Papers by Patrice Cartraud
Mechanical Systems and Signal Processing, 2013
The safety of turbomachines requires controlling the risks caused by contacts occurring between f... more The safety of turbomachines requires controlling the risks caused by contacts occurring between fixed and rotating parts. Undesirable phenomena induced by bladed wheel/ casing interactions are caused by the forced excitation of the natural modes of a blade leading to its damage or by potentially dangerous couplings between the modes of the casing and those of the wheel. Rotor-stator contacts may also lead to various types of dangerous behavior, including the well known configurations of dry whirl and dry whip. The paper proposes a large-scale literature review and examines existing numerical models and experimental setups used for highlighting the phenomenology involved in different rotor to stator contacts configurations. It confirms the great complexity of the problems which, by nature, are considerably nonlinear and involve multiphysics and multiscale coupled behaviors.
Wave Motion, 2011
Helical structures are designed to support heavy loads, which can significantly affect the dynami... more Helical structures are designed to support heavy loads, which can significantly affect the dynamic behaviour. This paper proposes a physical analysis of the effect of axial load on the propagation of elastic waves in helical beams. The model is based on the equations of motion of loaded helical Timoshenko beams. An eigensystem is obtained through a Fourier transform along the axis. The equations are made dimensionless for beams of circular cross-section and the number of parameters governing the problem is reduced to four (helix angle, helix index, Poisson coefficient, and axial strain). A parametric study is conducted. The effect of loading is quantified in high, medium and low frequency ranges. Noting that the effect is significant in low frequencies, dispersion curves of stretched and compressed helical beams are presented for different helix angles and radii. This effect is greater as the helix angle increases. Both the effects of stress and geometry deformation are shown to be non-negligible on elastic wave propagation.
Synthetic fiber ropes are characterized by a very complex architecture and a hierarchical structu... more Synthetic fiber ropes are characterized by a very complex architecture and a hierarchical structure. Considering the fiber rope architecture, to pass from fiber to rope structure behavior, two scale transition models are necessary, used in sequence: one is devoted to an assembly of a large number of twisted components (multilayered), whereas the second is suitable for a structure with a central straight core and six helical wires (1 + 6). The part I of this paper first describes the development of a model for the static behavior of a fibrous structure with a large number of twisted components. Tests were then performed on two different structures subjected to axial loads. Using the model presented here the axial stiffness of the structures has been predicted and good agreement with measured values is obtained. A companion paper (Ghoreishi, S.R. et al., in press. Analytical modeling of synthetic fiber ropes, part II: A linear elastic model for 1 + 6 fibrous structures, International Journal of Solids and Structures, doi:10.1016/j.ijsolstr.2006.08.032) presents the second model to predict the mechanical behavior of a 1 + 6 fibrous structure.
In part I of this study it was shown that, to model synthetic fiber ropes, two scale transition m... more In part I of this study it was shown that, to model synthetic fiber ropes, two scale transition models can be used in sequence. The first model (continuum model) has been presented in the part I and the present paper examines the behavior of a fibrous structure consisting of 6 helicoidal strands around a central core (1 + 6 structure). An analytical model will be presented which enables the global elastic behavior of such a cable under tension-torsion loading to be predicted. In this model, first, the core and the strands are described as Kirchhoff-Love beams and then the traction-torsion coupling behavior is taken into account for both of them. By modeling the contact conditions between the strands and the core, with certain assumptions, it is possible to describe the behavior of the cable section as a function of the degrees of freedom of the core. The behavior of the cable can thus be deduced from the tension-torsion coupling behavior of its constituents. Tensile tests have been performed on the core, the strands and then on a full scale 205 ton failure load cable. Finally, predicted stiffness from the analytical models is compared to the test results.
International Journal of Mechanical Sciences, 2007
In the field of cable modeling, many models have been proposed to describe the mechanical behavio... more In the field of cable modeling, many models have been proposed to describe the mechanical behavior of simple straight strands under axial loading, and the predictions of these models have been compared to experimental data when available. However, the validity domain of these models has not been evaluated yet because the experimental results reported in the literature are very limited. This problem is addressed here, the results from nine linear elastic models of a 6+1 wire single layered strand (simple straight strand) subjected to static axial loads being compared with values from 3D finite element modeling. The analytical models are shown to give satisfactory estimations of the elastic stiffness constants for lay angles below 20°.
