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Note on spatial gradient operators and gradient-based minimum length constraints in SIMP topology optimization

Abstract

Spatial gradient information of density field in SIMP (solid isotropic material with penalization) topology optimization is very useful for imposing overhang angle and minimum length (size) manufacturing constraints or achieving shell-infill optimization. However, the computation of density gradient is an approximation since the design space is discretized. There are several operators for this purpose, which arise from the image processing field. This note compares different gradient operators in the context of SIMP topology optimization method and suggests a new computation strategy to improve the accuracy of gradient estimation. We take a case study of spatial gradient-based minimum size constraints. New structural indicator functions are proposed to improve the general applicability of previous gradient-based minimum length constraints. This study is carried out in 2D structure examples to validate the methodology.

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Acknowledgments

The author Kaike Yang would like to thank the kindly hosting from Prof. Pierre Duysinx’s research group in the University of Liege.

Funding

This work is supported by the National Key Research and Development Program (2017YFB1102800), NSFC for Excellent Young Scholars (11722219), and Key Project of NSFC (51790171, 5171101743, 51735005, 11620101002, and 11432011). The author Kaike Yang received financial support from the CSC (China Scholarship Council).

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Correspondence to Eduardo Fernandez or Jihong Zhu.

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Responsible editor: Ole Sigmund

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Yang, K., Fernandez, E., Niu, C. et al. Note on spatial gradient operators and gradient-based minimum length constraints in SIMP topology optimization. Struct Multidisc Optim 60, 393–400 (2019). https://doi.org/10.1007/s00158-019-02269-9

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Keywords

  • Spatial gradient operators
  • Structural indicator functions
  • Minimum length constraints