Multi-material phase field approach to structural topology optimization

Luise Blank, M. Hassan Farshbaf-Shaker, Harald Garcke, Christoph Rupprecht, Vanessa Styles

Published 2013-12-09Version 1

Multi-material structural topology and shape optimization problems are formulated within a phase field approach. First-order conditions are stated and the relation of the necessary conditions to classical shape derivatives are discussed. An efficient numerical method based on an $H^1$-gradient projection method is introduced and finally several numerical results demonstrate the applicability of the approach.