Displaying similar documents to “Relaxation of an optimal design problem in fracture mechanic: the anti-plane case”

Vector variational problems and applications to optimal design

Pablo Pedregal (2005)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We examine how the use of typical techniques from non-convex vector variational problems can help in understanding optimal design problems in conductivity. After describing the main ideas of the underlying analysis and providing some standard material in an attempt to make the exposition self-contained, we show how those ideas apply to a typical optimal desing problem with two different conducting materials. Then we examine the equivalent relaxed formulation to end up with a new problem...

On an optimal shape design problem in conduction

José Carlos Bellido (2006)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this paper we analyze a typical shape optimization problem in two-dimensional conductivity. We study relaxation for this problem itself. We also analyze the question of the approximation of this problem by the two-phase optimal design problems obtained when we fill out the holes that we want to design in the original problem by a very poor conductor, that we make to converge to zero.

Optimal design in small amplitude homogenization

Grégoire Allaire, Sergio Gutiérrez (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

This paper is concerned with optimal design problems with a special assumption on the coefficients of the state equation. Namely we assume that the variations of these coefficients have a small amplitude. Then, making an asymptotic expansion up to second order with respect to the aspect ratio of the coefficients allows us to greatly simplify the optimal design problem. By using the notion of -measures we are able to prove general existence theorems for small amplitude optimal design...

On the minimum of the work of interaction forces between a pseudoplate and a rigid obstacle

Igor Bock, Ján Lovíšek (2001)

Mathematica Bohemica

Similarity:

An optimization problem for the unilateral contact between a pseudoplate and a rigid obstacle is considered. The variable thickness of the pseudoplate plays the role of a control variable. The cost functional is a regular functional only in the smooth case. The existence of an optimal thickness is verified. The penalized optimal control problem is considered in the general case.

Some remarks on existence results for optimal boundary control problems

Pablo Pedregal (2003)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

An optimal control problem when controls act on the boundary can also be understood as a variational principle under differential constraints and no restrictions on boundary and/or initial values. From this perspective, some existence theorems can be proved when cost functionals depend on the gradient of the state. We treat the case of elliptic and non-elliptic second order state laws only in the two-dimensional situation. Our results are based on deep facts about gradient Young measures. ...