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### On a robust phase field approach to topology optimization

##### Prof. Dietmar Hömberg, WIAS, Berlino

Sala conferenze IMATI-CNR, Pavia - Friday, April 28, 2017 h.9:30

**Abstract. ** The goal in topology optimization is to partition a given domain into regions occupied by either void or material by minimizing a given cost functional J_1 (typically a combination of compliance and tracking type) such that the displacement u solves a mechanical equilibrium problem. Here, the material distribution is described with the help of a phase field variable phi taking values in [0,1], corresponding to the phases void and material, respectively. To avoid homogenised microstructures, usually a perimeter penalisation is added to the cost functional. In the phase field approach to topology optimization the latter is relaxed by replacing it with a Ginzburg-Landau energy J_2, which can be shown to Gamma-converge to the perimeter functional.

In the presentation I will explain the phase field approach and include the effect of uncertainties in coefficients and loading data. I will present a numerical scheme and show numerical results in 2 and 3 D.

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