Search results for: Solitary structure

Authors: Buntara Sthenly Gan

Abstract:

A novel and versatile numerical technique to solve a self-stress equilibrium state is adopted herein as a form-finding procedure for an irregular tensegrity structure. The numerical form-finding scheme of a tensegrity structure uses only the connectivity matrix and prototype tension coefficient vector as the initial guess solution. Any information on the symmetrical geometry or other predefined initial structural conditions is not necessary to get the solution in the form-finding process. An eight-node initial condition example is presented to demonstrate the efficiency and robustness of the proposed method in the form-finding of an irregular tensegrity structure. Based on the conception from the form-finding of an eight-node irregular tensegrity structure, a monumental object is designed by considering the real world situation such as self-weight, wind and earthquake loadings.

Keywords: Tensegrity, Form-finding, Design, Irregular, Self-stress, Force density method.

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Authors: Li Yongfeng, Liu Yixing, Li Jian, Li Jun

Abstract:

A novel biomass composite inspired from wood porous structure was manufactured by impregnating vinyl monomer into wood cellular structure under vacuum conditions, and initiating the monomer for in situ polymerization through a thermal treatment. The vacuum condition was studied, and the mechanical properties of the composite were also tested. SEM observation shows that polymer generated in the wood porous structure, and strongly interacted with wood matrix; and the polymer content increased with vacuum value increasing. FTIR indicates that polymer grafted onto wood matrix, resulting chemical complex between them. The rate of monomer loading increased with increasing vacuum value and time, accordance with rate of polymer loading. The compression strength and modulus of elasticity linearly increased with the increasing rate of polymer loading. Results indicate that the novel biomass composite possesses good mechanical properties capable of applying in the fields of construction, traffic and so forth.

Keywords: Biomass composite, manufacture, vinyl monomer, wood cellular structure.

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Authors: J.W. Xiang, M. Liang

Abstract:

This paper presents a method to detect multiple cracks based on frequency information. When a structure is subjected to dynamic or static loads, cracks may develop and the modal frequencies of the cracked structure may change. To detect cracks in a structure, we construct a high precision wavelet finite element (EF) model of a certain structure using the B-spline wavelet on the interval (BSWI). Cracks can be modeled by rotational springs and added to the FE model. The crack detection database will be obtained by solving that model. Then the crack locations and depths can be determined based on the frequency information from the database. The performance of the proposed method has been numerically verified by a rotor example.

Keywords: Rotor, frequency measurement, multiple cracks, wavelet finite element method, identification.

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Authors: WooYoung Jung, Buntheng Chhorn, Min-Gi Kim

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Recently, damage to domestic facilities by strong winds and typhoons are growing. Therefore, this study focused on sign structure among various vulnerable facilities. The evaluation of the wind fragility was carried out considering the destruction of the anchor, which is one of the various failure modes of the sign structure. The performance evaluation of the anchor was carried out to derive the wind fragility. Two parameters were set and four anchor types were selected to perform the pull-out and shear tests. The resistance capacity was estimated based on the experimental results. Wind loads were estimated using Monte Carlo simulation method. Based on these results, we derived the wind fragility according to anchor type and wind exposure category. Finally, the evaluation of the wind fragility was performed according to the experimental parameters such as anchor length and anchor diameter. This study shows that the depth of anchor was more significant for the safety of structure compare to diameter of anchor.

Keywords: Sign structure, wind fragility, set anchor, pull-out test, shear test, Monte Carlo simulation.

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Authors: Thevaneyan K. David, John P. Forth

Abstract:

Integral Abutment Bridges (IAB) are defined as simple or multiple span bridges in which the bridge deck is cast monolithically with the abutment walls. This kind of bridges are becoming very popular due to different aspects such as good response under seismic loading, low initial costs, elimination of bearings, and less maintenance. However the main issue related to the analysis of this type of structures is dealing with soil-structure interaction of the abutment walls and the supporting piles. Various soil constitutive models have been used in studies of soil-structure interaction in this kind of structures by researchers. This paper is an effort to review the implementation of various finite elements model which explicitly incorporates the nonlinear soil and linear structural response considering various soil constitutive models and finite element mesh.

