878 resultados para Approximate Solution
Resumo:
A type of ZrO(2)center dot nH(2)O Was synthesized and its Cr(VI) removal potential was investigated in this study. The kinetic study, adsorption isotherm, pH effect, thermodynamic study and desorption were examined in batch experiments. The kinetic process was described by a pseudo-second-order rate model very well. The Cr(VI) adsorption tended to increase with a decrease of pH. The adsorption data fitted well to the Langmuir model. The adsorption capacity increased from 61 to 66 mg g(-1) when the temperature was increased from 298 to 338 K. The positive values of both Delta H degrees and Delta S degrees suggest an endothermic reaction and increase in randomness at the solid-liquid interface during the adsorption. Delta G degrees values obtained were negative indicating a spontaneous adsorption process. The effective desorption of Cr(VI) on ZrO(2)center dot nH(2)O could be achieved using distilled water at pH 12. (C) 2009 Elsevier B.V. All rights reserved.
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Ti-6Al-4V alloy has been widely used in restorative surgery due to its high corrosion resistance and biocompatibility. Nevertheless, some studies showed that V and Al release in the organism might induce cytotoxic effects and neurological disorders, which led to the development of V-free alloys and both V- and Al-free alloys containing Nb, Zr, Ta, or Mo. Among these alloys, Ti-13Nb-13Zr alloy is promising due to its better biomechanical compatibility than Ti-6Al-4V. In this work, the corrosion behavior of Ti, Ti-6Al-4V, and Ti-xNb-13Zr alloys (x=5, 13, and 20) was evaluated in Ringer`s solution (pH 7.5) at 37 degrees C through open-circuit potential measurements, potentiodynamic polarization, and electrochemical impedance spectroscopy. Spontaneous passivity was observed for all materials in this medium. Low corrosion current densities (in the order of 10(-7) A/cm(2)) and high impedance values (in the order of 10(5) Omega cm(2) at low frequencies) indicated their high corrosion resistance. EIS results showed that the passivating films were constituted of an outer porous layer (very low resistance) and an inner compact layer (high resistance), the latter providing the corrosion resistance of the materials. There was evidence that the Ti-xNb-13Zr alloys were more corrosion resistant than both Ti and Ti-6Al-4V in Ringer`s solution.
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This work presents the study and development of a combined fault location scheme for three-terminal transmission lines using wavelet transforms (WTs). The methodology is based on the low- and high-frequency components of the transient signals originated from fault situations registered in the terminals of a system. By processing these signals and using the WT, it is possible to determine the time of travelling waves of voltages and/or currents from the fault point to the terminals, as well as estimate the fundamental frequency components. A new approach presents a reliable and accurate fault location scheme combining some different solutions. The main idea is to have a decision routine in order to select which method should be used in each situation presented to the algorithm. The combined algorithm was tested for different fault conditions by simulations using the ATP (Alternative Transients Program) software. The results obtained are promising and demonstrate a highly satisfactory degree of accuracy and reliability of the proposed method.
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The purpose of this paper is to propose a multiobjective optimization approach for solving the manufacturing cell formation problem, explicitly considering the performance of this said manufacturing system. Cells are formed so as to simultaneously minimize three conflicting objectives, namely, the level of the work-in-process, the intercell moves and the total machinery investment. A genetic algorithm performs a search in the design space, in order to approximate to the Pareto optimal set. The values of the objectives for each candidate solution in a population are assigned by running a discrete-event simulation, in which the model is automatically generated according to the number of machines and their distribution among cells implied by a particular solution. The potential of this approach is evaluated via its application to an illustrative example, and a case from the relevant literature. The obtained results are analyzed and reviewed. Therefore, it is concluded that this approach is capable of generating a set of alternative manufacturing cell configurations considering the optimization of multiple performance measures, greatly improving the decision making process involved in planning and designing cellular systems. (C) 2010 Elsevier Ltd. All rights reserved.
Resumo:
In this paper, we address the problem of scheduling jobs in a no-wait flowshop with the objective of minimising the total completion time. This problem is well-known for being nondeterministic polynomial-time hard, and therefore, most contributions to the topic focus on developing algorithms able to obtain good approximate solutions for the problem in a short CPU time. More specifically, there are various constructive heuristics available for the problem [such as the ones by Rajendran and Chaudhuri (Nav Res Logist 37: 695-705, 1990); Bertolissi (J Mater Process Technol 107: 459-465, 2000), Aldowaisan and Allahverdi (Omega 32: 345-352, 2004) and the Chins heuristic by Fink and Voa (Eur J Operat Res 151: 400-414, 2003)], as well as a successful local search procedure (Pilot-1-Chins). We propose a new constructive heuristic based on an analogy with the two-machine problem in order to select the candidate to be appended in the partial schedule. The myopic behaviour of the heuristic is tempered by exploring the neighbourhood of the so-obtained partial schedules. The computational results indicate that the proposed heuristic outperforms existing ones in terms of quality of the solution obtained and equals the performance of the time-consuming Pilot-1-Chins.
