Optimization and Engineering

, Volume 16, Issue 1, pp 225–246 | Cite as

On the efficient solution of a patch problem with multiple elliptic inclusions

  • F. Schury
  • J. Greifenstein
  • G. Leugering
  • M. StinglEmail author


We present an asymptotic approach to find optimal rotations of orthotropic material inclusions inside an isotropic linear elastic matrix. We compute approximate optimal solutions with respect to compliance and a stress based cost functional. We validate the local and global quality of the candidate solutions by means of finite element based parametric optimization algorithms. In particular, we devise a lower bound algorithm based on the free material optimization approach. Several numerical experiments are performed for different traction scenarios.


Material optimization Material orientation Eshelby theorem Asymptotic expansions 



We would like to thank S. A. Nazarov for his valuable comments on a preprint of the manuscript. We also thank J. Sokołowski for fruitful discussions about the topics treated in this paper and for providing valuable insights. Furthermore, 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’. The authors are also indebted to the DFG for funding this research work within the Collaborative Research Centre 814: Additive Manufacturing (subproject C2).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • F. Schury
    • 1
  • J. Greifenstein
    • 1
  • G. Leugering
    • 1
  • M. Stingl
    • 1
    Email author
  1. 1.Chair of Applied Mathematics 2, Cluster of Excellence ‘Engineering of Advanced Materials’University of Erlangen-NurembergErlangenGermany

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