Stress distribution on dentin-cement-post interface varying root canal and glass fiber post diameters. A three-dimensional finite element analysis based on micro-C data

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A Numerical Study of the FENE-CR Model Applied to a Jet Flow Problem

The FENE-CR model is investigated through a numerical algorithm to simulate the time-dependent moving free surface flow produced by a jet impinging on a flat surface. The objective is to demonstrate that by increasing the extensibility parameter L, the numerical solutions converge to the solutions obtained with the Oldroyd-B model. The governing equations are solved by an established free surface flow solver based on the finite difference and marker-and-cell methods. Numerical predictions of the extensional viscosity obtained with several values of the parameter L are presented. The results show that if the extensibility parameter L is sufficiently large then the extensional viscosities obtained with the FENE-CR model approximate the corresponding Oldroyd-B viscosity. Moreover, the flow from a jet impinging on a flat surface is simulated with various values of the extensibility parameter L and the fluid flow visualizations display convergence to the Oldroyd-B jet flow results.

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.

Stability analysis and area spectrum of three-dimensional Lifshitz black holes

In this work, we probe the stability of a z = 3 three-dimensional Lifshitz black hole by using scalar and spinorial perturbations. We found an analytical expression for the quasinormal frequencies of the scalar probe field, which perfectly agree with the behavior of the quasinormal modes obtained numerically. The results for the numerical analysis of the spinorial perturbations reinforce the conclusion of the scalar analysis, i.e., the model is stable under scalar and spinor perturbations. As an application we found the area spectrum of the Lifshitz black hole, which turns out to be equally spaced.

Study of the thermal effects induced by magnetic resonance on endocardial leads: numerical models and experimental validation

Magnetic resonance imaging (MRI) is today precluded to patients bearing active implantable medical devices AIMDs). The great advantages related to this diagnostic modality, together with the increasing number of people benefiting from implantable devices, in particular pacemakers(PM)and carioverter/defibrillators (ICD), is prompting the scientific community the study the possibility to extend MRI also to implanted patients. The MRI induced specific absorption rate (SAR) and the consequent heating of biological tissues is one of the major concerns that makes patients bearing metallic structures contraindicated for MRI scans. To date, both in-vivo and in-vitro studies have demonstrated the potentially dangerous temperature increase caused by the radiofrequency (RF) field generated during MRI procedures in the tissues surrounding thin metallic implants. On the other side, the technical evolution of MRI scanners and of AIMDs together with published data on the lack of adverse events have reopened the interest in this field and suggest that, under given conditions, MRI can be safely performed also in implanted patients. With a better understanding of the hazards of performing MRI scans on implanted patients as well as the development of MRI safe devices, we may soon enter an era where the ability of this imaging modality may be more widely used to assist in the appropriate diagnosis of patients with devices. In this study both experimental measures and numerical analysis were performed. Aim of the study is to systematically investigate the effects of the MRI RF filed on implantable devices and to identify the elements that play a major role in the induced heating. Furthermore, we aimed at developing a realistic numerical model able to simulate the interactions between an RF coil for MRI and biological tissues implanted with a PM, and to predict the induced SAR as a function of the particular path of the PM lead. The methods developed and validated during the PhD program led to the design of an experimental framework for the accurate measure of PM lead heating induced by MRI systems. In addition, numerical models based on Finite-Differences Time-Domain (FDTD) simulations were validated to obtain a general tool for investigating the large number of parameters and factors involved in this complex phenomenon. The results obtained demonstrated that the MRI induced heating on metallic implants is a real risk that represents a contraindication in extending MRI scans also to patient bearing a PM, an ICD, or other thin metallic objects. On the other side, both experimental data and numerical results show that, under particular conditions, MRI procedures might be consider reasonably safe also for an implanted patient. The complexity and the large number of variables involved, make difficult to define a unique set of such conditions: when the benefits of a MRI investigation cannot be obtained using other imaging techniques, the possibility to perform the scan should not be immediately excluded, but some considerations are always needed.