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In this paper, the method of Galerkin and the Askey-Wiener scheme are used to obtain approximate solutions to the stochastic displacement response of Kirchhoff plates with uncertain parameters. Theoretical and numerical results are presented. The Lax-Milgram lemma is used to express the conditions for existence and uniqueness of the solution. Uncertainties in plate and foundation stiffness are modeled by respecting these conditions, hence using Legendre polynomials indexed in uniform random variables. The space of approximate solutions is built using results of density between the space of continuous functions and Sobolev spaces. Approximate Galerkin solutions are compared with results of Monte Carlo simulation, in terms of first and second order moments and in terms of histograms of the displacement response. Numerical results for two example problems show very fast convergence to the exact solution, at excellent accuracies. The Askey-Wiener Galerkin scheme developed herein is able to reproduce the histogram of the displacement response. The scheme is shown to be a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2009 Elsevier Ltd. All rights reserved.
Resumo:
We consider a class of two-dimensional problems in classical linear elasticity for which material overlapping occurs in the absence of singularities. Of course, material overlapping is not physically realistic, and one possible way to prevent it uses a constrained minimization theory. In this theory, a minimization problem consists of minimizing the total potential energy of a linear elastic body subject to the constraint that the deformation field must be locally invertible. Here, we use an interior and an exterior penalty formulation of the minimization problem together with both a standard finite element method and classical nonlinear programming techniques to compute the minimizers. We compare both formulations by solving a plane problem numerically in the context of the constrained minimization theory. The problem has a closed-form solution, which is used to validate the numerical results. This solution is regular everywhere, including the boundary. In particular, we show numerical results which indicate that, for a fixed finite element mesh, the sequences of numerical solutions obtained with both the interior and the exterior penalty formulations converge to the same limit function as the penalization is enforced. This limit function yields an approximate deformation field to the plane problem that is locally invertible at all points in the domain. As the mesh is refined, this field converges to the exact solution of the plane problem.
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The Darcy-Weisbach equation was used in the analysis of flow over spillways, furnishing theoretical tools to design stilling basins. Predictions for the length of hydraulic jump stilling basins downstream of stepped and smooth spillways are presented, together with ranges of values for the Darcy-Weisbach friction factor of both spillways. The experimental data were compared with results of the theoretical solution of the gradually varied flow equation. All comparisons were made in non-dimensional form. The values of the Darcy-Weisbach friction factor were roughly five times smaller for smooth spillways than for stepped spillways. The theoretical predictions and the experimental data allow to present approximate equations for a preliminary evaluation of the length and the bed level of hydraulic jump stilling basins. In the same way, approximate equations were presented for the evaluation of the friction factor in smooth and stepped spillways, as a function of the Froude number at the downstream cross-section.
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A modeling study was completed to develop a methodology that combines the sequencing and finite difference methods for the simulation of a heterogeneous model of a tubular reactor applied in the treatment of wastewater. The system included a liquid phase (convection diffusion transport) and a solid phase (diffusion reaction) that was obtained by completing a mass balance in the reactor and in the particle, respectively. The model was solved using a pilot-scale horizontal-flow anaerobic immobilized biomass (HAIB) reactor to treat domestic sewage, with the concentration results compared with the experimental data. A comparison of the behavior of the liquid phase concentration profile and the experimental results indicated that both the numerical methods offer a good description of the behavior of the concentration along the reactor. The advantage of the sequencing method over the finite difference method is that it is easier to apply and requires less computational time to model the dynamic simulation of outlet response of HAIB.
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Vibration-based energy harvesting has been investigated by several researchers over the last decade. The goal in this research field is to power small electronic components by converting the waste vibration energy available in their environment into electrical energy. Recent literature shows that piezoelectric transduction has received the most attention for vibration-to-electricity conversion. In practice, cantilevered beams and plates with piezoceramic layers are employed as piezoelectric energy harvesters. The existing piezoelectric energy harvester models are beam-type lumped parameter, approximate distributed parameter and analytical distributed parameter solutions. However, aspect ratios of piezoelectric energy harvesters in several cases are plate-like and predicting the power output to general (symmetric and asymmetric) excitations requires a plate-type formulation which has not been covered in the energy harvesting literature. In this paper. an electromechanically coupled finite element (FE) plate model is presented for predicting the electrical power output of piezoelectric energy harvester plates. Generalized Hamilton`s principle for electroelastic bodies is reviewed and the FE model is derived based on the Kirchhoff plate assumptions as typical piezoelectric energy harvesters are thin structures. Presence of conductive electrodes is taken into account in the FE model. The predictions of the FE model are verified against the analytical solution for a unimorph cantilever and then against the experimental and analytical results of a bimorph cantilever with a tip mass reported in the literature. Finally, an optimization problem is solved where the aluminum wing spar of an unmanned air vehicle (UAV) is modified to obtain a generator spar by embedding piezoceramics for the maximum electrical power without exceeding a prescribed mass addition limit. (C) 2009 Elsevier Ltd. All rights reserved.