Keywords: Constitutive Models, FEM, Integral AbutmentBridges, Soil-structure Interactions

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Authors: Ardeshir Karami Mohammadi

Abstract:

A Variable Structure Model Reference Adaptive Controller using state variables is proposed for a class of multi input-multi output systems. Adaptation law is of variable structure type and switching functions is designed based on stability requirements. Global exponential stability is proved based on Lyapunov criterion. Transient behavior is analyzed using sliding mode control and shows perfect model following at a finite time.

Keywords: Adaptive control, Model reference, Variablestructure, MIMO system.

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Authors: M.O. Makhmalbaf, M. GhanooniBagha, M.A. Tutunchian, M. Zabihi Samani

Abstract:

In this paper first, Two buildings have been modeled and then analyzed using nonlinear static analysis method under two different conditions in Nonlinear SAP 2000 software. In the first condition the interaction of soil adjacent to the walls of basement are ignored while in the second case this interaction have been modeled using Gap elements of nonlinear SAP2000 software. Finally, comparing the results of two models, the effects of soil-structure on period, target point displacement, internal forces, shape deformations and base shears have been studied. According to the results, this interaction has always increased the base shear of buildings, decreased the period of structure and target point displacement, and often decreased the internal forces and displacements.

Keywords: Seismic Rehabilitation, Soil-Structure Interaction, Short Structure, Nonlinear Static Analysis.

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Authors: Piotr Podlipniak

Abstract:

This paper proposes that in the course of evolution pitch structure became a human specific tool of communication the function of which is to induce emotional states such as uncertainty and cohesion. By the means of eliciting these emotions during collective music performance people are able to unconsciously give cues concerning social acceptance. This is probably one of the reasons why in all cultures people collectively perform tonal music. It is also suggested that tonal pitch structure had been invented socially before it became an evolutionary innovation of hominines. It means that a predisposition to tonally organize pitches evolved by the means of ‘Baldwin effect’ – a process in which natural selection transforms the learned response of an organism into the instinctive response. In the proposed, hypothetical evolutionary scenario of the emergence of tonal pitch structure social forces such as a need for closer cooperation play the crucial role.

Keywords: Emotion, evolution, tonality, social consolidation.

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Authors: Fatahian Dehkordi R.F, Parchami A.

Abstract:

Steroidal hormones with the efficient changes on the epiphyseal growth plate may influence tissue structure properties. Presents paper to investigate the effects of gonadectomy in the pattern distribution of the epiphyseal structure. Fifteen adult female New Zealand white rabbits were separated into three groups. One group was intact and others groups were selected for surgical operation. From these two groups, one group carried out steroidal administration. The results obtained showed that there is no statistically difference in the mean diameter of the growth plate cells between all three groups. The maximum value of the cartilage cells were allocated to the gonadectomized group and the minimum number were observed in Hormonal induced group significantly. Growth plate height was significantly greater in gonadectomized group than in two other groups.

Keywords: Steroidal hormones, Ovariectomy, Rabbit, Epiphyseal structure

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Authors: Young-Dal Kim, Jae-Myung Shim, Woo-Yong Park, Sung-joong Kim, Dong Seok Hyun, Dae-Dong Lee

Abstract:

The most common cause of power transformer failures is mechanical defect brought about by excessive vibration, which is formed by the combination of multiples of a frequency of 120 Hz. In this paper, the types of mechanical exciting forces applied to the power transformer were classified, and the mechanical damage mechanism of the power transformer was identified using the vibration transfer route to the machine or structure. The general effects of 120 Hz-vibration on the enclosure, bushing, Buchholz relay, pressure release valve and tap changer of the transformer were also examined.

Keywords: Structure-Vibration, Transformer.

