# Structural multiscale topology optimization with stress constraint for additive manufacturing

**Authors:** Ferdinando Auricchio, Elena Bonetti, Massimo Carraturo, Dietmar Hömberg, Alessandro Reali, Elisabetta Rocca  
**arXiv:** [1907.06355](https://arxiv.org/abs/1907.06355)  
**Date:** 2019-07-15  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1907.06355v1/

## Key points

- Phase-field approach for structural topology optimization in 3D-printing processes with stress constraints and potential for multiple materials or multiscales
- First-order necessary optimality conditions derived and numerical algorithm presented
- Sensitivity study conducted on parameters for a two-dimensional cantilever beam problem
- Workflow described to obtain a 3D-printed object from numerical solutions using fused deposition modeling (FDM) 3D printing technology
- Final structure printed using an FDM 3D printer
- Valuable insights provided into optimizing structures in additive manufacturing processes, particularly in applications where stress constraints are critical
- Importance emphasized of considering multiple materials or multiscales in topology optimization for 3D printing processes.

## Summary

This paper presents a phase-field approach for structural topology optimization in 3D-printing processes with stress constraints and the potential for multiple materials or multiscales. The authors derive first-order necessary optimality conditions and present a numerical algorithm to implement the method. They conduct a sensitivity study on parameters for a two-dimensional cantilever beam problem and describe a possible workflow to obtain a 3D-printed object from the numerical solutions, which involves using fused deposition modeling (FDM) 3D printing technology. The final structure is printed using an FDM 3D printer. This study provides valuable insights into optimizing structures in additive manufacturing processes, particularly in applications where stress constraints are critical and emphasizes the importance of considering multiple materials or multiscales in topology optimization for 3D printing processes.