Bending of stochastic Kirchhoff plates on Winkler foundations via the Galerkin method and the Askey-Wiener scheme

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.

Timoshenko versus Euler beam theory: Pitfalls of a deterministic approach

The selection criteria for Euler-Bernoulli or Timoshenko beam theories are generally given by means of some deterministic rule involving beam dimensions. The Euler-Bernoulli beam theory is used to model the behavior of flexure-dominated (or ""long"") beams. The Timoshenko theory applies for shear-dominated (or ""short"") beams. In the mid-length range, both theories should be equivalent, and some agreement between them would be expected. Indeed, it is shown in the paper that, for some mid-length beams, the deterministic displacement responses for the two theories agrees very well. However, the article points out that the behavior of the two beam models is radically different in terms of uncertainty propagation. In the paper, some beam parameters are modeled as parameterized stochastic processes. The two formulations are implemented and solved via a Monte Carlo-Galerkin scheme. It is shown that, for uncertain elasticity modulus, propagation of uncertainty to the displacement response is much larger for Timoshenko beams than for Euler-Bernoulli beams. On the other hand, propagation of the uncertainty for random beam height is much larger for Euler beam displacements. Hence, any reliability or risk analysis becomes completely dependent on the beam theory employed. The authors believe this is not widely acknowledged by the structural safety or stochastic mechanics communities. (C) 2010 Elsevier Ltd. All rights reserved.

Galerkin Solution of Stochastic Beam Bending on Winkler Foundations

In this paper, the Askey-Wiener scheme and the Galerkin method are used to obtain approximate solutions to stochastic beam bending on Winkler foundation. The study addresses Euler-Bernoulli beams with uncertainty in the bending stiffness modulus and in the stiffness of the foundation. Uncertainties are represented by parameterized stochastic processes. The random behavior of beam response is modeled using the Askey-Wiener scheme. One contribution of the paper is a sketch of proof of existence and uniqueness of the solution to problems involving fourth order operators applied to random fields. From the approximate Galerkin solution, expected value and variance of beam displacement responses are derived, and compared with corresponding estimates obtained via Monte Carlo simulation. Results show very fast convergence and excellent accuracies in comparison to Monte Carlo simulation. The Askey-Wiener Galerkin scheme presented herein is shown to be a theoretically solid and numerically efficient method for the solution of stochastic problems in engineering.

The random barrier-crossing problem

This paper addresses the time-variant reliability analysis of structures with random resistance or random system parameters. It deals with the problem of a random load process crossing a random barrier level. The implications of approximating the arrival rate of the first overload by an ensemble-crossing rate are studied. The error involved in this so-called ""ensemble-crossing rate"" approximation is described in terms of load process and barrier distribution parameters, and in terms of the number of load cycles. Existing results are reviewed, and significant improvements involving load process bandwidth, mean-crossing frequency and time are presented. The paper shows that the ensemble-crossing rate approximation can be accurate enough for problems where load process variance is large in comparison to barrier variance, but especially when the number of load cycles is small. This includes important practical applications like random vibration due to impact loadings and earthquake loading. Two application examples are presented, one involving earthquake loading and one involving a frame structure subject to wind and snow loadings. (C) 2007 Elsevier Ltd. All rights reserved.

Evaluation of rock mechanical behaviors under uniaxial compression with reference to assessed weathering grades

A weathering classification for granitic rock materials from southeastern Brazil was framed based on core characteristics. The classification was substantiated by a detailed petrographic study. Indirect assessment of weathering grades by density, ultrasonic and Schmidt hammer index tests was performed. Rebound values due to Schmidt hammer multiple impacts at one representative point were more efficient in predicting weathering grades than averaged single impact rebound values, P-wave velocities and densities. Uniaxial compression tests revealed that a large range of uniaxial compressive strength (214-153 MPa) exists in Grade I category where weathering does not seem to have played any role. It was concluded that variability in occurrences of quartz intragranular cracks and in biotite percentage, distribution and orientation might have played a key role in accelerating or decelerating the failure processes of the Grade I specimens. Deterioration of uniaxial compressive strength and elastic modulus and increase in Poisson`s ratio with increasing weathering intensity could be attributed to alteration of minerals, disruption of rock skeleton and microcrack augmentation. A crude relation between failure modes and weathering grades also emerged.