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Authors: Do Phuc, Nguyen Thi Kim Phung

Abstract:

In this paper, we represent protein structure by using graph. A protein structure database will become a graph database. Each graph is represented by a spectral vector. We use Jacobi rotation algorithm to calculate the eigenvalues of the normalized Laplacian representation of adjacency matrix of graph. To measure the similarity between two graphs, we calculate the Euclidean distance between two graph spectral vectors. To cluster the graphs, we use M-tree with the Euclidean distance to cluster spectral vectors. Besides, M-tree can be used for graph searching in graph database. Our proposal method was tested with graph database of 100 graphs representing 100 protein structures downloaded from Protein Data Bank (PDB) and we compare the result with the SCOP hierarchical structure.

Keywords: Eigenvalues, m-tree, graph database, protein structure, spectra graph theory.

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Authors: Shwe Wut Hmon Aye, Kay Thi Lwin, Waing Waing Kay Khine Oo

Abstract:

As the material used for fuselage structure must possess low density, high strength to weight ratio, the selection of appropriate materials for fuselage structure is one of the most important tasks. Aluminum metal itself is soft and low in strength. It can be made stronger by giving proper combination of suitable alloy addition, mechanical treatment and thermal treatment. The usual thermal treatment given to aluminum alloys is called age-hardening or precipitation hardening. In this paper, the studies are carried out on 7075 aluminum alloy which is how to improve strength level for fuselage structure. The marked effect of the strength on the ternary alloy is clearly demonstrated at several ageing times and temperatures. It is concluded that aluminum-zinc-magnesium alloy can get the highest strength level in natural ageing.

Keywords: Aluminum alloy, ageing, heat treatment, strength.

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Authors: Diego Ordonez, Carlos Dafonte, Minia Manteiga, Bernardino Arcayy

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This work presents a neural network model for the clustering analysis of data based on Self Organizing Maps (SOM). The model evolves during the training stage towards a hierarchical structure according to the input requirements. The hierarchical structure symbolizes a specialization tool that provides refinements of the classification process. The structure behaves like a single map with different resolutions depending on the region to analyze. The benefits and performance of the algorithm are discussed in application to the Iris dataset, a classical example for pattern recognition.

Keywords: Neural networks, Self-organizing feature maps, Hierarchicalsystems, Pattern clustering methods.

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Authors: Ladan Maijama’a, Jibril D. Jiya, Ejike C. Anene

Abstract:

This paper presents Differential Evolution Algorithm (DEA) based Variable Structure Position Control (VSPC) of Laboratory DC servomotor (LDCSM). DEA is employed for the optimal tuning of Variable Structure Control (VSC) parameters for position control of a DC servomotor. The VSC combines the techniques of Sliding Mode Control (SMC) that gives the advantages of small overshoot, improved step response characteristics, faster dynamic response and adaptability to plant parameter variations, suppressed influences of disturbances and uncertainties in system behavior. The results of the simulation responses of the VSC parameters adjustment by DEA were performed in Matlab Version 2010a platform and yield better dynamic performance compared with the untuned VSC designed.

Keywords: Differential evolution algorithm, laboratory DC servomotor, sliding mode control, variable structure control.

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Authors: M.B. Aryanezhad, J. Aliabadi

Abstract:

This paper considers the integration of assembly operations and product structure to Cellular Manufacturing System (CMS) design so that to correct the drawbacks of previous researches in the literature. For this purpose, a new mathematical model is developed which dedicates machining and assembly operations to manufacturing cells while the objective function is to minimize the intercellular movements resulting due to both of them. A linearization method is applied to achieve optimum solution through solving aforementioned nonlinear model by common programming language such as Lingo. Then, using different examples and comparing the results, the importance of integrating assembly considerations is demonstrated.

Keywords: Assembly operations and Product structure, CellFormation, Genetic Algorithm.