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The influence of the solvent-evaporation rate on the formation of of. and P crystalline phases in solution-cast poly(vinylidene fluoride) (PVDF) films was systematically investigated. Films were crystallized from PVDF/N,N-dimethylformamide solutions with concentrations of 2.5, 5.0, 10, and 20 wt % at different temperatures. During crystallization, the solvent evaporation rate was monitored in situ by means of a semianalytic balance. With this system, it was possible to determine the evaporation rate for different concentrations and temperatures of the solution under specific ambient conditions (pressure, temperature, and humidity). Fourier-Transform InfraRed spectroscopy with Attenuated Total Reflectance revealed the P-phase content in the PVDF films and its dependence on previous evaporation rates. Based on the relation between the evaporation rate and the PVDF phase composition, a consistent explanation for the different amounts of P phase observed at the upper and lower sample surfaces is achieved. Furthermore, the role of the sample thickness has also been studied. The experimental results show that not only the temperature but also the evaporation rate have to be controlled to obtain the desired crystalline phases in solution-cast PVDF films. (C) 2009 Wiley Periodicals, Inc. J Appl Polym Sci 116: 785-791, 2010
Resumo:
An exact non-linear formulation of the equilibrium of elastic prismatic rods subjected to compression and planar bending is presented, electing as primary displacement variable the cross-section rotations and taking into account the axis extensibility. Such a formulation proves to be sufficiently general to encompass any boundary condition. The evaluation of critical loads for the five classical Euler buckling cases is pursued, allowing for the assessment of the axis extensibility effect. From the quantitative viewpoint, it is seen that such an influence is negligible for very slender bars, but it dramatically increases as the slenderness ratio decreases. From the qualitative viewpoint, its effect is that there are not infinite critical loads, as foreseen by the classical inextensible theory. The method of multiple (spatial) scales is used to survey the post-buckling regime for the five classical Euler buckling cases, with remarkable success, since very small deviations were observed with respect to results obtained via numerical integration of the exact equation of equilibrium, even when loads much higher than the critical ones were considered. Although known beforehand that such classical Euler buckling cases are imperfection insensitive, the effect of load offsets were also looked at, thus showing that the formulation is sufficiently general to accommodate this sort of analysis. (c) 2008 Elsevier Ltd. All rights reserved.
Resumo:
This paper presents a study of the stationary phenomenon of superheated or metastable liquid jets, flashing into a two-dimensional axisymmetric domain, while in the two-phase region. In general, the phenomenon starts off when a high-pressure, high-temperature liquid jet emerges from a small nozzle or orifice expanding into a low-pressure chamber, below its saturation pressure taken at the injection temperature. As the process evolves, crossing the saturation curve, one observes that the fluid remains in the liquid phase reaching a superheated condition. Then, the liquid undergoes an abrupt phase change by means of an oblique evaporation wave. Across this phase change the superheated liquid becomes a two-phase high-speed mixture in various directions, expanding to supersonic velocities. In order to reach the downstream pressure, the supersonic fluid continues to expand, crossing a complex bow shock wave. The balance equations that govern the phenomenon are mass conservation, momentum conservation, and energy conservation, plus an equation-of-state for the substance. A false-transient model is implemented using the shock capturing scheme: dispersion-controlled dissipative (DCD), which was used to calculate the flow conditions as the steady-state condition is reached. Numerical results with computational code DCD-2D vI have been analyzed. Copyright (C) 2009 John Wiley & Sons, Ltd.
Resumo:
The exact vibration modes and natural frequencies of planar structures and mechanisms, comprised Euler-Bernoulli beams, are obtained by solving a transcendental. nonlinear, eigenvalue problem stated by the dynamic stiffness matrix (DSM). To solve this kind of problem, the most employed technique is the Wittrick-Williams algorithm, developed in the early seventies. By formulating a new type of eigenvalue problem, which preserves the internal degrees-of-freedom for all members in the model, the present study offers an alternative to the use of this algorithm. The new proposed eigenvalue problem presents no poles, so the roots of the problem can be found by any suitable iterative numerical method. By avoiding a standard formulation for the DSM, the local mode shapes are directly calculated and any extension to the beam theory can be easily incorporated. It is shown that the method here adopted leads to exact solutions, as confirmed by various examples. Extensions of the formulation are also given, where rotary inertia, end release, skewed edges and rigid offsets are all included. (C) 2008 Elsevier Ltd. All rights reserved.
Resumo:
This paper presents a family of algorithms for approximate inference in credal networks (that is, models based on directed acyclic graphs and set-valued probabilities) that contain only binary variables. Such networks can represent incomplete or vague beliefs, lack of data, and disagreements among experts; they can also encode models based on belief functions and possibilistic measures. All algorithms for approximate inference in this paper rely on exact inferences in credal networks based on polytrees with binary variables, as these inferences have polynomial complexity. We are inspired by approximate algorithms for Bayesian networks; thus the Loopy 2U algorithm resembles Loopy Belief Propagation, while the Iterated Partial Evaluation and Structured Variational 2U algorithms are, respectively, based on Localized Partial Evaluation and variational techniques. (C) 2007 Elsevier Inc. All rights reserved.