Baumann, P., Mazari, I., & Sturm, K. (2023, August 24). Topology optimisation with general dilatations via the topological state derivative [Conference Presentation]. 10th International Congress on Industrial and Applied Mathematics : ICIAM 2023 Tokyo, Tokyo, Japan. http://hdl.handle.net/20.500.12708/188546
10th International Congress on Industrial and Applied Mathematics : ICIAM 2023 Tokyo
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Event date:
20-Aug-2023 - 25-Aug-2023
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Event place:
Tokyo, Japan
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Keywords:
Topology optimisation; Shape optimisation
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Abstract:
In this work we introduce the topological state derivative, a noval approach to treat PDE-constrained topology optimisation problems. This notion allows to deal with point perturbations as well as more general perturbations like smooth hypersurfaces in a similar way. Furthermore, we draw a connection from the topological state derivative to the asymptotic expansion of the state equation, which is usually derived using boundary layer correctors. Finally, we present numerical results based on these ideas.