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Hochard C.,CNRS Laboratory of Mechanics and Acoustics
Materials and Design | Year: 2013

This study deals with the optimisation of hybrid composite drive shafts operating at subcritical or supercritical speeds, using a genetic algorithm. A formulation for the flexural vibrations of a composite drive shaft mounted on viscoelastic supports including shear effects is developed. In particular, an analytic stability criterion is developed to ensure the integrity of the system in the supercritical regime. Then it is shown that the torsional strength can be computed with the maximum stress criterion. A shell method is developed for computing drive shaft torsional buckling. The optimisation of a helicopter tail rotor driveline is then performed. In particular, original hybrid shafts consisting of high-modulus and high-strength carbon fibre reinforced epoxy plies were studied. The solutions obtained using the method presented here made it possible to greatly decrease the number of shafts and the weight of the driveline under subcritical conditions, and even more under supercritical conditions. This study yielded some general rules for designing an optimum composite shaft without any need for optimisation algorithms. © 2012 Elsevier Ltd.

Mitri F.G.,Los Alamos National Laboratory | Fellah Z.E.A.,CNRS Laboratory of Mechanics and Acoustics
Ultrasonics | Year: 2014

The present analysis investigates the (axial) acoustic radiation force induced by a quasi-Gaussian beam centered on an elastic and a viscoelastic (polymer-type) sphere in a nonviscous fluid. The quasi-Gaussian beam is an exact solution of the source free Helmholtz wave equation and is characterized by an arbitrary waist w0 and a diffraction convergence length known as the Rayleigh range zR. Examples are found where the radiation force unexpectedly approaches closely to zero at some of the elastic sphere's resonance frequencies for kw0 ≤ 1 (where this range is of particular interest in describing strongly focused or divergent beams), which may produce particle immobilization along the axial direction. Moreover, the (quasi)vanishing behavior of the radiation force is found to be correlated with conditions giving extinction of the backscattering by the quasi-Gaussian beam. Furthermore, the mechanism for the quasi-zero force is studied theoretically by analyzing the contributions of the kinetic, potential and momentum flux energy densities and their density functions. It is found that all the components vanish simultaneously at the selected ka values for the nulls. However, for a viscoelastic sphere, acoustic absorption degrades the quasi-zero radiation force. © 2013 Elsevier B.V. All rights reserved.

Ballard P.,CNRS Laboratory of Mechanics and Acoustics
Journal of the Mechanics and Physics of Solids | Year: 2016

The steady sliding frictional contact problem between a moving rigid indentor of arbitrary shape and an isotropic homogeneous elastic half-space in plane strain is extensively analysed. The case where the friction coefficient is a step function (with respect to the space variable), that is, where there are jumps in the friction coefficient, is considered. The problem is put under the form of a variational inequality which is proved to always have a solution which, in addition, is unique in some cases. The solutions exhibit different kinds of universal singularities that are explicitly given. In particular, it is shown that the nature of the universal stress singularity at a jump of the friction coefficient is different depending on the sign of the jump. © 2016 Elsevier Ltd.

Olive M.,CNRS Laboratory of Mechanics and Acoustics
Foundations of Computational Mathematics | Year: 2016

In this article, we present a modern viewpoint on the Gordan algorithm for binary forms. The symbolic method is recast in terms of (Formula presented.) equivariant homomorphisms. A graphical approach is used to define Gordan’s ideal, a central tool used to obtain an integrity basis for the covariant algebra of a binary form. To illustrate the power of this method, we compute for the first time a minimal integrity basis for the covariant algebra of (Formula presented.), (Formula presented.) and for the invariant algebra of (Formula presented.). © 2016 SFoCM

Hochard Ch.,CNRS Laboratory of Mechanics and Acoustics | Thollon Y.,CNRS Laboratory of Mechanics and Acoustics
International Journal of Fatigue | Year: 2010

A generalized non-linear cumulative damage model for woven ply laminates subjected to static and fatigue loading is developed in this paper. The damage, consisting of small cracks running parallel to the fibers, leads to a loss of stiffness in the warp, weft and shear directions. The model presented here describes the evolution of the damage up to failure of the first ply. By replacing the woven ply by two stacked unidirectional plies corresponding to the warp and weft thicknesses, this general model is extended to cover a broad range of plies, from quasi-unidirectional to balanced woven plies. A continuum damage approach (CDM) is then used to define the behaviour of the two virtual unidirectional plies under static and fatigue loading conditions. The model is applied here to an unbalanced woven ply with glass reinforcement and the results of the simulations are compared with experimental data. © 2009 Elsevier Ltd. All rights reserved.

