Robust topology optimization accounting for misplacement of material

Miche Jansen, Geert Lombaert, Moritz Diehl, Boyan Stefanov Lazarov, Ole Sigmund, Mattias Schevenels

Research output: Contribution to journalJournal articlepeer-review


The use of topology optimization for structural design often leads to slender structures. Slender structures are sensitive to geometric imperfections such as the misplacement or misalignment of material. The present paper therefore proposes a robust approach to topology optimization taking into account this type of geometric imperfections. A density filter based approach is followed, and translations of material are obtained by adding a small perturbation to the center of the filter kernel. The spatial variation of the geometric imperfections is modeled by means of a vector valued random field. The random field is conditioned in order to incorporate supports in the design where no misplacement of material occurs. In the robust optimization problem, the objective function is defined as a weighted sum of the mean value and the standard deviation of the performance of the structure under uncertainty. A sampling method is used to estimate these statistics during the optimization process. The proposed method is successfully applied to three example problems: the minimum compliance design of a slender column-like structure and a cantilever beam and a compliant mechanism design. An extensive Monte Carlo simulation is used to show that the obtained topologies are more robust with respect to geometric imperfections.
Original languageEnglish
JournalStructural and Multidisciplinary Optimization
Issue number3
Pages (from-to)317-333
Publication statusPublished - 2013


  • Topology optimization
  • Robust design optimization
  • Geometric imperfections
  • Random fields


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