Interpolation estimate for a finite-element space with embedded discontinuities

We consider a recently proposed finite-element space that consists of piecewise affine functions with discontinuities across a smooth given interface Γ (a curve in two dimensions, a surface in three dimensions). Contrary to existing extended finite element methodologies, the space is a variant of the standard conforming Formula space that can be implemented element by element. Further, it neither introduces new unknowns nor deteriorates the sparsity structure. It is proved that, for u arbitrary in Formula, the interpolant Formula defined by this new space satisfies Graphic where h is the mesh size, Formula is the domain, Formula, Formula, Formula and standard notation has been adopted for the function spaces. This result proves the good approximation properties of the finite-element space as compared to any space consisting of functions that are continuous across Γ, which would yield an error in the Formula-norm of order Graphic. These properties make this space especially attractive for approximating the pressure in problems with surface tension or other immersed interfaces that lead to discontinuities in the pressure field. Furthermore, the result still holds for interfaces that end within the domain, as happens for example in cracked domains.

Numerical assessment of stability of interface discontinuous finite element pressure spaces

The stability of two recently developed pressure spaces has been assessed numerically: The space proposed by Ausas et al. [R.F. Ausas, F.S. Sousa, G.C. Buscaglia, An improved finite element space for discontinuous pressures, Comput. Methods Appl. Mech. Engrg. 199 (2010) 1019-1031], which is capable of representing discontinuous pressures, and the space proposed by Coppola-Owen and Codina [A.H. Coppola-Owen, R. Codina, Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functions, Int. J. Numer. Methods Fluids, 49 (2005) 1287-1304], which can represent discontinuities in pressure gradients. We assess the stability of these spaces by numerically computing the inf-sup constants of several meshes. The inf-sup constant results as the solution of a generalized eigenvalue problems. Both spaces are in this way confirmed to be stable in their original form. An application of the same numerical assessment tool to the stabilized equal-order P-1/P-1 formulation is then reported. An interesting finding is that the stabilization coefficient can be safely set to zero in an arbitrary band of elements without compromising the formulation's stability. An analogous result is also reported for the mini-element P-1(+)/P-1 when the velocity bubbles are removed in an arbitrary band of elements. (C) 2012 Elsevier B.V. All rights reserved.

Analysis of elastic functionally graded materials under large displacements via high-order tetrahedral elements

The purpose of this study is to present a position based tetrahedral finite element method of any order to accurately predict the mechanical behavior of solids constituted by functionally graded elastic materials and subjected to large displacements. The application of high-order elements makes it possible to overcome the volumetric and shear locking that appears in usual homogeneous isotropic situations or even in non-homogeneous cases developing small or large displacements. The use of parallel processing to improve the computational efficiency, allows employing high-order elements instead of low-order ones with reduced integration techniques or strain enhancements. The Green-Lagrange strain is adopted and the constitutive relation is the functionally graded Saint Venant-Kirchhoff law. The equilibrium is achieved by the minimum total potential energy principle. Examples of large displacement problems are presented and results confirm the locking free behavior of high-order elements for non-homogeneous materials. (C) 2011 Elsevier B.V. All rights reserved.

GENERALIZED FINITE ELEMENT METHOD ON NONCONVENTIONAL HYBRID-MIXED FORMULATION

The generalized finite element method (GFEM) is applied to a nonconventional hybrid-mixed stress formulation (HMSF) for plane analysis. In the HMSF, three approximation fields are involved: stresses and displacements in the domain and displacement fields on the static boundary. The GFEM-HMSF shape functions are then generated by the product of a partition of unity associated to each field and the polynomials enrichment functions. In principle, the enrichment can be conducted independently over each of the HMSF approximation fields. However, stability and convergence features of the resulting numerical method can be affected mainly by spurious modes generated when enrichment is arbitrarily applied to the displacement fields. With the aim to efficiently explore the enrichment possibilities, an extension to GFEM-HMSF of the conventional Zienkiewicz-Patch-Test is proposed as a necessary condition to ensure numerical stability. Finally, once the extended Patch-Test is satisfied, some numerical analyses focusing on the selective enrichment over distorted meshes formed by bilinear quadrilateral finite elements are presented, thus showing the performance of the GFEM-HMSF combination.

