Analytical formulae for electromechanical effective properties of 3-1 longitudinally porous piezoelectric materials

A unidirectional fiber composite is considered here, the fibers of which are empty cylindrical holes periodically distributed in a transversely isotropic piezoelectric matrix, The empty-fiber cross-section is circular and the periodicity is the same in two directions at an angle pi/2 or pi/3. Closed-form formulae for all electromechanical effective properties of these 3-1 longitudinally periodic porous piezoelectric materials are presented. The derivation of such expressions is based on the asymptotic homogenization method as a limit of the effective properties of two-phase transversely isotropic parallel fiber-reinforced composites when the fibers properties tend to zero. The plane effective coefficients satisfy the corresponding Schulgasser-Benveniste-Dvorak universal type of relations, A new relation among the antiplane effective constants from the solutions of two antiplane strains and potential local problems is found. This relation is valid for arbitrary shapes of the empty-fiber cross-sections. Based on such a relation, and using recent numerical results for isotropic conductive composites, the antiplane effective properties are computed for different geometrical shapes of the empty-fiber cross-section. Comparisons with other analytical and numerical theories are presented. (c) 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

A simple way to introduce fibers into FEM models

This communication proposes a simple way to introduce fibers into finite element modelling. This is a promising formulation to deal with fiber-reinforced composites by the finite element method (FEM), as it 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 into the pre-existent finite element numerical system to consider any distribution 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 is the reduced work required by the user to introduce fibers, avoiding `rebar` elements, node-by-node geometrical definitions or even complex mesh generation. An additional characteristic of the technique is the possibility of representing unbounded stresses at the end of fibers using a finite number of degrees of freedom. Further studies are required for non-linear applications in which localization may occur. Along the text the linear formulation is presented and the bounded connection between fibers and continuum is considered. Four examples are presented, including non-linear analysis, to validate and show the capabilities of the formulation. Copyright (c) 2007 John Wiley & Sons, Ltd.

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.

Influence of physical and geometrical parameters on three-dimensional load transfer mechanism at tunnel face

Three-dimensional discretizations used in numerical analyses of tunnel construction normally include excavation step lengths much shorter than tunnel cross-section dimensions. Simulations have usually worked around this problem by using excavation steps that are much larger than the actual physical steps used in a real tunnel excavation. In contrast, the analyses performed in this study were based on finely discretized meshes capable of reproducing the excavation lengths actually used in tunnels, and the results obtained for internal forces are up to 100% greater than those found in other analyses available in the literature. Whereas most reports conclude that internal forces depend on support delay length alone, this study shows that geometric path dependency (reflected by excavation round length) is very strong, even considering linear elasticity. Moreover, many other solutions found in the literature have also neglected the importance of the relative stiffness between the ground mass and support structure, probably owing to the relatively coarse meshes used in these studies. The analyses presented here show that relative stiffness may account for internal force discrepancies in the order of 60%. A dimensionless expression that takes all these parameters into account is presented as a good approximation for the load transfer mechanism at the tunnel face.

Estimation of Mass Transfer Velocity Based on Measured Turbulence Parameters

The aim of this study is to quantify the mass transfer velocity using turbulence parameters from simultaneous measurements of oxygen concentration fields and velocity fields. The surface divergence model was considered in more detail, using data obtained for the lower range of beta (surface divergence). It is shown that the existing models that use the divergence concept furnish good predictions for the transfer velocity also for low values of beta, in the range of this study. Additionally, traditional conceptual models, such as the film model, the penetration-renewal model, and the large eddy model, were tested using the simultaneous information of concentration and velocity fields. It is shown that the film and the surface divergence models predicted the mass transfer velocity for all the range of the equipment Reynolds number used here. The velocity measurements showed viscosity effects close to the surface, which indicates that the surface was contaminated with some surfactant. Considering the results, this contamination can be considered slight for the mass transfer predictions. (C) 2009 American Institute of Chemical Engineers AIChE J, 56: 2005-2017; 2010

Effect of impeller type and mechanical agitation on the mass transfer and power consumption aspects of ASBR operation treating synthetic wastewater

The effect of flow type and rotor speed was investigated in a round-bottom reactor with 5 L useful volume containing 2.0 L of granular biomass. The reactor treated 2.0 L of synthetic wastewater with a concentration of 800 mgCOD/L in 8-h cycles at 30 degrees C. Five impellers, commonly used in biological processes, have been employed to this end, namely: a turbine and a paddle impeller with six-vertical-flat-blades, a turbine and a paddle impeller with six-45 degrees-inclined-flat-blades and a three-blade-helix impeller. Results showed that altering impeller type and rotor speed did not significantly affect system stability and performance. Average organic matter removal efficiency was about 84% for filtered samples, total volatile acids concentration was below 20 mgHAc/L and bicarbonate alkalinity a little less than 400 mgCaCO(3)/L for most of the investigated conditions. However, analysis of the first-order kinetic model constants showed that alteration in rotor speed resulted in an increase in the values of the kinetic constants (for instance, from 0.57 h(-1) at 50 rpm to 0.84 h(-1) at 75 rpm when the paddle impeller with six-45 degrees-inclined-flat-blades was used) and that axial flow in mechanically stirred reactors is preferable over radial-flow when the vertical-flat-blade impeller is compared to the inclined-flat-blade impeller (for instance at 75 rpm, from 0.52 h(-1) with the six-flat-blade-paddle impeller to 0.84 h(-1) with the six-45 degrees-inclined-flat-blade-paddle impeller), demonstrating that there is a rotor speed and an impeller type that maximize solid-liquid mass transfer in the reaction medium. Furthermore, power consumption studies in this reduced reactor volume showed that no high power transfer is required to improve mass transfer (less than 0.6 kW/10(3) m(3)). (C) 2008 Elsevier Ltd. All rights reserved.

