Optimization of an additively manufactured functionally graded lattice structure with liquid cooling considering structural performances

Akihiro Takezawa*, Xiaopeng Zhang, Mitsuru Kitamura

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


Effective cooling or heat exchange is a typical engineering issue related with various industrial products, and the lattice structure fabricated by additive manufacturing is expected to be useful for effective liquid cooling. Moreover, such a heat exchanger demands structural performances such as stiffness and small thermal deformation when, for example, casting die and transporters of heated objects. Thus, in this research, we develop an optimization method for lattice volume fraction distribution using lattice structure approximation and a gradient method considering three coupled physical problems: fluid flow, thermal conduction, and convection and linear elasticity. Fluid flow is approximated by deriving effective properties from the Darcy–Forchheimer law and analyzing the flow according to the Brinkman–Forchheimer equation. The basis lattice shape is formed as three orthogonally connected pillars. The effective performance of a representative dimension unit lattice was calculated based on the statically averaging theorem and the relationship between the design variable and effective properties were approximated by polynomial functions. Two types of optimization problems were considered: maximization of fluid cooling performance under strain energy constraint and unconstrained minimization of normal direction of the loading and heating surface. The validity of the proposed methodology was investigated through three-dimensional examples. Although observable errors in accuracy exist between results obtained from optimization and full-scale models, the relative performance optimization was considered successful.

Original languageEnglish
Article number118564
JournalInternational Journal of Heat and Mass Transfer
Publication statusPublished - 2019 Nov
Externally publishedYes


  • Additive manufacturing
  • Brinkman–Focheheimer equation
  • Focheheimer theory
  • Lattice density optimization
  • Thermal conduction–convection
  • Thermal deformation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


Dive into the research topics of 'Optimization of an additively manufactured functionally graded lattice structure with liquid cooling considering structural performances'. Together they form a unique fingerprint.

Cite this