Numerical implementation of composite Koiter shells including membrane/bending coupling coefficientsImplémentation numérique des coques composites de Koiter prenant en considération les coefficients de couplage membrane/flexions

We propose a way for determining the generalized coefficients of rigidity – some of which are membrane/bending coupling coefficients – which appear in the deformation energy of the Koiter model of thin shells. This is concerned with a heterogeneous material in the thickness direction. A new program to compute these coefficients is implemented in the finite element code Modulef, in order to simulate problems of thin multilayered shells with linearly elastic anisotropic layers. We propose an example of an inhibited multilayered thin shell, with hyperbolic middle surface, involving a composite material with unidirectional fibres. To cite this article: H. Ranarivelo, C. R. Mecanique 330 (2002) 273–278.     

On the stability of a Bingham fluid flow in an annular channelSur la stabilité de l'écoulement d'un fluide de Bingham dans une conduite annulaire

Linear stability of a fully developed Bingham fluid flow between two coaxial cylinders subject to infinitesimal axisymetric perturbations is investigated. The analysis leads to two uncoupled Orr–Sommerfeld equations with appropriate boundary conditions. The numerical solution is obtained using fourth order finite difference scheme. The computations were performed for various plug flow dimensions and radii ratios. Within the range of the parameters considered in this paper, the Poiseuille flow of Bingham fluid is found to be linearly stable. To cite this article: N. Kabouya, C. Nouar, C. R. Mecanique 331 (2003).     

Study of stabilization methods for computational aeroacoustics

The use of high-order centered finite difference to solve the Euler equations commonly requires a stabilization procedure. The present work is a theoretical analysis of these stabilization methods that make the whole algorithm (i) still consistent with the continuous problem and (ii) able to run long time simulations. In the present study, a theoretical analysis of the three commonly used methods resorting to the application of high-order filters is performed. An extension to non-periodic boundary conditions is studied to avoid numerical reflection and numerical instabilities due to the use of specific boundary schemes. To cite this article: R. Guénanff, M. Terracol, C. R. Mecanique 333 (2005).     

Eléments finis stochastiques en élasticité linéaireA stochastic finite element method in linear mechanics

The stochastic finite element method presented in this Note consists in representing in a probabilistic form the response of a linear mechanical system whose material properties and loading are random. Each input random variable is expanded into a Hermite polynomial series in standard normal random variables. The response (e.g., the nodal displacement vector) is expanded onto the so-called polynomial chaos. The coefficients of the expansion are obtained by a Galerkin-type method in the space of probability. To cite this article: B. Sudret et al., C. R. Mecanique 332 (2004).     

Optimal design of functionally graded plates with thermo-elastic plastic behaviourConfiguration optimale des plaques fonctionnellement graduées à plasticité thermo-élastique

The thermo-elastic plastic behaviour of functionally graded plates under extremal thermal loading at different boundary conditions is considered. The plates consist of two phases – ZrO₂ ceramics and Ti₆Al₄V alloy. The layers are distributed exponentially through the thickness. The mechanical and thermal properties of both materials strongly depend on temperature. The stress–strain behaviour is investigated by the FEM. To predict the stable state of the structures of interest, several failure criteria are applied. Two cost functions are introduced to optimize the design of the plate. The main results are discussed and graphically illustrated. To cite this article: L. Parashkevova et al., C. R. Mecanique 332 (2004).     

Mathematical modeling of an array of underground waste containersModélisation mathématique d'un réseau souterrain de stockage de déchets

We consider a mathematical model describing the behavior of an underground waste repository, once the containers start to leak. Due to the high contrast of the characteristic lengths, numerical simulations on a such model are unrealistic. After renormalization, a small parameter ε appears and the global model is obtained when ε tends to zero, by means of homogenization and boundary layers methods. The asymptotic model obtained could be used as a global repository model for large field numerical simulations. To cite this article: A. Bourgeat et al., C. R. Mecanique 330 (2002) 371–376.     

DNS of premixed turbulent V-flame: coupling spectral and finite difference methods

To allow for a reliable examination of the interaction between velocity fluctuations, acoustics and combustion, a novel numerical procedure is discussed in which a spectral solution of the Navier–Stokes equations is directly associated to a high-order finite difference fully compressible DNS solver (sixth order PADE). Using this combination of high-order solvers with accurate boundary conditions, simulations have been performed where a turbulent premixed V-shape flame develops in grid turbulence. In the light of the DNS results, a sub-model for premixed turbulent combustion is analyzed. To cite this article: R. Hauguel et al., C. R. Mecanique 333 (2005).     

Validation of averaged equations for thermal vibrational convection in near-critical fluidsValidation d'équations moyennées pour l'étude de la convection vibrationnelle dans les fluides supercritiques.

