Volume 51 Issue 4
Nov.  2021
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Huang M C, Huo W D, Liu C, Yang D S, Huang J, Du Z L, Guo X. Substructuring multi-resolution topology optimization with template. Advances in Mechanics, 2021, 51(4): 901-909 doi: 10.6052/1000-0992-21-030
Citation: Huang M C, Huo W D, Liu C, Yang D S, Huang J, Du Z L, Guo X. Substructuring multi-resolution topology optimization with template. Advances in Mechanics, 2021, 51(4): 901-909 doi: 10.6052/1000-0992-21-030

Substructuring multi-resolution topology optimization with template

doi: 10.6052/1000-0992-21-030
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  • Corresponding author: zldu@dlut.edu.cn
  • Received Date: 2021-05-27
  • Accepted Date: 2021-07-29
  • Available Online: 2021-08-10
  • Publish Date: 2021-11-26
  • In the multi-resolution topology optimization (MTOP) method, by decoupling the finite element mesh and discretization of density field, the finite element analysis is carried out with a coarser mesh (i.e., super-elements), and the computational cost is thus greatly reduced in the process of topology optimization. However, the elemental stiffness matrix is calculated each iteration using the average density of super-elements, and this treatment is actually not only inaccurate but also leads to the checkerboard phenomenon and QR patterns when the filter radius is relatively small. In order to alleviate such issues, the super-element is treated as a substructure and the corresponding elemental stiffness matrix is obtained using static condensation. Furthermore, a template library is developed for the substructure based on its density distribution during the topology optimization process. By this means, the elemental stiffness matrix is not required to be calculated repeatedly, the accuracy of the MTOP method is improved significantly and the checkerboard patterns are effectively inhibited as well.

     

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