Structural and Multidisciplinary Optimization

, Volume 59, Issue 1, pp 249–262 | Cite as

Topology optimization of shell-infill structures using a distance regularized parametric level-set method

  • Junjian Fu
  • Hao Li
  • Mi Xiao
  • Liang GaoEmail author
  • Sheng Chu
Research Paper


This paper presents a novel topology optimization formulation for shell-infill structures based on a distance regularized parametric level-set method (PLSM). In this method, the outer shell and the infill are represented by two distinct level sets of a single-level set function (LSF). In order to obtain a controllable and uniform shell thickness, a distance regularization (DR) term is introduced to formulate a weighted bi-objective function. The DR term is minimized along with the original objective, regularizing the parametric LSF close to a signed distance function. With the signed distance property, the area between the two-level sets can be contoured as the shell with a uniform thickness. Additionally, the presented formulation retains one important merit of the PLSM that new holes are able to nucleate during the optimization process. With respect to the material of the shell, the infill is filled with a weaker and lighter material with tunable parameters. Particularly, the infill can be pre-designed with isotropic microstructures. Three compliance minimization examples are provided to demonstrate the effectiveness of this formulation.


Topology optimization Shell-infill structures Parametric level-set method Distance regularization 



This research is partially supported by National Basic Scientific Research Program of China (JCKY2016110C012), China Equipment Pre-research Program (41423010102), National Natural Science Foundation of China (51705166, 51675196 and 51721092), China Postdoctoral Science Foundation (2017 M612446), and Program for HUST Academic Frontier Youth Team.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Lab of Digital Manufacturing Equipment and TechnologyHuazhong University of Science and TechnologyWuhanChina

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