A discontinuous-Galerkin-based immersed boundary method

A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of user-defined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous-Galerkin approximation and impose the Dirichlet boundary conditions strongly. By virtue of relaxing the continuity constraint at those elements. boundary locking is avoided and optimal-order convergence is achieved. This is shown through numerical experiments in reaction-diffusion problems. Copyright (c) 2008 John Wiley & Sons, Ltd.

Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures

We design and investigate a sequential discontinuous Galerkin method to approximate two-phase immiscible incompressible flows in heterogeneous porous media with discontinuous capillary pressures. The nonlinear interface conditions are enforced weakly through an adequate design of the penalties on interelement jumps of the pressure and the saturation. An accurate reconstruction of the total velocity is considered in the Raviart-Thomas(-Nedelec) finite element spaces, together with diffusivity-dependent weighted averages to cope with degeneracies in the saturation equation and with media heterogeneities. The proposed method is assessed on one-dimensional test cases exhibiting rough solutions, degeneracies, and capillary barriers. Stable and accurate solutions are obtained without limiters. (C) 2010 Elsevier B.V. All rights reserved.

Minimization of stock weight during close-die forging of a spindle

In this paper, Finite Element method and full-scale experiments have been used to study a hot forging method for fabri-cation of a spindle using reduced initial stock size. The forging sequence is carried out in two stages. In the first stage, the hot rolled cylindrical billet is pre-formed and pierced in a closed die using a spherical nosed punch to within 20 mm of its base. This process of piercing or impact extrusion leads to high strains within the work piece but requires high press loads. In the second stage, the resulting cylinder is placed in a die with a flange chamber and upset forged to form a flange. The stock mass is optimized for complete die filling. Process parameters such as effective strain distribution, material flow and forging load in different stages of the process are analyzed. It is concluded from the simulations that minor modifications of piercing punch geometry to reduce contact between the punch and emerging vertical walls of the cylinder appreciably reduces the piercing load. In the flange chamber, a die surfaces angle of 52° instead of 45° is pro-posed to ensure effective material flow and exert sufficient tool pressure to achieve complete cavity filling. In order to achieve better compression, it is also proposed to shorten both the length of the inserted punch and the die “tongues” by a few mm.

Experimental and computational investigation of the roll forming process

One of the first questions to consider when designing a new roll forming line is the number of forming steps required to produce a profile. The number depends on material properties, the cross-section geometry and tolerance requirements, but the tool designer also wants to minimize the number of forming steps in order to reduce the investment costs for the customer. There are several computer aided engineering systems on the market that can assist the tool designing process. These include more or less simple formulas to predict deformation during forming as well as the number of forming steps. In recent years it has also become possible to use finite element analysis for the design of roll forming processes. The objective of the work presented in this thesis was to answer the following question: How should the roll forming process be designed for complex geometries and/or high strength steels? The work approach included both literature studies as well as experimental and modelling work. The experimental part gave direct insight into the process and was also used to develop and validate models of the process. Starting with simple geometries and standard steels the work progressed to more complex profiles of variable depth and width, made of high strength steels. The results obtained are published in seven papers appended to this thesis. In the first study (see paper 1) a finite element model for investigating the roll forming of a U-profile was built. It was used to investigate the effect on longitudinal peak membrane strain and deformation length when yield strength increases, see paper 2 and 3. The simulations showed that the peak strain decreases whereas the deformation length increases when the yield strength increases. The studies described in paper 4 and 5 measured roll load, roll torque, springback and strain history during the U-profile forming process. The measurement results were used to validate the finite element model in paper 1. The results presented in paper 6 shows that the formability of stainless steel (e.g. AISI 301), that in the cold rolled condition has a large martensite fraction, can be substantially increased by heating the bending zone. The heated area will then become austenitic and ductile before the roll forming. Thanks to the phenomenon of strain induced martensite formation, the steel will regain the martensite content and its strength during the subsequent plastic straining. Finally, a new tooling concept for profiles with variable cross-sections is presented in paper 7. The overall conclusions of the present work are that today, it is possible to successfully develop profiles of complex geometries (3D roll forming) in high strength steels and that finite element simulation can be a useful tool in the design of the roll forming process.

