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B-DGTO: a new topology optimization approach enabling derivable signed distance feature in density method.

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Title: B-DGTO: a new topology optimization approach enabling derivable signed distance feature in density method.
Authors: Liang, Kaixian1 (AUTHOR), Liu, Jikai1 (AUTHOR) jikai_liu@sdu.edu.cn, Xu, Shuzhi2 (AUTHOR)
Source: Structural & Multidisciplinary Optimization. Jul2026, Vol. 69 Issue 7, p1-27. 27p.
Subjects: Level set methods, Implicit functions, Curvature, Mathematical equivalence, Structural optimization, Thermal conductivity
Abstract: Density method and level-set method (LSM) stand as the two most prevalent topology optimization approaches. The former boasts strong robustness but suffers from ambiguous boundary geometric information, while the latter describes structural boundaries via implicit functions, enabling accurate high-order boundary information, but suffers from issues of initial guess dependency and incompatibility to standard optimizers. These two approaches have long been isolated with rare mutual compensations. In this paper, we proposed a novel approach that starts from the density field and achieves its transformation to the signed distance function (SDF) by solving design-dependent transient diffusion equation and Poisson equation. The derived SDF maintains geometric equivalence with the original density field. On this foundation, we further developed two B-DGTO (Boundary-fitting Derivable Geodesics-coupled Topology Optimization) frameworks: the density-based B-DGTO and the SDF-based B-DGTO, in supporting the density-level-set co-topology optimization. The efficacy of these frameworks is validated through addressing mean curvature constraint and perimeter constraint on the L-brackets and thermal conduction structures. The proposed method provides a systematic framework integrating density method and LSM, holding profound implications for future development. [ABSTRACT FROM AUTHOR]
Copyright of Structural & Multidisciplinary Optimization is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: B-DGTO: a new topology optimization approach enabling derivable signed distance feature in density method.
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  Data: <searchLink fieldCode="AR" term="%22Liang%2C+Kaixian%22">Liang, Kaixian</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liu%2C+Jikai%22">Liu, Jikai</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jikai_liu@sdu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Xu%2C+Shuzhi%22">Xu, Shuzhi</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Structural+%26+Multidisciplinary+Optimization%22">Structural & Multidisciplinary Optimization</searchLink>. Jul2026, Vol. 69 Issue 7, p1-27. 27p.
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  Data: <searchLink fieldCode="DE" term="%22Level+set+methods%22">Level set methods</searchLink><br /><searchLink fieldCode="DE" term="%22Implicit+functions%22">Implicit functions</searchLink><br /><searchLink fieldCode="DE" term="%22Curvature%22">Curvature</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+equivalence%22">Mathematical equivalence</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+optimization%22">Structural optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Thermal+conductivity%22">Thermal conductivity</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: Density method and level-set method (LSM) stand as the two most prevalent topology optimization approaches. The former boasts strong robustness but suffers from ambiguous boundary geometric information, while the latter describes structural boundaries via implicit functions, enabling accurate high-order boundary information, but suffers from issues of initial guess dependency and incompatibility to standard optimizers. These two approaches have long been isolated with rare mutual compensations. In this paper, we proposed a novel approach that starts from the density field and achieves its transformation to the signed distance function (SDF) by solving design-dependent transient diffusion equation and Poisson equation. The derived SDF maintains geometric equivalence with the original density field. On this foundation, we further developed two B-DGTO (Boundary-fitting Derivable Geodesics-coupled Topology Optimization) frameworks: the density-based B-DGTO and the SDF-based B-DGTO, in supporting the density-level-set co-topology optimization. The efficacy of these frameworks is validated through addressing mean curvature constraint and perimeter constraint on the L-brackets and thermal conduction structures. The proposed method provides a systematic framework integrating density method and LSM, holding profound implications for future development. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Structural & Multidisciplinary Optimization is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00158-026-04363-1
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      – Code: eng
        Text: English
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        PageCount: 27
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      – SubjectFull: Level set methods
        Type: general
      – SubjectFull: Implicit functions
        Type: general
      – SubjectFull: Curvature
        Type: general
      – SubjectFull: Mathematical equivalence
        Type: general
      – SubjectFull: Structural optimization
        Type: general
      – SubjectFull: Thermal conductivity
        Type: general
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      – TitleFull: B-DGTO: a new topology optimization approach enabling derivable signed distance feature in density method.
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            NameFull: Liang, Kaixian
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            NameFull: Liu, Jikai
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            NameFull: Xu, Shuzhi
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            – D: 01
              M: 07
              Text: Jul2026
              Type: published
              Y: 2026
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            – TitleFull: Structural & Multidisciplinary Optimization
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