Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark beta algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples. Copyright (C) 2009 H. B. Coda and R. R. Paccola.

A positional FEM Formulation for geometrical non-linear analysis of shells

This work presents a fully non-linear finite element formulation for shell analysis comprising linear strain variation along the thickness of the shell and geometrically exact description for curved triangular elements. The developed formulation assumes positions and generalized unconstrained vectors as the variables of the problem, not displacements and finite rotations. The full 3D Saint-Venant-Kirchhoff constitutive relation is adopted and, to avoid locking, the rate of thickness variation enhancement is introduced. As a consequence, the second Piola-Kirchhoff stress tensor and the Green strain measure are employed to derive the specific strain energy potential. Curved triangular elements with cubic approximation are adopted using simple notation. Selected numerical simulations illustrate and confirm the objectivity, accuracy, path independence and applicability of the proposed technique.

Evaluation technique for determining wheel performance in the grinding of aerospace materials

Nickel-based super alloys are used in a variety of applications in which high-temperature strength and resistance to creep, corrosion, and oxidation are required, such as in aircraft gas turbines, combustion chambers, and automotive engine valves. The properties that make these materials suitable for these applications also make them difficult to grind. Grinding systems for such materials are often built around vitrified cBN (cubic boron nitride) wheels to realize maximum productivity and minimum cost per part. Conditions that yield the most economical combination of stock removal rate and wheel wear are key to the successful implementation of the grinding system. Identifying the transition point for excessive wheel wear is important. The aim of this study is to compare the performance of different cBN wheels when grinding difficult-to-grind (DTG) materials by determining the 'wheel wear characteristic curve', which correlates the G-ratio to the calculated tangential force per abrasive grain. With the proposed methodology, a threshold force per grit above which the wheel wear rate increases rapidly can be quickly identified. A comparison of performance for two abrasive product formulations in the grinding of three materials is presented. The obtained results can be applied for the development of grinding applications for DTG materials.

An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

Computational adjustment technique for digital mammographic images based on the digitizer characteristic curve

We evaluated the performance of a novel procedure for segmenting mammograms and detecting clustered microcalcifications in two types of image sets obtained from digitization of mammograms using either a laser scanner, or a conventional ""optical"" scanner. Specific regions forming the digital mammograms were identified and selected, in which clustered microcalcifications appeared or not. A remarkable increase in image intensity was noticed in the images from the optical scanner compared with the original mammograms. A procedure based on a polynomial correction was developed to compensate the changes in the characteristic curves from the scanners, relative to the curves from the films. The processing scheme was applied to both sets, before and after the polynomial correction. The results indicated clearly the influence of the mammogram digitization on the performance of processing schemes intended to detect microcalcifications. The image processing techniques applied to mammograms digitized by both scanners, without the polynomial intensity correction, resulted in a better sensibility in detecting microcalcifications in the images from the laser scanner. However, when the polynomial correction was applied to the images from the optical scanner, no differences in performance were observed for both types of images. (C) 2008 SPIE and IS&T [DOI: 10.1117/1.3013544]

Effects of Variations in Nonlinear Damping Coefficients on the Parametric Vibration of a Cantilever Beam with a Lumped Mass

Uncertainties in damping estimates can significantly affect the dynamic response of a given flexible structure. A common practice in linear structural dynamics is to consider a linear viscous damping model as the major energy dissipation mechanism. However, it is well known that different forms of energy dissipation can affect the structure's dynamic response. The major goal of this paper is to address the effects of the turbulent frictional damping force, also known as drag force on the dynamic behavior of a typical flexible structure composed of a slender cantilever beam carrying a lumped-mass on the tip. First, the system's analytical equation is obtained and solved by employing a perturbation technique. The solution process considers variations of the drag force coefficient and its effects on the system's response. Then, experimental results are presented to demonstrate the effects of the nonlinear quadratic damping due to the turbulent frictional force on the system's dynamic response. In particular, the effects of the quadratic damping on the frequency-response and amplitude-response curves are investigated. Numerically simulated as well as experimental results indicate that variations on the drag force coefficient significantly alter the dynamics of the structure under investigation. Copyright (c) 2008 D. G. Silva and P. S. Varoto.

Importance of considering a material micro-failure criterion in the numerical modelling of the shot peening process applied to parabolic leaf springs

Shot peening is a cold-working mechanical process in which a shot stream is propelled against a component surface. Its purpose is to introduce compressive residual stresses on component surfaces for increasing the fatigue resistance. This process is widely applied in springs due to the cyclical loads requirements. This paper presents a numerical modelling of shot peening process using the finite element method. The results are compared with experimental measurements of the residual stresses, obtained by the X-rays diffraction technique, in leaf springs submitted to this process. Furthermore, the results are compared with empirical and numerical correlations developed by other authors.

