Дисертації з теми "Méthode des element finis"
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Kergourlay, Erwan. "Eléments finis en transformations finies à base d'ondelettes." Thesis, Lorient, 2017. http://www.theses.fr/2017LORIS472/document.
The numerical modelling with the finite element method conventionally uses functions of polynomial form which, by their regularity, hardly represent singular evolutions such as those observed in the phenomena of localization in mechanics. To solve the issue, the aim of this thesis was to propose a new adaptive approximation support coupling the wavelet representation with the classical finite element method. In the field of signal processing, the wavelet method shows a real capacity to treat singular phenomena. This research study deals with the creation of a hybrid discretisation support, including a polynomial interpolation and a wavelet interpolation formulated with the scaling function of the Daubechies wavelet. The regular part of the solution is represented with the polynomial support and the singularities are visualised with the wavelet support. The adaptation of the hybrid support is carried out with the multiresolution contribution, which adjusts the support according to the importance of observed singularities. An automatic detection and enrichment method is carried out in order to obtain the optimum support. The Daubechies wavelet being known only in discrete points, a particular integration method is proposed. A modification of the not nodal naturally interpolated wavelet interpolation is also introduced, in order to impose classical nodal boundary conditions. An illustration of the method and its computer implementation is presented via a 1D academic study
Haidar, Sarwat. "Ouvrages renforcés par géosynthétiques : modélisation par la méthode des éléments finis, calcul équilibre limite et validation." Grenoble 1, 1992. http://www.theses.fr/1992GRE10199.
Pouzols, Virginie. "Optimisation d'opérations industrielles de pliage par la méthode des éléments finis." Phd thesis, Université de Grenoble, 2011. http://tel.archives-ouvertes.fr/tel-00722228.
Bert, Paul-Frédéric. "Modélisation des écoulements instationnaires dans les turbomachines par une méthode éléments finis." Grenoble INPG, 1996. http://www.theses.fr/1996INPG0218.
He, Tianlong. "A new approach based on finite element method for numerical computation of effective properties for composite materials : Phantom Domain Finite Element Method." Thesis, Normandie, 2020. http://www.theses.fr/2020NORMC204.
To circumvent the meshing difficulty of the existing numerical methods for composites homogenization, an original finite element method,named Phantom domain Finite Element Method (PFEM), is proposed in this thesis. The PFEM relies on computations of integrals with independent meshes based on a fictitious domain principle. In other words, one structured mesh is used for the entire domain, and independent meshes are used for the inclusions. The inclusion meshes will be related to the structured mesh through a substitution matrix. The PFEM is not only capable of calculating effective properties in homogenization technique with KUBC, SUBC and periodic condition, but also can be used in all the problems which can be solved by the FEM, such as the Dirichlet or Neumann boundary value problems. Numerical experiments in two or three dimensional cases, with inclusions of elementary geometry such as disk, square, sphere,cube and ellipsoid, have been performed to validate the PFEM method. Linear convergences of relative errors with respect to reference solutions such as the Mori-Tanaka model and the Fast Fourier Transform method are shown for thermal and elastic effective properties. We have illustrated some interesting features of the PFEM, such as the total flexibility concerning the inclusions meshes, by showing an example with a very thin pellicle sphere
Habchi, Wassim. "A full-system finite element approach to elastohydrodynamic lubrication problems : application to ultra-low-viscosity fluids." Lyon, INSA, 2008. http://theses.insa-lyon.fr/publication/2008ISAL0038/these.pdf.
Cette thèse présente un modèle éléments finis avec couplage fort des problèmes de lubrification élastohydrodynamique (EHD). La lubrification EHD consiste en une séparation complète des surfaces en contact par un film complet de lubrifiant dans lequel est générée une pression suffisamment élevée pour engendrer une déformation élastique significative des surfaces. Ainsi, un couplage fort entre les effets hydrodynamiques et les effets élastiques s’établit. Le système non-linéaire formé par les équations de Reynolds, d’élasticité linéaire et d’équilibre des charges est résolu de manière couplée par une approche de type Newton-Raphson. Cette approche permet d’avoir de très bons taux de convergence par rapport à l’approche classique avec couplage faible. Le problème de frontière libre de cavitation à la sortie du contact est traité par le biais d’une méthode de pénalisation. Des formulations de stabilisation appropriées sont utilisées pour étendre la résolution à des cas de contacts fortement chargés. Ensuite, le comportement non-Newtonien du lubrifiant et les effets thermiques sont pris en compte. Le modèle développé est utilisé pour étudier l’utilisation des Fluides de Très Faible Viscosité dans les contacts EHD. L’utilisation de tels fluides en tant que lubrifiants offre deux avantages principaux: tout d’abord, la dissipation d’énergie dans le contact par frottement est réduite et ensuite, dans le cadre de machines qui opèrent avec un fluide de fonction (généralement de faible viscosité) et un lubrifiant, le premier pourrait être utilisé pour remplir les deux fonctions. Cela permettrait une conception et une maintenance plus faciles de la machine en plus d’une amélioration de ses performances
Bossut, Régis. "Modélisation de transducteurs piézoélectriques annulaires immergés par la méthode des éléments finis." Valenciennes, 1985. https://ged.uphf.fr/nuxeo/site/esupversions/39364c80-50ea-4a42-9b4a-6380d9ebefdd.
Zouari, Wajdi. "Développement d'éléments finis ferroélectriques et ferroélastiques de type solide et coque curvilignes." Thesis, Nancy 1, 2010. http://www.theses.fr/2010NAN10015/document.
Piezoceramics like lead zirconate titanate or PZT can produce an electric potential when they are subjected to a mechanical stress and deform in the presence of an electric field. This electromechanical coupling can be described by linear constitutive equations for moderate loadings. Nevertheless, this coupling becomes highly non linear when piezoceramics are subjected to high electromechanical loadings due to the electric polarization switching. In this thesis work, a phenomenological material constitutive model that describe the electric polarization ferroelectric switching (by an electric field) and ferroelastic switching (by a mechanical stress) is proposed. To describe the loading history, two internal variables are considered and two electric and mechanical loading surfaces are defined to indicate the onset of domain switchings. A bi-dimensional version of this model is developed to study thin piezoelectric structures. The phenomenological model 2D and 3D versions are implicitly integrated by adopting the return-mapping algorithm. Two shell and hexahedral first-order finite elements are then formulated and implemented into the commercial finite element code Abaqus via the user subroutine UEL (User ELement)
Garambois, Pierre. "Modèles éléments-finis mixtes réduits pour l'optimisation en dynamique des structures." Thesis, Ecully, Ecole centrale de Lyon, 2015. http://www.theses.fr/2015ECDL0036/document.