Modelling and analysis of internally BFRP reinforced beams at elevated temperatures

The aim of the work is to conduct a finite element model analysis on a small – size concrete beam and on a full size concrete beam internally reinforced with BFRP exposed at elevated temperatures. Experimental tests performed at Kingston University have been used to compare the results from the numerical analysis for the small – size concrete beam. Once the behavior of the small – size beam at room temperature is investigated and switching to the heating phase reinforced beams are tested at 100°C, 200°C and 300°C in loaded condition. The aim of the finite element analysis is to reflect the three – point bending test adopted into the oven during the exposure of the beam at room temperature and at elevated temperatures. Performance and deformability of reinforced beams are straightly correlated to the material properties and a wide analysis on elastic modulus and coefficient of thermal expansion is given in this work. Develop a good correlation between the numerical model and the experimental test is the main objective of the analysis on the small – size concrete beam, for both modelling the aim is also to estimate which is the deterioration of the material properties due to the heating process and the influence of different parameters on the final result. The focus of the full – size modelling which involved the last part of this work is to evaluate the effect of elevated temperatures, the material deterioration and the deflection trend on a reinforced beam characterized by a different size. A comparison between the results from different modelling has been developed.

Fast and accurate numerical solutions in some problems of particle and radiation transport: synthetic acceleration for the method of short characteristics, Doppler-broadened scattering kernel, remote sensing of the cryosphere

The aim of this work is to present various aspects of numerical simulation of particle and radiation transport for industrial and environmental protection applications, to enable the analysis of complex physical processes in a fast, reliable, and efficient way. In the first part we deal with speed-up of numerical simulation of neutron transport for nuclear reactor core analysis. The convergence properties of the source iteration scheme of the Method of Characteristics applied to be heterogeneous structured geometries has been enhanced by means of Boundary Projection Acceleration, enabling the study of 2D and 3D geometries with transport theory without spatial homogenization. The computational performances have been verified with the C5G7 2D and 3D benchmarks, showing a sensible reduction of iterations and CPU time. The second part is devoted to the study of temperature-dependent elastic scattering of neutrons for heavy isotopes near to the thermal zone. A numerical computation of the Doppler convolution of the elastic scattering kernel based on the gas model is presented, for a general energy dependent cross section and scattering law in the center of mass system. The range of integration has been optimized employing a numerical cutoff, allowing a faster numerical evaluation of the convolution integral. Legendre moments of the transfer kernel are subsequently obtained by direct quadrature and a numerical analysis of the convergence is presented. In the third part we focus our attention to remote sensing applications of radiative transfer employed to investigate the Earth's cryosphere. The photon transport equation is applied to simulate reflectivity of glaciers varying the age of the layer of snow or ice, its thickness, the presence or not other underlying layers, the degree of dust included in the snow, creating a framework able to decipher spectral signals collected by orbiting detectors.

Numerical modelling of fluid-structure interaction with application in hemodynamics

The thesis deals with numerical algorithms for fluid-structure interaction problems with application in blood flow modelling. It starts with a short introduction on the mathematical description of incompressible viscous flow with non-Newtonian viscosity and a moving linear viscoelastic structure. The mathematical model consists of the generalized Navier-Stokes equation used for the description of fluid flow and the generalized string model for structure movement. The arbitrary Lagrangian-Eulerian approach is used in order to take into account moving computational domain. A part of the thesis is devoted to the discussion on the non-Newtonian behaviour of shear-thinning fluids, which is in our case blood, and derivation of two non-Newtonian models frequently used in the blood flow modelling. Further we give a brief overview on recent fluid-structure interaction schemes with discussion about the difficulties arising in numerical modelling of blood flow. Our main contribution lies in numerical and experimental study of a new loosely-coupled partitioned scheme called the kinematic splitting fluid-structure interaction algorithm. We present stability analysis for a coupled problem of non-Newtonian shear-dependent fluids in moving domains with viscoelastic boundaries. Here, we assume both, the nonlinearity in convective as well is diffusive term. We analyse the convergence of proposed numerical scheme for a simplified fluid model of the Oseen type. Moreover, we present series of experiments including numerical error analysis, comparison of hemodynamic parameters for the Newtonian and non-Newtonian fluids and comparison of several physiologically relevant computational geometries in terms of wall displacement and wall shear stress. Numerical analysis and extensive experimental study for several standard geometries confirm reliability and accuracy of the proposed kinematic splitting scheme in order to approximate fluid-structure interaction problems.

Survival Analysis with Large Dimensional Covariates: An Application in Microarray Studies

Use of microarray technology often leads to high-dimensional and low- sample size data settings. Over the past several years, a variety of novel approaches have been proposed for variable selection in this context. However, only a small number of these have been adapted for time-to-event data where censoring is present. Among standard variable selection methods shown both to have good predictive accuracy and to be computationally efficient is the elastic net penalization approach. In this paper, adaptation of the elastic net approach is presented for variable selection both under the Cox proportional hazards model and under an accelerated failure time (AFT) model. Assessment of the two methods is conducted through simulation studies and through analysis of microarray data obtained from a set of patients with diffuse large B-cell lymphoma where time to survival is of interest. The approaches are shown to match or exceed the predictive performance of a Cox-based and an AFT-based variable selection method. The methods are moreover shown to be much more computationally efficient than their respective Cox- and AFT- based counterparts.

