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.

Characterization of multiple reflections and phase space properties for a periodically corrugated waveguide

Dynamical properties for a beam light inside a sinusoidally corrugated waveguide are discussed in this paper. The beam is confined inside two-mirrors: one is flat and the other one is sinusoidally corrugated. The evolution of the system is described by the use of a two-dimensional and nonlinear mapping. The phase space of the system is of mixed type therefore exhibiting a large chaotic sea, periodic islands and invariant KAM curves. A careful discussion of the numerical method to solve the transcendental equations of the mapping is given. We characterize the probability of observing successive reflections of the light by the corrugated mirror and show that it is scaling invariant with respect to the amplitude of the corrugation. Average properties of the chaotic sea are also described by the use of scaling arguments.

Longitudinal dynamic hysteresis in single-domain particles

We present results for longitudinal dynamic hysteresis in single domain particles with uniaxial anisotropy. The combined influence of temperature, field-sweeping frequency, and field amplitude is discussed in detail. A novel and efficient numerical method is proposed, based on the direct solution of the infinite hierarchy of differential recurrence relations obtained from averaging over the stochastic realizations of the magnetic Langevin equation. (C) 2012 American Institute of Physics. [doi:10.1063/1.3676416]

Numerical analysis of different methods to calculate residual stresses in thin films based on instrumented indentation data

In this work, different methods to estimate the value of thin film residual stresses using instrumented indentation data were analyzed. This study considered procedures proposed in the literature, as well as a modification on one of these methods and a new approach based on the effect of residual stress on the value of hardness calculated via the Oliver and Pharr method. The analysis of these methods was centered on an axisymmetric two-dimensional finite element model, which was developed to simulate instrumented indentation testing of thin ceramic films deposited onto hard steel substrates. Simulations were conducted varying the level of film residual stress, film strain hardening exponent, film yield strength, and film Poisson's ratio. Different ratios of maximum penetration depth h(max) over film thickness t were also considered, including h/t = 0.04, for which the contribution of the substrate in the mechanical response of the system is not significant. Residual stresses were then calculated following the procedures mentioned above and compared with the values used as input in the numerical simulations. In general, results indicate the difference that each method provides with respect to the input values depends on the conditions studied. The method by Suresh and Giannakopoulos consistently overestimated the values when stresses were compressive. The method provided by Wang et al. has shown less dependence on h/t than the others.

A new method to analyze the subjective visual vertical in patients with bilateral vestibular dysfunction

OBJECTIVE: The aim of this study was to assess the subjective visual vertical in patients with bilateral vestibular dysfunction and to propose a new method to analyze subjective visual vertical data in these patients. METHODS: Static subjective visual vertical tests were performed in 40 subjects split into two groups. Group A consisted of 20 healthy volunteers, and Group B consisted of 20 patients with bilateral vestibular dysfunction. Each patient performed six measurements of the subjective visual vertical test, and the mean values were calculated and analyzed. RESULTS: Analyses of the numerical values of subjective visual vertical deviations (the conventional method of analysis) showed that the mean deviation was 0.326 +/- 1.13 degrees in Group A and 0.301 +/- 1.87 degrees in Group B. However, by analyzing the absolute values of the subjective visual vertical (the new method of analysis proposed), the mean deviation became 1.35 +/- 0.48 degrees in Group A and 2.152 +/- 0.93 degrees in Group B. The difference in subjective visual vertical deviations between groups was statistically significant (p < 0.05) only when the absolute values and the range of deviations were considered. CONCLUSION: An analysis of the absolute values of the subjective visual vertical more accurately reflected the visual vertical misperception in patients with bilateral vestibular dysfunction.

Analysis Methodology for Vortex-Induced Motion (VIM) of a Monocolumn Platform Applying the Hilbert-Huang Transform Method

Vortex-induced motion (VIM) is a highly nonlinear dynamic phenomenon. Usual spectral analysis methods, using the Fourier transform, rely on the hypotheses of linear and stationary dynamics. A method to treat nonstationary signals that emerge from nonlinear systems is denoted Hilbert-Huang transform (HHT) method. The development of an analysis methodology to study the VIM of a monocolumn production, storage, and offloading system using HHT is presented. The purposes of the present methodology are to improve the statistics analysis of VIM. The results showed to be comparable to results obtained from a traditional analysis (mean of the 10% highest peaks) particularly for the motions in the transverse direction, although the difference between the results from the traditional analysis for the motions in the in-line direction showed a difference of around 25%. The results from the HHT analysis are more reliable than the traditional ones, owing to the larger number of points to calculate the statistics characteristics. These results may be used to design risers and mooring lines, as well as to obtain VIM parameters to calibrate numerical predictions. [DOI: 10.1115/1.4003493]

The place of (explicit) grammar within the methods and approaches of foreign language teaching: in the north, in the centre or on the margins?

