Simultaneous Material and Topology Optimization Based on Topological Derivatives

Abstract : We use an asymptotic expansion of the compliance cost functional in linear elasticity to find the optimal material inside elliptic inclusions. We extend the proposed method to material optimization on the whole domain and compare the global quality of the solutions for different inclusion sizes. Specifically, we use an adjusted free material optimization problem, that can be solved globally, as a global lower material optimization bound. Finally, the asymptotic expansion is used as a topological derivative in a simultaneous material and topology optimization problem.
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Christian Pötzsche; Clemens Heuberger; Barbara Kaltenbacher; Franz Rendl. 26th Conference on System Modeling and Optimization (CSMO), Sep 2013, Klagenfurt, Austria. Springer Berlin Heidelberg, IFIP Advances in Information and Communication Technology, AICT-443, pp.118-127, 2014, System Modeling and Optimization. 〈10.1007/978-3-662-45504-3_11〉
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Jannis Greifenstein, Michael Stingl. Simultaneous Material and Topology Optimization Based on Topological Derivatives. Christian Pötzsche; Clemens Heuberger; Barbara Kaltenbacher; Franz Rendl. 26th Conference on System Modeling and Optimization (CSMO), Sep 2013, Klagenfurt, Austria. Springer Berlin Heidelberg, IFIP Advances in Information and Communication Technology, AICT-443, pp.118-127, 2014, System Modeling and Optimization. 〈10.1007/978-3-662-45504-3_11〉. 〈hal-01286404〉

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