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- ItemMulti-material phase field approach to structural topology optimization(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Blank, Luise; Farshbaf-Shaker, M. Hassan; Garcke, Harald; Rupprecht, Christoph; Styles, VanessaMulti-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.