Study of the water retention properties of a tropical soil

Some peculiarities of water retention in a tropical lateritic soil of clayey nature are presented and discussed. The typical soil microstructure is shown through thin-layer plates emphasizing soil microaggregation and pore distribution and their repercussion on the soil-water retention curve and on hysteresis. It is shown that the clayey soil has a behavior that to a large extent resembles sandy soil, which is characterized by the relatively high saturated hydraulic conductivity, low air-entry value, and small suction range at which water drainage takes place. The severe weathering processes that originated this soil have produced an altered soil that seems to be homogeneous in terms of physical indices, hydraulic conductivity, and soil-water retention characteristics, up to 4.5 m in depth.

Toxicity and recalcitrant compound removal from bleaching pulp plant effluents by an integrated system: anaerobic packed-bed bioreactor and ozone

Effluents originated in cellulose pulp manufacturing processes are usually toxic and recalcitrant, specially the bleaching effluents, which exhibit high contents of aromatic compounds (e.g. residual lignin derivates). Although biological processes are normally used, their efficiency for the removal of toxic lignin derivates is low. The toxicity and recalcitrance of a bleached Kraft pulp mill were assessed through bioassays and ultraviolet absorption measurements, i.e. acid soluble lignin (ASL), UV(280), and specific ultraviolet absorption (SUVA), before and after treatment by an integrated system comprised of an anaerobic packed-bed bioreactor and oxidation step with ozone. Furthermore, adsorbable organic halides (AOX) were measured. The results demonstrated not only that the toxic recalcitrant compounds can be removed successfully using integrated system, but also the ultraviolet absorption measurements can be an interesting control-parameter in a wastewater treatment.

An upflow fixed-bed anaerobic-aerobic reactor for removal of organic matter and nitrogen from L-lysine plant wastewater

This paper reports on the design of a new reactor configuration - an upflow fixed-bed combined anaerobic-aerobic reactor - can operate as a single treatment unit for the removal of nitrogen (approximate to 150 mg N/L) and organic matter (approximate to 1300 mg COD/L) from Lysine plant wastewater. L-Lysine, an essential amino acid for animal nutrition, is produced by fermentation from natural raw materials of agricultural origin, thus generating wastewater with high contents of organic matter and nitrogen. The best operational condition of the reactor was obtained with a hydraulic retention time of 35 h (21 h in the anaerobic zone and 14 h in the aerobic zone) and a recycling ratio (R) of 3.5. In this condition, the COD, total Kjeldahl nitrogen (TKN), and total nitrogen (TN) removal efficiencies were 97%, 96%, and 77%, respectively, with average effluent concentrations of 10 +/- 36 mg COD/L, 2 +/- 1 mg NH(4)(+)-N/L, 8 +/- 3 mg Org-N/L, 1 +/- 1 mg NH(2)(-)-N/L, and 26 +/- 23 mg NH(3)(-)-N/L.

Feasibility of a Sequencing Reactor Operated in Batch and Fed-batch Mode Applied to Nitrification and Denitrification Processes

The objective of this work was to study the operational feasibility of nitrification and denitrification processes in a mechanically stirred sequencing batch reactor (SBR) operated in batch and fed-batch mode. The reactor was equipped with a draft-tube to improve mass transfer and contained dispersed (aerobic) and granulated (anaerobic) biomass. The following reactor variables were adjusted: aeration time during the nitrification step; dissolved oxygen concentration, feed time defining batch and fed-batch phases, concentration of external carbon source used as electron donor during the denitrification stage and volumetric ammonium nitrogen load in the influent. The reactor (5 L volume) was maintained at 30 +/- 1 degrees C and treated either 1.0 or 1.5 L wastewater in 8-h cycles. Ammonium nitrogen concentrations assessed were: 50 (condition 1) and 100 mgN-NH(4)(+).L(-1) (condition 2), resulting in 29 and 67 mgN-NH(4)(+).L-1-d(-1), respectively. A synthetic medium and ethanol were used as external carbon sources (ECS). Total nitrogen removal efficiencies were 94.4 and 95.9% when the reactor was operated under conditions 1 and 2, respectively. Low nitrite (0.2 and 0.3 mgN-NO(2)(-).L(-1), respectively) and nitrate (0.01 and 0.3 mgN-NO(3)(-).L(-1), respectively) concentrations were detected in the effluent and ammonium nitrogen removal efficiencies were 97.6% and 99.6% under conditions 1 and 2, respectively.

