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.

Analyzing static three-dimensional elastic domains with a new infinite boundary element formulation

A new two-dimensionally mapped infinite boundary element (IBE) is presented. The formulation is based on a triangular boundary element (BE) with linear shape functions instead of the quadrilateral IBEs usually found in the literature. The infinite solids analyzed are assumed to be three-dimensional, linear-elastic and isotropic, and Kelvin fundamental solutions are employed. One advantage of the proposed formulation over quadratic or higher order elements is that no additional degrees of freedom are added to the original BE mesh by the presence of the IBEs. Thus, the IBEs allow the mesh to be reduced without compromising the accuracy of the result. Two examples are presented, in which the numerical results show good agreement with authors using quadrilateral IBEs and analytical solutions. (C) 2010 Elsevier Ltd. All rights reserved.

An alternative multi-region BEM technique for three-dimensional elastic problems

The main objective of this work is to present an alternative boundary element method (BEM) formulation for the static analysis of three-dimensional non-homogeneous isotropic solids. These problems can be solved using the classical boundary element formulation, analyzing each subregion separately and then joining them together by introducing equilibrium and displacements compatibility. Establishing relations between the displacement fundamental solutions of the different domains, the alternative technique proposed in this paper allows analyzing all the domains as one unique solid, not requiring equilibrium or compatibility equations. This formulation also leads to a smaller system of equations when compared to the usual subregion technique, and the results obtained are even more accurate. (C) 2008 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.

A critical reassessment of elastic unloading in sharp instrumented indentation experiments and the extraction of mechanical properties

This work examines the extraction of mechanical properties from instrumented indentation P-h(s) curves via extensive three-dimensional finite element analyses for pyramidal tips in a wide range of solids under frictional and frictionless contact conditions. Since the topography of the imprint changes with the level of pile-up or sink-in, a relationship is identified between correction factor beta in the elastic equation for the unloading indentation stage and the amount of surface deformation effects. It is shown that the presumption of a constant beta significantly affects mechanical property extractions. Consequently, a new best-fit function is found for the correlation between penetration depth ratios h(e)/h(max), h(r)/h(max) and n, circumventing the need for the assumption of a constant value for beta, made in our prior investigation [Acta Mater. 53 (2005) pp. 3545-3561]. Simulations under frictional contact conditions provide sensible boundaries for the influence of friction on both h(e)/h(max) and h(r)/h(max). Friction is essentially found to induce an overestimation in the inferred n. Instrumented indentation experiments are also performed in three archetypal metallic materials exhibiting distinctly different contact responses. Mechanical property extractions are finally demonstrated in each of these materials.

Finite element and dimensional analysis algorithm for the prediction of mechanical properties of bulk materials and thin films

In this work, the applicability of a new algorithm for the estimation of mechanical properties from instrumented indentation data was studied for thin films. The applicability was analyzed with the aid of both three-dimensional finite element simulations and experimental indentation tests. The numerical approach allowed studying the effect of the substrate on the estimation of mechanical properties of the film, which was conducted based on the ratio h(max)/l between maximum indentation depth and film thickness. For the experimental analysis, indentation tests were conducted on AISI H13 tool steel specimens, plasma nitrated and coated with TiN thin films. Results have indicated that, for the conditions analyzed in this work, the elastic deformation of the substrate limited the extraction of mechanical properties of the film/substrate system. This limitation occurred even at low h(max)/l ratios and especially for the estimation of the values of yield strength and strain hardening exponent. At indentation depths lower than 4% of the film thickness, the proposed algorithm estimated the mechanical properties of the film with accuracy. Particularly for hardness, precise values were estimated at h(max)/l lower than 0.1, i.e. 10% of film thickness. (C) 2010 Published by Elsevier B.V.

Characterization of the elastic-plastic region in AISI/SAE 1070 steel by the magnetic barkhausen noise

The magnetic Barkhausen energy in the rolling and transversal directions of AISI/SAE 1070 annealed surfaces is studied. The measurements were made in the samples under applied tension in the elastic-plastic region for different angular directions. The outcomes evidence that the magnetic anisotropy coefficient can be used to characterize the linear and nonlinear elastic limits of the material tinder tensile tresses. The results also show that the area of the curve corresponding to the angular dependence of the number of Barkhausen jumps with average energy presents a maximum value that corresponds to the elastic limit of the sample. (C) 2008 Elsevier Ltd. All rights reserved.