Design of laminated piezocomposite shell transducers with arbitrary fiber orientation using topology optimization approach

Sensor and actuator based on laminated piezocomposite shells have shown increasing demand in the field of smart structures. The distribution of piezoelectric material within material layers affects the performance of these structures; therefore, its amount, shape, size, placement, and polarization should be simultaneously considered in an optimization problem. In addition, previous works suggest the concept of laminated piezocomposite structure that includes fiber-reinforced composite layer can increase the performance of these piezoelectric transducers; however, the design optimization of these devices has not been fully explored yet. Thus, this work aims the development of a methodology using topology optimization techniques for static design of laminated piezocomposite shell structures by considering the optimization of piezoelectric material and polarization distributions together with the optimization of the fiber angle of the composite orthotropic layers, which is free to assume different values along the same composite layer. The finite element model is based on the laminated piezoelectric shell theory, using the degenerate three-dimensional solid approach and first-order shell theory kinematics that accounts for the transverse shear deformation and rotary inertia effects. The topology optimization formulation is implemented by combining the piezoelectric material with penalization and polarization model and the discrete material optimization, where the design variables describe the amount of piezoelectric material and polarization sign at each finite element, with the fiber angles, respectively. Three different objective functions are formulated for the design of actuators, sensors, and energy harvesters. Results of laminated piezocomposite shell transducers are presented to illustrate the method. Copyright (C) 2012 John Wiley & Sons, Ltd.

Contribution to assessing the stiffness reduction of structural elements in the global stability analysis of precast concrete multi-storey buildings

This study deals with the reduction of the stiffness in precast concrete structural elements of multi-storey buildings to analyze global stability. Having reviewed the technical literature, this paper present indications of stiffness reduction in different codes, standards, and recommendations and compare these to the values found in the present study. The structural model analyzed in this study was constructed with finite elements using ANSYS® software. Physical Non-Linearity (PNL) was considered in relation to the diagrams M x N x 1/r, and Geometric Non-Linearity (GNL) was calculated following the Newton-Raphson method. Using a typical precast concrete structure with multiple floors and a semi-rigid beam-to-column connection, expressions for a stiffness reduction coefficient are presented. The main conclusions of the study are as follows: the reduction coefficients obtained from the diagram M x N x 1/r differ from standards that use a simplified consideration of PNL; the stiffness reduction coefficient for columns in the arrangements analyzed were approximately 0.5 to 0.6; and the variation of values found for stiffness reduction coefficient in concrete beams, which were subjected to the effects of creep with linear coefficients from 0 to 3, ranged from 0.45 to 0.2 for positive bending moments and 0.3 to 0.2 for negative bending moments.

Finite element methods for the Stokes system based on a Zienkiewicz type N-simplex

Hermite interpolation is increasingly showing to be a powerful numerical solution tool, as applied to different kinds of second order boundary value problems. In this work we present two Hermite finite element methods to solve viscous incompressible flows problems, in both two- and three-dimension space. In the two-dimensional case we use the Zienkiewicz triangle to represent the velocity field, and in the three-dimensional case an extension of this element to tetrahedra, still called a Zienkiewicz element. Taking as a model the Stokes system, the pressure is approximated with continuous functions, either piecewise linear or piecewise quadratic, according to the version of the Zienkiewicz element in use, that is, with either incomplete or complete cubics. The methods employ both the standard Galerkin or the Petrov–Galerkin formulation first proposed in Hughes et al. (1986) [18], based on the addition of a balance of force term. A priori error analyses point to optimal convergence rates for the PG approach, and for the Galerkin formulation too, at least in some particular cases. From the point of view of both accuracy and the global number of degrees of freedom, the new methods are shown to have a favorable cost-benefit ratio, as compared to velocity Lagrange finite elements of the same order, especially if the Galerkin approach is employed.

