Shape design sensitivity of a membrane

Rousselet, Bernard

doi:10.1007/bf00933973

Cited by 48 publications

(13 citation statements)

References 9 publications

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“…Autrement dit, on pent renumeroter les valeurs propres de fagon a avoir la differentiabilite. Cette situation est generale, le lecteur interesse par le cas des valeurs propres multiples pourra consulter avec profit [76], [90] dans lesquels les auteurs choisissent d'introduire le sous-differentiel, ou [226] ou [203] ou est prouvee la derivabilite directionnelle des valeurs propres multiples. Enfin [176] reste une reference incontournable pour ce type de questions.…”

Section: X{at) = L-\t\ X^{at) = L + \T\unclassified

Variation et optimisation de formes

Henrot

Pierre

2005

Mathématiques &Amp; Applications

513

749

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Section: X{at) = L-\t\ X^{at) = L + \T\unclassified

Variation et optimisation de formes

Henrot

Pierre

2005

Mathématiques &Amp; Applications

513

749

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“…Following the classical setting in domain differentiation, (see [13,[17][18][19][20][21]), for m ≥ 1, we define…”

Section: The Density Of the Range Of D (0)mentioning

confidence: 99%

Controllability of an Elliptic equation and its Finite Difference Approximation by the Shape of the Domain

Chenais

Zuazua

2003

Numerische Mathematik

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In this article we study a controllability problem for an elliptic partial differential equation in which the control is the shape of the domain where the equation holds. The quantity to be controlled is the trace of the solution, with a given right hand side source term, into an open subdomain. The mapping that associates this trace to the shape of the domain is nonlinear. We first consider the linearized problem and show an approximate controllability property. We then address the same questions in the context of a finite difference discretization of the elliptic problem. We prove a local controllability result applying the Inverse Function Theorem together with a "unique continuation" property of the underlying adjoint discrete system. Subject Classification (1991): 35J05, 93B03, 65M06 Mathematics

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“…Dans cet article avaient 6t6 d6montr6es la continuit6 et la diff6rentiabilit6 directionnelle de 2 par rapport ~t ~o. Ce r6sultat a ensuite 6t6 6tendu dans Rousselet et et Rousselet [17] au cas off la variable de conception est la forme du domaine occup6 par la structure, en suivant les techniques indiqu6es dans (voir aussi [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]). Dans ce probl6me, on 6tudiait un probl6me de valeurs propres non auto-adjoint, issu de la physique nucl6aire.…”

Section: Introductionunclassified

Continuit� et diff�rentiabilit� d'�l�ments propres: Application � l'optimisation de structures

Rousselet

Chenais

1990

Appl Math Optim

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Abstract. The buckling load of a structure may usually be computed with an eigenvalue problem: it is the eigenvalue of smallest absolute value. In optimizing structures with a constraint on the buckling load, repeated eigenvalues are likely to occur. We prove continuity and differentiability results of eigenelements with respect to design variables using the variational characterization of eigenvalues. We illustrate these results with a classical problem: buckling of a beam. Application to arch buckling is presented in another article.

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Shape design sensitivity of a membrane

Cited by 48 publications

References 9 publications

Variation et optimisation de formes

Variation et optimisation de formes

Controllability of an Elliptic equation and its Finite Difference Approximation by the Shape of the Domain

Continuit� et diff�rentiabilit� d'�l�ments propres: Application � l'optimisation de structures

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