Abstract
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.KeywordsShape and topology optimizationPhase field approachShape sensitivity analysisGradient projection methodMathematics Subject Classification (2010)Primary 49Q10Secondary 74P0574P1590C5265K15
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