Chiavassa G.,École Centrale Marseille | Lombard B.,CNRS Laboratory of Mechanics and Acoustics
Journal of Computational Physics | Year: 2011

This paper deals with the numerical modeling of wave propagation in porous media described by Biot's theory. The viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity, which is valid in the low-frequency range. The coexistence of propagating fast compressional wave and shear wave, and of a diffusive slow compressional wave, makes numerical modeling tricky. To avoid restrictions on the time step, the Biot's system is splitted into two parts: the propagative part is discretized by a fourth-order ADER scheme, while the diffusive part is solved analytically. Near the material interfaces, a space-time mesh refinement is implemented to capture the small spatial scales related to the slow compressional wave. The jump conditions along the interfaces are discretized by an immersed interface method. Numerical experiments and comparisons with exact solutions confirm the accuracy of the numerical modeling. The efficiency of the approach is illustrated by simulations of multiple scattering. © 2011 Elsevier Inc.

Boussaa D.,CNRS Laboratory of Mechanics and Acoustics
Mechanics of Materials | Year: 2011

Effective thermoelastic properties - elasticities, thermal expansions, heat capacities - of composites with temperature-dependent constituents are derived all at the same time using a unified thermodynamic treatment within Kovalenko's thermoelasticity theory, which assumes the strain to be small but places no restrictions on temperature variations. Known results on elasticities and thermal expansions are rederived in a new way and new results on thermal expansions and heat capacities are obtained. In addition, the temperature-independent framework is revisited and expressions for the effective properties are obtained that are free of the restrictions placed on temperature variations within linear thermoelasticity. © 2011 Elsevier Ltd. All rights reserved.

Lebon F.,CNRS Laboratory of Mechanics and Acoustics | Rizzoni R.,University of Ferrara
International Journal of Solids and Structures | Year: 2011

The mechanical problem of two elastic bodies separated by a thin elastic film is studied here. The stiffness of the three bodies is assumed to be similar. The asymptotic behavior of the film as its thickness tends to zero is studied using a method based on asymptotic expansions and energy minimization. Several cases of interphase material symmetry are studied (from isotropy to triclinic symmetry). In each case, non-local relations are obtained relating the jumps in the displacements and stress vector fields at order one to these fields at order zero. © 2010 Elsevier Ltd. All rights reserved.

Ballard P.,CNRS Laboratory of Mechanics and Acoustics
Archive for Rational Mechanics and Analysis | Year: 2010

The linearized equilibrium equations for straight elastic strings, beams, membranes or plates do not couple tangential and normal components. In the quasi-static evolution occurring above a fixed rigid obstacle with Coulomb dry friction, the normal displacement is governed by a variational inequality, whereas the tangential displacement is seen to obey a sweeping process, the theory of which was extensively developed by Moreau in the 1970s. In some cases, the underlying moving convex set has bounded retraction and, in these cases, the sweeping process can be solved by directly applying Moreau's results. However, in many other cases, the bounded retraction condition is not fulfilled and this is seen to be connected to the possible event of moving velocity discontinuities. In such a case, there are no strong solutions and we have to cope with weak solutions of the underlying sweeping process. © 2010 Springer-Verlag.

Ogam E.,CNRS Laboratory of Mechanics and Acoustics
Mechanical Systems and Signal Processing | Year: 2013

The airflow resistivities of air-saturated poroelastic slender beams submitted to transient mechanical stress are recovered using fluid and solid borne compressional mode phase velocity expressions drawn from a modified Biot theory. A point where the two dilatational modes intersect and their phase velocities equal is first sought. This point also corresponds to the Biot transitional frequency indicating the frequency at which the solid and the pore fluid start disassociating due to the weakening of the viscous forces by the thinning of the viscous boundary layer in the pores. A bilinear time-frequency (TF) distribution is used to represent on the time-frequency plane, the captured transient mechanical stress waves from which the point of intersection/ separation of the two modes is located. The projection of the Eigenfrequencies obtained from a simple 3D finite element modeling of the thin poroelastic beam, on a (TF) diagram, facilitates the identification of the modes. The transition frequencies for the poroelastic beams thus retrieved are verified through the use of variable frequency, single cycle sine wave bursts. The anisotropy of the foams are also revealed by analyzing the transient responses of the poroelastic beam specimens cut from the same panel but in two perpendicular directions in orientation to each other. © 2012 Elsevier Ltd.

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