Pulse train fluorescence technique for measuring triplet state dynamics

We report on a method to study the dynamics of triplet formation based on the fluorescence signal produced by a pulse train. Basically, the pulse train acts as sequential pump-probe pulses that precisely map the excited-state dynamics in the long time scale. This allows characterizing those processes that affect the population evolution of the first excited singlet state, whose decay gives rise to the fluorescence. The technique was proven to be valuable to measure parameters of triplet formation in organic molecules. Additionally, this single beam technique has the advantages of simplicity, low noise and background-free signal detection. (C) 2011 Optical Society of America

Three-dimensional finite element thermal analysis of dental tissues irradiated with Er,Cr:YSGG laser

In the present study, a finite element model of a half-sectioned molar tooth was developed in order to understand the thermal behavior of dental hard tissues (both enamel and dentin) under laser irradiation. The model was validated by comparing it with an in vitro experiment where a sound molar tooth was irradiated by an Er,Cr:YSGG pulsed laser. The numerical tooth model was conceived to simulate the in vitro experiment, reproducing the dimensions and physical conditions of the typical molar sound tooth, considering laser energy absorption and calculating the heat transfer through the dental tissues in three dimensions. The numerical assay considered the same three laser energy densities at the same wavelength (2.79 mu m) used in the experiment. A thermographic camera was used to perform the in vitro experiment, in which an Er, Cr: YSGG laser (2.79 mu m) was used to irradiate tooth samples and the infrared images obtained were stored and analyzed. The temperature increments in both the finite element model and the in vitro experiment were compared. The distribution of temperature inside the tooth versus time plotted for two critical points showed a relatively good agreement between the results of the experiment and model. The three dimensional model allows one to understand how the heat propagates through the dentin and enamel and to relate the amount of energy applied, width of the laser pulses, and temperature inside the tooth. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.2953526]

Color-flavor locked strange matter and strangelets at finite temperature

It is possible that a system composed of up, down, and strange quarks exists as the true ground state of nuclear matter at high densities and low temperatures. This exotic plasma, called strange quark matter (SQM), seems to be even more favorable energetically if quarks are in a superconducting state, the so-called color-flavor locked state. Here we present calculations made on the basis of the MIT bag model, considering the influence of finite temperature on the allowed parameters characterizing the system for stability of bulk SQM (the so-called stability windows) and also for strangelets, small lumps of SQM, both in the color-flavor locking scenario. We compare these results with the unpaired SQM and also briefly discuss some astrophysical implications of them. Also, the issue of the strangelet's electric charge is discussed. The effects of dynamical screening, though important for nonpaired SQM strangelets, are not relevant when considering pairing among all three flavors and colors of quarks.

Finite-size particles, advection, and chaos: A collective phenomenon of intermittent bursting

We consider finite-size particles colliding elastically, advected by a chaotic flow. The collisionless dynamics has a quasiperiodic attractor and particles are advected towards this attractor. We show in this work that the collisions have dramatic effects in the system's dynamics, giving rise to collective phenomena not found in the one-particle dynamics. In particular, the collisions induce a kind of instability, in which particles abruptly spread out from the vicinity of the attractor, reaching the neighborhood of a coexisting chaotic saddle, in an autoexcitable regime. This saddle, not present in the dynamics of a single particle, emerges due to the collective particle interaction. We argue that this phenomenon is general for advected, interacting particles in chaotic flows.

Quantum statistical correlations in thermal field theories: Boundary effective theory

We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field phi(c), and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schrodinger field representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle point for fixed boundary fields, which is the classical field phi(c), a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally reduced effective theory for the thermal system. We calculate the two-point correlation as an example.

Thermodiffusion in a multicomponent lyotropic mixture in the vicinity of the critical micellar concentration by using the Z-scan technique

Thermodiffusion in a lyotropic mixture of water and potassium laurate is investigated by means of an optical technique (Z scan) distinguishing the index variations due to the temperature gradient and the mass gradients. A phenomenological framework allowing for coupled diffusion is developed in order to analyze thermodiffusion in multicomponent systems. An observable parameter relating to the mass gradients is found to exhibit a sharp change around the critical micellar concentration, and thus may be used to detect it. The change in the slope is due to the markedly different values of the Soret coefficients of the surfactant and the micelles. The difference in the Soret coefficients is due to the fact that the micellization process reduces the energy of interaction of the ball of amphiphilic molecules with the solvent.

Effective actions at finite temperature

This is a more detailed version of our recent paper where we proposed, from first principles, a direct method for evaluating the exact fermion propagator in the presence of a general background field at finite temperature. This can, in turn, be used to determine the finite temperature effective action for the system. As applications, we discuss the complete one loop finite temperature effective actions for 0+1 dimensional QED as well as for the Schwinger model in detail. These effective actions, which are derived in the real time (closed time path) formalism, generate systematically all the Feynman amplitudes calculated in thermal perturbation theory and also show that the retarded (advanced) amplitudes vanish in these theories. Various other aspects of the problem are also discussed in detail.