Vibro-Acoustography Beam Formation with Reconfigurable Arrays

In this work, we present a numerical study of the use of reconfigurable arrays (RCA) for vibro-acoustography (VA) beam formation. A parametric study of the aperture selection, number of channels, number of elements, focal distance, and steering parameters is presented to show the feasibility and evaluate the performance of VA imaging based on RCA. The transducer aperture was based on two concentric arrays driven by two continuous-wave or toneburst signals at slightly different frequencies. The mathematical model considers a homogeneous, isotropic, inviscid medium. The point-spread function of the system is calculated based on angular spectrum methods using the Fresnel approximation for rectangular sources. Simulations considering arrays with 50 x 50 to 200 x 200 elements with number of channels varying in the range of 32 to 128 are evaluated to identify the best configuration for VA. Advantages of two-dimensional and RCA arrays and aspects related to clinical importance of the RCA implementation in VA, such as spatial resolution, image frame rate, and commercial machine implementation, are discussed. It is concluded that RCA transducers can produce spatial resolution similar to confocal transducers and steering is possible in the elevational and azimuthal planes. Optimal settings for number of elements, number of channels, maximum steering, and focal distance are suggested for VA clinical applications. Furthermore, an optimization for beam steering based on the channel assignment is proposed for balancing the contribution of the two waves in the steered focus.

Atomically resolved study of the morphology change of InAs/GaAs quantum dot layers induced by rapid thermal annealing

The optoelectronic properties of InAs/GaAs quantum dots can be tuned by rapid thermal annealing. In this study, the morphology change of InAs/GaAs quantum dots layers induced by rapid thermal annealing was investigated at the atomic-scale by cross-sectional scanning tunneling microscopy. Finite elements calculations that model the outward relaxation of the cleaved surface were used to determine the indium composition profile of the wetting layer and the quantum dots prior and post rapid thermal annealing. The results show that the wetting layer is broadened upon annealing. This broadening could be modeled by assuming a random walk of indium atoms. Furthermore, we show that the stronger strain gradient at the location of the quantum dots enhances the intermixing. Photoluminescence measurements show a blueshift and narrowing of the photoluminescence peak. Temperature dependent photoluminescence measurements show a lower activation energy for the annealed sample. These results are in agreement with the observed change in morphology. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4770371]

Ultrastructural features of the myotendinous junction of the sternomastoid muscle in Wistar rats: from newborn to aging

The myotendinous junction (MTJ) is a major area for transmitting force from the skeletal muscle system and acts in joint position and stabilization. This study aimed to use transmission electron microscopy to describe the ultrastructural features of the MTJ of the sternomastoid muscle in Wistar rats from newborn to formation during adulthood and possible changes with aging. Ultrastructural features of the MTJ from the newborn group revealed pattern during development with interactions between muscle cells and extracellular matrix elements with thin folds in the sarcolemma and high cellular activity evidenced through numerous oval mitochondria groupings. The adult group had classical morphological features of the MTJ, with folds in the sarcolemma forming long projections called finger-like processes and sarcoplasmic invaginations. Sarcomeres were aligned in series, showing mitochondria near the Z line in groupings between collagen fiber bundles. The old group had altered finger-like processes, thickened in both levels of sarcoplasmic invaginations and in central connections with the lateral junctions. We conclude that the MTJ undergoes intense activity from newborn to its formation during adulthood. With increasing age, changes to the MTJ were observed in the shapes of the invaginations and finger-like processes due to hypoactivity, potentially compromising force transmission and joint stability. Microsc. Res. Tech. 75:12921296, 2012. (C) 2012 Wiley Periodicals, Inc.

Analysis, manufacture and characterization of Ni/Cu functionally graded structures

In this work, an experimental and numerical analysis and characterization of functionally graded structures (FGSs) is developed. Nickel (Ni) and copper (Cu) materials are used as basic materials in the numerical modeling and experimental characterization. For modeling, a MATLAB finite element code is developed, which allows simulation of harmonic and modal analysis considering the graded finite element formulation. For experimental characterization, Ni-Cu FGSs are manufactured by using spark plasma sintering technique. Hardness and Young's modulus are found by using microindentation and ultrasonic measurements, respectively. The effective gradation of Ni/Cu FGS is addressed by means of optical microscopy, energy dispersive spectrometry, scanning electron microscopy and hardness testing. For the purpose of comparing modeling and experimental results, the hardness curve, along the gradation direction, is used for identifying the gradation profile; accordingly, the experimental hardness curve is used for approximating the Young's modulus variation and the graded finite element modeling is used for verification. For the first two resonance frequency values, a difference smaller than 1% between simulated and experimental results is obtained. (C) 2012 Elsevier Ltd. All rights reserved.