Within an averaging approach, the governing equations and effective boundary conditions describing both the average and pulsation motion of a near-critical fluid subjected to high-frequency vibrations are obtained. Vibrations induce the non-homogeneities in average temperature. Owing to these non-homogeneities, the average flows can be generated even in isothermal cavity under weightlessness. These flows are examined for 1D and 2D configurations. The direct numerical simulations fulfilled earlier confirm the averaged model, we obtain the same flow structures by essentially smaller requirements for computational time. To cite this article: A.Vorobev et al., C. R. Mecanique 332 (2004).     

Simulation numérique directe de l'influence de la forme aval d'une plaque séparatrice sur une couche de mélangeDirect-numerical simulation of the splitting-plate downstream-shape influence upon a mixing layer

In this Note, we present direct numerical simulation results of a spatial mixing layer generated behind an upstream plate separating two boundary layers. The effect of the shape of the trailing edge of the plate is considered through comparisons between flows obtained from a bevelled or a blunt plate. In the former case, a spatial mixing layer consistent with previous experimental and numerical observations is obtained. In the latter case, the self-excited state that establishes in the near wake region dominates primary and secondary instability mechanisms while understating the importance of inflow perturbations. This behaviour is interpreted in terms of convective or absolute instability. The effects on turbulent statistics are also discussed. To cite this article: S. Laizet, E. Lamballais, C. R. Mecanique 334 (2006).     

Verification of higher-order discontinuous Galerkin method for hexahedral elements

A high-order implementation of the Discontinuous Galerkin (dg) method is presented for solving the three-dimensional Linearized Euler Equations on an unstructured hexahedral grid. The method is based on a quadrature free implementation and the high-order accuracy is obtained by employing higher-degree polynomials as basis functions. The present implementation is up to fourth-order accurate in space. For the time discretization a four-stage Runge–Kutta scheme is used which is fourth-order accurate. Non-reflecting boundary conditions are implemented at the boundaries of the computational domain.The method is verified for the case of the convection of a 1D compact acoustic disturbance. The numerical results show that the rate of convergence of the method is of order $p+1$ in the mesh size, with p the order of the basis functions. This observation is in agreement with analysis presented in the literature. To cite this article: H. Özdemir et al., C. R. Mecanique 333 (2005).     

Dispersion de particules solides en mouvement de saltation dans un écoulement turbulentDispersion of solid saltating particles in a turbulent flow

The solid particle dispersion in saltating motion is studied in an homogeneous turbulence and in a turbulent boundary layer. The fluid velocity along the particle trajectory is estimated using a continuous stochastic differential equation in which the correlation integral time takes into account gravity and inertia effects. As far as the boundary layer is concerned, the aerodynamic entrainment of particles and the rebound are modelised as random variables with Gaussian probability density functions. Compared with experimental results, the numerical results show good agreement for dispersion, although velocity fluctuations are slightly under evaluated. To cite this article: C. Aguirre et al., C. R. Mecanique 332 (2004).     

On the nature of the boundary layers instabilities in a flow between a rotating and a stationary discSur la nature des instabilités de couche limite dans un écoulement entre un disque fixe et un disque tournant

Both theoretical linear stability analysis and direct numerical simulation are performed to study the transition flow between a stationary and a rotating disc. This paper concerns three-dimensional spiral and annular patterns computed with a high-order (spectral) numerical method and related to Bödewadt layer instabilities. The characteristic parameters of these boundary layer patterns are compared to the theoretical results and interpreted in terms of type I and type II generic instabilities. Moreover, the absolute instability regions are also theoretically identified and the critical Reynolds numbers of the convective/absolute transition in both layers are given. To cite this article: E. Tuliska-Sznitko et al., C. R. Mecanique 330 (2002) 91–99.     

Computational aeroacoustics applications based on a discontinuous Galerkin method

caa simulation requires the calculation of the propagation of acoustic waves with low numerical dissipation and dispersion error, and to take into account complex geometries. To give, at the same time, an answer to both challenges, a Discontinuous Galerkin Method is developed for Computational AeroAcoustics. Euler's linearized equations are solved with the Discontinuous Galerkin Method using flux splitting technics. Boundary conditions are established for rigid wall, non-reflective boundary and imposed values. A first validation, for induct propagation is realized. Then, applications illustrate: the Chu and Kovasznay's decomposition of perturbation inside uniform flow in term of independent acoustic and rotational modes, Kelvin–Helmholtz instability and acoustic diffraction by an air wing. To cite this article: Ph. Delorme et al., C. R. Mecanique 333 (2005).     

