Finite Volume Methods

In this work, a new formulation for central schemes based on staggered grids is proposed. It is based on a novel approach, in which first a time discretization is carried out, followed by the space discretization. The schemes obtained in this fashion have a simpler structure than previous central schemes. For high order schemes, this simplification results in higher computational efficiency. In this work, schemes of order 2 to 5 are proposed and tested, although CRK schemes of any order of accuracy can be constructed in principle. The application to systems of equations is carefully studied, comparing algorithms based on a componentwise extension of the scalar scheme, and algorithms based on projection along characteristic directions.

This paper discusses the modelling of natural convection in air cavities using four eddy viscosity turbulence models. Two 2D closed cavities with deferentially heated walls opposite each other and one 3D open ended tall cavity with one side is heated and adiabatic for all the others were investigated. The CFD simulation results for the two 2D cases were compared with their corresponding experimental measurements and it was found that the komega turbulence model offered the best solution among the turbulence models tested. Close agreement was also achieved between the k-omega model and the experiments in the prediction of temperature and velocity fields for the 3D case with Monte Carlo radiation model. The work has demonstrated the ability of the eddy viscosity turbulence models for modelling natural convection and radiation in different types of cavities.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The numerical solution of the ideal magnetohidrodinamica equations (MHD) is presented. The study corresponds to a non-steady problem. The technique introduced by Powell [1] is used. The eigenvectors are normalized to avoid problems during the simulation. To carry out the numeric simulation an approximate Riemann solver is used in combined form with a TVD technique to evaluate the numeric flows. The analyzed problem to verify the appropriate behavior of the computacional code is of Riemann problem for the MHD. This is an extension of the shock tube used in gas dynamic. The obtained results show the richness of the single fluid MHD solution. Also the results here presented satisfies those found by other authors.

This paper describes the development and application of a frictionless contact stress solver based on the cell-centred finite volume method. The contact methodology, implemented in the open-source software OpenFOAM, is derived from the penalty method commonly used in finite element contact algorithms. The solver is verified on two benchmark tests using the available Hertzian analytical solutions.

The paper presents the solution of a three-dimensional (3-D) magnetostatic problem using the finite formulation of an electromagnetic field. Two different approaches, based on a primal-dual barycentric discretization of the 3-D space, are presented, considering as unknowns either the magnetic fluxes or the circulations of the vector potential. Results on simple reference configurations are reported and discussed.

Clawpack is a software package designed to solve nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. The package includes a number of variants aimed at different applications and user communities. Clawpack has been actively developed as an open source project for over 20 years. The latest major release, Clawpack 5, introduces a number of new features and changes to the code base and a new development model based on GitHub and Git submodules. This article provides a summary of the most significant changes, the rationale behind some of these changes, and a description of our current development model.

El factor de forma permite estimar el volumen de los árboles en pie de especies forestales, por tanto, es necesario determinar el factor para esta especie Juglans neotropica. Se planteó como objetivo determinar el factor de forma de Juglans neotropica en Ibarra, Imbabura, Ecuador. La investigación se realizó en el Campus Yuyucocha, de la Universidad Técnica del Norte, se realizó una adaptación la metodología de cubicación de madera, ya que no se apeó ningún árbol y la toma de datos fue de todos los árboles en árboles en pie de Juglans neotropica con un Dap ³ 10 cm, cuyo fuste se dividió en secciones de 1 m para registrar sus respectivos diámetros. Se utilizó las ecuaciones de Smalian y Newton para calcular el volumen y el factor de forma. Se empleó ocho modelos teóricos para la elaboración de las ecuaciones para la estimación de volumen, que se aplicaron con los valores de volumen obtenidos por los métodos de Smalian y Newton. Se registraron 76 árboles de Juglans neotropica, con val...

