# Combined length scale and overhang angle control in minimum compliance topology optimization for additive manufacturing

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## Abstract

This paper focuses on topology optimization for additive manufacturing. In order to ensure that the optimized design is immediately manufacturable, it is essential to take into account the appropriate geometric constraints during the optimization. Two important constraints are minimum length scale and maximum overhang angle. A minimum length scale is needed to ensure that the condition on minimal printable feature sizes is satisfied, while an imposed overhang angle eliminates the need for a temporary support structure. This paper first shows that both constraints cannot simultaneously be met by a straightforward coupling of existing methods for length scale and overhang angle control. Next, a new filtering scheme is introduced, based on a specific combination of spatial filters, which allows direct control over these constraints in a minimum compliance topology optimization problem. A 2D benchmark problem and a complex 3D case study are presented to demonstrate that the proposed filtering scheme successfully imposes a target length scale in both the solid and the void phase of the design domain, while simultaneously allowing control over the overhang angle.

## Keywords

Topology optimization Additive manufacturing Length scale control Overhang angle control Manufacturing constraints## Notes

### Acknowledgements

The first author is a doctoral fellow of the Research Foundation Flanders (FWO). The financial support is gratefully acknowledged. The authors also acknowledge Shibo Ren from ARUP for sharing the information required to perform the 3D case study.

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