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Relating phase field and sharp interface approaches to structural topology optimization
2013, Blank, Luise, Farshbaf-Shaker, M. Hassan, Garcke, Harald, Styles, Vanessa
A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement.
Multi-material phase field approach to structural topology optimization
2013, Blank, Luise, Farshbaf-Shaker, M. Hassan, Garcke, Harald, Rupprecht, Christoph, Styles, Vanessa
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.