Modeling and Analysis of Piezoelectric Energy Harvesting From Aeroelastic Vibrations Using the Doublet-Lattice Method

Multifunctional structures are pointed out as an important technology for the design of aircraft with volume, mass, and energy source limitations such as unmanned air vehicles (UAVs) and micro air vehicles (MAVs). In addition to its primary function of bearing aerodynamic loads, the wing/spar structure of an UAV or a MAV with embedded piezoceramics can provide an extra electrical energy source based on the concept of vibration energy harvesting to power small and wireless electronic components. Aeroelastic vibrations of a lifting surface can be converted into electricity using piezoelectric transduction. In this paper, frequency-domain piezoaeroelastic modeling and analysis of a canti-levered platelike wing with embedded piezoceramics is presented for energy harvesting. The electromechanical finite-element plate model is based on the thin-plate (Kirchhoff) assumptions while the unsteady aerodynamic model uses the doublet-lattice method. The electromechanical and aerodynamic models are combined to obtain the piezoaeroelastic equations, which are solved using a p-k scheme that accounts for the electromechanical coupling. The evolution of the aerodynamic damping and the frequency of each mode are obtained with changing airflow speed for a given electrical circuit. Expressions for piezoaeroelastically coupled frequency response functions (voltage, current, and electrical power as well the vibratory motion) are also defined by combining flow excitation with harmonic base excitation. Hence, piezoaeroelastic evolution can be investigated in frequency domain for different airflow speeds and electrical boundary conditions. [DOI:10.1115/1.4002785]

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

Analysis of two reinforced concrete pile caps with embedded sockets in the presence of a locking beam

The present research studies the behavior of reinforced concrete locking beams supported by two capped piles with the socket embedded; used as connections for pre-cast concrete structures. The effect provoked by locking the beam on the pile-caps when supported by the lateral socket walls was evaluated. Three-dimensional numerical analyses using software based on the finite element method (FEM) were developed considering the nonlinear physical behavior of the material. To evaluate the adopted software, a comparative analysis was made using the numerical and experimented results obtained from other software. In the pile caps studied, a variation in the wall thickness, socket interface, strut angle inclination and action on beam. The results show that the presence of a beam does not significantly change pile cap behavior and that the socket wall is able to effectively transfer the force from the beam to the pile caps. By the tensions on the bars of longitudinal reinforcement, it was possible to obtain the force on the tie and the strut angle inclination before the collapse of models. It was found that the angles present more inclinations than those used in the design, which was made based on a strut-and-tie model. More results are available at http://www.set.eesc.usp.br/pdf/download/2009ME_RodrigoBarros.pdf

Roughness and surface material effects on nucleate boiling heat transfer from cylindrical surfaces to refrigerants R-134a and R-123

This paper presents results of an experimental investigation carried out to determine the effects of the surface roughness of different materials on nucleate boiling heat transfer of refrigerants R-134a and R-123. Experiments have been performed over cylindrical surfaces of copper, brass and stainless steel. Surfaces have been treated by different methods in order to obtain an average roughness, Ra, varying from 0.03 mu m to 10.5 mu m. Boiling curves at different reduced pressures have been raised as part of the investigation. The obtained results have shown significant effects of the surface material, with brass being the best performing and stainless steel the worst. Polished surfaces seem to present slightly better performance than the sand paper roughened. Boiling on very rough surfaces presents a peculiar behavior characterized by good thermal performance at low heat fluxes, the performance deteriorating at high heat fluxes with respect to smoother surfaces. (C) 2008 Elsevier Inc. All rights reserved.

Wavelet-Galerkin method for one-dimensional elastoplasticity and damage problems: Constitutive modeling and computational aspects

This work presents an analysis of the wavelet-Galerkin method for one-dimensional elastoplastic-damage problems. Time-stepping algorithm for non-linear dynamics is presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spacial discretization we can use wavelet-Galerkin method instead of standard finite element method. This approach allows to locate singularities. The discrete formulation developed can be applied to the simulation of one-dimensional problems for elastic-plastic-damage models. (C) 2007 Elsevier Inc. All rights reserved.