Design and optimization of graded cellular structures with triply periodic level surface-based topological shapes

Dawei Li, Ning Dai, Yunlong Tang, Guoying Dong, Yaoyao Fiona Zhao

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107 Citations (Scopus)


Periodic cellular structures with excellent mechanical properties widely exist in nature. A generative design and optimization method for triply periodic level surface (TPLS)-based functionally graded cellular structures is developed in this work. In the proposed method, by controlling the density distribution, the designed TPLS-based cellular structures can achieve better structural or thermal performances without increasing its weight. The proposed technique can be divided into four steps. First, the modified 3D implicit functions of the triply periodic minimal surfaces are developed to design different types of cellular structures parametrically and generate spatially graded cellular structures. Second, the numerical homogenization method is employed to calculate the elastic tensor and the thermal conductivity tensor of the cellular structures with different densities. Third, the optimal relative density distribution of the object is computed by the scaling laws of the TPLS-based cellular structures added optimization algorithm. Finally, the relative density of the numerical results of structure optimization is mapped into the modified parametric 3D implicit functions, which generates an optimum lightweight cellular structure. The optimized results are validated subjected to different design specifications. The effectiveness and robustness of the obtained structures is analyzed through finite element analysis and experiments. The results show that the functional gradient cellular structure is much stiffer and has better heat conductivity than the uniform cellular structure.

Original languageEnglish
Article number071402
Number of pages13
JournalJournal of Mechanical Design
Issue number7
Publication statusPublished - Jul 2019
Externally publishedYes


  • computational design
  • functionally graded cellular structures
  • Generative design
  • triply periodic level surface

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