Treatment of industrial effluents of recalcitrant nature using ozone, hydrogen peroxide and ultraviolet radiation

Currently diverse industries have high pollution potential because their productive processes generate great volumes of refractory effluents. These effluents are problematic, mainly due to the presence of recalcitrant compounds that are detrimental in wastewater treatment plants using biological systems in their processes. In general, biological treatments do not remove refractory elements. Also, in most cases these compounds can inhibit the yield or are toxic for biota responsible to remove the polluting agents. The Advanced Oxidative Processes (AOPs) represent a technological alternative with a great potential for treatment of no biodegradable effluents. In this paper a review of the use of advanced oxidatives processes: Ozone (O(3)), peroxide of hydrogen (H(2)O(2)) and ultraviolet radiation (UV) is presented applied to the treatment of recalcitrant effluents.

Anaerobic sequencing batch biofilm reactor applied to automobile industry wastewater treatment: Volumetric loading rate and feed strategy effects

This paper presents a technological viability study of wastewater treatment in an automobile industry by an anaerobic sequencing batch biofilm reactor containing immobilized biomass (AnSBBR) with a draft tube. The reactor was operated in 8-h cycles, with agitation of 400 rpm, at 30 degrees C and treating 2.0 L wastewater per cycle. Initially the efficiency and stability of the reactor were studied when supplied with nutrients and alkalinity. Removal efficiency of 88% was obtained at volumetric loading rate (VLR) of 3.09 mg COD/L day. When VLR was increased to 6.19 mg COD/L day the system presented stable operation with reduction in efficiency of 71%. In a second stage the AnSBBR was operated treating wastewater in natura, i.e., without nutrients supplementation, only with alkalinity, thereby changing feed strategy. The first strategy consisted in feeding 2.0 L batch wise (10 min), the second in feeding 1.0 L of influent batch wise (10 min) and an additional 1.0 L fed-batch wise (4 h), both dewatering 2.0 L of the effluent in 10 min. The third one maintained 1.0 L of treated effluent in the reactor, without discharging, and 1.0 L of influent was fed fed-batch wise (4 h) with dewatering 1.0 L of the effluent in 10 min. For all implemented strategies (VLR of 1.40, 2.57 and 2.61 mg COD/L day) the system presented stability and removal efficiency of approximately 80%. These results show that the AnSBBR presents operational flexibility, as the influent can be fed according to industry availability. In industrial processes this is a considerable advantage, as the influent may be prone to variations. Moreover, for all the investigated conditions the kinetic parameters were obtained from fitting a first-order model to the profiles of organic matter, total volatile acids and methane concentrations. Analysis of the kinetic parameters showed that the best strategy is feeding 1.0 L of influent batchwise (10 min) and 1.0 L fed-batch wise (4 h) in 8-h cycle. (c) 2007 Elsevier B.V. All rights reserved.

The influence of immobilized biomass and particle size on the fluid dynamics of an anaerobic fluidized bed reactor

Fluid dynamic analysis is an important branch of several chemical engineering related areas, such as drying processes and chemical reactors. However, aspects concerning fluid dynamics in wastewater treatment bioreactors still require further investigation, as they highly influence process efficiency. Therefore, it is essential to evaluate the influence of biofilm on the reactor fluid dynamic behavior, through the analysis of a few important parameters, such as minimum fluidization velocity, bed expansion and porosity, and particle terminal velocity. The main objective of the present work was to investigate the fluid dynamics of an anaerobic fluidized bed reactor, having activated carbon particles as support media for biomass immobilization. Reactor performance was tested using synthetic residual water, which was prepared using the solution employed in BOD determination. The results showed that the presence of immobilized biomass increased particle density and altered the main fluid dynamic parameters investigated.

