Slope constrained material design

Authors:
Fabian Schury;Michael Stingl;Fabian Wein
Affiliations:
Chair of Applied Mathematics 2, Cluster of Excellence `Engineering of Advanced Materials', University of Erlangen-Nuremberg, Erlangen, Germany 91052;Chair of Applied Mathematics 2, Cluster of Excellence `Engineering of Advanced Materials', University of Erlangen-Nuremberg, Erlangen, Germany 91052;Chair of Applied Mathematics 2, Cluster of Excellence `Engineering of Advanced Materials', University of Erlangen-Nuremberg, Erlangen, Germany 91052
Venue:
Structural and Multidisciplinary Optimization
Year:
2012

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Abstract

We investigate a class of constrained inverse homogenization problems. The complexity of the topological solution is restricted using slope constraint regularization. We show existence of the solution for the inverse optimization problem in function space and outline a converging approximation scheme. We demonstrate how a proper numerical implementation can lead to a stable material design approach. We finally describe results for a comprehensive set of numerical test cases.