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 H1-gradient projection method is introduced and finally several numerical results demonstrate the applicability of the approach.
@article{arxiv.1312.2356,
title = {Multi-material phase field approach to structural topology optimization},
author = {Luise Blank and M. Hassan Farshbaf-Shaker and Harald Garcke and Christoph Rupprecht and Vanessa Styles},
journal= {arXiv preprint arXiv:1312.2356},
year = {2013}
}