International audienceIn 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 material interfaces, this is achieved by introducing a new enrichment strategy. Although the mesh does not need to conform to the physical surfaces, it needs to be fine enough to capture the geometry of these surfaces. A simple algorithm is described to adaptively refine the mesh to meet this geometrical requirement. Numerical experiments on the periodic homogenization of two-phase complex cells demonstrate the accuracy and simplicity of the X-FEM
The present work is devoted to the computation of the effective properties of corrugated core sandwich panels. Due to their periodic structure, the homogenization theory is used, based on the asymptotic expansion method. At the leading order, an equivalent Kirchhoff Love homogeneous plate is derived, with an overall behavior obtained from basic cell problems posed on the three dimensional period of the panel. The finite element computation of these effective properties is presented in this paper. The accuracy of the homogenization method is proved, since the real panel and equivalent plate responses are very close for membrane and pure bending loadings. However, a discrepancy appears for simple bending loading, underlining that transverse shear effects cannot be neglected. Therefore, a specific study is developed in order to derive the transverse shear stiffness, thus enabling to de termine an equivalent Reissner Mindlin homogeneous plate.
. Two-dimensional modeling of an aircraft engine structural bladed disk-casing modal interaction. Journal of Sound and Vibration, Elsevier, 2009, 319 (1-2) In modern turbo machines such as aircraft jet engines, structural contacts between the casing and bladed disk may occur through a variety of mechanisms: coincidence of vibration modes, thermal deformation of the casing, rotor imbalance due to design uncertainties to name a few. These nonlinear interactions may result in severe damage to both structures and it is important to understand the physical circumstances under which they occur. In this study, we focus on a modal coincidence during which the vibrations of each structure take the form of a k-nodal diameter traveling wave characteristic of axi-symmetric geometries. A realistic two-dimensional model of the casing and bladed disk is introduced in order to predict the occurrence of this very specific interaction phenomenon versus the rotation speed of the engine. The equations of motion are solved using an explicit time integration scheme in conjunction with the Lagrange multiplier method where friction is accounted for. This model is validated from the comparison with an analytical solution. The numerical results show that the structures may experience different kinds of behaviors (namely damped, sustained and divergent motions) mainly depending on the rotational velocity of the bladed disk.
International audienceThe 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
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.