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.

A simple method for non-linear analysis of steel fiber reinforced concrete

This paper proposes a physical non-linear formulation to deal with steel fiber reinforced concrete by the finite element method. The proposed formulation allows the consideration of short or long fibers placed arbitrarily inside a continuum domain (matrix). The most important feature of the formulation is that no additional degree of freedom is introduced in the pre-existent finite element numerical system to consider any distribution or quantity of fiber inclusions. In other words, the size of the system of equations used to solve a non-reinforced medium is the same as the one used to solve the reinforced counterpart. Another important characteristic of the formulation is the reduced work required by the user to introduce reinforcements, avoiding ""rebar"" elements, node by node geometrical definitions or even complex mesh generation. Bounded connection between long fibers and continuum is considered, for short fibers a simplified approach is proposed to consider splitting. Non-associative plasticity is adopted for the continuum and one dimensional plasticity is adopted to model fibers. Examples are presented in order to show the capabilities of the formulation.

Inverse analysis FOR two-dimensional structures using the boundary element method

Inverse analysis is currently an important subject of study in several fields of science and engineering. The identification of physical and geometric parameters using experimental measurements is required in many applications. In this work a boundary element formulation to identify boundary and interface values as well as material properties is proposed. In particular the proposed formulation is dedicated to identifying material parameters when a cohesive crack model is assumed for 2D problems. A computer code is developed and implemented using the BEM multi-region technique and regularisation methods to perform the inverse analysis. Several examples are shown to demonstrate the efficiency of the proposed model. (C) 2010 Elsevier Ltd. All rights reserved,

A coupled boundary element/differential equation method formulation for plate-beam interaction analysis

In this work, a new boundary element formulation for the analysis of plate-beam interaction is presented. This formulation uses a three nodal value boundary elements and each beam element is replaced by its actions on the plate, i.e., a distributed load and end of element forces. From the solution of the differential equation of a beam with linearly distributed load the plate-beam interaction tractions can be written as a function of the nodal values of the beam. With this transformation a final system of equation in the nodal values of displacements of plate boundary and beam nodes is obtained and from it, all unknowns of the plate-beam system are obtained. Many examples are analyzed and the results show an excellent agreement with those from the analytical solution and other numerical methods. (C) 2009 Elsevier Ltd. All rights reserved.

GENERALIZED FINITE ELEMENT METHOD FOR NONLINEAR THREE-DIMENSIONAL ANALYSIS OF SOLIDS

The Generalized Finite Element Method (GFEM) is employed in this paper for the numerical analysis of three-dimensional solids tinder nonlinear behavior. A brief summary of the GFEM as well as a description of the formulation of the hexahedral element based oil the proposed enrichment strategy are initially presented. Next, in order to introduce the nonlinear analysis of solids, two constitutive models are briefly reviewed: Lemaitre`s model, in which damage and plasticity are coupled, and Mazars`s damage model suitable for concrete tinder increased loading. Both models are employed in the framework of a nonlocal approach to ensure solution objectivity. In the numerical analyses carried out, a selective enrichment of approximation at regions of concern in the domain (mainly those with high strain and damage gradients) is exploited. Such a possibility makes the three-dimensional analysis less expensive and practicable since re-meshing resources, characteristic of h-adaptivity, can be minimized. Moreover, a combination of three-dimensional analysis and the selective enrichment presents a valuable good tool for a better description of both damage and plastic strain scatterings.

Analysis of stiffened plates by the boundary element method

In this paper, a formulation for representation of stiffeners in plane stress by the boundary elements method (BEM) in linear analysis is presented. The strategy is to adopt approximations for the displacements in the central line of the stiffener. With this simplification the Spurious oscillations in the stress along stiffeners with small thickness is prevented. Worked examples are analyzed to show the efficiency of these techniques, especially in the insertion of very narrow sub-regions, in which quasi-singular integrals are calculated, with stiffeners that are much stiffer than the main domain. The results obtained with this formulation are very close to those obtained with other formulations. (C) 2007 Elsevier Ltd. All rights reserved.

Consolidation of elastic-plastic saturated porous media by the boundary element method

This paper presents a domain boundary element formulation for inelastic saturated porous media with rate-independent behavior for the solid skeleton. The formulation is then applied to elastic-plastic behavior for the solid. Biot`s consolidation theory, extended to include irreversible phenomena is considered and the direct boundary element technique is used for the numerical solution after time discretization by the implicit Euler backward algorithm. The associated nonlinear algebraic problem is solved by the Newton-Raphson procedure whereby the loading/unloading conditions are fully taken into account and the consistent tangent operator defined. Only domain nodes (nodes defined inside the domain) are used to represent all domain values and the corresponding integrals are computed by using an accurate sub-elementation scheme. The developments are illustrated through the Drucker-Prager elastic-plastic model for the solid skeleton and various examples are analyzed with the proposed algorithms. (c) 2008 Elsevier B.V. All rights reserved.