We study numerical methods that are inspired by the active flux method of Eymann and Roe and present several new results for one and two-dimensional hyperbolic problems. For one-dimensional linear problems we show that the unlimited active flux method can be interpreted as an ADER method. This interpretation motivates the construction of new third order accurate methods for nonlinear hyperbolic conservation laws. In the two-dimensional case, equivalent methods are only obtained for scalar linear problems. For two-dimensional linear systems the methods are no longer equivalent. For the two-dimensional acoustic equations we compare the accuracy of the two resulting approaches. While commonly used methods for hyperbolic problems are based on discontinuous reconstructions, the active flux method uses a continuous, piecewise quadratic reconstruction. For nonlinear problems we identify a situation in which the continuous reconstruction leads to an unstable approximation. We propose a limiting strategy which overcomes this problem. Our limited version of the active flux method uses the same local stencil as the original method. Keywords Finite volume methods • Hyperbolic conservation laws • Active flux method • ADER method • High-order methods Recently, Eymann, Roe and coauthors introduced a new numerical method for hyperbolic conservation laws, which they called the active flux method. For sufficiently smooth linear problems the method is third order accurate . , third order accurate This work was supported by the DFG through HE 4858/4-1.

We study numerical methods that are inspired by the active flux method of Eymann and Roe and present several new results for one and two-dimensional hyperbolic problems. For one-dimensional linear problems we show that the unlimited active flux method can be interpreted as an ADER method. This interpretation motivates the construction of new third order accurate methods for nonlinear hyperbolic conservation laws. In the two-dimensional case, equivalent methods are only obtained for scalar linear problems. For two-dimensional linear systems the methods are no longer equivalent. For the two-dimensional acoustic equations we compare the accuracy of the two resulting approaches. While commonly used methods for hyperbolic problems are based on discontinuous reconstructions, the active flux method uses a continuous, piecewise quadratic reconstruction. For nonlinear problems we identify a situation in which the continuous reconstruction leads to an unstable approximation. We propose a limiting strategy which overcomes this problem. Our limited version of the active flux method uses the same local stencil as the original method. Keywords Finite volume methods • Hyperbolic conservation laws • Active flux method • ADER method • High-order methods Recently, Eymann, Roe and coauthors introduced a new numerical method for hyperbolic conservation laws, which they called the active flux method. For sufficiently smooth linear problems the method is third order accurate . , third order accurate This work was supported by the DFG through HE 4858/4-1.

We study a general approach to solving conservation laws of the form qt+f (q, x)x = 0, where the flux function f (q, x) has explicit spatial variation. Finite-volume methods are used in which the flux is discretized spatially, giving a function f i (q) over the ith grid cell and leading to a generalized Riemann problem between neighboring grid cells. A high-resolution wave-propagation algorithm is defined in which waves are based directly on a decomposition of flux differences ) into eigenvectors of an approximate Jacobian matrix. This method is shown to be second-order accurate for smooth problems and allows the application of wave limiters to obtain sharp results on discontinuities. Balance laws qt + f (q, x)x = ψ(q, x) are also considered, in which case the source term is used to modify the flux difference before performing the wave decomposition, and an additional term is derived that must also be included to obtain full accuracy. This method is particularly useful for quasi-steady problems close to steady state.

It is well-known that a successful cell destruction is a time-temperature-dependent process, so that the less temperature and the more freezing time, the more cell death will occur successfully. Hence, in order to be more effective ablation, the cryosurgery, whenever needed, should be done in a longer term and at a lower temperature in a more precise, controlled manner. To achieve the goal of targeted cancer therapy, we have proposed a ''pulsed-cryosurgery" as a simple and impressive planning framework to provide conditions for the ablation of deep tumors with minimum damaging impact on normal tissue. To do so, a 2D space-time-dependent model is developed with the help of the coupled Pennes' bio-heat, Navier-Stokes and Laplace equations to predict temperature distribution in the tumor, normal tissues and the microvascular network. Our results are in adequate harmony with the available ones in the literature. Furthermore, growing and shrinking of the ice-ball and lethal zone during and after the cryosurgery have been numerically studied. Subsequently, the effects of the heat generation produced by an electric field for hyperthermia treatment, the injection of nanofluid and spatial arrangement of cryoprobes on heat transfer in the biological tissues have been discussed. All the mentioned results have been supported and verified by illustrative simulations.