Identification of Elastic, Dielectric, and Piezoelectric Constants in Piezoceramic Disks

Three-dimensional modeling of piezoelectric devices requires a precise knowledge of piezoelectric material parameters. The commonly used piezoelectric materials belong to the 6mm symmetry class, which have ten independent constants. In this work, a methodology to obtain precise material constants over a wide frequency band through finite element analysis of a piezoceramic disk is presented. Given an experimental electrical impedance curve and a first estimate for the piezoelectric material properties, the objective is to find the material properties that minimize the difference between the electrical impedance calculated by the finite element method and that obtained experimentally by an electrical impedance analyzer. The methodology consists of four basic steps: experimental measurement, identification of vibration modes and their sensitivity to material constants, a preliminary identification algorithm, and final refinement of the material constants using an optimization algorithm. The application of the methodology is exemplified using a hard lead zirconate titanate piezoceramic. The same methodology is applied to a soft piezoceramic. The errors in the identification of each parameter are statistically estimated in both cases, and are less than 0.6% for elastic constants, and less than 6.3% for dielectric and piezoelectric constants.

Optimal design of periodic functionally graded composites with prescribed properties

The computational design of a composite where the properties of its constituents change gradually within a unit cell can be successfully achieved by means of a material design method that combines topology optimization with homogenization. This is an iterative numerical method, which leads to changes in the composite material unit cell until desired properties (or performance) are obtained. Such method has been applied to several types of materials in the last few years. In this work, the objective is to extend the material design method to obtain functionally graded material architectures, i.e. materials that are graded at the local level (e.g. microstructural level). Consistent with this goal, a continuum distribution of the design variable inside the finite element domain is considered to represent a fully continuous material variation during the design process. Thus the topology optimization naturally leads to a smoothly graded material system. To illustrate the theoretical and numerical approaches, numerical examples are provided. The homogenization method is verified by considering one-dimensional material gradation profiles for which analytical solutions for the effective elastic properties are available. The verification of the homogenization method is extended to two dimensions considering a trigonometric material gradation, and a material variation with discontinuous derivatives. These are also used as benchmark examples to verify the optimization method for functionally graded material cell design. Finally the influence of material gradation on extreme materials is investigated, which includes materials with near-zero shear modulus, and materials with negative Poisson`s ratio.

Stochastic stability analysis for the constant-modulus algorithm

We derive an easy-to-compute approximate bound for the range of step-sizes for which the constant-modulus algorithm (CMA) will remain stable if initialized close to a minimum of the CM cost function. Our model highlights the influence, of the signal constellation used in the transmission system: for smaller variation in the modulus of the transmitted symbols, the algorithm will be more robust, and the steady-state misadjustment will be smaller. The theoretical results are validated through several simulations, for long and short filters and channels.

Numerical study of tensile tests conducted on systems with elastic-plastic films deposited onto elastic-plastic substrates

In this work, a series of two-dimensional plane-strain finite element analyses was conducted to further understand the stress distribution during tensile tests on coated systems. Besides the film and the substrate, the finite element model also considered a number of cracks perpendicular to the film/substrate interface. Different from analyses commonly found in the literature, the mechanical behavior of both film and substrate was considered elastic-perfectly plastic in part of the analyses. Together with the film yield stress and the number of film cracks, other variables that were considered were crack tip geometry, the distance between two consecutive cracks and the presence of an interlayer. The analysis was based on the normal stresses parallel to the loading axis (sigma(xx)), which are responsible for cohesive failures that are observed in the film during this type of test. Results indicated that some configurations studied in this work have significantly reduced the value of sigma(xx) at the film/substrate interface and close to the pre-defined crack tips. Furthermore, in all the cases studied the values of sigma(xx) were systematically larger at the film/substrate interface than at the film surface. (C) 2010 Elsevier B.V. All rights reserved.

Collagen and Elastic Content of Abdominal Skin After Surgical Weight Loss

Collapsed skin folds after bariatric weight loss are often managed by plastic procedures, but changes in dermal composition and architecture have rarely been documented. Given the potential consequences on surgical outcome, a prospective histochemical study was designed. The hypothesis was that a deranged dermal fiber pattern would accompany major changes in adipose tissue. Female surgical candidates undergoing postbariatric abdominoplasty (n = 40) and never obese women submitted to control procedures (n = 40) were submitted to double abdominal biopsy, respectively in the epigastrium and hypogastrium. Histomorphometric assessment of collagen and elastic fibers was executed by the Image Analyzer System (Kontron Electronic 300, Zeiss, Germany). Depletion of collagen, but not of elastic fibers, in cases with massive weight loss was confirmed. Changes were somewhat more severe in epigastrium (P = 0.001) than hypogastrium (P = 0.007). Correlation with age did not occur. (1) Patients displayed lax, soft skin lacking sufficient collagen fiber network. (2) Elastic fiber content was not damaged, and was even moderately increased in epigastrium; (3) Preoperative obesity negatively correlated with hypogastric collagen concentration; (4) Future studies should pinpoint the roles of obesity, and especially of massive weight loss, on dermal architecture and response to surgery.

