A novel subdomain level set method for structural topology optimization and its application in graded cellular structure design

  • Hui LiuEmail author
  • Hongming Zong
  • Ye Tian
  • Qingping Ma
  • Michael Yu WangEmail author
Research Paper


A novel subdomain structural topology optimization method is proposed for the minimum compliance problem based on the level sets with the parameterization of radial basis function (RBF). In this method, the level set function evolves on each subdomain separately and independently according to the requirements of objective functions and additional constraints. This makes the parameterization in the proposed subdomain method much faster and more cost-effective than that in the classical global method, as well as the evolution of the level set function since it can be achieved on each subdomain in parallel. In addition, the microstructures on arbitrary two adjacent subdomains can be connected perfectly, without any mismatch around the interfaces of the microstructures. Several typical examples are conducted to verify the correctness and effectiveness of the developed subdomain method. The effects of some factors on the optimized results are also investigated in detail, such as the RBF types, the connectivity types of microstructures, and the size of subdomain division. Without scale separation assumption, several layered graded cellular structures are successfully designed by employing the proposed method under the condition of corresponding repetition constraints. To improve the computational efficiency, a multi-node extended multiscale finite element method (EMsFEM) is used to solve the structural static equilibrium equation for the three-dimensional layered structure optimization problems. Furthermore, a MATLAB code is also provided in the Appendix for readers to reproduce the results of the two-dimensional problems in this work.


Subdomain level set method Topology optimization Layered graded structure Cellular graded structure Multiscale finite element method (MsFEM) 


Funding information

This work is supported by the Hong Kong Scholars Program (XJ2016024) and the Fundamental Research Funds for the Central Universities (2042018kf0016).

Compliance with ethical standards

Conflict of interest

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled “A novel subdomain level set method for structural topology optimization”.

Supplementary material

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Copyright information

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

Authors and Affiliations

  1. 1.Department of Mechanics Engineering, School of Civil EngineeringWuhan UniversityWuhanPeople’s Republic of China
  2. 2.Department of Mechanical and Aerospace EngineeringThe Hong Kong University of Science and TechnologyClear Water BayHong Kong

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