It is well-known that a successful cell destruction is a time-temperature-dependent process, so that the less temperature and the more freezing time, the more cell death will occur successfully. Hence, in order to be more effective ablation, the cryosurgery, whenever needed, should be done in a longer term and at a lower temperature in a more precise, controlled manner. To achieve the goal of targeted cancer therapy, we have proposed a ''pulsed-cryosurgery" as a simple and impressive planning framework to provide conditions for the ablation of deep tumors with minimum damaging impact on normal tissue. To do so, a 2D space-time-dependent model is developed with the help of the coupled Pennes' bio-heat, Navier-Stokes and Laplace equations to predict temperature distribution in the tumor, normal tissues and the microvascular network. Our results are in adequate harmony with the available ones in the literature. Furthermore, growing and shrinking of the ice-ball and lethal zone during and after the cryosurgery have been numerically studied. Subsequently, the effects of the heat generation produced by an electric field for hyperthermia treatment, the injection of nanofluid and spatial arrangement of cryoprobes on heat transfer in the biological tissues have been discussed. All the mentioned results have been supported and verified by illustrative simulations.

Ce manuel propose des méthodes pratiques pour le calcul de quelques structures par la méthode des éléments finis, notamment avec l’utilisation d’une feuille de calcul MS EXCEL. Il est destiné aux apprenants de niveau licence ou ingénieur désireux de s’initier à la méthode des éléments finis pour la modélisation des structures. La théorie de la méthode des éléments finis n’y est pas développée mais un bref rappel des démarches et formules y est fait. Le lecteur désireux d’en savoir davantage est invité à se référer à d’autres ouvrages pour plus de détail (voir en annexe les références bibliographiques).

Chemotaxis is a biological phenomenon widely studied these last years, at the biological level but also at the mathematical level. Various models have been proposed, from microscopic to macroscopic scales. In this article, we consider in particular two hyperbolic models for the density of organisms, a semi-linear system based on the hyperbolic heat equation (or dissipative waves equation) and a quasi-linear system based on incompressible Euler equation. These models possess relatively stiff solutions and well-balanced and asymptotic-preserving schemes are necessary to approximate them accurately. The aim of this article is to present various techniques of well-balanced and asymptotic-preserving schemes for the two hyperbolic models for chemotaxis.

We consider two models which were both designed to describe the movement of eukaryotic cells responding to chemical signals. Besides a common standard parabolic equation for the diffusion of a chemoattractant, like chemokines or growth factors, the two models differ for the equations describing the movement of cells. The first model is based on a quasilinear hyperbolic system with damping, the other one on a degenerate parabolic equation. The two models have the same stationary solutions, which may contain some regions with vacuum. We first explain in details how to discretize the quasilinear hyperbolic system through an upwinding technique, which uses an adapted reconstruction, which is able to deal with the transitions to vacuum. Then we concentrate on the analysis of asymptotic preserving properties of the scheme towards a discretization of the parabolic equation, obtained in the large time and large damping limit, in order to present a numerical comparison between the asymptotic behavior of these two models. Finally we perform an accurate numerical comparison of the two models in the time asymptotic regime, which shows that the respective solutions have a quite different behavior for large times.

In this article, we consider a simple hyperbolic relaxation system on networks which models the movement of fibroblasts on an artificial scaffold. After proving the uniqueness of stationary solutions with a given total mass, we present an adapted numerical scheme which takes care of boundary conditions and display some numerical tests.

We introduce a new class of finite difference schemes for approximating the solutions to an initial-boundary value problem on a bounded interval for a one dimensional dissipative hyperbolic system with an external source term, which arises as a simple model of chemotaxis. Since the solutions to this problem may converge to non constant asymptotic states for large times, standard schemes usually fail to yield a good approximation. Therefore, we propose a new class of schemes, which use an asymptotic higher order correction, second and third order in our examples, to balance the effects of the source term and the influence of the asymptotic solutions. A special care is needed to deal with boundary conditions, to avoid harmful loss of mass. Convergence results are proven for these new schemes, and several numerical tests are presented and discussed to verify the effectiveness of their behavior.