Safety of Active Implantable Devices during MRI Examinations: A Finite Element Analysis of an Implantable Pump

The goal of this study was to propose a general numerical analysis methodology to evaluate the magnetic resonance imaging (MRI)-safety of active implants. Numerical models based on the finite element (FE) technique were used to estimate if the normal operation of an active device was altered during MRI imaging. An active implanted pump was chosen to illustrate the method. A set of controlled experiments were proposed and performed to validate the numerical model. The calculated induced voltages in the important electronic components of the device showed dependence with the MRI field strength. For the MRI radiofrequency fields, significant induced voltages of up to 20 V were calculated for a 0.3T field-strength MRI. For the 1.5 and 3.0T MRIs, the calculated voltages were insignificant. On the other hand, induced voltages up to 11 V were calculated in the critical electronic components for the 3.0T MRI due to the gradient fields. Values obtained in this work reflect to the worst case situation which is virtually impossible to achieve in normal scanning situations. Since the calculated voltages may be removed by appropriate protection circuits, no critical problems affecting the normal operation of the pump were identified. This study showed that the proposed methodology helps the identification of the possible incompatibilities between active implants and MR imaging, and can be used to aid the design of critical electronic systems to ensure MRI-safety

Numerical Error Prediction and its applications in CFD using tau-estimation

Nowadays, Computational Fluid Dynamics (CFD) solvers are widely used within the industry to model fluid flow phenomenons. Several fluid flow model equations have been employed in the last decades to simulate and predict forces acting, for example, on different aircraft configurations. Computational time and accuracy are strongly dependent on the fluid flow model equation and the spatial dimension of the problem considered. While simple models based on perfect flows, like panel methods or potential flow models can be very fast to solve, they usually suffer from a poor accuracy in order to simulate real flows (transonic, viscous). On the other hand, more complex models such as the full Navier- Stokes equations provide high fidelity predictions but at a much higher computational cost. Thus, a good compromise between accuracy and computational time has to be fixed for engineering applications. A discretisation technique widely used within the industry is the so-called Finite Volume approach on unstructured meshes. This technique spatially discretises the flow motion equations onto a set of elements which form a mesh, a discrete representation of the continuous domain. Using this approach, for a given flow model equation, the accuracy and computational time mainly depend on the distribution of nodes forming the mesh. Therefore, a good compromise between accuracy and computational time might be obtained by carefully defining the mesh. However, defining an optimal mesh for complex flows and geometries requires a very high level expertize in fluid mechanics and numerical analysis, and in most cases a simple guess of regions of the computational domain which might affect the most the accuracy is impossible. Thus, it is desirable to have an automatized remeshing tool, which is more flexible with unstructured meshes than its structured counterpart. However, adaptive methods currently in use still have an opened question: how to efficiently drive the adaptation ? Pioneering sensors based on flow features generally suffer from a lack of reliability, so in the last decade more effort has been made in developing numerical error-based sensors, like for instance the adjoint-based adaptation sensors. While very efficient at adapting meshes for a given functional output, the latter method is very expensive as it requires to solve a dual set of equations and computes the sensor on an embedded mesh. Therefore, it would be desirable to develop a more affordable numerical error estimation method. The current work aims at estimating the truncation error, which arises when discretising a partial differential equation. These are the higher order terms neglected in the construction of the numerical scheme. The truncation error provides very useful information as it is strongly related to the flow model equation and its discretisation. On one hand, it is a very reliable measure of the quality of the mesh, therefore very useful in order to drive a mesh adaptation procedure. On the other hand, it is strongly linked to the flow model equation, so that a careful estimation actually gives information on how well a given equation is solved, which may be useful in the context of _ -extrapolation or zonal modelling. The following work is organized as follows: Chap. 1 contains a short review of mesh adaptation techniques as well as numerical error prediction. In the first section, Sec. 1.1, the basic refinement strategies are reviewed and the main contribution to structured and unstructured mesh adaptation are presented. Sec. 1.2 introduces the definitions of errors encountered when solving Computational Fluid Dynamics problems and reviews the most common approaches to predict them. Chap. 2 is devoted to the mathematical formulation of truncation error estimation in the context of finite volume methodology, as well as a complete verification procedure. Several features are studied, such as the influence of grid non-uniformities, non-linearity, boundary conditions and non-converged numerical solutions. This verification part has been submitted and accepted for publication in the Journal of Computational Physics. Chap. 3 presents a mesh adaptation algorithm based on truncation error estimates and compares the results to a feature-based and an adjoint-based sensor (in collaboration with Jorge Ponsín, INTA). Two- and three-dimensional cases relevant for validation in the aeronautical industry are considered. This part has been submitted and accepted in the AIAA Journal. An