Homogenization of helical beam-like structures: application to single-walled carbon nanotubes

International audienceThis work is devoted to the computation of axial stiffness of helical beam-like structures. Starting from the homogenization theory of periodic slender domains and taking benefit of the property of helical symmetry, the overall elastic behavior can be obtained from the solution of three-dimensional problems posed on a reduced basic cell. The mechanical analysis of this reduced basic cell performed using a concise FE model allows therefore to compute easily the anisotropic beam homogenized stiffness coefficients. The accuracy and usefulness of this approach is demonstrated by comparisons with reference solutions and large FE model results for two numerical volume structure examples: a wire spring and a stranded “6 + 1” rope. The homogenization procedure is then applied to single-walled carbon nanotubes and it is shown from the two helical symmetries that their basic cell can be reduced to three beam elements

Continuum modelling of beamlike lattice trusses using averaging methods

International audienceA general procedure to determine the equivalent beam properties of beam-like lattice trusses is presented. The method is based on the energy equivalence. Its main features are the use of piecewise linear functions to represent the displacements, and the definition of the continuum stress and strain parameters by their average values over the continuum cell. This allows a unifying approach to be obtained to derive methods for computing the effective beam properties. It is shown that there is only one rigorous method, and this method takes the lattice periodicity into account. Moreover, the classical method based on static condensation is found to be only approximate, The procedure is applied to examples of planar lattice trusses in static analysis. The results prove the effectiveness and the reliability of the present approach, and comparisons are made with results obtained from other classical methods

Application de la Méthode X-FEM pour l'Analyse Multi-Echelles de Matériaux

International audienceLa méthode X-FEM permet d'enrichir les fonctions de formé eléments finis, et donc de prendre en compte des discontinuités au sein d'unélémentun´unélément. Elle est appliquée icì a la résolution deprobì emes cellulaires d'homogénéisation, pour faciliter le maillage de la cellule, qui peut ne pas respecter l'interface matériau. Une nouvelle fonction d'enrichisse-ment est proposée, et une solution numérique de même qualité qu'une approché eléments finis classique est obtenue

On the use of the eXtended Finite Element Method with Quatree/Octree meshes

International audienceThis paper describes the use of the eXtended Finite Element Method in the context of quadtree/octree meshes. Particular attention is paid on the enrichment of hanging nodes that inevitably arise with these meshes. An approach for enforcing displacement continuity along hanging edges and faces is proposed and validated on various numerical examples (holes, material interfaces and singularities) in both 2D and 3D

A beam to 3D model switch in transient dynamic analysis

International audienceTransient structural dynamic analyses often exhibit different phases, which enable one to use an adaptive modeling. Thus, a 3D model is required for a better understanding of local or non-linear effects, whereas a simplified beam model is sufficient for simulating the linear phenomena occurring for a long period of time. This paper proposes a method which enables one to switch from a beam to a 3D model during a transient dynamic analysis, and thus, allows one to reduce the computational cost while preserving a good accuracy. The method is validated through comparisons with a 3D reference solutioncomputed during all the simulation

Bascule d'un modèle poutre à un modèle 3D en dynamique des machines tournantes

National audienceLes problèmes de machines tournantes incluant un contact rotor-stator, nécessitent un maillage 3D de la zone de contact. Cependant, un modèle 3D pour toute la durée de simulation conduit à des temps de calcul rédhibitoires. Or un modèle poutre est suffisant pour décrire la dynamique de la machine tournante hors contact. Une stratégie qui permet d'utiliser un modèle poutre et un autre 3D, pendant deux phases différentes durant la même simulation, permet donc de gagner en temps de calcul pour une précision équivalente. Cet article propose une bascule d'un modèle poutre à un modèle 3D, en dynamique des rotors transitoire, avec une résolution par intégration temporelle implicite. Si on démarre la simulation avec le modèle poutre, on construit à l'instant de la bascule, une solution 3D, telle que les déplacements 3D soient la somme d'un déplacement corps rigide de la section correspondant à la solution poutre et d'une correction qui tient en compte des déformations dans la section. Cette correction résulte de la résolution d'un problème statique. Cette correction statique peut être cal-culée sur trois pas de temps consécutifs (l'instant de bascule, le pas temps qui la précède et celui qui la suit) pour l'obtention d'une correction en vitesses. La bascule est validée par comparaison avec une solution 3D de référence obtenue en effectuant la simulation entière sur le modèle 3D