The use of thin structures is increasing in many industries. Their mechanical representation and optimization is therefore a major challenge in modern research. Usually, the optimization is done with a stress criterion which is determined through displacements finite-element model. The idea of this work is to build a mixed displacements-stresses finite-element model and to develop adapted reduction procedures, in order to improve the efficiency of existing optimization methods. On the one hand, we build two mixed displacements-generalized stresses finite element models, for thin and thick dynamic plate structures analysis. They afford the advantage of giving identical results as classical displacements models with a better computational time to re-build the stress fields. Nevertheless, they turn out to be tricky for some reasons : the bigger matrices size, the difficulty of modal analysis and an assembling time higher. That is the reason why we develop afterwards some sub-structuring methods and double modal synthesis specifically dedicated to mixed models. The idea is to use modal basis taken from the equivalent displacement model so as to build a new mixed reduced basis. Ten methods are implemented, based on fixed modes, free modes, and branch modes. Some of them turn out to be very efficient to drastically reduce the amount of degrees of freedom of the mixed model, without using its eigenmodes. Finally, we embed the sub-structured mixed model in the form of Mixed Super- Element in a genetic algorithm, with the aim of conducting a multi-objective optimization of academic plate structures under dynamic loads, with stresses criterion and thicknesses parameters. The models previously defined are configured with thicknesses as parameters, and therefore don’t need to be re-assembled for each configuration. We now dispose of a powerful thickness-parametrized mixed reduced plate finite element model : it keeps the advantages of an easy access to the stresses and is free of its important size thanks to the reduction method and of its assembling thanks to the parametrization. The result is an original and efficient mechanical model that reduces the computational cost of classical optimization algorithms. That type of model, coupled with powerful genetic algorithms, permits a global optimization with a good overview of the solutions and promises interesting perspectives for industrial uses
Chaumont, Frelet Théophile. "Approximation par éléments finis de problèmes d'Helmholtz pour la propagation d'ondes sismiques." Thesis, Rouen, INSA, 2015. http://www.theses.fr/2015ISAM0011/document.
The main objective of this work is the design of an efficient numerical strategy to solve the Helmholtz equation in highly heterogeneous media. We propose a methodology based on coarse meshes and high order polynomials together with a special quadrature scheme to take into account fine scale heterogeneities. The idea behind this choice is that high order polynomials are known to be robust with respect to the pollution effect and therefore, efficient to solve wave problems in homogeneous media. In this work, we are able to extend so-called "asymptotic error-estimate" derived for problems homogeneous media to the case of heterogeneous media. These results are of particular interest because they show that high order polynomials bring more robustness with respect to the pollution effect even if the solution is not regular, because of the fine scale heterogeneities. We propose special quadrature schemes to take int account fine scale heterogeneities. These schemes can also be seen as an approximation of the medium parameters. If we denote by h the finite-element mesh step and by e the approximation level of the medium parameters, we are able to show a convergence theorem which is explicit in terms of h, e and f, where f is the frequency. The main theoretical results are further validated through numerical experiments. 2D and 3D geophysica benchmarks have been considered. First, these experiments confirm that high-order finite-elements are more efficient to approximate the solution if they are coupled with our multiscale strategy. This is in agreement with our results about the pollution effect. Furthermore, we have carried out benchmarks in terms of computational time and memory requirements for 3D problems. We conclude that our multiscale methodology is able to greatly reduce the computational burden compared to the standard finite-element method
Dujc, Jaka. "Finite element analysis of limit load and localized failure of structures." Cachan, Ecole normale supérieure, 2008. http://tel.archives-ouvertes.fr/tel-00505153/fr/.
The dissertation deals with limit load and limit ductility analysis of structures by the finite element method. When structure is at its limit load, several structural components behave inelastically, while in the critical parts of the structure, due to localization of inelastic strains, failure of material appears. Localized effects in brittle materials are related to appearance and formation of a large (macro) crack, while failure in ductile materials is governed by localized shear bands. The study of limit load is thus related to modeling both standard inelastic material effects, as well as modeling of localized failure of material, often reffered to as material softening. Standard inelastic material effects are in this work described with elastoplastic, elastoviscoplastic and nonlinear elastic material models. All the material models are defined at the level of stress-resultants. Several mathematical approaches and numerical algorithms for modeling localized effects are at hand, but they are often inefficient or inaccurate. Therefor, we use an up-to-date approach, based on a finite element method with embedded discontinuity. We derive new finite element formulations with a quite complex kinematics of the basic elements, as well as rather complex description of discontinuous displacement fields. We derived several finite element formulations for analysis of different structural components. First we present a finite element for limit load analysis of reinforced concrete plates. Stress-resultant elastoplastic and elastoviscoplastic plate finite element formulation along with a unified computational procedure that covers both formulations are presented next. Further, a nonlinear shell finite element, based on a two-surface yield function, that includes both isotropic and kinematic material hardening is presented. The last two finite elements derived in this work are intended to model the localized failure in planar beams and 2D solids. The embedded discontinuity in rotations was built into elastoplastic Euler-Bernoulli beam finite element, and a procedure, based on a precomputed analysis of a part of a structure, by using a refined numerical model, is proposed to obtain the beam constitutive model parameters. Finally, we derive an elastoplastic quadrilateral two-dimensional finite element formulation with embedded strong discontinuity, whose kinematics can model linear jumps in both normal and tangential displacements along the discontinuity line. Numerical simulations show, that the derived finite elements, along with the accompanied numerical algorithms, are an efficient and a rather robust tool for limit load and failure analysis of structures. Among other examples, we present a simulation of crack growth in brittle material and a simulation of shear band failure in ductile material. All the computer codes of the finite element formulations presented in this work have been generated through the symbolic programming of the finite element computer code and the expression optimization in AceGen computer program. The performance of these elements has been presented in numerous numerical examples, all performed by the AceFem computer program
Droniuc, Niculai. "Développement et applications géotechniques du calcul à la rupture par la méthode des éléments finis." Marne-la-vallée, ENPC, 2001. http://www.theses.fr/2001ENPC0109.
