Michel Salaun - Academia.edu (original) (raw)
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The modelization of bending plates with through the thickness cracks is investigated. We consider... more The modelization of bending plates with through the thickness cracks is investigated. We consider the Kirchhoff-Love plate model which is valid for very thin plates. Reduced HCT and FVS elements are used for the numerical discretization. We apply the eXtended Finite Element Method (XFEM) strategy: enrichment of the finite element space with the asymptotic bending singularities and with the discontinuity across the crack. The main point, adressed in this paper, is the numerical computation of stress intensity factors. For this, two strategies, direct estimate and J-integral, are described and tested. Some practical rules, dealing with the choice of some numerical parameters, are underlined.
Comptes Rendus De L Academie Des Sciences Series I Mathematics, 1994
La Recherche Aerospatiale, 1990
Nous proposons une variante de la méthode des éléments finis étendue permettant d’obtenir, en méc... more Nous proposons une variante de la méthode des éléments finis étendue permettant d’obtenir, en mécanique de la rupture, une vitesse de convergence égale à celle d’une méthode d’éléments finis standard pour un problème régulier. La première amélioration consiste à enrichir une zone élargie autour du fond de fissure. On considère ensuite une condition de liaison entre degrés de liberté d’enrichissement
ESAIM: Mathematical Modelling and Numerical Analysis, 2015
Our purpose is to describe and compare some families of fully discretized approximations and thei... more Our purpose is to describe and compare some families of fully discretized approximations and their properties, in the case of vibro-impact of plates between rigid obstacles with non-penetration Signorini's conditions. To this aim, the dynamical Kirchhoff-Love plate model is considered and an extension to plates of the singular dynamic method, introduced by Renard and previously adapted to beams by Pozzolini and Salaün, is described. A particular emphasis is given in the use of an adapted Newmark scheme in which intervene a discrete restitution coefficient. Finally, various numerical results are presented and energy conservation capabilities of several numerical schemes are investigated and discussed.
This study takes place in the context of dynamical prediction for satellite structures. Aims of s... more This study takes place in the context of dynamical prediction for satellite structures. Aims of such studies are to survey the dynamical response of satellite equipment and components, to check that requirements are correct and to give prediction of vibration levels, which are inputs for the experimental test validation according to the launcher specification. This prediction is done by modal analysis performed on a numerical model built by finite element method. Uncertainties on equipment and components properties lead to random frequency response function (FRF). This paper aims at understanding how modal approach can be adapted to probabilistic framework in order to calculate cumulative density function or, at least, some quantiles of a FRF. Starting point of deterministic modal analysis is the study of a single degree of freedom (DOF) system. C. Heinkelé analytically expresses the probability density function (PDF) of the FRF of an oscillator with a random natural pulsation following a uniform law. We have generalized this work to random natural pulsation following a law of finite variance. Then, the expression of a FRF between two DOF of the structure is a linear function of random oscillators FRF and DOF components of random eigenvectors. Assuming that random eigenvectors are close to their means, we have access to the characteristic function of the random FRF between two DOF as a multi-dimensional integral with respect to the joint PDF of the oscillators FRF. This paper mainly focuses on two major points which are calculation of oscillators joint PDF and inversion of characteristic functions. The first one is tackled by copulas theory. Dependence structure of random eigenvalues are identified and modeled by a copula. Then we apply results on copulas transformations to obtain joint PDF of oscillators FRF. Classical results concern monotonic transformations but we extended these ones to non-monotonic cases. Concerning inversion of characteristic function, several methods are studied to numerically compute the Gil-Pelaez formula. This approach allows to access some FRF quantiles by numerical integration which error can be controlled. Moreover, an interesting point is the flexibility in the identification of the random eigenvalues PDF. This is especially interesting in order to couple parametric identification with nonparametric one, when only few dispersion informations are given for equipments, housed in the satellite primary structure.
The modelization of bending plates with through the thickness cracks is investigated. We consider... more The modelization of bending plates with through the thickness cracks is investigated. We consider the Kirchhoff-Love plate model which is valid for very thin plates. Reduced HCT and FVS elements are used for the numerical discretization. We apply the eXtended Finite Element Method (XFEM) strategy: enrichment of the finite element space with the asymptotic bending singularities and with the discontinuity across the crack. The main point, adressed in this paper, is the numerical computation of stress intensity factors. For this, two strategies, direct estimate and J-integral, are described and tested. Some practical rules, dealing with the choice of some numerical parameters, are underlined.
Comptes Rendus De L Academie Des Sciences Series I Mathematics, 1994
La Recherche Aerospatiale, 1990
Nous proposons une variante de la méthode des éléments finis étendue permettant d’obtenir, en méc... more Nous proposons une variante de la méthode des éléments finis étendue permettant d’obtenir, en mécanique de la rupture, une vitesse de convergence égale à celle d’une méthode d’éléments finis standard pour un problème régulier. La première amélioration consiste à enrichir une zone élargie autour du fond de fissure. On considère ensuite une condition de liaison entre degrés de liberté d’enrichissement
ESAIM: Mathematical Modelling and Numerical Analysis, 2015
Our purpose is to describe and compare some families of fully discretized approximations and thei... more Our purpose is to describe and compare some families of fully discretized approximations and their properties, in the case of vibro-impact of plates between rigid obstacles with non-penetration Signorini's conditions. To this aim, the dynamical Kirchhoff-Love plate model is considered and an extension to plates of the singular dynamic method, introduced by Renard and previously adapted to beams by Pozzolini and Salaün, is described. A particular emphasis is given in the use of an adapted Newmark scheme in which intervene a discrete restitution coefficient. Finally, various numerical results are presented and energy conservation capabilities of several numerical schemes are investigated and discussed.
This study takes place in the context of dynamical prediction for satellite structures. Aims of s... more This study takes place in the context of dynamical prediction for satellite structures. Aims of such studies are to survey the dynamical response of satellite equipment and components, to check that requirements are correct and to give prediction of vibration levels, which are inputs for the experimental test validation according to the launcher specification. This prediction is done by modal analysis performed on a numerical model built by finite element method. Uncertainties on equipment and components properties lead to random frequency response function (FRF). This paper aims at understanding how modal approach can be adapted to probabilistic framework in order to calculate cumulative density function or, at least, some quantiles of a FRF. Starting point of deterministic modal analysis is the study of a single degree of freedom (DOF) system. C. Heinkelé analytically expresses the probability density function (PDF) of the FRF of an oscillator with a random natural pulsation following a uniform law. We have generalized this work to random natural pulsation following a law of finite variance. Then, the expression of a FRF between two DOF of the structure is a linear function of random oscillators FRF and DOF components of random eigenvectors. Assuming that random eigenvectors are close to their means, we have access to the characteristic function of the random FRF between two DOF as a multi-dimensional integral with respect to the joint PDF of the oscillators FRF. This paper mainly focuses on two major points which are calculation of oscillators joint PDF and inversion of characteristic functions. The first one is tackled by copulas theory. Dependence structure of random eigenvalues are identified and modeled by a copula. Then we apply results on copulas transformations to obtain joint PDF of oscillators FRF. Classical results concern monotonic transformations but we extended these ones to non-monotonic cases. Concerning inversion of characteristic function, several methods are studied to numerically compute the Gil-Pelaez formula. This approach allows to access some FRF quantiles by numerical integration which error can be controlled. Moreover, an interesting point is the flexibility in the identification of the random eigenvalues PDF. This is especially interesting in order to couple parametric identification with nonparametric one, when only few dispersion informations are given for equipments, housed in the satellite primary structure.