Sensitivity analysis and lattice density optimization for sequential inherent strain method used in additive manufacturing process

Akihiro Takezawa*, Albert C. To, Qian Chen, Xuan Liang, Florian Dugast, Xiaopeng Zhang, Mitsuru Kitamura

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)


Compensation of the thermal distortion that occurs during the fabrication process is an important issue in the field of metal additive manufacturing. Considering the problem in forming a lattice structure inside an object to reduce the thermal distortion, we developed a lattice volume fraction distribution optimization method. Assuming that the linear elastic problem is solved using the finite element method (FEM), an inherent strain method applying a layer-by-layer process utilizing the element activation during the FEM is formed as a recurrence relation, and the sensitivity of an objective function is derived based on the adjoint method. The unit lattice shape is a simple cube with a cube or a sphere-shaped air hole, and its distribution is optimized by considering the minimum thickness of the wall surrounding it as a design variable. The effective stiffness tensor of the lattice is derived using a homogenization method. The functions of the effective properties with respect to the design variables are approximated through polynomial functions. The optimization problem is formulated as an unconstrained minimization problem. The design variables are optimized using the method of moving asymptotes. Herein, the validity of the proposed method is discussed based on quasi two-dimensional and three-dimensional numerical studies including a re-analysis through full-scale thermo-mechanical analysis.

Original languageEnglish
Article number113231
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 2020 Oct 1


  • Additive manufacturing
  • Inherent strain method
  • Lattice density optimization
  • Recurrence relation
  • Sensitivity analysis
  • Thermal distortion

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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