Otimização topológica de estruturas termoelásticas tridimensionais

This work presents an optimization technique based on structural topology optimization methods, TOM, designed to solve problems of thermoelasticity 3D. The presented approach is based on the adjoint method of sensitivity analysis unified design and is intended to loosely coupled thermomechanical problems. The technique makes use of analytical expressions of sensitivities, enabling a reduction in the computational cost through the use of a coupled field adjoint equation, defined in terms the of temperature and displacement fields. The TOM used is based on the material aproach. Thus, to make the domain is composed of a continuous distribution of material, enabling the use of classical models in nonlinear programming optimization problem, the microstructure is considered as a porous medium and its constitutive equation is a function only of the homogenized relative density of the material. In this approach, the actual properties of materials with intermediate densities are penalized based on an artificial microstructure model based on the SIMP (Solid Isotropic Material with Penalty). To circumvent problems chessboard and reduce dependence on layout in relation to the final optimal initial mesh, caused by problems of numerical instability, restrictions on components of the gradient of relative densities were applied. The optimization problem is solved by applying the augmented Lagrangian method, the solution being obtained by applying the finite element method of Galerkin, the process of approximation using the finite element Tetra4. This element has the ability to interpolate both the relative density and the displacement components and temperature. As for the definition of the problem, the heat load is assumed in steady state, i.e., the effects of conduction and convection of heat does not vary with time. The mechanical load is assumed static and distributed

Método de Otimização Topológica em Estruturas Tridimensionais

The topology optimization problem characterize and determine the optimum distribution of material into the domain. In other words, after the definition of the boundary conditions in a pre-established domain, the problem is how to distribute the material to solve the minimization problem. The objective of this work is to propose a competitive formulation for optimum structural topologies determination in 3D problems and able to provide high-resolution layouts. The procedure combines the Galerkin Finite Elements Method with the optimization method, looking for the best material distribution along the fixed domain of project. The layout topology optimization method is based on the material approach, proposed by Bendsoe & Kikuchi (1988), and considers a homogenized constitutive equation that depends only on the relative density of the material. The finite element used for the approach is a four nodes tetrahedron with a selective integration scheme, which interpolate not only the components of the displacement field but also the relative density field. The proposed procedure consists in the solution of a sequence of layout optimization problems applied to compliance minimization problems and mass minimization problems under local stress constraint. The microstructure used in this procedure was the SIMP (Solid Isotropic Material with Penalty). The approach reduces considerably the computational cost, showing to be efficient and robust. The results provided a well defined structural layout, with a sharpness distribution of the material and a boundary condition definition. The layout quality was proporcional to the medium size of the element and a considerable reduction of the project variables was observed due to the tetrahedrycal element

Biossorção utilizando alga marinha (sargassum sp.) aplicada em meio orgânico

In this work, biosorption process was used to remove heavy metals from used automotive lubricating oils by a bus fleet from Natal-RN-Brazil. This oil was characterized to determine the physical-chemistry properties. It was also characterized the used oil with the aim of determining and quantifying the heavy metal concentration. Fe and Cu were the metals existent in large concentration and these metals were choused to be studied in solubilization process. For the biosorption process was used the seaweed Sargassum sp for the study of influencing of the metals presents separately and with other metals. It was also studied the effect of the protonation treatment of alga with the objective to know the best efficiency of heavy metals removal. The study of the solubilization showed that the presence of more than a metal favors the solubilization of the metals presents in the oil and consequently, it favors the biosorption process, what becomes interesting the perspective application in the heavy metals removal in lubricating oils used, because the presence of more than a heavy metal favors the solubility of all metals present. It was observed that the iron and copper metals, which are present in large concentration, the protonated biosorbtent was more effective. In this study we used as biomass the marine alga Sargassum sp to study the influence of agitation velocity, temperature and initial biomass concentration on the removal of iron and copper from used lubricant oils. We performed an experimental design and a kinetic study. The experiments were carried out with samples of used lubricant oil and predetermined amounts of algae, allowing sufficient time for the mixture to obtain equilibrium under controlled conditions. The results showed that, under the conditions studied, the larger the amount of biomass present, the lower the adsorption capacity of the iron and of the copper, likely due to a decrease in interface contact area. The experimental design led us to conclude that a function can be obtained that shows the degree of influence of each one of the system variables

Influência do tipo de chanfro, tecimento e sentido de laminação na distorção angular em soldagem GMAW-P robotizada de alumínio

The industry's interest in having a greater control of the deformations caused by welding is due to the geometric and dimensional tolerances been more and more precise in the project specifications, motivating the manufacturing engineering to develop stable processes and to ensure routine production. Aiming at it, the main goal of this present work is to analyze how much routine situations used in automatic aluminum welding can influence on the angular deformations of this material. Using the alloy AA 5052 H34, and the automatic welding in pulsed GMAW process, three types of weaving were applied throughout the length of the weld, in butt joints assembled without groove and with 60 degrees single-V-groove, arranged transversely as well as longitudinally to the rolling direction of the plate. The measurement of the deformations was made by a three-dimensional equipment, before and after the welding, in three distinct regions in the specimens. The profile of the weld bead was the main factor for the different types of deformations found, as revealed by macrographical analysis. The 60 degrees single-V-groove had higher amplitudes of deformations as the joint without groove. The torch oscillation wasn't a variable of statistically significant influence on this amplitudes.