Bouizi, Abdelillah. "Résolution des équations de l'acoustique linéaire par une méthode d'éléments finis mixtes." Ecully, Ecole centrale de Lyon, 1989. http://www.theses.fr/1989ECDL0005.
Petin, Pascal. "Étude de sensibilité à l'aide des dérivées d'ordre élevé dans la méthode des éléments finis : application à l'électromagnétisme." Grenoble INPG, 1996. http://www.theses.fr/1996INPG0102.
Feng, Qingqing. "Développement d'une méthode d'éléments finis multi-échelles pour les écoulements incompressibles dans un milieu hétérogène." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLX047/document.
The nuclear reactor core is a highly heterogeneous medium crowded with numerous solid obstacles and macroscopic thermohydraulic phenomena are directly affected by localized phenomena. However, modern computing resources are not powerful enough to carry out direct numerical simulations of the full core with the desired accuracy. This thesis is devoted to the development of Multiscale Finite Element Methods (MsFEMs) to simulate incompressible flows in heterogeneous media with reasonable computational costs. Navier-Stokes equations are approximated on the coarse mesh by a stabilized Galerkin method, where basis functions are solutions of local problems on fine meshes by taking precisely local geometries into account. Local problems are defined by Stokes or Oseen equations with appropriate boundary conditions and source terms. We propose several methods to improve the accuracy of MsFEMs, by enriching the approximation space of basis functions. In particular, we propose high-order MsFEMs where boundary conditions and source terms are chosen in spaces of polynomials whose degrees can vary. Numerical simulations show that high-order MsFEMs improve significantly the accuracy of the solution. A multiscale simulation chain is constructed to simulate successfully flows in two- and three-dimensional heterogeneous media
Alves, Rade Domingos. "Correction parametrique de modeles elements finis : elargissement de l'espace de connaissance." Besançon, 1994. http://www.theses.fr/1994BESA2014.
Nabeta, Silvio Ikuyo. "Étude des régimes transitoires des machines synchrones par la méthode des éléments finis." Grenoble INPG, 1994. http://www.theses.fr/1994INPG0069.
Fau, Amélie. "Finite Element Approach of Electronic Structures." Phd thesis, Ecole Centrale Paris, 2012. http://tel.archives-ouvertes.fr/tel-00997398.
Normand, Pierre-Elie. "Application de méthodes d'ordre élevé en éléments finis pour l'aérodynamique." Thesis, Bordeaux 1, 2011. http://www.theses.fr/2011BOR14416/document.
The areas of research and analysis covered in this thesis focus on methods using high order finite elements applied for solving Navier-Stokes equations and turbulence models. It consists of two main parts:-The implementation of high-order methods in an industrial computer code -The development of a methodology for creating curved meshes on 3D geometries A series of test cases of increasing difficulty were conducted to validate these methods. We present, moreover, a case of a full aircraft where the process used to obtain the full mesh and the Navier-Stokes/turbulence model calculation are fully described and discussed. Motivation, contribution and technical barriers are finally discussed
Rostand, Virgile. "Analysis of discrete finite element shallow-water models." Doctoral thesis, Québec : Université Laval, 2007. http://www.theses.ulaval.ca/2007/24911/24911.pdf.
Badri, Mohd Afeef. "Efficient finite element strategies for solving the radiative transfer equation." Thesis, Nantes, 2018. http://www.theses.fr/2018NANT4050/document.
The discrete ordinate method coupled with the finite element method is often used for numerically solving the radiative transfer equation. The main goal of this thesis is to improve upon such numerical technique. Instead of using standard finite elements, this thesis reformulates the radiative transfer equation using vectorial finite elements. In comparison to standard finite elements, this reformulation yields faster timings for the linear system assemblies, as well as for the solution phase when solving scattering media problems. Preconditioned Krylov subspace methods like the GMRES and the BiCGSTAB are employed for solving the linear systems arising from the proposed vectorial finite element discretization. The developed methods are validated against benchmark problems available in literature. In addition, the method of manufactured solutions is used for verifying the proposed method. For solving large problems of radiation on parallel computers, the vectorial finite element method is parallelized using domain decomposition and angular decomposition approaches. The proposed parallel methods possess quasi-linear scaling capabilities on a large number of processes. The developed parallel solvers are used to perform large scale numerical simulations with billions of unknowns. Overall it is shown how to perform complex numerical simulations of radiation at scales that were previously unattainable by standard radiative transfer equation solvers
Ben, Hassine Mohamed Rafik. "Étude asymptotique et numérique d’inclusions fines dans des domaines élastiques." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEI086/document.
This work focused on mathematical modeling and numerical approximation of the influence of a very thin inclusion on an elastic substrate of different stiffness. The study is motivated by applications in tires and is not based on conventional homogenization techniques. Indeed, the objective was to treat the interaction between a single inclusion and its elastic medium and not a density of inclusions. The study consisted of three parts, the first concerning mathematical modeling for linear behavior laws leading to an expression of the contribution of the inclusion in the form of the inclusion-free field corrected by correctors at different orders. These correctors are independent of the characteristic size of the inclusion. The second relates to the numerical approximation of this influence by means of the finite element method and that of the inverted finite elements. A numerical strategy for taking into account the influence of several inclusions is also presented. The last part is prospective and discusses the possibility of extending the approach for nonlinear behavioral laws
Al-Akhrass, Dina. "Méthodes éléments finis mixtes robustes pour gérer l’incompressibilité en grandes déformations dans un cadre industriel." Thesis, Saint-Etienne, EMSE, 2014. http://www.theses.fr/2014EMSE0733/document.
