metal casting process. The model is validated with past studied at same conditions. The solidification process is analyzed by including the effect of pouring velocity as well as natural convection from the wall and geometry of the cavity. These studies show the possibility of various defects during solidification process.

Keywords: Buoyancy driven flow, natural convection driven flow, residual flow, secondary flow, volume of fluid.

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Authors: Maha BenHamad, Ali Snoussi, Ammar Ben Brahim

Abstract:

A steady-state analysis of triple-effect thermal vapor compressor desalination unit was performed. A mathematical model based on mass, salinity and energy balances is developed. The purpose of this paper is to develop a connection between process simulator and process optimizer in order to study the influence of several operating variables on the performance and the produced water cost of the unit. A MATLAB program is used to solve the model equations, and Aspen HYSYS is used to model the plant. The model validity is examined against a commercial plant and showed a good agreement between industrial data and simulations results. Results show that the pressures of the last effect and the compressed vapor have an important influence on the produced cost, and the increase of the difference temperature in the condenser decreases the specific heat area about 22%.

Keywords: Steady-state, triple effect, thermal vapor compressor, MATLAB, Aspen HYSYS.

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Authors: Eduardo C. Guardia, Jose W. M. Lima, Afonso H. M. Santos

Abstract:

This paper presents a nonparametric method to obtain the hazard rate “Bathtub curve” for power system components. The model is a mixture of the three known phases of a component life, the decreasing failure rate (DFR), the constant failure rate (CFR) and the increasing failure rate (IFR) represented by three parametric Weibull models. The parameters are obtained from a simultaneous fitting process of the model to the Kernel nonparametric hazard rate curve. From the Weibull parameters and failure rate curves the useful lifetime and the characteristic lifetime were defined. To demonstrate the model the historic time-to-failure of distribution transformers were used as an example. The resulted “Bathtub curve” shows the failure rate for the equipment lifetime which can be applied in economic and replacement decision models.

Keywords: Bathtub curve, failure analysis, lifetime estimation, parameter estimation, Weibull distribution.

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Authors: Ramaswamy Palaniappan

Abstract:

This paper reports a new approach on identifying the individuality of persons by using parametric classification of multiple mental thoughts. In the approach, electroencephalogram (EEG) signals were recorded when the subjects were thinking of one or more (up to five) mental thoughts. Autoregressive features were computed from these EEG signals and classified by Linear Discriminant classifier. The results here indicate that near perfect identification of 400 test EEG patterns from four subjects was possible, thereby opening up a new avenue in biometrics.

Keywords: Autoregressive, Biometrics, Electroencephalogram, Linear discrimination, Mental thoughts.

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Authors: A. Izadbakhsh, M. M. Fateh

Abstract:

A model-free robust control (MFRC) approach is proposed for position control of robot manipulators in the state space. The control approach is verified analytically to be robust subject to uncertainties including external disturbances, unmodeled dynamics, and parametric uncertainties. There is a high flexibility to work on different systems including actuators by the use of the proposed control approach. The proposed control approach can guarantee the robustness of control system. A PUMA 560 robot driven by geared permanent magnet dc motors is simulated. The simulation results show a satisfactory performance for control system under technical specifications. KeywordsModel-free, robust control, position control, PUMA 560.

Keywords: Model-free, robust control, position control, PUMA 560.

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Authors: Naci Büyükkaracığan

Abstract:

Hydroclimatic observation values ​​are used in the planning of the project of water resources. Climate variables are the first of the values ​​used in planning projects. At the same time, the climate system is a complex and interactive system involving the atmosphere, land surfaces, snow and bubbles, the oceans and other water structures. The amount and distribution of precipitation, which is an important climate parameter, is a limiting environmental factor for dispersed living things. Trend analysis is applied to the detection of the presence of a pattern or trend in the data set. Many trends work in different parts of the world are usually made for the determination of climate change. The detection and attribution of past trends and variability in climatic variables is essential for explaining potential future alteration resulting from anthropogenic activities. Parametric and non-parametric tests are used for determining the trends in climatic variables. In this study, trend tests were applied to annual total precipitation data obtained in period of 1972 and 2012, in the Konya Basin. Non-parametric trend tests, (Sen’s T, Spearman’s Rho, Mann-Kendal, Sen’s T trend, Wald-Wolfowitz) and parametric test (mean square) were applied to annual total precipitations of 15 stations for trend analysis. The linear slopes (change per unit time) of trends are calculated by using a non-parametric estimator developed by Sen. The beginning of trends is determined by using the Mann-Kendall rank correlation test. In addition, homogeneities in precipitation trends are tested by using a method developed by Van Belle and Hughes. As a result of tests, negative linear slopes were found in annual total precipitations in Konya.