In this paper we deal with a semilinear hyperbolic chemotaxis model in one space dimension evolving on a network, with suitable transmission conditions at nodes. This framework is motivated by tissue-engineering scaffolds used for improving wound healing. We introduce a numerical scheme, which guarantees global mass densities conservation. Moreover our scheme is able to yield a correct approximation of the effects of the source term at equilibrium. Several numerical tests are presented to show the behavior of solutions and to discuss the stability and the accuracy of our approximation.

We introduce a numerical scheme to approximate a quasi-linear hyperbolic system which models the movement of cells under the influence of chemotaxis. Since we expect to find solutions which contain vacuum parts, we propose an upwinding scheme which handles properly the presence of vacuum and, besides, which gives a good approximation of the time asymptotic states of the system. For this scheme we prove some basic analytical properties and study its stability near some of the steady states of the system. Finally, we present some numerical simulations which show the dependence of the asymptotic behavior of the solutions upon the parameters of the system.

Aims: This study seeks to examine the relationship between cerebrospinal fluid (CSF) biomarkers (Aβ1-42, Phospho-Tau181p, Total-Tau) and brain volumetric changes measured by Brain Shift Integral (BSI) in Alzheimer's disease (AD) spectrum. We explore the potential of BSI as a complementary, non-invasive tool for early diagnosis and progression monitoring of AD.

The shallow water equations are derived from the Navier-Stokes equations for incompressible fluids and are valid when the vertical velocity and acceleration of the fluid are small. The equations are adequate to model a big range of the hydrodynamic flows which appear in practical engineering situations. The shallow water equations can account for the effects of the bed slope, wind and bottom friction, turbulence, varying channel section and mass source due to superficial waters or infiltration. It has been proved by Bermúdez and Vázquez [3] the convenience of upwinding the bed slope source term in order to reduce discretization errors introduced in the upwinded convective flux terms. showed also the need of upwinding the source terms which account for the varying geometry of the transversal section. This paper focus on the study of the mass and turbulent terms in the shallow water equations, analyzing the convenience of upwinding them from an accurate as well as a stability point of view. A steady solution to the equations which relate the bed slope with the mass and turbulent terms is proposed.

This paper presents a robust finite volume shock-capturing scheme based on the rotated approximate Riemann solver. A general framework for constructing the rotated Riemann solver is described and a rotated Roe scheme is discussed in detail. It is found that the robustness of the rotated shock-capturing scheme is closely related to the way in which the direction of upwind differencing is determined. When the upwind direction is determined by the velocity-difference vector, the rotated Roe scheme demonstrates a robust shock-capturing capability and the shock instabilities or carbuncle phenomena can be eliminated completely. The dissipation property associated with the linear field of the rotated flux-difference splitting scheme is analyzed, and several test cases are presented to validate the proposed scheme.

A class of augmented approximate Riemann solvers due to GEORGE (2008) (J. Comput. Phys. 227, 3089-3113) is extended to solve the shallow-water equations in a moving vessel with variable bottom topography and variable cross-section with wetting and drying. A class of Roe-type upwind solvers for the system of balance laws is derived which respects the steady-state solutions. The numerical solutions of the new adapted augmented f-wave solvers are validated against the Roe-type solvers. The theory is extended to solve the shallow-water flows in moving vessels with arbitrary cross-section with influx-efflux boundary conditions motivated by the shallow-water sloshing in the ocean wave energy converter (WEC) proposed by Offshore Wave Energy Ltd (OWEL) [1]. A fractional step approach is used to handle the time-dependent forcing functions. The numerical solutions are compared to an extended new Roe-type solver for the system of balance laws with a time-dependent source function. The shallow-water sloshing finite volume solver can be coupled to a Runge-Kutta integrator for the vessel motion.

La présence des singularités géométriques dans les structures telles que les trous est une nécessité technologique pour des besoins mécaniques comme l’assemblage des pièces et les canalisations. Cette présence peut conduire à un affaiblissement de la structure en raison de l’augmentation locale de la contrainte. Ce phénomène, appelé concentration des contraintes, peut provoquer l’endommagement des structures métalliques ou composites et influe négativement sur leur sécurité. Dans cette ensemble d’études analytiques, numériques et expérimentales nous présentons l’effet de la présence des trous circulaire et elliptique sur le comportement mécanique des plaques en matériaux composites. Il s’agit de déterminer la distribution des contraintes autour et loin du trou sous les sollicitations de traction, compressions et cisaillement. L’étude est focalisée sur la détermination du facteur de concentration des contraintes qui est considéré comme un inducteur de l’augmentation locale de la cont...

