Structural and Multidisciplinary Optimization

, Volume 60, Issue 6, pp 2571–2595 | Cite as

Topology optimization of continuum structures under hybrid additive-subtractive manufacturing constraints

  • Yong Sheng Han
  • Bin XuEmail author
  • Lei Zhao
  • Yi Min Xie
Industrial Application


Additive manufacturing (AM) makes it possible to fabricate complicated parts that are otherwise difficult to manufacture by subtractive machining. However, such parts often require temporary support material to prevent the component from collapsing or warping during fabrication. The support material results in increased material consumption, manufacturing time, and clean-up costs. The surface precision and dimensional accuracy of the workpieces from AM are far from the engineering requirement due to layer upon layer manufacturing. Subtractive machining (SM), by contrast, can fabricate parts to satisfy the requirements of surface precision and dimensional accuracy. Nevertheless, the components need to be relatively uncomplicated for subtractive manufacturing. Thus, hybrid additive-subtractive manufacturing (HASM) is gaining increasing attention in order to take advantages of both processes. There is little research on the topological design methodology for this hybrid manufacturing technology. To address this issue, a method based on geometry approach for topology optimization of continuum structure is proposed in this paper. Both additive manufacturing and subtractive machining constraints are simultaneously considered in each topology optimization iteration. The topology optimization is performed by the bi-directional evolutionary structural optimization (BESO) method. The effectiveness of the proposed method is demonstrated by several 3D compliance minimization problems.


Topology optimization Additive manufacturing Subtractive machining Hybrid additive-subtractive manufacturing BESO method Manufacturability 


Funding information

This work was sponsored by the National Natural Science Foundation of China (11872311).

Compliance with ethical standards

Conflict of interest

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

  • Yong Sheng Han
    • 1
  • Bin Xu
    • 1
    Email author
  • Lei Zhao
    • 1
  • Yi Min Xie
    • 2
    • 3
  1. 1.Institute of Structural Health Monitoring and Control, School of Mechanics, Civil Engineering & ArchitectureNorthwestern Polytechnical UniversityXi’anChina
  2. 2.Centre for Innovative Structures and Materials, School of EngineeringRMIT UniversityMelbourneAustralia
  3. 3.XIE Archi-Structure Design (Shanghai) Co., Ltd.ShanghaiChina

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