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On a level set and topological derivative-based strategy for connectivity constraints in topology optimization.

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Title: On a level set and topological derivative-based strategy for connectivity constraints in topology optimization.
Authors: Andrade, Giovanna C.1 (AUTHOR) gcandrade@ime.usp.br, Donoso, Alberto2 (AUTHOR), Ruiz, David2 (AUTHOR), Ferrer, Alex3 (AUTHOR)
Source: Structural & Multidisciplinary Optimization. Jun2026, Vol. 69 Issue 6, p1-21. 21p.
Subjects: Level set methods, Topological derivatives, Solid freeform fabrication, Graph theory, Structural optimization
Abstract: This work addresses a level set-based framework for connectivity constraints in shape and topology optimization, using the concept of topological derivative. By controlling the presence of disconnected material components in optimal designs, the goal is to ensure that optimal solutions are also physically realizable in terms of additive manufacturing and of its final application. The proposed strategy is an extension of the continuous spectral graph approach, originally introduced in Donoso et al. (Struct Multidisc Optim 66(4):71, 2023. https://doi.org/10.1007/s00158-023-03526-8) in the density-based framework, which identifies and enforces connectivity based on the spectrum of a two-phase differential operator. The effectiveness of the strategy is demonstrated through several benchmark problems in structural optimization, in two and three dimensions. Numerical challenges and limitations such as filtering strategies and parameter dependence are illustrated and successful simulations are obtained with either the addition of perimeter penalization or a dilation operator. [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: On a level set and topological derivative-based strategy for connectivity constraints in topology optimization.
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  Data: <searchLink fieldCode="DE" term="%22Level+set+methods%22">Level set methods</searchLink><br /><searchLink fieldCode="DE" term="%22Topological+derivatives%22">Topological derivatives</searchLink><br /><searchLink fieldCode="DE" term="%22Solid+freeform+fabrication%22">Solid freeform fabrication</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+optimization%22">Structural optimization</searchLink>
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  Data: This work addresses a level set-based framework for connectivity constraints in shape and topology optimization, using the concept of topological derivative. By controlling the presence of disconnected material components in optimal designs, the goal is to ensure that optimal solutions are also physically realizable in terms of additive manufacturing and of its final application. The proposed strategy is an extension of the continuous spectral graph approach, originally introduced in Donoso et al. (Struct Multidisc Optim 66(4):71, 2023. https://doi.org/10.1007/s00158-023-03526-8) in the density-based framework, which identifies and enforces connectivity based on the spectrum of a two-phase differential operator. The effectiveness of the strategy is demonstrated through several benchmark problems in structural optimization, in two and three dimensions. Numerical challenges and limitations such as filtering strategies and parameter dependence are illustrated and successful simulations are obtained with either the addition of perimeter penalization or a dilation operator. [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/s00158-026-04327-5
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        Text: English
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        PageCount: 21
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      – SubjectFull: Level set methods
        Type: general
      – SubjectFull: Topological derivatives
        Type: general
      – SubjectFull: Solid freeform fabrication
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      – SubjectFull: Graph theory
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      – SubjectFull: Structural optimization
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            – D: 01
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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