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Notre but est de proposer un modèle d'un géomatériau composite aléatoirement renforcé de type TexSol T M [1, 2] (un mélange sable-fil). La stratégie de modélisation consiste à découper un cube de TexSol T M en fines plaques, le problème initial est alors décomposé en n modèles plaque donnant une formulation 2D homogène et déterministe après passage à la limite par Γ-convergence (voir [3] pour la méthode). Nous reconstruisons alors une structure 3D homogène et déterministe par une intégration variationnelle. Nos différents résultats sont validés par une étude numérique. Mots clés -Modélisation variationnelle, homogénéisation de matériaux composites, analyse numérique, analyse asymptotique, problème non-local.

A new method for computing the fluid flow in complex geometries using highly non‐smooth and non‐orthogonal staggered grid is presented. In a context of the SIMPLE algorithm, pressure and physical tangential velocity components are used as dependent variables in momentum equations. To reduce the sensitivity of the curvature terms in response to coordinate line orientation change, these terms are exclusively computed using Cartesian velocity components in momentum equations. The method is then used to solve some fairly complicated 2‐D and 3‐D flow field using highly non‐smooth grids. The accuracy of results on rough grids (with sharp grid line orientation change and non‐uniformity) was found to be high and the agreement with previous experimental and numerical results was quite good. Copyright © 2008 John Wiley & Sons, Ltd.

Cette these porte sur la modelisation de l’ecoulement et du transport en milieu poreux ;nous effectuons des simulations numeriques et demontrons des resultats de convergence d’algorithmes.Au Chapitre 1, nous appliquons des methodes de volumes finis pour la simulation d’ecoulements a densite variable en milieu poreux ; il vient a resoudre une equation de convection diffusion parabolique pour la concentration couplee a une equation elliptique en pression.Nous nous appuyons sur la methode des volumes finis standard pour le calcul des solutions de deux problemes specifiques : une interface en rotation entre eau salee et eau douce et le probleme de Henry. Nous appliquons ensuite la methode de volumes finis generalises SUSHI pour la simulation des memes problemes ainsi que celle d’un probleme de bassin sale en dimension trois d’espace. Nous nous appuyons sur des maillages adaptatifs, bases sur des elements de volume carres ou cubiques.Au Chapitre 2, nous nous appuyons de nouveau sur la me...

Submitted for the DFD13 Meeting of The American Physical Society von Neumann Stability Analysis of Pressure-Based Formulation of 1D and 2D Euler Equations SANTOSH KONANGI, URMILA GHIA, University of Cincinnati -The stability properties of a pressure-based scheme for the Euler equations are investigated, as such schemes are widely employed in commercial computational fluid dynamics codes. The published literature often focusses on model equations, and does not consider the solution scheme used in the parent code. The present study conducts a von Neumann stability analysis for a pressure-based, segregated scheme, SIMPLE (Semi-Implicit Method for Pressure-Linked Equations). The 1D and 2D Euler equations, closed by an "artificial" equation of state, are discretized using finite differences on a staggered grid, which permits equivalence to finite-volume discretization. As a first effort, first-order accurate spatial and temporal schemes are analyzed, to determine error amplification matrices, identify stable and unstable regimes, and predict practical stability limits in terms of the maximum allowable CFL number as a function of Mach number. The predictions are verified using the Riemann problem at several Mach numbers, and very good agreement is obtained between the predicted and the "numerically" observed CFL values. Hence, the present results should prove useful in guiding the stability of a simulation using the parent-code and the scheme tested here.

