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Spatial heterogeneity in 3D-2D dimensional reduction

Jean-François Babadjian, Gilles A. Francfort (2005)

ESAIM: Control, Optimisation and Calculus of Variations

A justification of heterogeneous membrane models as zero-thickness limits of a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is proposed in the spirit of Le Dret (1995). Specific characterizations of the 2D elastic energy are produced. As a generalization of Bouchitté et al. (2002), the case where external loads induce a density of bending moment that produces a Cosserat vector field is also investigated. Throughout, the 3D-2D dimensional reduction is viewed as a problem...

Spatial heterogeneity in 3D-2D dimensional reduction

Jean-François Babadjian, Gilles A. Francfort (2010)

ESAIM: Control, Optimisation and Calculus of Variations

A justification of heterogeneous membrane models as zero-thickness limits of a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is proposed in the spirit of Le Dret (1995). Specific characterizations of the 2D elastic energy are produced. As a generalization of Bouchitté et al. (2002), the case where external loads induce a density of bending moment that produces a Cosserat vector field is also investigated. Throughout, the 3D-2D dimensional reduction is viewed as a problem...

Special exact curved finite elements

Jitka Křížková (1991)

Applications of Mathematics

Special exact curved finite elements useful for solving contact problems of the second order in domains boundaries of which consist of a finite number of circular ares and a finite number of line segments are introduced and the interpolation estimates are proved.

Spectral estimates of vibration frequencies of anisotropic beams

Luca Sabatini (2023)

Applications of Mathematics

The use of one theorem of spectral analysis proved by Bordoni on a model of linear anisotropic beam proposed by the author allows the determination of the variation range of vibration frequencies of a beam in two typical restraint conditions. The proposed method is very general and allows its use on a very wide set of problems of engineering practice and mathematical physics.

Spectral/hp elements in fluid structure interaction

Pech, Jan (2021)

Programs and Algorithms of Numerical Mathematics

This work presents simulations of incompressible fluid flow interacting with a moving rigid body. A numerical algorithm for incompressible Navier-Stokes equations in a general coordinate system is applied to two types of body motion, prescribed and flow-induced. Discretization in spatial coordinates is based on the spectral/hp element method. Specific techniques of stabilisation, mesh design and approximation quality estimates are described and compared. Presented data show performance of the solver...

Stabilisation d’une poutre. Étude du taux optimal de décroissance de l’énergie élastique

Francis Conrad, Fatima-Zahra Saouri (2002)

ESAIM: Control, Optimisation and Calculus of Variations

On se propose d’étudier la stabilité d’une poutre flexible homogène, encastrée à une extrémité. À l’autre extrémité est attachée une masse ponctuelle où on applique un moment proportionnel à la vitesse de déplacement angulaire. On montre par une analyse spectrale que le taux optimal de décroissance de l’énergie est déterminé par l’abscisse spectrale du générateur infinitésimal du semi-groupe associé au problème.

Stabilisation d'une poutre. Étude du taux optimal de décroissance de l'énergie élastique

Francis Conrad, Fatima-Zahra Saouri (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study the stability of a flexible beam clamped at one end. A mass is attached at the other end, where a control moment is applied. The boundary control is proportional to the angular velocity at the end. By spectral analysis, we prove that the optimal decay rate of the energy is given by the spectrum of the generator of the semigroup associated to the system.

Stabilisation exponentielle d’une équation des poutres d’Euler-Bernoulli à coefficients variables

My Driss Aouragh, Naji Yebari (2009)

Annales mathématiques Blaise Pascal

Dans ce travail, nous étudions la propriété de base de Riesz et la stabilisation exponentielle pour une équation des poutres d’Euler-Bernoulli à coefficients variables sous un contrôle frontière linéaire dépendant de la position (resp. l’angle de rotation), de la vitesse et de la vitesse de rotation dans le contrôle force (resp. moment). Nous montrons qu’il existe une suite de fonctions propres généralisées qui forme une base de Riesz de l’espace d’énergie considéré, et qu’il y a stabilité exponentielle...

Currently displaying 101 – 120 of 220