Minimum length scale constraints in multi-scale topology optimisation for additive manufacturing

ABSTRACT

This paper performs a combined numerical and experimental study to explore the role of minimum length scale constraints in multi-scale topology optimisation. Multi-scale topology optimisation is generally performed without considering the actual unit cell size, while an arbitrary value considerably smaller than the part is selected afterwards. However, this procedure would be problematic if including geometric constraints, e.g. minimum length scale constraints, since geometric constraints cannot be applied without knowing the unit cell dimensions. To address this issue, unit cell size should be defined beforehand, and guidelines will be provided in this work through a thorough numerical exploration, i.e. compliance minimisation multi-scale topology optimisation with different unit cell sizes and a consistent minimum length scale limit will be performed. The numerical results indicate that selecting the unit cell size considerably smaller than the part and larger than the length scale limit would be recommended. Then, experiments are conducted to explore the effect of minimum length scale limit on the stiffness and strength of the multi-scale design. It is observed that increasing the minimum length scale limit would reduce the structural mechanical performance in both aspects.

KEYWORDS:

• Multi-scale
• topology optimisation
• additive manufacturing
• unit cell size
• length scale

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes on contributors

Dr Jikai Liu is a Professor at the School of Mechanical Engineering of Shandong University. He received his Ph.D. degree from the University of Alberta, Canada, and used to work as a Postdoctoral Research Associate at the ANSYS Additive Manufacturing Research Laboratory at the University of Pittsburgh, USA. His main research is focused on topology optimisation and additive manufacturing.

Yufan Zheng is a Ph.D. student from the Laboratory of Intelligent Manufacturing, Design and Automation (LIMDA), Mechanical Engineering Department, University of Alberta. His research areas of interest include remanufacturing, hybrid manufacturing, and process planning.

Dr Rafiq Ahmad is Assistant Professor in the Department of Mechanical Engineering, University of Alberta. He has established and is leading a research group of the Laboratory of Intelligent Manufacturing, Design and Automation (LIMDA) focusing on ‘hybrid & Smart systems’. His research interest includes smart systems design and development for industry 4.0, hybrid manufacturing combining additive and subtractive technologies, and industrial robotics.

Dr Jinyuan Tang is a full professor at the School of Mechanical and Electrical Engineering of Central South University. His main research is focused on design and fabrication of complex gear transmission systems.

Dr Yongsheng Ma is a full professor at the University of Alberta where he joined since 2007. Dr Ma is also a member of ASEE, SME, SPE, CSME and an Alberta registered Professional Engineer. His main research areas include feature-based engineering informatics for design and manufacturing, CADCAM, and product lifecycle management.

ORCID

Yongsheng Ma http://orcid.org/0000-0002-6155-0167

Additional information

Funding

The authors would like to acknowledge the support from the Qilu Young Scholar award, Shandong University, and the Open Research Fund of Key Laboratory of High Performance Complex Manufacturing, Central South University [grant number Kfkt2016-07].