Simulations in solid mechanics exhibit difficulties as dealing with incompressibility or nonlinearities due to finite strains, constitutive laws and contact. The basic motivation of our work is to propose efficient finite element methods capable of dealing with incompressibility in finite strain context, and using low order elements. Among the approaches in the literature, mixed formulations offer an interesting theoretical framework. In this work, a three-field mixed formulation (displacement, pressure, volumetric strain) is investigated. In some cases, this formulation can be condensed in a two-field formulation. However, it is well-known that the discrete problem given by the Galerkin finite element technique, does not inherit the “inf-sup” stability condition from the continuous problem: the finite elements used, and in particular the interpolation orders must be chosen so as to satisfy this stability condition. However, it is possible to circumvent it, by adding terms stabilizing the FE Galerkin formulation. The latter approach allows the use of equal order interpolation. In this work, stable finite elements of type P2/P1 are used as reference, and compared to a P1/P1 formulation, stabilized with a bubble function, or with a VMS method (Variational Multi-Scale) based on a sub-grid-space orthogonal to the FE space. Combined to a finite strain model based on logarithmic strain, these approaches are first validated on academic cases and then on industrial cases
Kaliche, Keltoum. "Méthode des éléments finis inversés pour des domaines non bornés." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLV014.
Inverted finite element method (IFEM) is a non runcature method which was introduced for solving partial differential equations in unbounded domains. The objective of this thesis is to analyze, to adapt and to implement IFEM for solving several problems arising in physics, especially when the domain is the whole space R3. We first give a presentation in which we detail the principles and the main features of the method. Then, we adapt IFEM for solving some div-curl systems and vector potential problems in the whole space. In a second part, we successfully develop an IFEM based approach for computing the stray-field energy in micromagnetism. In the last part, we are interested in the study of the polarizable continuum model arising in quantum chemistry. The manuscript contains a large number of numerical results obtained with some 3D codes, especially when the domain is the whole space R3. It also contains some theoretical results in relation with weighted Sobolev spaces. We give in particular a constructive proof of some div-curl inequalities in unbounded domains
Razafimahery, Fulgence. "Analyse numerique par elements finis d'ecoulements s'etablissant en domaines non bornes." Rennes 1, 1988. http://www.theses.fr/1988REN10023.
Boukari, Nabil. "Modélisation du mouvement à l'aide de codes de calcul par éléments finis en 3D : application à la machine homopolaire et au microactionneur électrostatique." Toulouse, INPT, 2000. http://www.theses.fr/2000INPT008H.
Peyre, Georges. "Méthode EF2 et hyperréduction de modèle : vers des calculs massifs à l'échelle micro." Thesis, Paris, ENMP, 2015. http://www.theses.fr/2015ENMP0026/document.
Model Order Reduction (MOR) methods are used to cope with high computational costs typically involved in parametric analysis of structures requiring a huge number of almost similar simulations. Among them, a so-called hyperreduction method suitable for non-linear mechanical finite element (FE) problems is studied. An objected-oriented approach to deal with it in the framework of a FE software is carried out. The software design takes advantage of a two-level process : a so-called offline computation step in which the reduced model is set up based on collected snapshots of mechanical system states and an online high-speed reduced computation which runs the reduced model. The code design relying on a reduced element is expected to enhance performance, to give a clearer view over the process and to favour code reuse in subsequent developments of the method. Futhermore, the hyperreduction method is reviewed and is deeply improved : vector and tensor bases are introduced to deal with non-scalar fields which arise in non-linear mechanical FE problems and the mechanical balance is ensured in the extrapolation phase. A particular emphasis is placed on the treatment of free and periodic boundary conditions. In this approach, the boundary conditions at the edge of the reduced integration domain are enforced in the reduced balance equations. Numerical toy examples of elasticity fiber/matrix inclusions as well as a full adaptative non-linear simluation are provided to show the capabilities of the implementation. To take into account microstructural behaviors, FE2 methods consist in splitting the computation into two scales. At the micro scale the material constitutive equations are integrated over periodic RVEs. The behavior of the macro structure is carried out by a homogeneized process. A multidimensional hyperreduction method is applied to the massive micro problem composed of the set of the periodic RVEs. A BFGS algorithm is used to update the macro tangent matrices at each integration Gauss point. Some speed-ups are recorded for low dimensional models. However, as the number of degrees of freedom increases, the multidimensional hyperreduction method is proved to be far less efficient to cut computational costs down
Resk, Héba. "Finite element modelling of grain-scale heterogeneities in polycrystalline aggregates." Paris, ENMP, 2010. http://pastel.archives-ouvertes.fr/pastel-00577855.
Macroscopic properties of crystalline solids depend inherently on their underlying mi-croscopic structure. Studying the mechanisms operating at the microstructural scale during the various thermomechanical processes to which such materials may be subjected offers a valuable insight into their final in-use properties. The objective of this work is to investigate grain scale heterogeneities in polycrystalline aggregates subjected to large strains using the Crystal Plasticity Finite Element Method (CPFEM). For this purpose, highly resolved simulations, where each grain is represented explicitly, are needed. The first part of this work is devoted to a detailed account of the numerical framework implemented for such simulations. A classical elastic-viscoplastic crystal plasticity model is combined to a non-linear parallel finite element framework. The discretization of the digital microstructures is performed using non- conforming unstructured meshes. Most importantly, a level set approach is used to describe grain boundaries and to guide an adaptive anisotropic meshing strategy. Automatic remeshing, with appropriate transport of variables, is introduced in the proposed framework. In the second part of this work, the robustness and flexibility of our approach is demonstrated via different CPFEM applications. The deformation energy is used to assess heterogeneities in polycrystalline aggregates, highlighting the need to perform adaptive meshing so as to achieve a good compromise between accuracy and computation time. These grain-scale heterogeneities are to be accurately predicted during the deformation simulation if subsequent static recrystallization modelling is to be performed. An example of linking between the deformation and static recrystallization steps, using the proposed common approach, is illustrated. In terms of global texture predictions, the CPFEM framework is validated for a highly resolved model polycrystal subjected to more than 90 % thickness reduction in rolling. The importance of automatic remeshing in avoiding excessive mesh distortion, in such applications, is demonstrated. Most importantly, microtexture analysis is performed on digital microstructures that correspond, in a discrete sense, to an actual microstructure observed experimentally. Intragranular misorientation predictions and virtual 2D orientation maps are compared to the experimental ones, highlighting the difficulties pertaining to the validation of such grain-scale predictions
Dib, Serena. "Méthodes d'éléments finis pour le problème de Darcy couplé avec l'équation de la chaleur." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066294/document.
