Venerdi' 28/4/2017, alle ore 09:30 precise, presso la sala conferenze dell’IMATI-CNR di Pavia, il
Prof. Dietmar Hömberg, WIAS, Berlino
terrà un seminario dal titolo:
ON A ROBUST PHASE FIELD APPROACH TO TOPOLOGY OPTIMIZATION
nell'ambito del Seminario di Matematica Applicata (IMATI-CNR e Dipartimento di Matematica, Pavia), http://matematica.unipv.it/it/seminari-matematica-applicata
Al termine della conferenza sarà organizzato un piccolo rinfresco.
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.