Displaying similar documents to “A level set method in shape and topology optimization for variational inequalities”

Topology optimization of quasistatic contact problems

Andrzej Myśliński (2012)

International Journal of Applied Mathematics and Computer Science

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This paper deals with the formulation of a necessary optimality condition for a topology optimization problem for an elastic contact problem with Tresca friction. In the paper a quasistatic contact model is considered, rather than a stationary one used in the literature. The functional approximating the normal contact stress is chosen as the shape functional. The aim of the topology optimization problem considered is to find the optimal material distribution inside a design domain occupied...

Optimal internal dissipation of a damped wave equation using a topological approach

Arnaud Münch (2009)

International Journal of Applied Mathematics and Computer Science

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We consider a linear damped wave equation defined on a two-dimensional domain Ω, with a dissipative term localized in a subset ω. We address the shape design problem which consists in optimizing the shape of ω in order to minimize the energy of the system at a given time T . By introducing an adjoint problem, we first obtain explicitly the (shape) derivative of the energy at time T with respect to the variation in ω. Expressed as a boundary integral on ∂ω, this derivative is then used...

On the ersatz material approximation in level-set methods

Marc Dambrine, Djalil Kateb (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The level set method has become widely used in shape optimization where it allows a popular implementation of the steepest descent method. Once coupled with a ersatz material approximation [Allaire , (2004) 363–393], a single mesh is only used leading to very efficient and cheap numerical schemes in optimization of structures. However, it has some limitations and cannot be applied in every situation. This work aims at exploring such a limitation. We estimate the systematic...

Selfadjoint Extensions for the Elasticity System in Shape Optimization

Serguei A. Nazarov, Jan Sokołowski (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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Two approaches are proposed to modelling of topological variations in elastic solids. The first approach is based on the theory of selfadjoint extensions of differential operators. In the second approach function spaces with separated asymptotics and point asymptotic conditions are introduced, and a variational formulation is established. For both approaches, accuracy estimates are derived.

Topological derivatives for semilinear elliptic equations

Mohamed Iguernane, Serguei A. Nazarov, Jean-Rodolphe Roche, Jan Sokolowski, Katarzyna Szulc (2009)

International Journal of Applied Mathematics and Computer Science

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The form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in the L∞ norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.