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Authors: Yacine Ait Ali Yahia, Abderazak Guessoum

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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: Carlos H. Cuadra

Abstract:

Seismic isolation can be used as a retrofit method for historical buildings with the advantage that minimum intervention on super-structure is required. However, selection of isolation devices depends on weight and stiffness of upper structure. In this study, two buildings are considered for analyses to evaluate the applicability of this retrofitting methodology. Both buildings are located at Akita prefecture in the north part of Japan. One building is a wooden structure that corresponds to the old council meeting hall of Noshiro city. The second building is a brick masonry structure that was used as house of a foreign mining engineer and it is located at Ani town. Ambient vibration measurements were performed on both buildings to estimate their dynamic characteristics. Then, target period of vibration of isolated systems is selected as 3 seconds is selected to estimate required stiffness of isolation devices. For wooden structure, which is a light construction, it was found that natural rubber isolators in combination with friction bearings are suitable for seismic isolation. In case of masonry building elastomeric isolator can be used for its seismic isolation. Lumped mass systems are used for seismic response analysis and it is verified in both cases that seismic isolation can be used as retrofitting method of historical construction. However, in the case of the light building, most of the weight corresponds to the reinforced concrete slab that is required to install isolation devices.

Keywords: Historical building, finite element method, masonry structure, seismic isolation, wooden structure.

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Authors: Radim Cajka, Pavlina Mateckova, Martina Janulikova, Marie Stara

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Use of a sliding joint is an effective method to decrease the stress in foundation structure where there is a horizontal deformation of subsoil (areas afflicted with underground mining) or horizontal deformation of a foundation structure (pre-stressed foundations, creep, shrinkage, temperature deformation). A convenient material for a sliding joint is a bitumen asphalt belt. Experiments for different types of bitumen belts were undertaken at the Faculty of Civil Engineering - VSB Technical University of Ostrava in 2008. This year an extension of the 2008 experiments is in progress and the shear resistance of a slide joint is being tested as a function of temperature in a temperature controlled room. In this paper experimental results of temperature dependant shear resistance are presented. The result of the experiments should be the sliding joint shear resistance as a function of deformation velocity and temperature. This relationship is used for numerical analysis of stress/strain relation between foundation structure and subsoil. Using a rheological slide joint could lead to a decrease of the reinforcement amount, and contribute to higher reliability of foundation structure and thus enable design of more durable and sustainable building structures.

Keywords: Pre-stressed foundations, sliding joint, soil-structure interaction, subsoil horizontal deformation.

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Authors: Rosidah Musa, Rezian-na Muhammad Kassim

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The purpose of this research is to disentangle and validate the underlying factorial-structure of Ecotourism Experiential Value (EEV) measurement scale and subsequently investigate its psychometric properties. The analysis was based on a sample of 225 eco-tourists, collected at the vicinity of Taman Negara National Park (TNNP) via interviewer-administered questionnaire. Exploratory factor analysis (EFA) was performed to determine the factorial structure of EEV. Subsequently, to confirm and validate the factorial structure and assess the psychometric properties of EEV, confirmatory factor analysis (CFA) was executed. In addition, to establish the nomological validity of EEV a structural model was developed to examine the effect of EEV on Total Eco-tourist Experience Quality (TEEQ). It is unveiled that EEV is a secondorder six-factorial structure construct and it scale has adequately met the psychometric criteria, thus could permit interpretation of results confidently. The findings have important implications for future research directions and management of ecotourism destination.

Keywords: ecotourism, experiential value, experience quality, national park,

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Authors: E. A. Asabina, V. I. Pet'kov, P. A. Mayorov, A. V. Markin, N. N. Smirnova, A. M. Kovalskii, A. A. Usenko

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The purpose of this work was to synthesize and investigate phase formation, structure and thermophysical properties of the phosphates M_0.5+xM'_xZr_2–x(PO₄)₃ (M – Cd, Sr, Pb; M' – Mg, Co, Mn). The compounds were synthesized by sol-gel method. The results showed formation of limited solid solutions of NZP/NASICON type. The crystal structures of triple phosphates of the compositions MMg_0.5Zr_1.5(PO₄)₃ were refined by the Rietveld method using XRD data. Heat capacity (8–660 K) of the phosphates Pb_0.5+xMg_xZr_2-x(PO₄)₃ (x = 0, 0.5) was measured, and reversible polymorphic transitions were found at temperatures, close to the room temperature. The results of Rietveld structure refinement showed the polymorphism caused by disordering of lead cations in the cavities of NZP/NASICON structure. Thermal expansion (298−1073 K) of the phosphates MMg_0.5Zr_1.5(PO₄)₃ was studied by XRD method, and the compounds were found to belong to middle and low-expanding materials. Thermal diffusivity (298–573 K) of the ceramic samples of phosphates slightly decreased with temperature increasing. As was demonstrated, the studied phosphates are characterized by the better thermophysical characteristics than widespread fire-resistant materials, such as zirconia and etc.

