Displaying similar documents to “A shape optimization approach for a class of free boundary problems of Bernoulli type”

A note on contact shape optimization with semicoercive state problems

Jaroslav Haslinger (2002)

Applications of Mathematics

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This note deals with contact shape optimization for problems involving “floating” structures. The boundedness of solutions to state problems with respect to admissible domains, which is the basic step in the existence analysis, is a consequence of Korn’s inequality in coercive cases. In semicoercive cases (meaning that floating bodies are admitted), the Korn inequality cannot be directly applied and one has to proceed in another way: to use a decomposition of kinematically admissible...

Shape optimization of elasto-plastic bodies

Zuzana Dimitrovová (2001)

Applications of Mathematics

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Existence of an optimal shape of a deformable body made from a physically nonlinear material obeying a specific nonlinear generalized Hooke’s law (in fact, the so called deformation theory of plasticity is invoked in this case) is proved. Approximation of the problem by finite elements is also discussed.

An existence result for a quadrature surface free boundary problem

Mohammed Barkatou, Diaraf Seck, Idrissa Ly (2005)

Open Mathematics

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The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.

Boundary integral representations of second derivatives in shape optimization

Karsten Eppler (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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For a shape optimization problem second derivatives are investigated, obtained by a special approach for the description of the boundary variation and the use of a potential ansatz for the state. The natural embedding of the problem in a Banach space allows the application of a standard differential calculus in order to get second derivatives by a straight forward "repetition of differentiation". Moreover, by using boundary value characerizations for more regular data, a complete boundary...