Mixed projection- and density-based topology optimization with applications to structural assemblies

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In this paper, we present a mixed projection- and density-based topology optimization approach. The aim is to combine the benefits of both parametrizations: the explicit geometric representation provides specific controls on certain design regions while the implicit density representation provides the ultimate design freedom elsewhere. While mixing projection and density representations in one formulation can serve many applications, our focus herein is only on the particular case of structural assemblies: the optimization of the structural topology is coupled with the optimization of the shape of the interface between the sub-components in a unified formulation. The interface between the assemblies is defined by a segmented profile made of linear geometric entities. The geometric coordinates of the nodes connecting the profile segments are used as shape variables in the problem, together with density variables as in conventional topology optimization. The variable profile is used to locally impose specific geometric constraints or to project particular material properties. Examples of the properties considered herein are a local volume constraint, a local maximum length scale control, a variable Young’s modulus for the distributed solid material, and spatially variable minimum and maximum length scale. The resulting optimization approach is general and various geometric entities can be used. The potential for complex design manipulations is demonstrated through several numerical examples.

Original languageEnglish
Pages (from-to)687-710
Number of pages24
JournalStructural and Multidisciplinary Optimization
Issue number2
StatePublished - 1 Feb 2020


  • Projection methods
  • Robust approach
  • Shape optimization
  • Structural assembly
  • Topology optimization

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Software
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization


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