Structural and Multidisciplinary Optimization

, Volume 46, Issue 6, pp 813–827 | Cite as

Slope constrained material design

  • Fabian SchuryEmail author
  • Michael Stingl
  • Fabian Wein
Research Paper


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.


Slope constraints Inverse homogenization Topology optimization SIMP 



We would like to thank the reviewers for their valuable comments, which helped to improve the manuscript.

The authors gratefully acknowledge the support of the Cluster of Excellence ‘Engineering of Advanced Materials’ at the University of Erlangen-Nuremberg, which is funded by the German Research Foundation (DFG) within the framework of its ‘Excellence Initiative’.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Chair of Applied Mathematics 2, Cluster of Excellence ‘Engineering of Advanced Materials’University of Erlangen-NurembergErlangenGermany

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