Homogénéisation de frontières par épi-convergence en élasticité linéaire

Brillard, Alain; Лобо, М.; Pérez, Eugenia

doi:10.1051/m2an/1990240100051

Cited by 25 publications

(28 citation statements)

References 5 publications

(3 reference statements)

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“…Consequently, e = O(T) 2 ) is the critical dimension of the stuck zones that gives a Fourier-type limit problem that is intermediate between the unstuck case, which we obtain for JT = 0, and the totally stuck case, for X = oo.…”

Section: E->0mentioning

confidence: 65%

“…where all the surface is stuck to the plane, or all the surface is unstuck. The « critical size » of these zones is given by the relation e = O(r\ 2 ). For this size, the boundary conditions that we find in the limit problem, give us a relation between the stresses and the displacements from a « matrix of capacities » obtained from the solution of the « local problem ».…”

Section: E->0mentioning

confidence: 89%

“…Let T = dfl -% and T l9 T 2 be two open domains in F such that T 2 has a positive measure and T = T 1 U T 2 (cf. fig.…”

Section: Setting Of the Problemmentioning

confidence: 99%

“…The boundary value problem (2.1)-(2.5) is the problem of elasticity for a isotropic homogeneous material with coefficients of elasticity a l}kh under the action of the forces ƒ. The boundary conditions express the f act that the body Ci is fixed by the parts F 2 where C is a constant independent of e.…”

Section: Setting Of the Problemmentioning

confidence: 99%

See 3 more Smart Citations

Asymptotic behaviour of an elastic body with a surface having small stuck regions

Лобо¹,

Pérez²

1988

ESAIM: M2AN

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Section: E->0mentioning

confidence: 65%

Section: E->0mentioning

confidence: 89%

“…Let T = dfl -% and T l9 T 2 be two open domains in F such that T 2 has a positive measure and T = T 1 U T 2 (cf. fig.…”

Section: Setting Of the Problemmentioning

confidence: 99%

Section: Setting Of the Problemmentioning

confidence: 99%

See 2 more Smart Citations

Asymptotic behaviour of an elastic body with a surface having small stuck regions

Лобо¹,

Pérez²

1988

ESAIM: M2AN

Self Cite

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“…We stress that the estimates (4), (6), (8) are best possible. More concretely, under hypothesis of each theorem there exist function a j and b j , for those the degree of convergence has the smallness order exactly as given in the estimates (4), (6), (8). This statement will be established in the proofs of Theorems 2.1-2.3.…”

Section: Theorem 22 Suppose the Inequalitiesmentioning

confidence: 99%

On a problem with nonperiodic frequent alternation of boundary conditions imposed on fast oscillating sets

Борисов¹

2006

Comput. Math. and Math. Phys.

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We consider singular perturbed eigenvalue problem for Laplace operator in a cylinder with frequent and nonperiodic alternation of boundary conditions imposed on narrow strips lying in the lateral surface. The width of strips depends on a small parameter in a arbitrary way and may oscillate fast, moreover, the nature of oscillation is arbitrary, too. We obtain two-sided estimates for degree of convergences of the perturbed eigenvalues.

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The skin effect in vibrating systems with many concentrated masses

Лобо¹,

Prez²

2000

Math. Meth. Appl. Sci.

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We address the asymptotic behaviour of the vibrations of a body occupying a domain \documentclass{article}\usepackage{amsfonts}\begin{document}\pagestyle{empty}$\Omega\subset\mathbb{R}^n, n=2,3$\end{document}. The density, which depends on a small parameter $\varepsilon$\nopagenumbers\end , is of the order $O(1)$\nopagenumbers\end out of certain regions where it is $O(\varepsilon^{‐m})$\nopagenumbers\end with $m>2$\nopagenumbers\end. These regions, the concentrated masses with diameter $O(\varepsilon)$\nopagenumbers\end, are located near the boundary, at mutual distances $O(\eta)$\nopagenumbers\end, with $\eta=\eta(\varepsilon)\rightarrow 0$\nopagenumbers\end. We impose Dirichlet (resp. Neumann) conditions at the points of $\partial\Omega$\nopagenumbers\end in contact with (resp. out of) the masses. We look at the asymptotic behaviour, as $\varepsilon\rightarrow 0$\nopagenumbers\end, of the eigenvalues of order $O(1)$\nopagenumbers\end, the high frequencies, of the corresponding eigenvalue problem. We show that they accumulate on the whole positive real axis and characterize those giving rise to global vibrations of the whole system. We use the fact that the corresponding eigenfunctions, microscopically, present a skin effect in the concentrated masses. Copyright © 2001 John Wiley & Sons, Ltd.

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Homogénéisation de frontières par épi-convergence en élasticité linéaire

Cited by 25 publications

References 5 publications

Asymptotic behaviour of an elastic body with a surface having small stuck regions

Asymptotic behaviour of an elastic body with a surface having small stuck regions

On a problem with nonperiodic frequent alternation of boundary conditions imposed on fast oscillating sets

The skin effect in vibrating systems with many concentrated masses

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