The renewable energy sources like wind energy takes an important role to achieve sustainable goal. The wind energy is freely available pollution-free source by which electricity can be produced by the help of wind turbine. Small wind is available in Kota of speed 3m/s to 5 m/s for whole year. So small windmill which can be operated on the small and medium wind can be installed in Kota along with the Chambal River in plain areas and nearby hills. This study focuses on the design and simulation of a 1 kW grid-connected wind energy power plant for a Department of Renewable Energy building in Kota, India. The project aims to harness wind energy as a sustainable source of power to meet the energy demands of the building. By integrating a small-scale wind turbine with the existing grid infrastructure, this system ensures both renewable energy generation and reliability through grid support. The wind energy potential of the Kota region is analyzed, and the system is designed based on local wind speed patterns. The design includes key components such as the wind turbine, power electronics for grid interfacing, and battery storage for energy stability. Simulations are conducted using MATLAB/Simulink to evaluate the system's performance in terms of energy output, efficiency, and grid compatibility. The study demonstrates the feasibility of implementing small-scale wind energy systems in urban institutional buildings and highlights the potential of renewable energy integration in India's energy mix.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The chaotic mixing of miscible liquids in gas-segmented serpentine channels is studied computationally in a two-dimensional setting. Passive tracer particles are used to visualize and quantify the mixing. The molecular diffusion is ignored and only the mixing due to chaotic stirring is considered. Mixing is quantified using the entropy and intensity of segregation measures. The effects of various non-dimensional parameters on the quality of mixing are investigated and it is found that the relative bubble size, the capillary number and the non-dimensional channel corrugation length are the most important parameters influencing the mixing. The mixing is found to be weakly dependent on Reynolds number and nearly independent of viscosity ratio.

This study is devoted to the three-dimensional numerical simulation of developing secondary flows of Newtonian and viscoelastic fluids through a curved duct of square cross-section. The Phan-Thien-Tanner (PTT) model is used to represent viscoelastic effects. The numerical method uses a finite volume discretization with a staggered grid, and the equations are written in general orthogonal coordinates. The numerical simulations produced for 3 different Dean numbers (125, 137 and 150) show clearly the presence of two steady Dean cells and the upstream development of a four-cell pattern when the centrifugal forces become significant. The comparison between Newtonian and PTT flows shows that the transition from twin-cells to four-cells is anticipated for the viscoelastic fluid. To cite this article: M.

This paper analytically examines the effects of adding nanoparticle on the entropy generation of water-Al 2 O 3 nanofluid flows through a coiled tube under uniform wall heat flux condition in turbulent regime. It is found that adding nanoparticles improves the thermal performance of water-Al 2 O 3 flow with Re numbers less than 40,000. The pumping power to heat transfer rate ratio by adding nanoparticles in constant δ anddifferent δ investigated. Moreover optimum conditions (based on the entropy generation sense) for turbulent nanofluid flows are obtained.

Temperatura crítica, Resistência ao fogo, Elementos mistos aço betão Resumo. Neste trabalho são apresentados resultados de ensaios realizados sob acção do fogo em elementos mistos de aço e betão, constituídos por perfis laminados, parcialmente revestidos com betão armado. Os ensaios foram realizados de acordo com a norma europeia de ensaios de resistência ao fogo EN1363 parte 1. Os elementos foram ensaiados à flexão sob acção da curva de incêndio padrão ISO834. A temperatura crítica e a resistência ao fogo foram determinadas para o estado limite último de doze elementos, para três graus de utilização (40, 60 e 80%) e para diferentes configurações dos estribos (soldados e não soldados). Foi utilizado um modelo de elementos finitos para validar a temperatura medida nos diferentes materiais (aço do perfil, betão e reforço) e o deslocamento sofrido pelo elemento. O modelo termo-mecânico foi comparado com os ensaios realizados, utilizando elementos tridimensionais e elementos de interface para simular a transferência de calor e a adesão entre os blocos de betão armado e o perfil metálico. Os resultados numéricos confirmam as medições experimentais em todas as vertentes, quando comparados deslocamentos e temperaturas.