On the analysis of notched concrete beams: From measurement with digital image correlation to identification with boundary element method of a cohesive model

A way of coupling digital image correlation (to measure displacement fields) and boundary element method (to compute displacements and tractions along a crack surface) is presented herein. It allows for the identification of Young`s modulus and fracture parameters associated with a cohesive model. This procedure is illustrated to analyze the latter for an ordinary concrete in a three-point bend test on a notched beam. In view of measurement uncertainties, the results are deemed trustworthy thanks to the fact that numerous measurement points are accessible and used as entries to the identification procedure. (C) 2010 Elsevier Ltd. All rights reserved.

Characterization and kinetics of sulfide-oxidizing autotrophic denitrification in batch reactors containing suspended and immobilized cells

Sulfide-oxidizing autotrophic denitrification is an advantageous alternative over heterotrophic denitrification, and may have potential for nitrogen removal of low-strength wastewaters, such as anaerobically pre-treated domestic sewage. This study evaluated the fundamentals and kinetics of this process in batch reactors containing suspended and immobilized cells. Batch tests were performed for different NO(x)(-)/S(2-) ratios and using nitrate and nitrite as electron acceptors. Autotrophic denitrification was observed for both electron acceptors, and NO(x)(-)/S(2-) ratios defined whether sulfide oxidation was complete or not. Kinetic parameter values obtained for nitrate were higher than for nitrite as electron acceptor. Zero-order models were better adjusted to profiles obtained for suspended cell reactors, whereas first-order models were more adequate for immobilized cell reactors. However, in the latter, mass transfer physical phenomena had a significant effect on kinetics based on biochemical reactions. Results showed that sulfide-oxidizing autotrophic denitrification can be successfully established for low-strength wastewaters and have potential for nitrogen removal from anaerobically pre-treated domestic sewage.

Full-scale anaerobic sequencing batch biofilm reactor for sulfate-rich wastewater treatment

This paper describes the performance and biofilm characteristics of a full-scale anaerobic sequencing batch biofilm reactor (ASBBR; 20 m(3)) containing biomass immobilized on an inert support (mineral coal) for the treatment of industrial wastewater containing a high sulfate concentration. The ASBBR reactor was operated during 110 cycles (48 h each) at sulfate loading rates ranging from 6.9 to 62.4 kgSO(4)(2-)/cycle corresponding to sulfate concentrations of 0.58-5.2 gSO(4)(2-)/L. Domestic sewage and ethanol were utilized as electron donors for sulfate reduction. After 71 cycles the mean sulfate removal efficiency was 99%, demonstrating a high potential for biological sulfate reduction. The biofilm formed in the reactor occurred in two different patterns, one at the beginning of the colonization and the other of a mature biofilm. These different colonization patterns are due to the low adhesion of the microorganisms on the inert support in the start-up period. The biofilm population is mainly made up of syntrophic consortia among sulfate-reducing bacteria and methanogenic archaea such as Methanosaeta spp.

Influence of carbon sources and C/N ratio on EPS production in anaerobic sequencing batch biofilm reactors for wastewater treatment

The objective of this work was to evaluate the influence of different carbon sources and the carbon/nitrogen ratio (C/N) on the production and main composition of insoluble extracellular polymers (EPS) produced in an anaerobic sequencing batch biofilm reactor (ASBBR) with immobilized biomass in polyurethane foam. The yield of EPS was 23.6 mg/g carbon, 13.3 mg/g carbon, 9.0 mg/g carbon and 1.4 mg/g carbon when the reactor was fed with glucose, soybean oil. fat acids, and meat extract, respectively. The yield of EPS decreased from 23.6 to 2.6 mg/g carbon as the C/N ratio was decreased from 13.6 to 3.4 gC/gN, using glucose as carbon source. EPS production was not observed under strict anaerobic conditions. The results suggest that the carbon source, microaerophilic conditions and high C/N ratio favor EPS production in the ASBBR used for wastewater treatment. Cellulose was the main exopolysaccharide observed in all experimental conditions. (C) 2009 Elsevier Ltd. All rights reserved.

Nitrogen removal in a sequencing batch biofilm reactor with liquid circulation: Effect of feed strategy and carbon source in the denitrifying step

Ammonium nitrogen removal from a synthetic wastewater by nitrification and denitrification processes were performed in a sequencing batch biofilm reactor containing immobilized biomass on polyurethane foam with circulation of the liquid-phase. It was analyzed the effect of four external carbon sources (ethanol, acetate, carbon synthetic medium and methanol) acting as electron donors in the denitrifying process. The experiments were conducted with intermittent aeration and operated at 30+/-1 degrees C in 8-h cycles. The synthetic wastewater (100 mgCOD/L and 50 mgNH(4)(+)-N/L) was added batch-wise, while the external carbon sources were added fed-batch-wise during the periods where aeration was suspended. Ammonium nitrogen removal efficiencies obtained were 95.7, 94.3 and 97.5% for ethanol, acetate and carbon synthetic medium, respectively. As to nitrite, nitrate and ammonium nitrogen effluent concentrations, the results obtained were, respectively: 0.1, 5.7 and 1.4 mg/L for ethanol; 0.2, 4.1 and 1.8 mg/L for acetate and 0.2, 6.7 and 0.8 for carbon synthetic medium. On the other hand using methanol, even at low concentrations (50% of the stoichiometric value calculated for complete denitrification), resulted in increasing accumulation of nitrate and ammonium nitrogen in the effluent over time.