Artificial boundary conditions on polyhedral truncation surfaces for three-dimensional elasticity systemsConditions aux limites artificielles sur des surfaces polyhédrales de troncature pour des systèmes d'élasticité tridimensionalle

For a three-dimensional exterior problem in the framework of anisotropic elasticity, artificial boundary conditions are constructed on a polyhedral truncation surface. These conditions do not need an explicit formula for the fundamental matrix. An approach to adapt the shape of truncation surfaces to the shape of the enclosed cavity is discussed. To cite this article: S. Langer et al., C. R. Mecanique 332 (2004).     

Asymptotic decomposition of a singular perturbation problem with unbounded energyDécomposition asymptotique d'une perturbation singulière d'énergie sans limite

We consider a singular perturbation with unbounded energy. We propose here an effective method of finite element computation, fit for accounting for the linear behavior of the solution. The Hilbert space of the variational formulation, H²₀(0,1), is replaced by a simpler subspace containing an asymptotic solution of the initial problem. Error estimates are derived by eliminating some degrees of freedom and a numerical experiment is developped. To cite this article: F. Fontvieille et al., C. R. Mecanique 330 (2002) 507–512.     

Drapage géométrique des compositesGeometrical draping of composite fabrics

This paper presents a study devoted to the composite fabric shaping simulation in finite strain analysis. We introduce a new geometrical approach based on the fishnet method for which the deformation of a fabric mesh element consists in a pure trellis effect. Such a fabric mesh element is then defined by a curved quadrilateral whose edges are geodesic lines with the same length plotted onto the surface to drape. Given three vertices of the fabric mesh element on the surface, we propose an optimization algorithm to define the fourth vertex of the fabric mesh element. This algorithm allows us to drape the surface using an advancing front approach from the data of an initial impact point between the fabric and the surface and the initial fibre directions at this point. A numerical draping simulation example using this approach is given. To cite this article: H. Borouchaki, A. Cherouat, C. R. Mecanique 331 (2003).     

A penalization method applied to the wave equation

In this Note we investigate the mathematical properties of the volume penalization method applied to the one-dimensional wave equation. Generally speaking, the penalization method allows one to handle complex geometries by simply adding a term to the equation to impose the boundary conditions. We study the convergence of the method with regards to the penalization parameter and we present error and stability analyses for the wave equation. Numerical simulations using a finite difference scheme illustrate the results. To cite this article: A. Paccou et al., C. R. Mecanique 333 (2005).     

Sur la réponse transitoire d'une couche solidaire d'un milieu semi-infini ; application à un impact sur le thoraxOn the transient response of a layer welded to a half-space; an insvestigation of impact on the thorax

The theory of generalized rays is dedicated to the investigation of the transient response of elastic layered media. It yields exact solutions, whatever the duration of the applied impulse (i.e., for any frequency content of the excitation). This Note is part of a research project on the modeling of non-penetrating impact on thorax. We investigate a simplified model of the thoracic wall – a layer welded to a semi-infinite medium – submitted to an impulse of variable duration. Among other things, it is found that the response computed for a “long” impulse is consistent with a result of the classical plate theory. To cite this article: Q. Grimal et al., C. R. Mecanique 331 (2003).     

A symmetry-preserving Cartesian grid method for computing a viscous flow past a circular cylinder

This article deals with a numerical method for solving the unsteady, incompressible Navier–Stokes equations in domains with arbitrarily-shaped boundaries, where the boundary is represented using the Cartesian grid approach. We introduce a novel cut-cell discretization which preserves the spectral properties of convection and diffusion. Here, convection is discretized by a skew-symmetric operator and diffusion is approximated by a symmetric, positive-definite coefficient matrix. Such a symmetry-preserving discretization conserves the kinetic energy (if the dissipation is turned off) and is stable on any grid. The method is successfully tested for an incompressible, unsteady flow around a circular cylinder at $\mathit{Re}=100$. To cite this article: R. Verstappen, M. Dröge, C. R. Mecanique 333 (2005).     

‘Les fleurs du mal’ – an adaptive wavelet method of arbitrary lines I: convection–diffusion problems« Les fleurs du MAL » – une méthode d'ondelettes adaptive de lignes arbitraires I : problèmes de convection–diffusion

Baudelaire's ‘les fleurs du mal’ refers to various new developments (‘les fleurs’) of the method ofarbitrarylines (mal), since it was first published (in C. R. Acad. Sci. Paris, Sér. I, in 1991). Here we revisit the basic mal (semi-discretization) methodology for stationary convection–diffusion problems and develop an adaptive, wavelet-based solver that is capable of capturing the thin layers that arise in such problems. We show the efficacy and high accuracy of the wavelet-mal solver by applying it to a challenging 2D problem involving both boundary and interior layers. To cite this article: X. Ren, L.S. Xanthis, C. R. Mecanique 332 (2004).