Optimally variable density lattice to reduce warping thermal distortion of laser powder bed fusion

Akihiro Takezawa*, Qian Chen, Albert C. To

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


Reduction of the thermal distortion caused by the fabrication process of metal additive manufacturing is an important issue. Considering the problem of forming an object having lattices inside it to reduce the thermal distortion, we perform a lattice density distribution optimization and its experimental verification. In the optimization, assuming a cube with a sphere void as the base lattice shape, the lattice's distribution optimization is constructed based on the recurrent formula inherent strain method and a gradient method. The lattices are approximately handled as solid materials having effective stiffness calculated by the homogenization method. In the experiment, the laser powder bed fusion is introduced to fabricate test pieces. The test pieces are partially cut from the baseplate by a wire electric discharge machine, and the edge clearance caused by warping deformation is measured. The thermo-mechanical analysis is also introduced for the mechanical interpretation of the results. The reduction rate of the clearance caused by warping deformation in the experiment was 10.4%–24.8% in the quasi 2D example (comparison with 61.0%–91.4% volume fraction uniform lattices and a solid test piece) and 6.0% in the 3D example (comparison with the same volume fraction uniform lattice with the optimal lattice).

Original languageEnglish
Article number102422
JournalAdditive Manufacturing
Publication statusPublished - 2021 Dec


  • Inherent strain method
  • Powder bed fusion
  • Thermal distortion
  • Thermo-mechanical analysis
  • Variable lattice density optimization

ASJC Scopus subject areas

  • Biomedical Engineering
  • Materials Science(all)
  • Engineering (miscellaneous)
  • Industrial and Manufacturing Engineering


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