The treatment of sulfate-rich wastewater using an anaerobic sequencing batch biofilm pilot-scale reactor

This paper presents the results from 92 cycles of an anaerobic sequencing batch biofilm reactor containing biomass immobilized on inert support (mineral coal) applied for the treatment of an industrial wastewater containing high sulfate concentration. The pilot-scale reactor, with a total volume of 1.2 m(3), was operated at sulfate loading rates ranging from 0.15 to 1.90 kgSO(4)(2-)/cycle (48 It - cycle) corresponding to sulfate concentrations of 0.25 to 3.0 gSO(4)(2-) l(-1). Domestic sewage and ethanol were utilized as electron donors for sulfate reduction. Influent sulfate concentrations were increased in order to evaluate the minimum COD/sulfate ratio at which high reactor performance could be maintained. The mean sulfate removal efficiency remained between the range of 88 to 92% at several sulfate concentrations. Temporal profiles along the 48 h cycles were carried out under stable operation at sulfate concentrations of 1.0, 2.0 and 3.0 gSO(4)(2-) l(-1). Sulfate removal reached 99% for cycle times of 15, 25, and 30 h, and the effluents sulfate concentrations were lower than 8 mgSO(4)(2-) l(-1). The results demonstrate the potential applicability of the anaerobic configuration for the biological treatment of sulfate-rich wastewaters. (C) 2009 Elsevier B.V. All rights reserved.

Effect of specific feed volume on the performance of an anaerobic sequencing batch biofilm reactor (AnSBBR) with circulation treating different wastewaters under different organic loads

The objective of this research was to study the behavior of two anaerobic sequencing batch reactors, containing immobilized biomass (AnSBBR), as a function of the ratio of the volume of treated medium in each cycle to the total volume of reaction medium. The reactors, in which mixing was accomplished by recirculation of the liquid phase, were maintained at 30 +/- 1 degrees C and treated different wastewaters in 8-h cycles. The operational conditions imposed had the objective to investigate whether maintenance of a residual volume in the reactor would affect, at the end of each cycle, process efficiency and stability, as well as to verify the intensity of the effect for different types of wastewaters and organic loading rates. The first reactor, with work volume of 2.5 L, treated reconstituted cheese whey at an organic loading rate of 12 g COD.L(-1).d(-1) and presented similar effluent quality for the four conditions under which it was operated: renewal of 100, 70, 50 and 25 % of its work volume at each cycle. Despite the fact that reduction in the renewed volume did not significantly affect effluent quality, in quantitative terms, this reduction resulted in an increase in the amount of organic matter removed by the first reactor. The second reactor, with work volume of 1.8 L, treated synthetic wastewater at organic loading rates of 3 and 5 g COD.L(-1).d(-1) and operated under two conditions for each loading: renewal of 100 and 50 % of its work volume. At the organic loading rate of 3 g COD.L(-1).d(-1), the results showed that both effluent quality and amount of organic matter removed by the second reactor were independent of the treated volume per cycle. At the organic loading rate of 5 g COD.L(-1).d(-1), although the reduction in the renewed volume did not affect the amount of organic matter removed by the reactor, effluent quality improved during reactor operation with total discharge of its volume. In general, results showed process stability under all conditions, evidencing reactor flexibility and the potential to apply this technology in the treatment of different types of wastewater.

Degradation of formaldehyde in anaerobic sequencing batch biofilm reactor (ASBBR)

The present study evaluated the degradation of formaldehyde in a bench-scale anaerobic sequencing batch reactor, which contained biomass immobilized in polyurethane foam matrices. The reactor was operated for 212 days at 35 C with 8 h sequential cycles, under different affluent formaldehyde concentrations ranging from 31.6 to 1104.4 mg/L (formaldehyde loading rates from 0.08 to 2.78 kg/m(3) day). The results indicate excellent reactor stability and over 99% efficiency in formaldehyde removal, with average effluent formaldehyde concentration of 3.6 + 1.7 mg/L. Formaldehyde degradation rates increased from 204.9 to 698.3 mg/L h as the initial concentration of formaldehyde was increased from around 100 to around 1100 mg/L. However, accumulation of organic matter was observed in the effluent (chemical oxygen demand (COD) values above 500 mg/L) due to the presence of non-degraded organic acids, especially acetic and propionic acids, This observation poses an important question regarding the anaerobic route of formaldehyde degradation, which might differ Substantially from that reported in the literature. The anaerobic degradation pathway can be associated with the formation of long-chain oligomers from formaldehyde. Such long- or short-chain polymers are probably the precursors of organic acid formation by means of acidogenic anaerobic microorganisms. (C) 2008 Elsevier B.V. All rights reserved.