Quality of martensitic stainless steel type AISI-420 utilized in the manufacture surgical implements

Until now the martensitic stainless steel type AISI-420 is widely used in the manufacture of surgical implements. These implements present premature corrosion problems identified after cleaning, sterilization and cutting edge loss and/or rupture during the surgical processes.. This study evaluates the steel as to the chemical composition, hardness, microstructure and pitting corrosion resistance in a solution of enzyme detergent diluted in water by anodic cyclic polarization. This mixture is used in the cleaning of surgical implements that are submerged in this solution for 2 h before cleaning and sterilization. The results show steels with martensite microstructures in the ferrite phase, together with impurities. These presented low pitting potential values in compariston to steels with a fully martensitic microstructure.

Development of new rapid prototyping process

Purpose - The purpose of this paper is to identify the key elements of a new rapid prototyping process, which involves layer-by-layer deposition of liquid-state material and at the same time using an ultraviolet line source to cure the deposited material. This paper reports studies about the behaviour of filaments, deposition accuracy, filaments interaction and functional feasibility of system. Additionally, the author describes the process which has been proposed, the equipment that has been used for these studies and the material which was developed in this application. Design/methodology/approach - The research has been separated into three study areas in accordance with their goals. In the first, both the behaviour of filament and deposition accuracy was studied. The design of the experiment is described with focus on four response factors (bead width, filament quality, deposition accuracy and deposition continuity) along with function of three control factors (deposition height, deposition velocity and extrusion velocity). The author also studied the interaction between filaments as a function of bead centre distance. In addition, two test samples were prepared to serve as a proof of the methodology and to verify the functional feasibility of the process which has been studied. Findings - The results show that the proposed process is functionally feasible, and that it is possible to identify the main effects of control factors over response factors. That analysis is used to predict the condition of process as a function of the parameters which control the process. Also identified were distances of centre beads which result in a specific behaviour. The types of interaction between filaments were analysed and sorted into: union, separation and indeterminate. At the end, the functional feasibility of process was proved whereby two test parts could be built. Originality/value - This paper proposes a new rapid prototyping process and also presents test studies related to this proposition. The author has focused on the filament behaviour, deposition accuracy, interaction between filaments and studied the functional feasibility of process to provide new information about this process, which at the same time is useful to the development of other rapid prototyping processes.

Combination of an anaerobic process with O(3), UV and O(3)/UV for cellulose pulp bleaching effluent treatment

Recent studies have shown that partial oxidation by advanced oxidation processes (AOP) is able to transform hard-to-degrade compounds and increase their biodegradability. In this work, anaerobic treatment was followed by ozonation, UV radiation and ozonation in the presence of UV radiation, to treat bleaching effluents from a cellulose kraft Pulp plant. The anaerobic reactor (horizontal anaerobic immobilized Sludge bed, HAISB) was Used as a pretreatment to reduce the efficient organic load before applying ACIP. The ozone treatments were applied in three different pH environments (3, 8 and 10) with retention times of 10, 30, 45 and 60 min. COD and adsorbable organic halogens (AOX) removal efficiencies at the HAISB were approximately 50%, while the BOD removal efficiency reached 80%. Ozonation promoted further removal of AOX and COD so that the combined efficiency reached 96% for AOX and 70% for COD. In the oxidation process, BOD was either removed in small quantities or actually increased, as intended, so that a second biological treatment would be able to complete the treatment. The maximum increase in the BOD(5)/COD ratio (biodegradability indicator) Occurred at pH 8, reaching 104% for ozonation at a dosage of 1540 mg(O3).L(-1). Applying UV radiation alone resulted in lower values: a 34% increase ill the BOD(5)/COD ratio and a 76% AOX removal efficiency. These results indicate that the combination of anaerobic treatment with ozonation or ozonation/UV radiation improves the treatability of cellulose pulp bleaching efficients and that the resulting wastewater is suitable for further biological treatment under aerobic conditions with a low level of toxic compounds from the halogenated family.