This article is concerned with a multi-scale domain decomposition method (DDM), based on the FETI... more This article is concerned with a multi-scale domain decomposition method (DDM), based on the FETI-DP solver, for large-scale structural elastic analysis and suited to problems that exhibit structural heterogeneities, such as plate assemblies in the presence of structural details. In this approach once a partition of the global fine mesh into subdomains has been performed (all subdomains possess a fine mesh) and to optimize the computational time, the fine mesh is preserved only in the zones of interest (with local phenomena due to discontinuity, hole, etc.) while the remaining subdomains are replaced by numerical homogenized coarse elements. Indeed, the multi-scale aspect is introduced by the description of subdomains with either a fine or a coarse scale mesh. As a result, an extension of the FETI-DP DDM is proposed in this article (called herein FETI-DP micro-macro) that allows the simultaneous usage of different discretizations: fine (microscopic) mesh for subdomains in zones of interest and coarse (macroscopic or homogenized) mesh for the complementary part of the structure. Using this strategy raises the problem of the determination of the stiffness of coarse subdomains, and of the incompatible finite element connection between fine and coarse subdomains. Two approaches (collocation and Mortar) are presented and compared. The article ends with patch tests and some numerical examples in 2D and 3D. The obtained numerical results exemplify the efficiency and capability of the FETI-DP micro-macro approach and reveal that the Mortar approach is more accurate, at constant cost, than the collocation approach.
Mechanics of Sandwich Structures, 1998
... le temps total d'analyse doit être suffisamment long pour permettre aux ondes les plus l... more ... le temps total d'analyse doit être suffisamment long pour permettre aux ondes les plus lentes issues du pied de l'ACU, en l ... Le modèle ainsi obtenu, « 5ddls Cs nida », retranscrit très bien le comportement dynamique hors-plan à 3kHz, mais présente un retard important sur le ...
41st Structures, Structural Dynamics, and Materials Conference and Exhibit, 2000
Guided waves are used to control large components such as plates and tubes. They have the advanta... more Guided waves are used to control large components such as plates and tubes. They have the advantage to spread over long distances with little loss of energy. Because of the dispersive and multimodal behavior of guided waves, simulation becomes a very helpful tool for a proper analysis of these tests. The aim of this work is to model the elastic waves propagation in helical waveguides subjected to axial load. This study requires the development of elastodynamics equations in a helical coordinate system, which is translationally invariant along the helix centerline. The semi-analytical finite element (SAFE) method may then be applied, reducing the mesh to the section of the guide (two dimensional). The eigen-problem can be solved by fixing the wavenumber k or frequency . Moreover, the computation of the prestressed state is solved by a 2D model based on the asymptotic expansion in which the invariance of the helical structure is taken into account. Results for single straight and he...
The goal of this paper is to numerically investigate the effect of prestress on the propagation o... more The goal of this paper is to numerically investigate the effect of prestress on the propagation of elastic waves in straight and helical waveguides. The simulation technique, based on a semi-analytical finite element (SAFE) method, reduces the problem to the two-dimensional cross-section. The three-dimensional equilibrium equations of prestressed structures are written in the covariant and contravariant bases and used for the SAFE method. The eigenproblem can be solved by fixing the wavenumber and finding the angular frequency or inversely. Dispersion curves for single straight and helical wires will be computed to quantify the effect of prestress on the wave propagation.
Guided waves are commonly used to control large components such as plates and tubes since they ha... more Guided waves are commonly used to control large components such as plates and tubes since they have the advantage to spread over long distances with little loss of energy. Because of the dispersive and multimodal behaviour of guided waves, simulation becomes a very helpful tool for a proper analysis of these tests. The purpose of this paper is to numerically investigate the effect of axial preload on the propagation of elastic waves in helical waveguides. Typical applications are springs and multi-wire strands. The study of wave propagation in prestressed helical structures requires the development of the equation of dynamics in a helical coordinate system. The three dimensional equilibrium equations of prestressed dynamics are rewritten in the helical covariant and contravariant bases. The problem then becomes translationnally invariant along the waveguide axis and can be solved with a semi-analytical finite element (SAFE) technique. The problem is hereby reduced to the two-dimensi...