Extracellular Matrix Composition of the Cricopharyngeus Muscle

The aim of this study was to analyze the presence and distribution of total collagen, type I and type III collagen, elastic fibers, fibronectin, and versican in the endomysium of cricopharyngeus muscles from adults of various ages. The study was a cross-sectional analysis of human cricopharyngeus muscles. Twenty-seven muscles obtained from autopsies of men and women ranging in age from 28 to 92 years were analyzed with the Picrosirius method, oxidized Weigert resorcin-fuchsin, immunohistochemistry, and image analysis. Collagen had the highest density among the analyzed components. Elastic fibers surrounded each muscle cell; they were aligned longitudinally by their long axis and associated with traversing fibers, thereby forming a fiber network with embedded muscle cells. The fibronectin and versican contents varied widely among the specimens. We found no statistically significant differences between the proportion of extracellular matrix (ECM) components and factors such as gender and race. We conclude that the higher proportion of type I and type III collagen is compatible with the cricopharyngeus muscle's sphincteric behavior, and the arrangement of the elastic fibers may also contribute to the muscle's elasticity. We found no statistically significant correlation between the ECM components and age.

The production of critical-reflexive narratives and their effect on nursing students' portfolios

The objective of this study is to analyze the process of producing reflexive narratives on nursing students' portfolios. This qualitative study performed an analysis of the portfolios of the class discipline Health Promotion in Primary Education, taught in the fourth semester of the Nursing Licensure Course. Results showed an initial predominance of descriptive records, with the incipient approach of theoretical aspects associated with the aspects regarding their experience. Further, in the group and experience discussions, there were narratives containing more critical and reflexive elements, with justifications for the described actions and the relationships with the theoretical-practical aspects studied in the class and in the course. In conclusion, there is a process of producing critical-reflexive narratives in portfolios that could include a summarized description, using common sense and idealization which allows for including the differences and the theoretical review.

On Site Stripping Voltammetric Determination of Zn(II), Cd(II) and Pb(II) in Water Samples of the Cananeia-Iguape Estuarine-Lagoon Complex in Sao Paulo State, Brazil

Estuarine systems play an important role in the retention of toxic trace elements owing to the affinity of these elements with particles dissolved in water. This work presents the use of a voltammetric sensor to monitor heavy metal (Zn (II), Cd(II) and Pb (II)) concentrations in the Cananeia-Iguape Estuarine-Lagoon region (Sao Paulo State, Brazil). Lower concentrations were found in the Southern estuarine system (Cananeia City) and increased concentrations observed in the Northern sector (Iguape City) were promoted by anthropogenic activities, with particular influence from the historical introduction of mining wastes and inputs from agricultural, industrial and domestic effluents. The proposed method is reliable, inexpensive and fast, can simultaneously provide information on the concentration of these metallic ions and can be easily used for field measurements aboard oceanographic ships.

An ecological economic interpretation of the Jevons effect

This article develops an ecological economic interpretation of the Jevons effect. Moreover, it is argued that under the neoclassical paradigm there are no elements with which to foresee the long-term existence of this phenomenon. The objective of these arguments is to demonstrate that the Jevons effect can be used to compare the ability of neoclassical and ecological economics describing the social appropriation of nature. This is elaborated in two steps. First, we show the importance of the thesis that the economy cannot be cut off from the biophysical materiality of what is produced to give consistency to the so-called Khazzoom-Brookes postulate. It is made clear that this supposition is exogenous to the neoclassical paradigm. Second, the supposition of the biophysical materiality of what is produced is utilized to make an ecological economic interpretation of the Jevons effect. Afterwards, a comparison is made between the neoclassical and the ecological economic perspectives. This comparison leads to the following conclusions: (i) the persistent presence of the Jevons effect in the long run is an anomaly in the neoclassical paradigm; (ii) the observation of the non-existence of the Jevons effect is a refutation of the supposition that economic growth and biophysical materiality are not separable, a central thesis defended by ecological economists. This situation makes possible to use the Jevons effect as a 'laboratory test' to compare the ability of neoclassical and ecological economic paradigms to describe the social appropriation of nature. (C) 20111 Elsevier B.V. All rights reserved.