A planar flexible robotic manipulator

Presents the dynamic modelling of a flexible robotic manipulator with two flexible links and two revolute joints, which rotates in the horizontal plane. The dynamic equations are derived using the Newton-Euler formulation and the finite element method, based on elementary beam theory, which is used to discretize the displacements such that the small motion is represented in terms of nodal displacements. Computer simulation results are presented to illustrate this study. The dynamic model becomes necessary for use in future design and control applications.

BEM Formulations Based on Kirchhoff's Hypoyhesis to Perform Linear Bending Analysis of Plates Reinforced by Beams

In this work, are discussed two formulations of the boundary element method - BEM to perform linear bending analysis of plates reinforced by beams. Both formulations are based on the Kirchhoffs hypothesis and they are obtained from the reciprocity theorem applied to zoned plates, where each sub-region defines a beam or a stab. In the first model the problem values are defined along the interfaces and the external boundary. Then, in order to reduce the number of degrees of freedom kinematics hypothesis are assumed along the beam cross section, leading to a second formulation where the collocation points are defined along the beam skeleton, instead of being placed on interfaces. on these formulations no approximation of the generalized forces along the interface is required. Moreover, compatibility and equilibrium conditions along the interface are automatically imposed by the integral equation. Thus, these formulations require less approximation and the total number of the degrees of freedom is reduced. In the numerical examples are discussed the differences between these two BEM formulations, comparing as well the results to a well-known finite element code.

Experimental Active Vibration Control in Truss Structures Considering Uncertainties in System Parameters

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

Modelagem Matemática e Computacional de fenômenos eletrocinéticos em meios porosos carregados eletricamente

In this work we present a mathematical and computational modeling of electrokinetic phenomena in electrically charged porous medium. We consider the porous medium composed of three different scales (nanoscopic, microscopic and macroscopic). On the microscopic scale the domain is composed by a porous matrix and a solid phase. The pores are filled with an aqueous phase consisting of ionic solutes fully diluted, and the solid matrix consists of electrically charged particles. Initially we present the mathematical model that governs the electrical double layer in order to quantify the electric potential, electric charge density, ion adsorption and chemical adsorption in nanoscopic scale. Then, we derive the microscopic model, where the adsorption of ions due to the electric double layer and the reactions of protonation/ deprotanaç~ao and zeta potential obtained in modeling nanoscopic arise in microscopic scale through interface conditions in the problem of Stokes and Nerst-Planck equations respectively governing the movement of the aqueous solution and transport of ions. We developed the process of upscaling the problem nano/microscopic using the homogenization technique of periodic structures by deducing the macroscopic model with their respectives cell problems for effective parameters of the macroscopic equations. Considering a clayey porous medium consisting of kaolinite clay plates distributed parallel, we rewrite the macroscopic model in a one-dimensional version. Finally, using a sequential algorithm, we discretize the macroscopic model via the finite element method, along with the interactive method of Picard for the nonlinear terms. Numerical simulations on transient regime with variable pH in one-dimensional case are obtained, aiming computational modeling of the electroremediation process of clay soils contaminated

Petrologia do magmatismo tardi-brasiliano no Maciço São José de Campestre(RN/PB), com ênfase no Plúton Alcalino Caxexa

