Self-connected multi-domain topology optimization of structures with multiple dissimilar microstructures

Abstract

Multi-domain topology optimization allows the design of lattice structures with multiple dissimilar microstructures. However, how to handle the connectivity issue between the dissimilar microstructures is a very important and difficult topic. In this paper, a self-connected material interpolation is proposed to handle the topology optimization of structures with multiple dissimilar-but-connected microstructures. Due to this interpolation, the material in the interface domains between the dissimilar microstructures can be separately defined, which enables us to carefully design the material of interface to guarantee good connectivity. An advantage of this way is that the connectivity requirement is only considered for these microstructures in the small interface domain while other microstructures can be freely designed in the remaining relatively much bigger design domain. In this paper, the connectivity requirement is realized by simply using a non-design solid domain in the interface microstructures. Based on the proposed interpolation, a two-scale multi-objective optimization formulation is proposed for concurrently designing the topologies and the lattice materials. In addition to the traditional mechanical performance, a geometric feature, i.e., the mass of the interface, is also taken as an objective in this method to control the material usage of interface. Several examples with parameterized lattice microstructures are provided to illustrate the effectiveness of the proposed method.

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Funding

This work is financially supported by the National Natural Science Foundation of China (Grant Nos. U1808215), the 111 Project (B14013), and the Fundamental Research Funds for the Central Universities of China (DUT18ZD103).

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Correspondence to Shutian Liu.

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The results provided in this paper are generated by MATLAB codes developed by the authors. The codes can be available upon request by contacting the corresponding author via email.

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Luo, Y., Hu, J. & Liu, S. Self-connected multi-domain topology optimization of structures with multiple dissimilar microstructures. Struct Multidisc Optim (2021). https://doi.org/10.1007/s00158-021-02865-8

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Keywords

  • Topology optimization
  • Two-scale optimization
  • Multi-objective optimization
  • Interface connectivity