extension to Reynolds Averaged Navier- Stokes equations is also included, where _ -estimation-based mesh adaptation and _ -extrapolation are applied to viscous wing profiles. The latter has been submitted in the Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering. Keywords: mesh adaptation, numerical error prediction, finite volume Hoy en día, la Dinámica de Fluidos Computacional (CFD) es ampliamente utilizada dentro de la industria para obtener información sobre fenómenos fluidos. La Dinámica de Fluidos Computacional considera distintas modelizaciones de las ecuaciones fluidas (Potencial, Euler, Navier-Stokes, etc) para simular y predecir las fuerzas que actúan, por ejemplo, sobre una configuración de aeronave. El tiempo de cálculo y la precisión en la solución depende en gran medida de los modelos utilizados, así como de la dimensión espacial del problema considerado. Mientras que modelos simples basados en flujos perfectos, como modelos de flujos potenciales, se pueden resolver rápidamente, por lo general aducen de una baja precisión a la hora de simular flujos reales (viscosos, transónicos, etc). Por otro lado, modelos más complejos tales como el conjunto de ecuaciones de Navier-Stokes proporcionan predicciones de alta fidelidad, a expensas de un coste computacional mucho más elevado. Por lo tanto, en términos de aplicaciones de ingeniería se debe fijar un buen compromiso entre precisión y tiempo de cálculo. Una técnica de discretización ampliamente utilizada en la industria es el método de los Volúmenes Finitos en mallas no estructuradas. Esta técnica discretiza espacialmente las ecuaciones del movimiento del flujo sobre un conjunto de elementos que forman una malla, una representación discreta del dominio continuo. Utilizando este enfoque, para una ecuación de flujo dado, la precisión y el tiempo computacional dependen principalmente de la distribución de los nodos que forman la malla. Por consiguiente, un buen compromiso entre precisión y tiempo de cálculo se podría obtener definiendo cuidadosamente la malla, concentrando sus elementos en aquellas zonas donde sea estrictamente necesario. Sin embargo, la definición de una malla óptima para corrientes y geometrías complejas requiere un nivel muy alto de experiencia en la mecánica de fluidos y el análisis numérico, así como un conocimiento previo de la solución. Aspecto que en la mayoría de los casos no está disponible. Por tanto, es deseable tener una herramienta que permita adaptar los elementos de malla de forma automática, acorde a la solución fluida (remallado). Esta herramienta es generalmente más flexible en mallas no estructuradas que con su homóloga estructurada. No obstante, los métodos de adaptación actualmente en uso todavía dejan una pregunta abierta: cómo conducir de manera eficiente la adaptación. Sensores pioneros basados en las características del flujo en general, adolecen de una falta de fiabilidad, por lo que en la última década se han realizado grandes esfuerzos en el desarrollo numérico de sensores basados en el error, como por ejemplo los sensores basados en el adjunto. A pesar de ser muy eficientes en la adaptación de mallas para un determinado funcional, este último método resulta muy costoso, pues requiere resolver un doble conjunto de ecuaciones: la solución y su adjunta. Por tanto, es deseable desarrollar un método numérico de estimación de error más asequible. El presente trabajo tiene como objetivo estimar el error local de truncación, que aparece cuando se discretiza una ecuación en derivadas parciales. Estos son los términos de orden superior olvidados en la construcción del esquema numérico. El error de truncación proporciona una información muy útil sobre la solución: es una medida muy fiable de la calidad de la malla, obteniendo información que permite llevar a cabo un procedimiento de adaptación de malla. Está fuertemente relacionado al modelo matemático fluido, de modo que una estimación precisa garantiza la idoneidad de dicho modelo en un campo fluido, lo que puede ser útil en el contexto de modelado zonal. Por último, permite mejorar la precisión de la solución resolviendo un nuevo sistema donde el error local actúa como término fuente (_ -extrapolación). El presenta trabajo se organiza de la siguiente manera: Cap. 1 contiene una breve reseña de las técnicas de adaptación de malla, así como de los métodos de predicción de los errores numéricos. En la primera sección, Sec. 1.1, se examinan las estrategias básicas de refinamiento y se presenta la principal contribución a la adaptación de malla estructurada y no estructurada. Sec 1.2 introduce las definiciones de los errores encontrados en la resolución de problemas de Dinámica Computacional de Fluidos y se examinan los enfoques más comunes para predecirlos. Cap. 2 está dedicado a la formulación matemática de la estimación del error de truncación en el contexto de la metodología de Volúmenes Finitos, así como a un procedimiento de verificación completo. Se estudian varias características que influyen en su estimación: la influencia de la falta de uniformidad de la malla, el efecto de las no linealidades del modelo matemático, diferentes condiciones de contorno y soluciones numéricas no convergidas. Esta parte de verificación ha sido presentada y aceptada para su publicación en el Journal of Computational Physics. Cap. 3 presenta un algoritmo de adaptación de malla basado en la estimación del error de truncación y compara los resultados con sensores de featured-based y adjointbased (en colaboración con Jorge Ponsín del INTA). Se consideran casos en dos y tres dimensiones, relevantes para la validación en la industria aeronáutica. Este trabajo ha sido presentado y aceptado en el AIAA Journal. También se incluye una extensión de estos métodos a las ecuaciones RANS (Reynolds Average Navier- Stokes), en donde adaptación de malla basada en _ y _ -extrapolación son aplicados a perfiles con viscosidad de alas. Este último trabajo se ha presentado en los Actas de la Institución de Ingenieros Mecánicos, Parte G: Journal of Aerospace Engineering. Palabras clave: adaptación de malla, predicción del error numérico, volúmenes finitos

