Dependence of the buckling load of a nonshallow arch with respect to the shape of its midcurve

Chenais, Denise; Rousselet, Bernard

doi:10.1051/m2an/1990240303071

Cited by 8 publications

(4 citation statements)

References 5 publications

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“…O n pourait traiter de la m~me faqon les autres exemples indiqu6s dans H a u g et Rousselet [7] (vibration de m e m b r a n e et de plaque). D a n s Chenais et Rousselet (/L paraltre) [2], on d6veloppe l'exemple plus compliqu6 de la diff6rentiabilit6 par r a p p o r t / l l'6paisseur et/L la surface moyenne de la charge critique de flambement d'une arche.…”

Section: Kfi2z -P Fi2z : -F I 2 K Z -Fik Fiz + Fiz#z + Fip Fiz Et Dounclassified

“…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

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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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Section: Kfi2z -P Fi2z : -F I 2 K Z -Fik Fiz + Fiz#z + Fip Fiz Et Dounclassified

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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“…We prove the existence of the minimizer and derive the first order optimality conditions by computing the directional derivative of the cost. Similar problems were studied by Rousselet, Piekarski, and Myslinski [17], Chenais and Rousselet [9], and Chenais, Rousselet, and Benedict [10] under differentiability assumptions.…”

Section: Introductionmentioning

confidence: 78%

Analysis and Optimization of Nonsmooth Arches

Ignat¹,

Sprekels²,

Tiba³

2002

SIAM J. Control Optim.

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It is our aim to present a new treatment for some classical models of arches and for their optimization. In particular, our approach allows us to study nonsmooth arches, while the standard assumptions from the literature require W 3,∞ -regularity for the parametric representation. Moreover, by a duality-type argument, the deformation of the arches may be explicitly expressed by integral formulas.As examples for the shape optimization problems under study, we mention the design of the middle curve of a clamped arch such that, under a prescribed load, the obtained deflection satisfies certain desired properties. In all cases, no smoothness is required for the design parameters.

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“…Some applications of shape optimization in fluids can be found in [27,68,69]. Some related references on optimization of nonlinear elastic curves are [4,11,12,48].…”

Section: Optimization Approach and Algorithmmentioning

confidence: 99%

Analysis of Shape Optimization for Magnetic Microswimmers

Walker¹,

Keaveny²

2013

SIAM J. Control Optim.

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We analyze an infinite dimensional, geometrically constrained shape optimization problem for magnetically driven microswimmers (locomotors) in three-dimensional (3-D) Stokes flow and give a well-posed descent scheme for computing optimal shapes. The problem is inspired by recent experimental work in this area. We show the existence of a minimizer of the optimization problem using analytical tools for elastic rods that respect the excluded volume constraint. We derive a variational gradient descent method for computing optimal locomotor shapes using the tools of shape differential calculus. The descent direction is obtained by solving a saddle-point system, which we prove is well-posed. We also introduce a finite element approximation of the gradient descent method and prove its stability. We present numerical results illustrating our method and the effect that finite aspect ratio and external cargo can have on the optimal shape. The 3-D Stokes equations are solved by a boundary integral method.

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Dependence of the buckling load of a nonshallow arch with respect to the shape of its midcurve

Cited by 8 publications

References 5 publications

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

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

Analysis and Optimization of Nonsmooth Arches

Analysis of Shape Optimization for Magnetic Microswimmers

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