In this thesis, we study the heat equation coupled with Darcy's law by a nonlinear viscosity depending on the temperature in dimension d=2,3 (Hooman and Gurgenci or Rashad). We analyse this problem by setting it in an equivalent variational formulation and reducing it to an diffusion-convection equation for the temperature where the velocity depends implicitly on the temperature.Existence of a solution is derived without restriction on the data by Galerkin's method and Brouwer's Fixed Point. Global uniqueness is established when the solution is slightly smoother and the dataare suitably restricted. We also introduce an alternative equivalent variational formulation. Both variational formulations are discretized by four finite element schemes in a polygonal or polyhedral domain. We derive existence, conditional uniqueness, convergence, and optimal a priori error estimates for the solutions of the three schemes. Next, these schemes are linearized by suitable convergent successive approximation algorithms. We present some numerical experiments for a model problem that confirm the theoretical rates of convergence developed in this work. A posteriori error estimates are established with two types of errors indicators related to the linearisation and discretization. Finally, we show numerical results of validation
Alachaher, Abderrahim. "Abd : une nouvelle loi de comportement incrémentalement non linéaire et applications par la méthode des éléments finis." Université Joseph Fourier (Grenoble), 1994. http://www.theses.fr/1994GRE10136.
Manet, Vincent. "Methodes d'analyse par elements finis des contraintes aux interfaces dans les structures sandwich." Clermont-Ferrand 2, 1998. https://tel.archives-ouvertes.fr/tel-00663078.
Tounsi, Chakroun Douha. "Formulation et mise en oeuvre d'un élément continu de coque axisymétrique raidie." Thesis, Châtenay-Malabry, Ecole centrale de Paris, 2015. http://www.theses.fr/2015ECAP0005/document.
This thesis focuses on the development of a continuous stiffened axisymmetric shell element of type Reissner/Mindlin. The approach consist in using the axisymmetric shell element developed in LISMMA for which distributed loads were applied on it.The introduction of longitudinal stiffeners is achieved by using a straight beam element coupled to the shell. The introduction of circumferential stiffeners requires the development of circular beam element according to a formulation similar to that used for the axisymmetric shell.In fact, this continuous element method is based on the development of the unknown fields on the Fourier series according to the circumferential dimensions and on the determination of the dynamic stiffness matrix of the studied structure.Two coupling configuration were considered: First of all the coupling of axisymmetric shell with circular Timoshenko beam element acting as circumferential stiffeners, then with straight Timoshenko beam element acting as longitudinal stiffener. Harmonic analyzes are conducted in order to validate the formulations presented in comparison with the results obtained from finite element model
Shan, Ju-Lin. "Research and application of adaptive finite element Mesh generation algorithm." Reims, 2007. http://theses.univ-reims.fr/exl-doc/GED00000709.pdf.
Assaad, Jamal. "Modélisation des transducteurs piézoélectriques haute fréquence à l'aide de la méthode des éléments finis." Valenciennes, 1992. https://ged.uphf.fr/nuxeo/site/esupversions/daff1271-db25-4894-82dd-828d666c589c.
Sahraoui, Omar. "Calcul des paramètres du schéma équivalent de la machine asynchrone par la méthode des éléments finis." Grenoble INPG, 1994. http://www.theses.fr/1994INPG0056.
Marouby, Eric. "Analyse d'elements de connectique microondes par la methode des elements finis." Limoges, 1990. http://www.theses.fr/1990LIMO0102.
Dinh, Van Quang. "Vers une simulation par éléments finis en temps réel pour le génie électrique." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAT093/document.
The physical phenomena in the electrical engineering field are based on Maxwell's equations in which solutions are functions verifying the material properties and satisfying certain boundary conditions on the field. The finite element method (FEM) is the most commonly used method to calculate the solutions of these equations and deduce the magnetic and electric fields.Nowadays, the parallel computing on graphics processors offers a very high computing performance over traditional calculation by CPU. The GPU-accelerated computing makes use of a graphics processing unit (GPU) together with a CPU to accelerate many applications in science and engineering. It enables massively parallelized tasks and thus accelerate the performance by offloading the compute-intensive portions of the application to the GPU while the remainder of the application still runs on the CPU.The thesis deals with the modeling in the magnetic field using the finite element method. The aim of the thesis is to improve the performance of the MEF by taking advantage of the high performance parallel computing on the GPU. Thus if the calculation can be performed in near real-time, the simulation tools would become an intuitive design tool which allow for example to "feel" the sensitivity of a design modification of geometric and physical parameters. A new field of use of simulation codes would open. This is the theme of this work, which tries to accelerate the different phases of a simulation to make the whole almost instantaneous. So in this thesis, the meshing, the numerical integration, the assembly, the resolution and the post processing are discussed respectively. For each phase, the methods in the literature are examined and new approaches are proposed. The performances are analyzed and compared. The implementation details are described as the overall performance of GPU approaches are closely linked to these choices
Mazor, Alon. "Modelling of roll compaction process by finiite element method." Thesis, Ecole nationale des Mines d'Albi-Carmaux, 2017. http://www.theses.fr/2017EMAC0009/document.