Numerical simulation of tangling in jet engine turbines

The numerical analysis of certain safety related problems presents serious difficulties, since the large number of components present leads to huge finite elementmodels that can only be solved by using large and expensive computers or by making rough approaches to the problem. Tangling, or clashing, in the turbine of a jet engine airplane is an example of such problems. This is caused by the crash and friction between rotor and stator blades in the turbine after an eventual shaft failure. When facing the study of an event through numerical modelling, the accurate simulation of this problem would require the engineer to model all the rotor and stator blades existing in the turbine stage, using a small element size in all pieces. Given that the number of stator and rotor blades is usually around 200, such simulations would require millions of elements. This work presents a new numerical methodology, specifically developed for the accurate modelling of the tangling problem that, depending on the turbine configuration, is able to reduce the number of nodes up to an order of magnitude without losing accuracy. The methodology, which benefits from the cyclic configuration of turbines, is successfully applied to the numerical analysis of a hypothetical tangling event in a turbine, providing valuable data such as the rotating velocity decrease of the turbine, the braking torque and the damage suffered by the blades. The methodology is somewhat general and can be applied to any problem in which damage caused by the interaction between a rotating and static piece is to be analysed.

Some theoretical aspects in computational analysis of adhesive lap joints

This paper is devoted to the numerical analysis of bidimensional bonded lap joints. For this purpose, the stress singularities occurring at the intersections of the adherend-adhesive interfaces with the free edges are first investigated and a method for computing both the order and the intensity factor of these singularities is described briefly. After that, a simplified model, in which the adhesive domain is reduced to a line, is derived by using an asymptotic expansion method. Then, assuming that the assembly debonding is produced by a macro-crack propagation in the adhesive, the associated energy release rate is computed. Finally, a homogenization technique is used in order to take into account a preliminary adhesive damage consisting of periodic micro-cracks. Some numerical results are presented.

A non-linear analysis of lying a floating pipeline on the seabed

In this article, a model for the determination of displacements, deformations and tensions of a submarine pipeline during the construction is presented. The process is carried out from an initial floating situation to the final laying position on the seabed. The existence of currents and small waves are also considered. Firstly, this technique, usually applied to polyethylene pipelines, is described in this paper as well as some real world examples, as well as the variables that can be modified to control the behavior of the structure. A detailed description of the actions in this process is considered, specially the ones related to marine environment, as Archimedes force, current and sea waves. The behavior of the pipeline is modeled with a non linear elasto dynamic model where geometric non linearities are taken into account. A 3-D beam model, without cross section deformation effects, is developed. Special care is taken in the numerical analysis, developed within an updated lagrangian formulation framework, with the sea bed contact, the follower forces due to the external water pressures and the dynamic actions. Finally, some subroutines are implemented into ANSYS to simulate the two dimensional case, where the whole construction process is achieved. With this software, a sensibility analysis of the bending moments, axial forces and stresses obtained with different values of the control variables in order to optimize the construction steps. These control variables are, the axial load in the pipe, the inundated inner length and the distance of the control barge from the coast.