O aço inoxidável tem reconhecidamente uma resistência ao fogo superior ao aço carbono pelo que é de prever uma crescente utilização deste tipo de aço para fins estruturais. De facto, embora mais caro que o aço carbono, o aço inoxidável pode conduzir a estruturas competitivas em virtude de necessitarem de uma menor quantidade de material de protecção térmica ou mesmo, em alguns casos, não ser necessária protecção contra incêndio, como sucede na estrutura apresentada neste artigo. Com o objectivo de modelar pelo Método dos Elementos Finitos o comportamento de uma estrutura porticada de um edifício em aço inoxidável em situação de incêndio, introduziu-se a sua lei constitutiva no programa SAFIR, um programa de elementos finitos para análise não-linear geométrica e material, especialmente desenvolvido na Universidade de Liège para estudo de estruturas sujeitas à acção do fogo. Neste programa as propriedades térmicas e mecânicas do aço são função da temperatura, de acordo com o Eurocódigo 3. Compara-se o comportamento da estrutura em aço inoxidável 1.4301 (também conhecido como 304) com o comportamento que teria se a estrutura fosse em aço carbono S235 e realçam-se os benefícios da utilização do aço inoxidável resultantes da sua maior resistência ao fogo. A utilização do aço inoxidável para fins estruturais tem estado reservada a projectos de elevado valor arquitectónico em que o carácter inovador das soluções adoptadas constitui

Foi utilizado um forno de resistência ao fogo, com a prescrição da curva ISO834. Neste trabalho são apresentados os resultados da evolução da temperatura nos painéis perfurados, nas vigas, conetores, superfície não exposta e apresentados resultados da taxa de carbonização de cada célula.

As lajes em madeira são estruturas leves, de fácil montagem, com excelentes características arquitetónicas, térmicas e acústicas. No entanto, a sua elevada vulnerabilidade ao fogo, obriga a que se determine e avalie o seu comportamento com rigor. Com base em ensaios experimentais, realizados para a determinação da resistência ao fogo, será possível validar um modelo de laje numérico desenvolvido com a utilização de um programa de elementos finitos, ANSYS. O modelo numérico é transiente térmico, não linear e utiliza elementos hexaédricos. Considerou-se a não linearidade das propriedades a temperaturas elevadas. As condições de fronteira, admitidas no problema, são de convecção e radiação, sendo consideradas curvas típicas para a evolução da temperatura. Estas curvas foram registadas durante os ensaios experimentais e permitiram simular o efeito da ação do fogo na superfície exposta, interior das cavidades celulares e nas aberturas ou perfurações da laje. O comportamento físico da laje é também condicionado pela formação da carbonização, sendo este fenómeno considerado no modelo numérico.

An improved design of an axial flux permanent magnet machine is obtained using finite element method and sensitivity analyses. A 9-phase axial flux permanent magnet machine with one-rotor-two-stators configuration equipped with concentrated winding is investigated and condition for minimum cogging torque and voltage harmonics is deduced. Owing to three dimensional structure of axial flux permanent magnet machines, 3-D finite element model is used to model and analysis of the generator performance characteristics. Sensitivity of the machine is evaluated respect to variation of its geometric parameters

Les choix technologiques sont naturellement orientés vers l'utilisation des pièces légères dont au moins une des dimensions est beaucoup plus petite que les autres, tels que des profils ou des plaques, mais le comportement des pièces souples présente des défis particuliers pour les ingénieurs lors de la spécification géométrique, la raison est que les pièces souples peuvent prendre à l'état libre une forme substantiellement différente de leur géométrie nominale. Avec le développement de la conception des systèmes mécaniques, les méthodes traditionnelles d'analyse des tolérances, tels que la méthode pire des cas et la simulation de Monte Carlo, ne sont pas applicables à des assemblages flexibles en raison de la déformation possible de la pièce pendant le processus d'assemblage. Cette communication porte sur la présentation du tolérancement des mécanismes déformables à travers l'illustration de la problématique générale afin d'aborder dans un deuxième temps une étude des mécanismes déformables (flexibles) en utilisant la méthode des coefficients d'influence et enfin la modélisation d'un mécanisme de ce type à travers un exemple en vue d'une analyse des tolérances dimensionnelles et géométriques. Mots clefs -tolérancement, analyse des tolérances; mécanismes déformables ; méthode de Monte Carlo ; méthode des coefficients d'influence.