Increased elastic microfibrils and thickening of fibroblastic nuclear lamina in canine cutaneous asthenia

Cutaneous asthenia is a hereditary connective tissue disease, primarily of dogs and cats, resembling Ehlers-Danlos syndrome in man. Collagen dysplasia results in skin hyperextensibility, skin and vessel fragility, and poor wound healing. The purpose of this study was to describe the histological findings in a dog with a collagenopathy consistent with cutaneous asthenia. An 8-month-old crossbreed female dog presented with lacerations and numerous atrophic and irregular scars. The skin was hyperextensible and easily torn by the slightest trauma. Ultrastructurally, the dermis was comprised of elaunin and oxytalan microfibrils. These are immature fibres in which the fibrillar component is increased but elastin is reduced. Collagen fibres were profoundly disorganized. The fibrils had a highly irregular outline and a corroded appearance when viewed in cross-section, and were spiralled and fragmented in a longitudinal view. Dermal fibroblasts displayed a conspicuous thickening of the nuclear lamina. Nuclear lamins form a fibrous nucleoskeletal network of intermediate-sized filaments underlying the inner nuclear membrane. Mutations in lamins or lamin-associated proteins cause a myriad of genetic diseases collectively called laminopathies. Disruption of the nuclear lamina seems to affect chromatin organization and transcriptional regulation of gene expression. A common link among all laminopathies may be a failure of stem cells to regenerate mesenchymal tissue. This could contribute to the connective tissue dysplasia seen in cutaneous asthenia.

Elastic Fibers in Reinke`s Edema

Objectives: We describe the distribution of elastic system fibers in the superficial layer of the lamina propria of Reinke`s edema, as compared with normal vocal folds. Methods: Weigert`s resorcin-fuchsin stain after oxidation with 10% oxone was used to study the arrangement of elastic fibers. The findings were categorized and afterward compared with the severity of Reinke`s edema. Results: Analysis of 20 specimens of vocal folds with Reinke`s edema showed that the network of thin elastic fibers in Reinke`s space lost their undulated appearance and had a tangled aspect. In addition, these fibers were no longer parallel to the epithelial basement membrane, but had a random distribution scattered throughout Reinke`s space. The elastic fiber network immediately below the epithelial basement membrane also appeared more fragmented in Reinke`s edema because of some alteration in organization combined with the 5-mu m-thick histologic sectioning plane. No significant difference in the degree of elastic system fiber disarrangement was observed between severity grades II and III (p = 0.382). Large areas of disarrangement were predominant (80% of cases). Conclusions: The disarrangement of elastic fibers in Reinke`s edema may cause insufficient tissue resistance and resilience, contributing to the hypermobility observed in Reinke`s edema.

Is the wearing of elastic stockings for half a day as effective as wearing them for the entire day?

P>Background There is good evidence for the use of compression for some clinical indications but little is known about dosimetry in compression. Objective The aim of this work was to evaluate whether or not the use of compression stockings during part of the day would help in the reduction of evening oedema in patients with clinical, epidemiological, anatomical and physiopathological (CEAP) classifications C0 and C1. Methods The effects of elastic compression stockings on volumetric variations during the working day were evaluated for the legs of two men and 18 women (40 legs). The inclusion criterion was classification as C0 (10 legs) or C1 (30 legs) according to the CEAP criteria. Participants used three-quarter-length elastic compression stockings (20-30 mmHg) on three consecutive days for the entire day or only for the morning or they did not use the stockings at all. Volumetry using the water displacement technique was performed in the morning and in the evening. When the patients wore the stockings only during the morning, volumetry was also performed at 13:00 h. Results Significant increases in volume were observed for both legs when stockings were not used compared with the use of stockings in the morning only. After removing the stockings, both legs had significant increases in volume in the afternoon. However, use for half the day was better than not using the stockings at all. Conclusions The use of elastic compression stockings can reduce volumetric variations during working hours, with the use of stockings for the entire day being better than for just half the day.