In the pharmaceutical industry, dry granulation by roll compaction is a process of size enlargement of powder into granules with good flowability for subsequent die compaction process. Understanding the roll compaction process and optimizing manufacturing efficiency is limited using the experimental approach due to the high cost of powder, time-consuming and the complexity of the process. In this work, a 3D Finite Element Method (FEM) model was developed to identify the critical material properties, roll press designs and process parameters controlling the quality of the product. The Drucker-Prager Cap (DPC) model was used to describe the powder compaction behavior and was determined based on standard calibration method. To overcome the complexity involving two different mechanisms of powder feeding by the screw and powder compaction between rolls, a novel combined approach of Discrete Element Method (DEM), used to predict the granular material flow in the feed zone and the Finite Elements Method (FEM) employed for roll compaction, was developed. Lastly, for a more realistic roll compaction modelling, allowing the fluctuation of the gap between rolls, a Coupled-Eulerian Lagrangian (CEL) approach was developed. FEM simulation results clearly show the effect of different process parameters on roll pressure and density distribution in the compaction zone of powder between the rolls. Moreover, results show that using a cheek-plates sealing system causes a nonuniform roll pressure and density distribution with the highest values in the middle and the lowest at the edges. On the other hand, the resultant pressure and density distributions with the rimmed-roll obtained higher values in the edges than in the middle and overall a more uniform distribution. The combined DEM-FEM methodology clearly shows a direct correlation between the particle velocity driven by the screw conveyor to the feed zone and the roll pressure, both oscillating in the same period. This translates into an anisotropic ribbon with a density profile varying sinusoidally along its length. To validate the results, the simulations are compared with literature and experimentally measured values in order to assess the ability of the model to predict the properties of the produced ribbons
El, Bechari Reda. "Optimisation et analyse de fiabilité des machines électriques modélisées par la méthode des éléments finis." Thesis, Ecole centrale de Lille, 2020. http://www.theses.fr/2020ECLI0007.
The finite element method is the most sophisticated tool to model the electromagnetic phenomenon. However, it is computationally expensive. Thus, its usage for optimization and reliability analysis (iterative processes) should be made with caution since only a limited number of evaluations of the model can be tolerated. Furthermore, the impact of the manufacturing process on the electrical machines is scarcely studied in the literature. The integration of this aspect in the design phase is one of the contributions of this thesis alongside the main contribution, which is the development and comparison of optimization approaches for electrical machines.We present the approaches adapted to the subject and develop new ones. On the one hand, the finite element model can be seen as a "black-box" for which we develop a non-intrusive approach based on Kriging meta-models. On the other hand, we consider an intrusive approach as we look inside the "black-box," we upgrade the model to provide the derivatives of the quantities of interest. The derivatives are essential to some optimization and reliability analysis tools. They are computed efficiently using the adjoint variable method. Finally, the methods are compared to give insight into the advantages and the shortcomings of each of them.Lastly, a real case study is considered; it consists of studying the impact of the manufacturing process on the claw-pole machine manufactured by Valeo. From the production line, machines are withdrawn to measure their dimensions and characterize their deviation from the nominal one. Then a statistical analysis is conducted to assess the reliability and impact on the performances
El, Bechari Reda. "Optimisation et analyse de fiabilité des machines électriques modélisées par la méthode des éléments finis." Thesis, Centrale Lille Institut, 2020. http://www.theses.fr/2020CLIL0007.
The finite element method is the most sophisticated tool to model the electromagnetic phenomenon. However, it is computationally expensive. Thus, its usage for optimization and reliability analysis (iterative processes) should be made with caution since only a limited number of evaluations of the model can be tolerated. Furthermore, the impact of the manufacturing process on the electrical machines is scarcely studied in the literature. The integration of this aspect in the design phase is one of the contributions of this thesis alongside the main contribution, which is the development and comparison of optimization approaches for electrical machines.We present the approaches adapted to the subject and develop new ones. On the one hand, the finite element model can be seen as a "black-box" for which we develop a non-intrusive approach based on Kriging meta-models. On the other hand, we consider an intrusive approach as we look inside the "black-box," we upgrade the model to provide the derivatives of the quantities of interest. The derivatives are essential to some optimization and reliability analysis tools. They are computed efficiently using the adjoint variable method. Finally, the methods are compared to give insight into the advantages and the shortcomings of each of them.Lastly, a real case study is considered; it consists of studying the impact of the manufacturing process on the claw-pole machine manufactured by Valeo. From the production line, machines are withdrawn to measure their dimensions and characterize their deviation from the nominal one. Then a statistical analysis is conducted to assess the reliability and impact on the performances
Rusaouen, Gilles. "Éléments finis déformables applicables aux problèmes d'aérodynamique interne." Ecully, Ecole centrale de Lyon, 1987. http://www.theses.fr/1987ECDL0002.
Christophe-Argenvillier, Alexandra. "Méthode des éléments finis avec joints en recouvrement non-conforme de maillages : application au contrôle non destructif par courants de Foucault." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112341/document.
This thesis aims at studying and developing a domain decomposition method with overlapping subdomains for the modeling in eddy current (EC) non-Destructive testing (NDT). The idea behind such an approach is the possibility to avoid the systematic remeshes of the whole studying domain when some of its components are modified (for example the displacement of the coil above the conductor). More precisely, this work aims at designing a domain decomposition method with overlapping based on the theory of the mortar finite element method. In addition to remove the constraint owing to an coupling interface which is invariant with the displacement, the technique described, in this work, realizes reciprocal transfers of information between subdomains. This study presents the theoretical and numerical results attached to the magnetodynamic simulation. Moreover, the interest of such a method is illustrated by applications in some 2D modeling cases of EC NDT
Qin, Zhi. "Finite element modelling and PGD based model reduction for piezoelectric and magnetostrictive materials." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066566/document.
The energy harvesting technology that aims to enable wireless sensor networks (WSN) to be maintenance-free, is recognized as a crucial part for the next generation technology mega- trend: the Internet of Things (IoT). Piezoelectric and magnetostrictive materials, which can be used in a wide range of energy harvesting systems, have attracted more and more interests during the past few years. This thesis focuses on multiphysics finite element (FE) modeling of these two materials and performing model reduction for resultant systems, based on the Prop- er Generalized Decomposition (PGD). Modeling these materials remains challenging although research in this area has been under- going over decades. A multitude of difficulties exist, among which the following three issues are largely recognized. First, mathematically describing properties of these materials is com- plicated, which is particularly true for magnetostrictive materials because their properties depend on factors including temperature, stress and magnetic field. Second, coupling effects between electromagnetic, elastic, and thermal fields need to be considered, which is beyond the capability of most existing simulation tools. Third, as systems becoming highly integrated whole-scale simulations become necessary, which means three dimensional (3D) numerical models should be employed. 3D models, on the other hand, quickly turns intractable if not properly built. The work presented here provides solutions in respond to the above challenges. A differential forms based multiphysics FE framework is first established. Within this frame- work quantities are discreted using appropriate Whitney elements. After discretization, the system is solved as a single block, thus avoiding iterations between different physics solutions and leading to rapid convergences. Next, the linear piezoelectric, and a free energy based nonlinear magnetostrictive constitutive model called Discrete Energy Averaged Model (DE- AM) are incorporated into the framework. Our implementation describes underlying material behaviors at reasonable numerical costs. Eventually, two novel PGD based algorithms for model reduction are proposed. With our algorithms, problem size of multiphysics models can be significantly reduced while final results of very good accuracy are obtained. Our algo- rithms also provide means to handle coupling and nonlinearity conveniently. All our methodologies are demonstrated and verified via representative examples
Virgaux, Nicolas. "Modélisation par éléments finis et évaluation clinique d'un système innovant de fusion percutanée pour les pathologies rachidiennes." Electronic Thesis or Diss., Paris, ENSAM, 2019. http://www.theses.fr/2019ENAM0035.