This article analyzes the role that has been attributed to grammar throughout the history of foreign language teaching, with special emphasis on methods and approaches of the twentieth century. In order to support our argument, we discuss the notion of grammar by proposing a conceptual continuum that includes the main meanings of the term which are relevant to our research. We address as well the issue of "pedagogical grammar" and consider the position of grammar in the different approaches of the "era of the methods" and the current "post-method condition" in the field of language teaching and learning. The findings presented at the end of the text consist of recognizing the central role that grammar has played throughout the history of the methods and approaches, where grammar has always been present by the definition of the contents' progression. The rationale that we propose for this is the recognition of the fact that the dissociation between what is said and how it is said can not be more than theoretical and, thus, artificial.

Numerical simulation of drop impact and jet buckling problems using the eXtended Pom-Pom model

This work presents numerical simulations of two fluid flow problems involving moving free surfaces: the impacting drop and fluid jet buckling. The viscoelastic model used in these simulations is the eXtended Pom-Pom (XPP) model. To validate the code, numerical predictions of the drop impact problem for Newtonian and Oldroyd-B fluids are presented and compared with other methods. In particular, a benchmark on numerical simulations for a XPP drop impacting on a rigid plate is performed for a wide range of the relevant parameters. Finally, to provide an additional application of free surface flows of XPP fluids, the viscous jet buckling problem is simulated and discussed. (C) 2011 Elsevier B.V. All rights reserved.

Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization

At each outer iteration of standard Augmented Lagrangian methods one tries to solve a box-constrained optimization problem with some prescribed tolerance. In the continuous world, using exact arithmetic, this subproblem is always solvable. Therefore, the possibility of finishing the subproblem resolution without satisfying the theoretical stopping conditions is not contemplated in usual convergence theories. However, in practice, one might not be able to solve the subproblem up to the required precision. This may be due to different reasons. One of them is that the presence of an excessively large penalty parameter could impair the performance of the box-constraint optimization solver. In this paper a practical strategy for decreasing the penalty parameter in situations like the one mentioned above is proposed. More generally, the different decisions that may be taken when, in practice, one is not able to solve the Augmented Lagrangian subproblem will be discussed. As a result, an improved Augmented Lagrangian method is presented, which takes into account numerical difficulties in a satisfactory way, preserving suitable convergence theory. Numerical experiments are presented involving all the CUTEr collection test problems.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal-Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient. (C) 2012 Elsevier B.V. All rights reserved.

The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems

Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented.

Numerical combination for nonlinear analysis of structures coupled to layered soils

This paper presents an alternative coupling strategy between the Boundary Element Method (BEM) and the Finite Element Method (FEM) in order to create a computational code for the analysis of geometrical nonlinear 2D frames coupled to layered soils. The soil is modeled via BEM, considering multiple inclusions and internal load lines, through an alternative formulation to eliminate traction variables on subregions interfaces. A total Lagrangean formulation based on positions is adopted for the consideration of the geometric nonlinear behavior of frame structures with exact kinematics. The numerical coupling is performed by an algebraic strategy that extracts and condenses the equivalent soil's stiffness matrix and contact forces to be introduced into the frame structures hessian matrix and internal force vector, respectively. The formulation covers the analysis of shallow foundation structures and piles in any direction. Furthermore, the piles can pass through different layers. Numerical examples are shown in order to illustrate and confirm the accuracy and applicability of the proposed technique.

Numeric reconstruction of cytoskeleton with finite element method and topology optimization method

The importance of mechanical aspects related to cell activity and its environment is becoming more evident due to their influence in stem cell differentiation and in the development of diseases such as atherosclerosis. The mechanical tension homeostasis is related to normal tissue behavior and its lack may be related to the formation of cancer, which shows a higher mechanical tension. Due to the complexity of cellular activity, the application of simplified models may elucidate which factors are really essential and which have a marginal effect. The development of a systematic method to reconstruct the elements involved in the perception of mechanical aspects by the cell may accelerate substantially the validation of these models. This work proposes the development of a routine capable of reconstructing the topology of focal adhesions and the actomyosin portion of the cytoskeleton from the displacement field generated by the cell on a flexible substrate. Another way to think of this problem is to develop an algorithm to reconstruct the forces applied by the cell from the measurements of the substrate displacement, which would be characterized as an inverse problem. For these kind of problems, the Topology Optimization Method (TOM) is suitable to find a solution. TOM is consisted of an iterative application of an optimization method and an analysis method to obtain an optimal distribution of material in a fixed domain. One way to experimentally obtain the substrate displacement is through Traction Force Microscopy (TFM), which also provides the forces applied by the cell. Along with systematically generating the distributions of focal adhesion and actin-myosin for the validation of simplified models, the algorithm also represents a complementary and more phenomenological approach to TFM. As a first approximation, actin fibers and flexible substrate are represented through two-dimensional linear Finite Element Method. Actin contraction is modeled as an initial stress of the FEM elements. Focal adhesions connecting actin and substrate are represented by springs. The algorithm was applied to data obtained from experiments regarding cytoskeletal prestress and micropatterning, comparing the numerical results to the experimental ones