Optimality conditions for shape and topology optimization subject to a cone constraint

Description

Niveau: Supérieur, Doctorat, Bac+8
OPTIMALITY CONDITIONS FOR SHAPE AND TOPOLOGY OPTIMIZATION SUBJECT TO A CONE CONSTRAINT SAMUEL AMSTUTZ AND MARC CILIGOTTRAVAIN Abstra t. This paper provides rst order ne essary optimality onditions for simultaneous shape and topology optimization subje t to a one onstraint. These onditions are expressed with the help of the shape and topologi al derivatives of the obje tive and onstraint fun tionals. Several examples of appli ations are given. 1. Introdu tion The lassi al theory of shape optimization onsists in analyzing the behavior of a shape fun - tional with respe t to a small deformation of the domain, where ea h point moves along a dire tion represented by a displa ement eld [20, 24, 30?. In the formulation of [20, 24?, the shape deriva- tive is dened as a Fré het derivative, whi h allows to re ast, at least lo ally, shape optimization problems as dierentiable optimization problems. Therefore, optimality onditions an be derived straightforwardly by applying general results of nonlinear programming in Bana h spa es. Unfor- tunately, this approa h does not apply any more when one wants to allow topology variations. In fa t, in this ontext, the set of attainable domains annot be equipped with a stru ture of ve tor spa e in a natural and onvenient way.

• fritz-john multipliers whi


• lassi al


• optimality ondition


• ?? ?


• perturbation


• tion ?


• shape optimization


• simultaneous shape


• lagrange multipliers


• dire tional

Sujets

• Perturbation
• Shape optimization
• Lagrange multiplier

Informations

• Publié par: profil-zyak-2012
• Nombre de lectures: 11
• Langue: English

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