Suffering from low back pain can be disabling and may lead to a surgical intervention. The predominant surgical technique consists in bridging two vertebrae with a bony bridge. A new technique has been developed to create such a bridge with the minimal impact. The objective of our work is to determine the results of this technique with a three complementary axes approach. The first axe consists in evaluating the clinical results in a real-life setting. The second axe consists in determining the influence of parameters specific to the technique on the mechanical response of an instrumented lumbar spine by in-vitro testing. The last axe consists in a finite element model of this technique in a human spine to measure the influence of properties of the graft on the mechanical response. The three-axes approach allowed us to highlight the clinical interests of such a technique as well of its limitations. The in-vitro and numeric axes allowed us to analyze in detail the mechanical response of an instrumented spine and to determine its specificities. Clinical and scientific conclusions have been drawn based on the combination of the three axes as well as future potential evolutions of the technique. These evolutions could lead to technical innovations and future research projects. From a more general perspective, the benefits of the three-panes approach have been demonstrated for throughout understanding of the complementarity key parameters that could yield aa given clinical outcome, from a biomechanical point of view
Kunhappan, Deepak. "Modélisation numérique de l’écoulement de suspensions de fibres souples en régime inertiel." Thesis, Université Grenoble Alpes (ComUE), 2018. http://www.theses.fr/2018GREAI045/document.
A numerical model describing the behavior of flexible fibers under inertial flows was developed by coupling a discrete element solver with a finite volume solver.Each fiber is discretized into several beam segments, such that the fiber can bend, twist and rotate. The equations of the fiber motion were solved usinga second order accurate explicit scheme (space and time). The three dimensional Navier-Stokes equations describing the motion of the fluid phase was discretizedusing a fourth th order accurate (space and time) unstructured finite volume scheme. The coupling between the discrete fiber phase and the continuous fluid phasewas obtained by a pseudo immersed boundary method as the hydrodynamic force on the fiber segments were calculated based on analytical expressions.Several hydrodynamic force models were analyzed and their validity and short-comings were identified. For Reynolds numbers (Re) at the inertial regime(0.01 < Re < 100, Re defined at the fiber scale), non linear drag force formulations based on the flow past an infinite cylinder was used. For rigid fibers in creeping flow, the drag force formulation from the slender body theory was used. A per unit length hydrodynamic torque model for the fibers was derived from explicit numerical simulations of shear flow past a high aspect ratio cylinder. The developed model was validated against several experimental studies and analytical theories ranging from the creeping flow regime (for rigid fibers) to inertial regimes. In the creeping flow regime, numerical simulations of semi dilute rigid fiber suspensions in shear were performed.The developed model wasable to capture the fiber-fiber hydrodynamic and non-hydrodynamic interactions. The elasto-hydrodynamic interactions at finite Reynolds was validated with against two test cases. In the first test case, the deflection of the free end of a fiber in an uniform flow field was obtained numerically and the results were validated. In the second test case the conformation of long flexible fibers in homogeneous isotropic turbulence was obtained numerically and the results were compared with previous experiments. Two numerical studies were performed to verify the effects of the suspended fibers on carrier phase turbulence and the numerical model was able to reproduce the damping/enhancement phenomena of turbulence in channel and pipe flows as a consequence of the micro-structural evolution of the fibers
Bouayed, Mohamed Amine. "Modélisation stochastique par éléments finis en géomécanique." Vandoeuvre-les-Nancy, INPL, 1997. http://www.theses.fr/1997INPL087N.
Sedira, Lakhdar. "Contribution à la Modélisation de Composites 2D/3D à l'Aide d'Eléments Finis Spéciaux." Thesis, Reims, 2013. http://www.theses.fr/2013REIMS019/document.
This doctoral thesis deals with the finite element formulation and evaluation of a modified Mindlin's discrete variational model for static, dynamic, linear and non-linear composite plates and shells analysis. Including additional terms of zigzag type, in order to improve the accuracy of stress, the model has been reformulated to take into account the linear picewise of displacement variation. Consequently, two finite plate and shell elements with four nodes, called DMQP and DMQS (Discrete Quadrilateral Mindlin Plates and Shells respectively), enhanced by quadratic field rotations, have been developed and validated under REFLEX and ABAQUS codes.Both elements including the zigzag effect have been also developed in a second version, and validated through several static and dynamic test problems known from the literature, highlighting the independence towards the transverse shear correction and in particular the stress accuracy with respect to the initial model without the zigzag effect.The satisfactory results of this model found through cases of linear isotropic shell tests, motivated us to extend this approach to the non-linear geometric applications. An isoparametric curve element of shell has been developed for this purpose, where small elastic deformation assumptions of and large displacements and moderate rotations are adopted. It is geometrically simple and has only four nodes at corners and 6 DOF/node. The elementary calculation of the tangent stiffness matrix consists in combining the linear part of the curved shell element (DMQS) with that of the membrane Q4 non-linear part. An Updated Lagrangian Formulation at each Iteration (ULFI) is used with Newton-Raphson resolution Method. Some standard tests of nonlinear geometrical shell structures are presented; they show a very good convergence and global behavior better than such elements
Simon, Jessy. "Numerical simulation and experimental investigation of the forming of tailored fibre placement preforms : a mixed embedded-ALE finite element formulation." Thesis, Ecole centrale de Nantes, 2022. http://www.theses.fr/2022ECDN0024.
