Displaying similar documents to “On an optimal shape design problem in conduction”

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...

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...

Relaxation of an optimal design problem in fracture mechanic: the anti-plane case

Arnaud Münch, Pablo Pedregal (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In the framework of the linear fracture theory, a commonly-used tool to describe the smooth evolution of a crack embedded in a bounded domain Ω is the so-called energy release rate defined as the variation of the mechanical energy with respect to the crack dimension. Precisely, the well-known Griffith's criterion postulates the evolution of the crack if this rate reaches a critical value. In this work, in the anti-plane scalar case, we consider the shape design problem which consists...

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.