Résumé — La modélisation par la méthode X-Fem et level-sets permet de s'affranchir de maillag... more Résumé — La modélisation par la méthode X-Fem et level-sets permet de s'affranchir de maillages conformes, amenant à utiliser des maillages structurés (octree/quadtree), plus faciles à mettre en oeuvre. L'objet de cette étude est donc la mise en place d'un algorithme de maillage octree adap-tatif, avec un raffinement de type h. Les applications concernent des modèles bi-dimensionnels de thermique stationnaire (problèmes de conduction). Cet algorithme s'appuie sur un indicateur d'erreur basé sur la différence entre la solution courante et celle issue d'un maillage plus fin. Mots clés — maillage adaptatif, erreur, X-Fem, octree, quadtree.
In this contribution an integrated strategy is proposed for image-based computations. Indeed, it ... more In this contribution an integrated strategy is proposed for image-based computations. Indeed, it is still difficult to handle the amount of geometrical information contained in the images produced by modern acquisition techniques such as microtomographs. Classically, voxel-based finite element models are used as the model can be automatically constructed by converting each voxel into a finite element. This approach leads to huge numerical models and a poor geometrical description if the resolution is not sufficient. An integrated computational approach was presented in in order to circumvent these limitations. The proposed strategy is based on the X-FEM and levelsets in order to avoid the meshing of complex geometries. More recently [9], the approach was improved in order to uncouple the computational model from the geometrical one. Validations against the voxel-based Finite Elements is 2D and 3D proposed in order to assess the accuracy of the approach.
Many industrial problems involving slender structures in transient dynamics require a 3D model fo... more Many industrial problems involving slender structures in transient dynamics require a 3D model for a better understanding of local or non linear effects that occur along a small period of time, whereas a simplified beam model can be sufficient for simulating the linear phenomena occurring for a long period of time. This paper proposes a method which enables to switch from a beam to a 3D model during a transient dynamic analysis solved with a time integration technique. Thus, this method allows to reduce the computational cost while preserving a good accuracy. Starting with the beam model, at switch moment ts, a 3D solution is constructed as the sum of a cross-section rigid body displacement corresponding to the classical Timoshenko kinematical assumption and a 3D correction which accounts for cross-section deformation. This correction is obtained from the solution of a static problem and may be computed on three consecutive time steps (the switch instant, the previous and the follow...
Les problèmes de machines tournantes incluant un contact rotor-stator, nécessitent un maillage 3D... more Les 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 transitoire des rotors, avec une résolution par intégration temporelle implicite. Si on démarre la simulation avec le modèle poutre, on construit à l’instant de la bascule tb, 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 compte des déformations dans la section. Cette...
La caractérisation des matériaux est en progrès constant, ce qui implique un niveau de développem... more La caractérisation des matériaux est en progrès constant, ce qui implique un niveau de développement similaire des méthodes numériques utilisées. Ce travail présente une application de la méthode X-FEM couplée aux level-sets pour la résolution de problèmes de micromécanique. Les level-sets sont utilisées pour réaliser le traitement de l'image, puis exploitées dans le calcul X-FEM où le maillage peut ne pas respecter l'interface matériau. Un exemple d'homogénéisation est présenté.
Computer Methods in Applied Mechanics and Engineering, 2003
In multiscale analysis of components, there is usually a need to solve microstructures with compl... more In multiscale analysis of components, there is usually a need to solve microstructures with complex geometries. In this paper, we use the extended finite element method (X-FEM) to solve scales involving complex geometries. The X-FEM allows one to use meshes not necessarily matching the physical surface of the problem while retaining the accuracy of the classical finite element approach. For
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Papers by Patrice Cartraud