Keywords: NASICON, NZP, phosphate, structure, synthesis, thermophysical properties.

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Authors: Emna Benmohamed, Hela Ltifi, Mounir Ben Ayed

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Bayesian Network (BN) is one of the most efficient classification methods. It is widely used in several fields (i.e., medical diagnostics, risk analysis, bioinformatics research). The BN is defined as a probabilistic graphical model that represents a formalism for reasoning under uncertainty. This classification method has a high-performance rate in the extraction of new knowledge from data. The construction of this model consists of two phases for structure learning and parameter learning. For solving this problem, the K2 algorithm is one of the representative data-driven algorithms, which is based on score and search approach. In addition, the integration of the expert's knowledge in the structure learning process allows the obtainment of the highest accuracy. In this paper, we propose a hybrid approach combining the improvement of the K2 algorithm called K2 algorithm for Parents and Children search (K2PC) and the expert-driven method for learning the structure of BN. The evaluation of the experimental results, using the well-known benchmarks, proves that our K2PC algorithm has better performance in terms of correct structure detection. The real application of our model shows its efficiency in the analysis of the phosphate laundry effluents' impact on the watershed in the Gafsa area (southwestern Tunisia).

Keywords: Classification, Bayesian network; structure learning, K2 algorithm, expert knowledge, surface water analysis.

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Authors: H. Katkhuda

Abstract:

A time domain approach is used in this paper to identify unknown dynamic forces applied on two dimensional frames using the measured dynamic structural responses for a sub-structure in the two dimensional frame. In this paper a sub-structure finite element model with short length of measurement from only three or four accelerometers is required, and an iterative least-square algorithm is used to identify the unknown dynamic force applied on the structure. Validity of the method is demonstrated with numerical examples using noise-free and noise-contaminated structural responses. Both harmonic and impulsive forces are studied. The results show that the proposed approach can identify unknown dynamic forces within very limited iterations with high accuracy and shows its robustness even noise- polluted dynamic response measurements are utilized.

Keywords: Dynamic Force Identification, Dynamic Responses, Sub-structure and Time Domain.

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Authors: Yasser F. Hassan

Abstract:

Deep learning structure is a branch of machine learning science and greet achievement in research and applications. Cellular neural networks are regarded as array of nonlinear analog processors called cells connected in a way allowing parallel computations. The paper discusses how to use deep learning structure for representing neural cellular automata model. The proposed learning technique in cellular automata model will be examined from structure of deep learning. A deep automata neural cellular system modifies each neuron based on the behavior of the individual and its decision as a result of multi-level deep structure learning. The paper will present the architecture of the model and the results of simulation of approach are given. Results from the implementation enrich deep neural cellular automata system and shed a light on concept formulation of the model and the learning in it.

Keywords: Cellular automata, neural cellular automata, deep learning, classification.

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Authors: Maria V. Morozova, Yulia V. Emelyanova, Anastasia A. Levina, Elena S. Buyanova, Zoya A. Mikhaylovskaya, Sofia A. Petrova

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The solid solutions of lanthanum niobates substituted by yttrium, bismuth and tungsten were synthesized. The structure of the solid solutions is either LaNbO₄-based monoclinic or BiNbO₄-based triclinic. The series where niobium is substituted by tungsten on B site reveals phase-modulated structure. The values of cell parameters decrease with increasing the dopant concentration for all samples except the tungsten series although the latter show higher total conductivity.

Keywords: Impedance spectroscopy, LaNbO4, lanthanum ortho-niobates.