Keywords: Trend analysis, precipitation, hydroclimatology, Konya, Turkey.

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Authors: Qassun S. Mohammed Shafiqu, Murtadha A. Abdulrasool

Abstract:

The design of shallow foundations to withstand different dynamic loads has given considerable attention in recent years. Dynamic loads may be due to the earthquakes, pile driving, blasting, water waves, and machine vibrations. But, predicting the behavior of shallow foundations during earthquakes remains a difficult task for geotechnical engineers. A database for dynamic and static parameters for different soils in seismic active zones in Iraq is prepared which has been collected from geophysical and geotechnical investigation works. Then, analysis of a typical 3-D soil-raft foundation system under earthquake loading is carried out using the database. And a parametric study has been carried out taking into consideration the influence of some parameters on the dynamic behavior of the raft foundation, such as raft stiffness, damping ratio as well as the influence of the earthquake acceleration-time records. The results of the parametric study show that the settlement caused by the earthquake can be decreased by about 72% with increasing the thickness from 0.5 m to 1.5 m. But, it has been noticed that reduction in the maximum bending moment by about 82% was predicted by decreasing the raft thickness from 1.5 m to 0.5 m in all sites model. Also, it has been observed that the maximum lateral displacement, the maximum vertical settlement and the maximum bending moment for damping ratio 0% is about 14%, 20%, and 18% higher than that for damping ratio 7.5%, respectively for all sites model.

Keywords: Shallow foundation, seismic behavior, raft thickness, damping ratio.

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Authors: Yacine Ait Ali Yahia, Abderazak Guessoum

Abstract:

In this paper, a new method of image edge-detection and characterization is presented. “Parametric Filtering method" uses a judicious defined filter, which preserves the signal correlation structure as input in the autocorrelation of the output. This leads, showing the evolution of the image correlation structure as well as various distortion measures which quantify the deviation between two zones of the signal (the two Hamming signals) for the protection of an image edge.

Keywords: Edge detection, parametrable recursive filter, autocorrelation structure, distortion measurements.

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Authors: José Julio de C. Pituba

Abstract:

This work deals with the initial applications and formulation of an anisotropic plastic-damage constitutive model proposed for non-linear analysis of reinforced concrete structures submitted to a loading with change of the sign. The original constitutive model is based on the fundamental hypothesis of energy equivalence between real and continuous medium following the concepts of the Continuum Damage Mechanics. The concrete is assumed as an initial elastic isotropic medium presenting anisotropy, permanent strains and bimodularity (distinct elastic responses whether traction or compression stress states prevail) induced by damage evolution. In order to take into account the bimodularity, two damage tensors governing the rigidity in tension or compression regimes are introduced. Then, some conditions are introduced in the original version of the model in order to simulate the damage unilateral effect. The three-dimensional version of the proposed model is analyzed in order to validate its formulation when compared to micromechanical theory. The one-dimensional version of the model is applied in the analyses of a reinforced concrete beam submitted to a loading with change of the sign. Despite the parametric identification problems, the initial applications show the good performance of the model.

Keywords: Damage model, plastic strain, unilateral effect.

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Authors: Abdelrahman Elsehsah, Hany Madkour, Khalid Farah

Abstract:

This article presents a 3-D modified non-linear elastic model in the strain space. The Helmholtz free energy function is introduced with the existence of a dissipation potential surface in the space of thermodynamic conjugate forces. The constitutive equation and the damage evolution were derived as well. The modified damage has been examined to model the nonlinear behavior of reinforced concrete (RC) slabs with an opening. A parametric study with RC was carried out to investigate the impact of different factors on the behavior of RC slabs. These factors are the opening area, the opening shape, the place of opening, and the thickness of the slabs. And the numerical results have been compared with the experimental data from literature. Finally, the model showed its ability to be applied to the structural analysis of RC slabs.

Keywords: 3-D numerical analysis, damage mechanics, RC slab with opening.

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