A density-and-strain-based K-clustering approach to microstructural topology optimization

  • Tej KumarEmail author
  • Krishnan Suresh
Research Paper


Microstructural topology optimization (MTO) is the simultaneous optimization of macroscale topology and microscale structure. MTO holds the promise of enhancing product-performance beyond what is possible today. Furthermore, with the advent of additive manufacturing, the resulting multiscale structures can be fabricated with relative ease. There are however two significant challenges associated with MTO: (1) high computational cost, and (2) potential loss of microstructural connectivity. In this paper, a novel density-and-strain-based K-means clustering method is proposed to reduce the computational cost of MTO. Further, a rotational degree of freedom is introduced to fully utilize the anisotropic nature of microstructures. Finally, the connectivity issue is addressed through auxiliary finite element fields. The proposed concepts are illustrated through several numerical examples applied to two-dimensional single-load problems.


Topology optimization Microstructural optimization design Clustering Principal strain 


Funding information

The authors would like to thank the support of the National Science Foundation through grant 1561899. Prof. Krishnan is a consulting Chief Scientific Officer of SciArt, Corp, which has licensed the Pareto technology, developed in Prof. Suresh’s lab, through Wisconsin Alumni Research Foundation.

Compliance with ethical standards

Conflict of interests

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of Wisconsin-MadisonMadisonUSA

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