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"... Noname manuscript No. (will be inserted by the editor) Edge detection using topological gradients: a scale-space approach ..."

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Noname manuscript No. (will be inserted by the editor) Edge detection using topological gradients: a scale-space approach

### Project-Team CORIDA Robust Control Of Infinite Dimensional Systems and Applications

"... c t i v it y e p o r t 2008 Table of contents ..."

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### TOPOLOGY OPTIMIZATION OF QUASISTATIC CONTACT PROBLEMS

"... 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 ..."

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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 by the body in unilateral contact with the rigid foundation to obtain the optimally shaped domain for which the normal contact stress along the contact boundary is minimized. The volume of the body is assumed to be bounded. Using the material derivative and asymptotic expansion methods as well as the results concerning the differentiability of solutions to quasistatic variational inequalities, the topological derivative of the shape functional is calculated and a necessary optimality condition is formulated.

### TOPOLOGICAL SENSITIVITY ANALYSIS FOR SOURCE PERTURBATION IN TRANSIENT PROBLEMS

"... In this work we calculate the topological derivative for a quite general heat transfer problem when perturbing the reactive coefficient and the source term as well. This is ob-tained for two cost functionals, one depending upon a given function on a portion of the boundary and the other based on a K ..."

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In this work we calculate the topological derivative for a quite general heat transfer problem when perturbing the reactive coefficient and the source term as well. This is ob-tained for two cost functionals, one depending upon a given function on a portion of the boundary and the other based on a Kohn–Vogelius criterion. Then, we use this expression as an indicator function in order to devise an iterative algo-rithm to apply it in the context of an optimization problem and of an inverse problem.