Tailored Fibre Placement (TFP) allows manufacturing flat, net shape fibrous reinforcements with continuously varying orientation and thickness. The hybridisation of TFP and forming is an attractive solution to manufacture mechanically optimized 3D shelllike composite parts. During the forming of complex parts, inevitable fibre path changes occur in the TFP preform. Prediction of the final state of TFP preforms is required to take full advantage of this hybrid solution in the industry.A first numerical modelling strategy is proposed to address the forming of flat TFP preforms. Two semi-discrete models based on an embedded formulation are developed to offer the possibility of removing or keeping the backing material. Both finite element models use an explicit discretisation of the fibre tows using beam elements and assumes no slippage between the preform constituents. Full-scale validations of the model without backing material are successfully addressed by forming hemispherical and tetrahedral parts with final orthotropic orientations. Finally, a mixed embedded element-ALE (Arbitrary Lagrangian Eulerian) formulation is proposed to introduce fibre slippage into the models without modifying their initial ingredients. A parametric study of pull-out experiments is performed to characterize the friction behaviour to be implemented in the models. Numerical validations for TFP preforms and an extension to model fibre slippage in conventional textiles are proposed
Martin, Guillaume. "Méthode de corrélation calcul/essai pour l'analyse du crissement." Thesis, Paris, ENSAM, 2017. http://www.theses.fr/2017ENAM0012/document.
Brake squeal is a nuisance commonly encountered in the car industry which often results in financial penalties towards brake manufacturers, even if no robust solution exists for the conception. Numerical simulation and experimental characterizations are the classical two-track approaches to analyze squeal phenomena. Numerical simulation allows a fine analysis of vibration behaviors and the evaluation of conception modification impacts, but models are not perfect and their validity domain must be defined. Measurement guarantees that every parameter is taken into account, but it is often spatially poor and not really suited for modification prediction. In this context, the thesis objectives are to make an overview of test operating methods, to provide tools allowing an easier interaction between both test and simulation teams and to enforce the developments in a business application.After a review of the hypotheses and methods for modal identification, a critical analysis of the identification results leads to the characterization of biases and the introduction of detailed criteria to evaluate the quality of the result. Calculation/test correlation allows to qualify the models and tools are integrated to facilitate its implementation. Several criteria are defined to highlight the sources of bad correlation coming from the measure on the one hand and the model on the other hand. Sources of poor correlation are also identified with the MDRE expansion algorithm, whose limitations are compared with those of static and dynamic expansions.Model updating is then processed by a systematic procedure imbricating the steps of updating of geometry, material properties and contacts between components. A contact parametrization is proposed with a multi-model reduction allowing calculation times compatible with industrial time. It also allows sensitivity studies with the introduction of the notion of component modes in an assembly.Finally, a detailed analysis of a measurement campaign on a braking system under squeal conditions is carried out. A parallel between the changes of the limit cycle and the degree of coupling of the complex modes is proposed. In the time-frequency domain, variability, repeatability, reproducibility and the ability to aggregate sequential measurements are evaluated. The result is finally extended on the finite element model, which allows useful interpretations
Mint, brahim Maimouna. "Méthodes d'éléments finis pour le problème de changement de phase en milieux composites." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0157/document.
In this thesis we aim to develop a numerical tool that allow to solve the unsteady heatconduction problem in a composite media with a graphite foam matrix infiltrated witha phase change material such as salt, in the framework of latent heat thermal energystorage.In chapter 1, we start by explaining the model that we are studying which is separated in three sub-parts : a heat conduction problem in the foam, a phase change problem in the pores of the foam which are filled with salt and a contact resistance condition at the interface between both materials which results in a jump in the temperature field.In chapter 2, we study the steady heat conduction problem in a composite media withcontact resistance. This allow to focus on the main difficulty here which is the treatment of the thermal contact resistance at the interface between the carbon foam and the salt. Two Finite element methods are proposed in order to solve this problem : a finite element method based on Lagrange P1 and a hybrid dual finite element method using the lowest order Raviart-Thomas elements for the heat flux and P0 for the temperature. The numerical analysis of both methods is conducted and numerical examples are given to assert the analytic results. The work presented in this chapter has been published in the Journal of Scientific Computing [10].The phase change materials that we study here are mainly pure materials and as a consequence the change in phase occurs at a single point, the melting temperature. This introduces a jump in the liquid fraction and consequently in the enthalpy. This discontinuity represents an additional numerical difficulty that we propose to overcome by introducing a smoothing interval around the melting temperature. This is explained in chapter 3 where an analytical and numerical study shows that the error on the temperature behaves like " outside of the mushy zone, where _ is the width of the smoothing interval. However, inside the error behaves like p " and we prove that this estimation is optimal due to the energy trapped in the mushy zone. This chapter has been published in Communications in Mathematical Sciences [58].The next step is to determine a suitable time discretization scheme that allow to handle the non-linearity introduced by the phase change. For this purpose we present in chapter 4 four of the most used numerical schemes to solve the non-linear phase change problem : the update source method, the enthalpy linearization method, the apparent heat capacity method and the Chernoff method. Various numerical tests are conducted in order to test and compare these methods for various types of problems. Results show that the enthalpy linearization is the most accurate at each time step while the apparent heat capacity gives better results after a given time. This indicates that if we are interestedin the transitory states the first scheme is the best choice. However, if we are interested in the asymptotic thermal behavior of the material the second scheme is better. Results also show that the Chernoff scheme is the fastest in term of calculation time and gives comparable results to the one given by the first two methods.Finally, in chapter 5 we use the Chernoff method combined with the hybrid-dual finiteelement method with P0 and the lowest order Raviart-Thomas elements to solve thenon-linear heat conduction problem in a realistic composite media with a phase change material. Numerical simulations are realised using 2D-cuts of X-ray images of two real graphite matrix foams infiltrated with a salt. The aim of these simulations is to determine if the studied composite materials could be assimilated to an equivalent homogeneous phase change material with equivalent thermo-physical properties. For all simulationsconducted in this work we used the free finite element software FreeFem++ [41]