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Authors: Shreya Thusoo, Karan Modi, Ankit Kumar Jha, Rajesh Kumar

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Since the evolution of computational tools and simulation software, there has been considerable increase in research on Soil Structure Interaction (SSI) to decrease the computational time and increase accuracy in the results. To aid the designer with a proper understanding of the response of structure in different soil types, the presented paper compares the deformation, shear stress, acceleration and other parameters of multi-storey building for a specific input ground motion using Response-spectrum Analysis (RSA) method. The response of all the models of different heights have been compared in different soil types. Finite Element Simulation software, ANSYS, has been used for all the computational purposes. Overall, higher response is observed with SSI, while it increases with decreasing stiffness of soil.

Keywords: Soil-structure interaction, response-spectrum analysis, finite element method, multi-storey buildings.

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Authors: Krestina V. Alsaraeva, Victor E. Gromov, Sergey V. Konovalov, Anna A. Atroshkina

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Processing of Al-19.4Si alloy by high intensive electron beam has been carried out and multiple increases in fatigue life of the material have been revealed. Investigations of structure and surface modified layer destruction of Al-19.4Si alloy subjected to multicycle fatigue tests to fracture have been carried out by methods of scanning electron microscopy. The factors responsible for the increase of fatigue life of Al-19.4Si alloy have been revealed and analyzed.

Keywords: Al-19.4Si alloy, high intensive electron beam, multicycle fatigue, structure.

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Authors: Sung-Chul Hwang, Di Ren, Sang-Moon Yoon, Jong-Chun Park, Abbas Khayyer, Hitoshi Gotoh

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This paper presents a fully Lagrangian coupled Fluid-Structure Interaction (FSI) solver for simulations of fluid-structure interactions, which is based on the Moving Particle Semi-implicit (MPS) method to solve the governing equations corresponding to incompressible flows as well as elastic structures. The developed solver is verified by reproducing the high velocity impact loads of deformable thin wedges with three different materials such as mild steel, aluminium and tin during water entry. The present simulation results for aluminium are compared with analytical solution derived from the hydrodynamic Wagner model and linear Wan’s theory. And also, the impact pressure and strain on the water entry wedge with three different materials, such as mild steel, aluminium and tin, are simulated and the effects of hydro-elasticity are discussed.

Keywords: Fluid-structure interaction (FSI), Moving Particle Semi-implicit (MPS) method, Elastic structure, Incompressible fluid Wedge slamming impact.

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Authors: A. Eman Mohammed

Abstract:

Algae-based fuel are considered a promising sources of clean energy, and because it has many advantages over traditional biofuel, research and business ventures have driven into developing and producing Algal-biofuel. But its production stages create a cost structure that it is not competitive with traditional fuels. Therefore, cost becomes the main obstacle in commercial production purpose. However, the present research which aims at using cost structure model, and designed MS-Dose program, to investigate the a mount of production cost and determined the parameter had great effect on it, second to measured the amount of contribution rate of algae in process the pollution by capturing Co2 from air . The result generated from the model shows that the production cost of biomass is between $0.137 /kg for 100 ha and $0.132 /kg for 500 ha which was less than cost of other studies, while gallon costs between $3.4 - 3.5, more than traditional sources of oil about $1 ,which regarded as a rate of contribution of algal in capturing CO2 from air.

Keywords: Cost Structure Model, Operation Costs(Production Cost), Capital Costs, Algae.

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Authors: Jebari Chaker, Ounalli Habib

Abstract:

This paper presents a new approach for automatic document categorization. Exploiting the logical structure of the document, our approach assigns a HTML document to one or more categories (thesis, paper, call for papers, email, ...). Using a set of training documents, our approach generates a set of rules used to categorize new documents. The approach flexibility is carried out with rule weight association representing your importance in the discrimination between possible categories. This weight is dynamically modified at each new document categorization. The experimentation of the proposed approach provides satisfactory results.

Keywords: categorization rule, document categorization, flexible categorization, logical structure.

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Authors: O. M. Bamigbola, A. A. Ibrahim

Abstract:

Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined apriori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss- Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss- Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.

Keywords: Linear system of equations, Gauss-Seidel iteration, algebraic structure, convergence.

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