Additive manufacturing oriented topology optimization of structures with self-supported enclosed voids

Yunfeng Luo, Ole Sigmund, Quhao Li, Shutian Liu*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


It is challenging to remove the supports in an enclosed void of an additively manufactured structure, while it is much easier in open regions. This paper presents a novel approach to control the minimal overhang angle only in enclosed voids in order to improve the manufacturability of AM structures with as little performance loss as possible. Firstly, a nonlinear virtual temperature method (N-VTM) is proposed to identify the enclosed voids. In the N-VTM method, void areas are assumed to be filled with a temperature-dependent heating material with high heat conductivity while the solid parts have low heat conductivity. Due to a nonlinear heat source term, the maximum temperature is controlled to a prescribed value, making the temperature in enclosed voids uniform over the whole structures. Hence, the enclosed voids can be easily identified without a careful selection of parameters. Then, the gradient of the filtered density field is applied to evaluate the overhang angle of the interface. Finally, a multiple filtering/projection process is developed to identify the overhang interface of enclosed voids, and then a logarithmic function-based constraint is developed to control overhang angle in enclosed voids by restricting the area of overhang interface of enclosed voids. Enhanced by the robust formulation, a topology optimization method for the design of structures with self-supported enclosed voids is then established. Several numerical examples are used to illustrate the effectiveness of the proposed method.

Original languageEnglish
Article number113385
JournalComputer Methods in Applied Mechanics and Engineering
Number of pages21
Publication statusPublished - 2020


  • Additive manufacturing
  • Enclosed voids
  • Overhang angle
  • Topology optimization

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