Tensor-based methods for numerical homogenization from high-resolution images

International audienceWe present a complete numerical strategy based on tensor approximation techniques for the solution of numerical homogenization problems with geometrical data coming from high resolution images. We first introduce specific numerical treatments for the translation of image-based homogenization problems into a tensor framework. It includes the tensor approximations in suitable tensor formats of fields of material properties or indicator functions of multiple material phases recovered from segmented images. We then introduce some variants of proper generalized decomposition (PGD) methods for the construction of tensor decompositions in different tensor formats of the solution of boundary value problems. A new definition of PGD is introduced which allows the progressive construction of a Tucker decomposition of the solution. This tensor format is well adapted to the present application and improves convergence properties of tensor decompositions. Finally, we use a dual-based error estimator on quantities of interest which was recently introduced in the context of PGD. We exhibit its specificities when it is used for assessing the error on the homogenized properties of the heterogeneous material. We also provide a complete goal-oriented adaptive strategy for the progressive construction of tensor decompositions (of primal and dual solutions) yielding to predictions of homogenized quantities with a prescribed accuracy

A micro-macro strategy for ship structural analysis with FETI-DP method

International audienceIn the analysis of ship structures at small scale, with structural details heterogeneities and because there is only one prototype produced, which is the final product, the designers rely on finite element simulations. The finite element discretization of such structure, leads to a huge global numerical model, that suffers for computational cost and memory resource that may be unaffordable. In such a case, a multi-scale analysis should be performed. The classical local-global analysis that is used by engineers has several limitations such as: - structure details are not periodic, therefore classical homogenization methods are not easily applicable; - edge effects are not take into account; - zooming techniques are not easy to use: the gluing they require with the global scale often introduces artificial edge effects. This paper presents a micro-macro strategy based on the domain decomposition FETI-DP method as the solver in analysis of ship structure. With this approach, the two scales (micro and macro) are coupled during the iterations of the solver and we can consider the structural details in areas of interest, area where the fine mesh is used and a sub-domain is located. Performances are discussed and results in term of convergence are presented for several examples

An X-FEM and Level Set computational approach for image-based modeling. Application to homogenization.

International audienceThe advances in material characterization by means of imaging techniques require powerful computational methods for numerical analysis. The present contribution focuses on highlighting the advantages of coupling the Extended Finite Elements Method (X-FEM) and the level sets method, applied to solve microstructures with complex geometries. The process of obtaining the level set data starting from a digital image of a material structure and its input into an extended finite element framework is presented. The coupled method is validated using reference examples and applied to obtain homogenized properties for heterogeneous structures. Although the computational applications presented here are mainly two dimensional, the method is equally applicable for three dimensional problems

Prediction of Transient Engine Loads and Damage due to Hollow Fan Blade-off

International audienceThe loss of a fan blade causes serious damages on an engine and can endanger the aircraft integrity and the safety of passengers. Commercial aircraft engines must then meet the FAA (Federal Aviation Administration) and JAA (Joint Aviation Authorities) certification requirements concerning the fan blade containment. The certification is validated through a Fan Blade-Off (FBO) test on a whole engine. The success in this test requires destructive and expensive development tests performed at the different stages of the design process. To reduce the number of these experiments and thus, the costs and the time of development, the engine behaviour under FBO can be understood and even predicted thanks to finite element (FE) analysis. This paper shows a comparison between a FBO simulation of hollow blades, computed with an explicit integration FE code, and experimental data obtained during an intermediate FBO test carried out by Snecma Moteurs. The results of the load levels and the similarity on the sequence of events show good agreement.La perte d’une aube fan peut causer de graves dommages dans un moteur, et mettre en danger l’intégrité de l’avion et la sécurité des passagers. Les moteurs d’avion civil doivent donc répondre aux exigences de certification de la FAA et de la JAA sur la perte d’aube. La certification est validée par un essai de perte d’aube sur moteur complet. La réussite de cet essai nécessite la réalisation d’essais partiels destructifs, coûteux et qui ne peuvent être réalisés qu’à la fin du cycle de conception. Pour réduire le nombre d’essais et donc les coûts et délais de développement, la simulation par éléments finis peut permettre de comprendre et même de prédire le comportement du moteur en perte d’aube. Cet article présente la comparaison entre la simulation d’une perte d’aube creuse, effectuée à l’aide d’un code explicite, et des données expérimentales mesurées lors d’un essai intermédiaire effectué par Snecma Moteurs. Les résultats sur les niveaux de charges et la similarité de la séquence d’événements montrent une bonne corrélation