The area studied is located on the north-easternmost portion of the Borborema Province, on the so-called São José de Campestre Massif, States of RN and PB, Northeast Brazil. Field relations and petrographic, geochemical and isotope data permitted the separation of five suites of plutonic rocks: alkali-feldspar granite (Caxexa Pluton), which constitutes the main subject of this dissertation, amphibole-biotite granite (Cabeçudo Pluton), biotite microgranite, gabbronorite to monzonite (Basic to Intermediate Suite) and aluminous granitoid. The Caxexa Pluton is laterally associated to the Remígio Pocinhos Shear Zone, with its emplacement along the mylonitic contact between the gneissic basement and the micashists. This pluton corresponds to a syntectonic intrusion elongated in the N-S direction, with about 50 km2 of outcropping surface. It is composed exclusively of alkali-feldspar granites, having clinopyroxene (aegirine-augite and hedenbergite), andradite-rich garnet, sphene and magnetite. It is classified geochemically as high silica rocks (>70 % wt), metaluminous to slightly peraluminous (normative corindon < 1%), with high total alkalis (>10% wt), Sr, iron number (#Fe=90-98) and agpaitic index (0.86-1.00), and positive europium anomaly. The Cabeçudo Pluton is composed of porphyritic rocks, commonly containing basic to intermediate magmatic enclaves often with mingling and mixing textures. Petrographically, it presents k-feldspar and plagioclase phenocrysts as the essential minerals, besides the accessories amphibole, biotite, sphene and magnetite. It is metaluminous and shows characteristics transitional between the calc-alkaline and alkaline series (or monzonitic subalkaline). Its REE content is greater than those ones of the Caxexa Pluton and biotite microgranite, and all spectra have negative europium anomalies. The biotite microgranites occur mainly on the central and eastern portion of the mapped area, as dykes and sheets with decimetric thickness, hosted principally in orthogneisses and micashists. Their field relationships as regards the Caxexa and Cabeçudo plutons suggested that they are late-tectonic intrusions. They are typically biotite granites, having also sphene, amphibole, allanite, opaques and zircon in the accessory assemblage. Geochemically they can be distinguished from the porphyritic types because the biotite microgranites are more evolved, peraluminous, and have more fractionated REE spectra. The Basic to Intermediate rocks form a volumetrically expressive elliptical, kilometric scale body on the Southeast, as well as sheets in micashists. They are classified as gabbronorites to monzonites, with the two pyroxenes and biotite, besides subordinated amounts of amphibole, sphene, ilmenite and allanite. These rocks do not show a well-defined geochemical trend, however they may possibly represent a monzonitic (shoshonitic) series. Their REE spectra have negative europium anomalies and REE contents greater than the other suites. The aluminous granitoids are volumetrically restricted, and have been observed in close association with migmatised micashists bordering the gabbronorite pluton. They are composed of almandine-rich garnet, andalusite, biotite and muscovite, and are akin to the peraluminous suites. Rb-Sr (whole rock) and Sm-Nd (whole-rock and mineral) isotopes furnished a minimum estimate of the crystallization (578±14 Ma) and the final resetting age of the Rb-Sr system (536±4 Ma) in the Caxexa Pluton. The aluminous granitoid has a Sm-Nd garnet age similar to that one of the Caxexa Pluton, that is 574±67 Ma. The strong interaction of shear bands and pegmatite dykes favoured the opening of the Rb-Sr system for the Caxexa Pluton and biotite microgranite. The amphibole-plagioclase geothermometer and the Al-in amphibole geobarometer indicate minimum conditions of 560°C and 7 kbar for the Cabeçudo Pluton, 730°C and 6 kbar for the microgranite and 743°C and 5 kbar for the basic to intermediate suite. The Zr saturation geothermometer reveals temperatures of respectively 855°C, 812°C and 957°C for those suites, whereas the Caxexa Pluton shows temperatures of around 757°C. The Caxexa, Cabeçudo and microgranites suites crystallized under high fO2 (presence of magnetite). On the other hand, the occurrence of ilmenite suggests less oxidant conditions in the basic to intermediate suite. Field relations demonstrate the intrusive character of the granitoids into a tectonically relatively stable continental crust. This is corroborated by petrographic and geochemical data, which suggest a late- or post-collisional tectonic context. It follows that the generation and emplacement of those granitoid suites is related to the latest events of the Brasiliano orogeny. Finally, the relationships between eNd (600 Ma), TDM (Nd) and initial Sr isotope ratio (ISr) do not permit to define the precise sources of the granitoids. Nevertheless, trace element modelling and isotopic comparisons suggest the participation of the metasomatised mantle in the generation of these suites, probably modified by different degrees of crustal contamination. In this way, a metasomatised mantle would not be a particular characteristic of the Neoproterozoic lithosphere, but a remarkable feature of this portion of the Borborema Province since Archaean and Paleoproterozoic times.

Short Implant to Support Maxillary Restorations: Bone Stress Analysis Using Regular and Switching Platform

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

Influence of customized composite resin fibreglass posts on the mechanics of restored treated teeth

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